CONTENTS
PREFACE 1. INTRODUCTION
2. BACKGROUND PND EXPLANATION
79-
8 54
3. DESIGN
55 — 69
4. DESIGNEXAMPLES
71 — 113 71 — 93
Example 1 Example2 Example3 Example4
Price £ 10.00
93 — 109 109—111
111—113
Edited by Robert G. D. Brown MA CEng MICE
Handbook to BI 5628: Structural use of masonry
Part 1: Unreinforced Masonry B. A. HASELTINE BSc AGGI DIC CEng FICE FlStructE
MConsE
J. F. A. MOORE MA BSc PhD DIC ARSM
The Brick Development Association 1
FOREWORD
by Professor A. W. Hendry
The purpose of BS 5628 is to provideessential data and guide-lines for the structural design of masonry buildings, based on acceptedgood practice and researchresults. The writersof codesofpractice are invariablyfaced with the problem of having to write succinct and rather specific statements,without being allowed to spell out the frequentlyimprecise basis of these statements.Similarly, it is not possible in a code to envisage all the possible situationsto which a particular clausemay be applied by others, nor are the drafterspermitted to set out the limitations inherent in a particular statement. Finally, there is the dilemmaof making rules which are sufficiently clearly defined, but whichdo not, at the same time, limit innovation.
To overcomethese problems, it is extremely helpful for codes to be accompanied by explanatory documents, written by authors who have played a large part in the draftingprocessand who are, therefore,aware ofthe backgroundto the code formulations. This is the more necessary when, as in the case of BS 5628, the code is more than a revision of a previous edition, long familiar to designers. This handbook includes detaileddiscussion of every clause in the code, supported by references from the nowvery extensive literature on masonry constructionand by a large number of illustrative examples. The latter are presentedin full numerical detail, and cover practically all likely design problems.
The authors are exceptionally well qualified for the taskwhich they have undertaken. Mr Haseltine is a consultingengineer of manyyears standingwho has been responsible for the design and constructionofmany major buildings in masonry, who was an extremely active member of the drafting committee of BS 5628, andhas also played a largepart in the formulationand reporting of extensive researchprojects — the results ofwhich were essential in the preparation of the code. Subsequent to the publication of the new code, Mr Haseltine took over chairmanship of the code committee.
Dr Moore, a senior member of the staff of the Building Research Establishment, also played a large part in the lengthy process of drafting BS 5628, on the basis of his extensive knowledge ofthe research backgroundto the masonry code, much of which originatedat BRE. This handbook is, therefore, authoritativeon the basis ofthe authors' direct knowledge of the subject, and ofthe discussions in the drafting committee. It is also practical because of theirextensive experience in masonry design, constructionand research. Users of BS 5628 will be much indebted to the authors of the handbook for their work in clarifying the basis of the code, and its applicationto practical design.
2
INDEX BY CODE CLAUSES
References are arranged in three groups. Those to Chapter 2, lead to background and explanatory material. References to Chapter 3, show the sequence and significance of specific clauses, or groups of clauses, in the design process. Chapter 4 demonstrates the practical application of clauses to typical design problems. Note: In Chapters 2 & 3, sub-clausesquoted in bracketsare discussed in the context oftheprincipalclause, rather than being consideredseparately.
CODE SECTION 1. GENERAL Chapter 2 Chapter 3 Chapter 4 1. Scope
3. Definitions 3.1 actual dimension 3.2 category I building 3.3 category 2 building
9 9 9 9 9 9
3.4 characteristic load
9—10
3.5 characteristic strength of masonry 3.6compressive strength of structural units
10 10
3.7column
10
3.8 design load 3.9 design strength 3.10 effective height or length
10
3.11 effective thickness 3.12 laterallyloaded wallpanels 3.13 lateral support 3.14 loadbearing walls
10
2. References
3.15 masonry 3.16 orthogonal ratio
3.l7pier 3.18 protected member 3.19 slendernessratio 3.20 structuralunits 3.21 types ofwall 3.21.1 single-leaf wall 3.21.2 double-leaf (collar-jointed) wall 3.21.3 cavity wall 3.21.4 grouted cavity wall 3.21.5facedwall 3.21.6 veneered wall 3.22 wallette 4. Symbols 5. Alternative materials and methods ofdesign and construction
Handbook to BS 5628: Part 1
74—75, 96—97
87
10 10
10 10
10 10 10—Il 11
11
II 11 11
11 11 11 11
II 11 11
11—12
12
3
CODE SECTION 2. MATERIALS,COMPONENTS ANDWORKMANSHIP Chapter 2 Chapter 3 Chapter 4 6. General
12
55
7. Structural Units 8. Laying of structuralUnits 8.1 General 8.2 Bricks with frogs 8.3 Perforated bricks 8.4 1-lollow and cellular blocks (8.4.! Ho/lowclay blocks) (8.4.2 Hollow and cellularconcrete blocks) 9. Rateof laying 10. Formingof chasesand holes
12
55
12—13
55
12
55
12
55
13
55
13
55
13
55
13
55
13
55
13
55
13
55
13
55
13
55
14
55
14
55
14
55
II. Pallet slips
12. Dampproof courses 13. Wall ties 14. Cements 15. Mortars 15.1 General 15.2 Ready mixed mortars 16. Colouring agents 17. Plasticisers 18.
Frost inhibitors
14
55
14
55
14
55
14
55
CODE SECTION 3. DESIGN: OBJECTIVES & GENERAL RECOMMENDATIONS Chapter 2 Chapter 3 Chapter 4 19. Basis ofdesign 20. Stability 20.1 General considerations 20.2 Accidental forces 20.3 During construction 21. Loads 22. Design loads: partial safety factor, 1f
15—17 17—20
55—56
74, 84
17—19
19 19
20 20—21
72 56—57,
76—77, 79, 81, 83, 85, 87, 90, 92, 108, 112
63—64, 68—69
23. Characteristic compressive strength of masonry, fk 23.1 Normal masonry 23.1.1 Walls orcolumnsofsmall plan area 23.1.2 Narrow brick walls 23.1.3 Walls constructed in modularbricks 23.1.4 WaIls constructed of wide bricks 23.1.5 Hollow blockwalls 23.1.6 Solid concrete block walls 23.1.7 Walls ofhollow concrete blocks filled within situ concrete 23.1.8 Natural stone masonry 23.1.9 Random rubblemasonry 23.2 Structuralunits laid other than on the normal bed face 23.3 Perforated bricks and hollow blocks 24. Characteristic fiexuralstrength of masonry, fkx (24.1 General) (24.2 Flexuralstrength) 25. Characteristic shear strength ofmasonry, 26. Coefficient offriction 27. Partial safety factors
f
21—24 21—22
84, 88, 110 80, 84, 87, 100, 102
22—23
23 23 23 23 23
23 23 23 23 23 24—26
63—64
91, 108,
63
77, 79, 81,86
112
24—26 24—26 26—27
27
for materialstrength,
27—29
27.1 General 27.2 Quality control
27
(27.2.! Manufacturing control) (27.2.1.1 Normal category) (27.2.1.2 Special category) (27.2.2 Construction control) (27.2 .2.1 Normal category) (27.2.2.2 Specialcategory)
27—29
4
58
27—29 27—29
27—29 27—29 27—29 27—29
27.3 Valuesofm for normal and accidental loads 27.4 Values of Ymv for shearloads 27.5 Valuesof for use withties
y
27-29 27—29
80,110
63
77, 81, 86, 89
27—29
CODE SECTION4. DESIGN: DETAILED CONSIDERATIONS Chapter 2 Chapter 3 Chapter 4 28. Consideration of slenderness of wallsand columns 28.1 Slenderness ratio 28.2 Lateralsupport 28.2.1 Horizontal or vertical lateral supports 28.2.2 Horizontal lateralsupports (28.2.2.!) (28.2.2.2) 28.2.3 Vertical lateralsupports (28.2.3.1) (28.2.3.2) (28.2.3.3) 28.3 Effectiveheight or length 28.3.1 Effectiveheight (28.3.1.1 Walls) (28.3.1.2 Columns) (28.3.1.3 Columnsformedbyadjacent openings in walls) (28.3.1.4 Piers) 28.3.2 Effectivelength 28.4 Effective thickness 28.4.1 Walls and columnsnot stiffened by piers or intersecting walls 28.4.2 Walls stiffened by piers or intersecting walls 29. Special typesofwall 29.1 Cavity walls 29.1.1 General 29.1.2 Minimum thicknessofleaves 29.1.3 Width of cavity 29.1.4 Spacing ofties 29.1.5 Embedment ofties 29.2 External cavitywalls 29.3 Faced walls 29.4 Veneered walls 29.5 Double-leaf (collar-jointed) walls 29.6 Groutedcavitywalls 30. Eccentricity in the plane of the wall 31. Eccentricity at rightangles to the wall
29—34
58, 58—9
29
79, 84, 85, 87, 97, 99, 102, 103, 104, 106, 79, 84, 85, 87, 97, 99, 102, 103, 104
110
29 29—30 30—31
79, 84, 85
30—31
97, 102, 104
30—31
102, 103
31 31
106
31 31
31—33 79, 84, 85, 87,97 102, 103, 104
31—32
31—32 31—32
87
3 1—32 31—32
110
32 33
84, 106 79, 84, 85, 87, 97, 102, 103, 104
33
87
33—34 34—35
58
34 34 34 34 34 34 71
34—35
35 35 35 35 35—39
58
35—39
59—60
to vertical loading
35—39
58, 68—69
(32.1 Loads ecce,,Iric in theplane ofthe waIl) (32.2 Design strength ofmasonry) (32.2.! Design vertical loadresistanceof walls) (32.2.2 Design vertical loadresistance
35—39
ofcolumns)
35—39
(32.2.3 Design vertical load resistance ofcavitywalls andcolumns)
35—39
77, 106 79, 81, 82, 84, 85, 86, 87, 88, 92, 97, 99, 102, 103, 104,106,110
32. Wallsand columns subjected
33. Wallssubjected to shearforces 34. Concentrated loads: stresses underand close to a bearing 35. Composite action between wallsand their supporting beams 36. Wallssubjected to lateralload 36.1 General 36.2Supportconditions and continuity 36.3 Limiting dimensions 36.4 Methods ofdesign for laterally loaded wall panels (36.4.1 General) (36.4.2 Calculation ofdesign momentsinpanels)
Handbook to BS 5628: Part 1
35—39
60—62
80, 84, 85, 86, 87, 88, 98, 99, 103, 104, 105,107,110
35—39
81
39—40
63
77, 78—79, 80, 81, 84, 86
40—42
58, 62—63
97, 100
42—43 43—50
63—64
43 43—44 44—45
64
45—47
64—66
45—46
64—66
45—46
64—66
91, 107,112
91, 109, 110, 113
5
CODE SECTION 4 continued Chapter 2 Chapter 3 Chapter 4 (36.4.3 Calculation ofdesign moment ofresistance ofpanels) 36.4.4 Arching (36.4.5 Design moment ofresistance for cavitywalls) 36.5 Method ofdesign for free -standing walls (36.5.1 General) (36.5.2 Calculation ofdesign moment
45—46
64—66
46
91, 92, 108, 112
47—49
66—67
47—49
66—67
47—49
66—67
ofresistanceoffreestanding walls)
47—49
66—67
36.6 Retaining walls 36.7 Foundation walls 36.8 Design lateralstrength of axially loaded wallsand columns
49
infreestanding walls)
ItO, 112
47
(36.5.3 Calculation ofdesign moment
49 49—50
67—68
90
CODE SECTION5. DESIGN:ACCIDENTAL DAMAGE Chapter 2 Chapter 3 Chapter 4 37. Design: accidental damage
50—54
(37.1 General) (37.1.1 Protected member) (37.2 Partial safety factors)
50—54
37.3 Horizontal ties 37.4 Vertical ties 37.5 Loadbearing elements
51—52
6
50—54
88 90
50—54 52—53 53—54
89
INTRODUCTION
A draft Code of Practicefor 'Structural
Recommendations for Load-bearing Walls' was circulatedfor commentin 1946. It had been
prepared by the Institution ofStructural Engineers on behalf of the British Standards Institution (BSI). It included a general section on loadbearingwalls, followed by sections on masonry, including brickwork(unreinforced), on reinforcedmasonry and on concretecast in situ. After appropriate discussion andrevision the documentwas publishedin 1948 as CP ill. The first revision ofthisCode of Practicewas publishedin 1964. The main change affecting brickwork wasan increase, usuallysubstantial,in the permissible stresses. The basic stresses were altered slightly but the reductionfactors for slenderness were made less onerous and were extended to includethe effects of eccentric loads. From the beginning, the codewas based on the assumptionthat normal principles of structural design would be used to assess the loads produced by a structure on its masonry elements. The detailed clauses of the code then gave guidance to enable wallthicknesses to be determinedin relation to stresses that were considered to be safe and permissible, based on an assessment of experimental data and practicalexperience. The experimental tests were carried through to collapse in most cases, so that even at that time design was related effectively to ultimate stresses. The changesin 1964 reflected an increased body of experimental knowledge coupled with satisfactoryresults from usingthe first code.
A further revision was published in 1970as part of the programmedchange in the construction
industry from Imperialto SI units. The existing codewas renamed CP Ill :Part 1:1964, still in Imperialunits, and CP 111 :Part 2:1970 was published as its SI equivalent. Rounding ofvalues occurredon conversion but, althoughthere were other minor changes, the new code did not constitutea technical revision. Howevera proposedrevisionof the code had beenpublished as a 'draft for comment' but in July 1970 it was decided to delaypublicationso that the code couldbe redrafted in limit state termswhich had beendevelopedover the previous 10—15years. A Handbook to BS 5628: Part I
1
'draft for comment'of the proposed unified concretecode had been publishedalready in 1969. Followingassimilation ofthe commentsCP 110 waspublishedin 1972 and effectivelysuperseded those clauses of CP Ill dealingwith plain concretewalls.
A number of the changesenvisaged in the new draft of CP Ill were still appropriate,quite separately from the change to the limitstate approach, and amendments were issued to both parts ofCP Ill in 1971. The changes included the amendmentfrom nominal to actual thickness, further changesto the reduction factor for slenderness, an increase in the maximum slenderness ratio, and a change in the permissible shear stress. Minor editorial amendmentswere published in 1976 and at the same time CP Ill :Part 1:1964 was withdrawnand Part 2 wasrenamed CP 111:1970.
After the 1970 draft revision hadbeen converted to the limit state philosophy,together with the inclusion ofsome new technical matter, a further 'draftfor publiccomment' wasissued in 1974 and wasdiscussed extensively at an Institution of Structural Engineers symposium. A large volume of commentwas received and sub-committees sat for 2 years revising the text. It was, perhaps, inevitable that the newaccidentaldamage and lateral loading sections took the longestto finalise, especially as researchinto lateral loading wasproceedingduring the drafting; indeed this researchis still continuing,and refinement ofthe design methods may be possible in the future. With the requirement that British Standards are approvedby committees unanimously, considerablediscussion was needed on the combinedwork ofthe four sub-committees before final agreement to publish was reachedin May 1978; the code was published in October 1978. In duecourse, it may be expected to be deemed to satisfythe BuildingRegulations. Two amendments,largely containingcorrections,have now been published. Work has started on Part 2 to the code whichwill deal with reinforcedand, possibly, prestressed masonry. After Part 2 has been published it will 7
be possible to withdraw CP 111, but in the
meantimeboth codes willexist side by side. This handbook sets out (in Chapter 2) to give backgroundand explanatorymaterial on many of the clauses in the newcode; where possible, references have been given so that the source of informationcan be examinedby those who wish so to do.
In Chapter 3, those formulae neededfor design
are given together with detailed recommendations for the analytical aspectsof design. Chapter 4 Consists of worked examples, extensively crossreferenced to the code clauses and to the explanatorysections of this handbook. Acknowledgements The grateful thanks of the authorsare extended to the British Standards Institution for permissionto publish extracts from BS 5628:Part 1 and to Neil Tutt ofJenkins and Potter for all his work on the calculations.
8
BACKGROUND AND EXPLANATION
Thenumbers of the paragraphs which follow correspond to the clause numbers in the code. References to the code in the text are prefixed with the word 'code'. SECTION 1: GENERAL Basic guidance for the applicationof the code of practice is given under five headings which indicate the context in which the code should be used and set down certaincriteria relatingto
BS 3921 Clay bricks andblocks BS 4027 Sulphate-resisting Portland cement Part 2 Metric units BS 4551 Methodsof testingmortars and specification for mortar testing sand BS 4721 Ready-mixed lime: sand for mortar BS 4887 Mortar plasticizers BS 5224 Specification for masonry cement BS 5390 Code of practice for stone masonry CP 3 Code of basic datafor the design of
its objectives. 1. Scope
In commonwith most recentstructural codesof practice,a presumption is made about the qualifications of the designer and the supervisor during construction.This condition arises, not because the code is necessarily more involved or sophisticatedthan hitherto, but because by its nature a code does not purport to be a comprehensive design manual. It gives detailed guidance in some places, but in others only draws attention to factors to which the designershould attend when devising a structural scheme for a specific building.In doing so the designerwill haveofnecessity to makeassumptionsappropriate to the circumstances in addition to those inherent in the detailed recommendations of the code. In order to ensure the satisfactory realisationof a design it is essential that these assumptions are justified in practice by the provisionofthe necessary supervision.
2. References The following standards publications are referred to in the code. BS 12 Specification for ordinary and rapidhardeningPortlandcement BS 146
Portland-blastfurnace cement Part2 Metric units BS 187 Specification for calcium silicate (sandlimeandflintlime) bricks BS 743 Materials for damp proofcourses Metricunits BS 1014 Pigments for Portland cement and Portland cementproducts BS 1180 Concrete bricks and fixing bricks BS 1217 Cast stone BS 1243 Metal ties for cavity wall construction BS 2028, 1364Precast concrete blocks Handbook to BS 5628: Part 1
2
CP 110 CP 111 CP 121
buildings Chapter V. Loading Part 1 Dead and imposed loads Part 2 Wind loads The structural use ofconcrete Structural recommendations for loadbearingwalls Walling Part I Brick andblock masonry
CP 2004 Foundations DD 34 Clay brickswith modular dimensions DD 59 Calcium silicate bricks with modular dimensions
3. Definitions 3.1 actual dimension Either the work size ofthe unit or, where applicable for solid walls,the sum of the work size of the units together with the work size of the joints between them. The use of'actual dimensions'follows its introductioninto CP Ill by the 1970 amendment. The expression 'solid walls' includes all those types defined in clause 3.21, except for 'cavity wall'. 3.2 category 1 building A buildinghaving 4 storeys (including basement storeys),or less. A classification introduced in relationto design to resist accidental damage(section 5). 3.3 category 2 building A building having 5 storeys (including basement storeys), or more. Complementary classification to that in clause 3.2. 3.4 characteristic load Ideally, wherethe load acts unfavourably,the load whichhas a probabilityofnot more than 5% 9
ofbeingexceeded or, wherethe load acts
favourably, the load which has a probability of at least 95% of beingexceeded. In practice,the load
obtained from the appropriate British Standard. This definition follows from the recognitionthat real values ofloads will have a statistical distributionabout a mean value. The 5% fractile is an arbitrary cut-off, used by most if not all limit state codes, as a means ofcharacterisingthe tails or extreme values of the distribution— hence 'characteristic'value. Probabilistic conceptsare thereby introduced into the design. Depending on the effect ofa load on stabilityit is necessary to distinguish maximumor minimumextremevalues. The practical method of obtainingcharacteristic loads at present arisesfrom the lack ofadequate statistical data about some types of loading. 3.5 characteristic strengthofmasonry The valueofthe strength ofmasonry below which the probabilityoftest results falling is not more than 5%. The meaning of 'characteristic'is the same as discussed under clause 3.4 except that, for strength,only minimumvalues are of interest to a limit state design. In this context, however, the reference to 'test results' implies that the characteristic strength has been determined from tests on specimens of masonryconstructedin the laboratory.
3.6 compressivestrengthofstructural units For the normal categoryofmanufacturing
control, the compressive strengthof structural units is the strength of a sample tested according to the appropriate British Standard. Note: Whenmanufacturing control is within the special categor)'. as defined in 27.2.1.2, compressivestrength is taken as the acceptance
limit, therein defined. This general statementacknowledges the range of methods specifiedfor determiningthe compressive strengthof different types of structural unit. The significance ofthe two categories ofmanufacturing control of quality is discussed below.
3.7 column An isolatedvertical loadbearingmemberwhose width is not more than four times its thickness. In the case of a memberwith a cavity, this definition should be appliedto the overall thickness ofthe memberunlessonly one leaf is loaded, whenit should be applied to the loaded leaf.
3.12 laterallyloadedwallpanels Walls subjected mainly to loads normal to the face of the wall. This definition draws attention to a type of element whichwas not covered by CP Ill. However, its definition, in commonwith that of 'load-bearingwalls' in clause 3.14, is not mutually exclusive. Between the extremes of high lateral load and only self-weight vertically, and high verticalload only, all combinationsoflateral and verticalloads may be envisaged. The appropriate definition and design approach must be decided dependingon the load whichpredominates. 3.13 lateralsupport The support, in relationto a wall or pier, which will restrict movement in the direction of the thickness of the wall or, in relation to a column, whichwillrestrict movement in the directionof its thickness or width. Lateral supports may be horizontalor vertical. This definition emphasises the requirement for lateral supports to resist movement, althoughin the relevant design clauses (28.2) the forces necessary to prevent movement are usually considered. The elements providing lateral (ie horizontal)support may be arranged in either vertical planes eg piers and buttressing walls, or horizontalplanes eg roofs and floors. 3.14 loadbearing walls Walls primarilydesigned to carry an imposed vertical load in addition to their own weight. 3.15 masonry An assemblage ofstructural units, either laid in-situ or constructedin prefabricatedpanels,in which the structural units are bonded and solidly put together with mortar or grout. Masonrymay
be reinforced or unreinforced. The reference to reinforcedmasonry recognises the scope of masonry beyond Part 1 of BS 5628.
3.16 orthogonal ratio The ratio of the flexural strengthofmasonry when failure is parallel to the bed joints to that when failure is perpendicularto the bed joints. Although a commonterm in structural engineering it has not been applied previously to masonry. It now refers to the ratio ofthe flexural strengths of masonry determined in two directionsat right angles to each other. These directionsare depictedin Figure 1 and are called 'parallel' when the failure surface due to bendingis parallel to the beddingjoints, and 'perpendicular'when failure occursat right angles
3.8 designload The characteristicload multipliedby a partial safety factor for loads. 3.9 design strength The characteristic strengthdivided by a partial safety factor for material strength. 3.10 effectiveheightor length The height or length of a wall, pier or column assumed for calculating the slenderness ratio. 3.11 effective thickness The thickness of a wall, pier or columnassumed for calculating the slenderness ratio. 10
Figure 1 Orthogonalfailuredirections.
to the beddingjoints. This terminologyshould
notbe confused with that used to describethe momentswhich cause failure andwhich act in planes at right angles to the failuresurfaces, and whichare therefore oppositeto the definition used in thiscode.
The strengthin the paralleldirectionis usually the lower so that the orthogonal ratio of the masonryitselfis usuallyless than unity. 3.17 pier A member which forms an integralpart of a wall, in the form of a thickened section placed at intervals alongthe wall. 3.18 protectedmember A structural member capableof resisting a specified pressure. Note: See section 5, page 50 3.19 slendernessratio The ratio of the effective heightor lengthto the effective thickness.
3.20 structuralunits Bricks or blocks or square dressed natural stone. This definition implies that structural units are right paralielepipeds. However, clause7 'Structural Units' includes BS 5390: Stone masonry which coversrandom rubblemasonry ie non rectangularunits, to which reference is also made in clause 23.1.9 for characteristic compressive strength. 3.21 types ofwall 3.21.1 single-leaf wall
A wall of bricks or blockslaid to overlapin one
or more directionsand set solidly in mortar.
3.21.2 double-leaf(collar-jointed) itall Two parallel single-leaf walls, with a space betweennot exceeding 25 mm, filled solidly with mortar and so tied together as to result in commonaction under load. The name given to thisform ofwall may vary locally but the constructionis designed essentially to achievea finished wallfair-faced on both sides. 3.21.3 cavity i'aIl Two parallel single-leaf walls, usuallyat least 50 mm apart, and effectivelytied togetherwith wall ties, the spacebetweenbeingleft as a continuous cavity or filled with non-loadbearingmaterial. The definition ofsingle-leaf walls includes walls wider than the minimumplan dimension of the structural units used. The definition ofcavity walls therefore includesleaves of different thicknesses. The non-loadbearingmaterial in the cavity will usuallybe a thermalinsulatingmaterial whichmay not necessarily occupythe full width of the cavity. 3.21.4 groutedcavitywall Two parallelsingle-leaf walls, spaced at least 50 mm apart, effectively tied together with wallties and with the interveningcavity filled with fine aggregate concrete(grout), which may be reinforced, so as to result in common action
under load. Althoughdefined here andreferredto in clause 29.6the more usual application for a grouted cavitywall is in reinforcedmasonry.
Handbook to BS 5628: Part I
3.21.5 faced iiall
A wall in which the facing andbacking are so
bonded as to result in commonaction under load. 3.21.6 veneeredit'alls A wallhavinga facingwhich is attached to the backing,but not so bonded as to result in commonaction under load. 3.22 wallette A smallmasonry panel constructedfor test purposes.
Although panelsrangingfrom a few stackbonded units to a half-storey heightwall could be includedin this definition the main size of walletteenvisaged is similar to that described in AppendixA.3 for the determinationofflexural strength,ie several courses high and a few units long.
4. Symbols
For ease ofreference the symbols used in the
code are reproducedhere. The notation follows closely that used in CP 110 based on the following convention: Roman capitalsto denoteforces, areaor related functions,andconstants. Roman lowercase to denote length andforce per unit area or per unit length. The meaning of subscriptsis more variablebut k denotesa characteristicvalue andm denotesa mean valueexcept when subscript to a Greek symbol.
Greek lowercase to denote factorsor coefficients.
The use of L for length is an exceptionand a particular difference from CP 110 is the use oft for width or thicknessand h for height.
A B
b ea ex et em
Fk Fm
F fk fkx
fGk gg h
ha
hL hef
horizontalcross-sectional area width of a bearingunder a concentrated load width of column additional eccentricity dueto deflection in walls eccentricity at top ofa wall total design eccentricity in the mid-height regionofa wall the larger of ex or et
characteristicload average ofthe maximum loads carried by two test panels
tie force
characteristic compressive strength of masonry
characteristicflexuralstrength(tension)of masonry
characteristicshear strengthof masonry characteristicdead load designvertical load per unit area designvertical dead load per unit area clear heightofwall or column between lateral supports clear heightofwall between concrete surfaces or other constructioncapable of providingadequate resistanceto rotation across the full thickness of a wall clear height ofwallto point ofapplication ofa lateral load effective height or lengthof wall or column 11
k K
L La
N n
n Plim
o
Pu Qk qiat
multiplicationfactor for lateral strengthof axially loaded walls stiffness coefficient length a span in accidental damage calculation number of storeys in a building axial load per unit length of wall, available to resist an arch thrust design vertical load per unit length of wall acceptancelimit for compressive strength of units specified compressive strength of units mean compressive strengthof units characteristic imposed load design lateral strength per unit area
Wk yu
overall thickness of a wall or column effective thickness of a wall or column thickness ofa pier thickness ofleaf 1 of a cavitywall thickness ofleaf2 of a cavitywall design shear stress characteristicwind load deflection oftest wall in the mid-height
Z
region section modulus
t
tef tp
ti t2 Vh
i m my Ym Yu
bendingmoment coefficient for laterally loaded panels capacityreduction factor for walls allowing for effects of slenderness and eccentricity partial safetyfactor for load partial safety factor for material partial safety factor for material in shear orthogonal ratio reduction factor for strengthofmortar unit reductionfactor
5. Alternative materialsand methods of design and construction
The concept of 'good practice' embodiedin BS 5628: Part 1 does not necessarily representan exclusive approach to the design of masonry structuresand to the use ofappropriate materials. Such a rigid view would prejudice and inhibit developmentand innovation,or even individual preference. However, the code does set or indicate required standards and guidingprinciples which may be used as bases of comparison against which to judge the use ofalternative procedures and materials.
SECTION 2. MATERIALS, COMPONENTS AND WORKMANSHIP As a logical sequel to clause 5 this section defines the standards of materialsnecessary to achieve masonry constructionof the requiredquality and reliability envisaged by the code. It does so by referringto the principalexisting British Standards.
6. General
Althoughthis code relies on the recommendations in CP 121 and BS 5390 to providegenerally acceptable standards, in many cases, to achieve higher quality brickwork,certain clauses in CP 121 (see particularlyclause27, below) will require particular emphasis or amplification by the designer. 7. Structuralunits The value of a particular property of a structural unit, especially compressive strength is strongly dependenton the method of testing. Therefore use of the recommendations in the code can be justified only if unit strength or other property has been determined in accordance with the appropriate British Standard.
8. Laying of structuralunits 8.1 General
Speculationmay be raised over the precise definition of bed faces, stretcherand end faces in the 'General' clause 8. I, since it could be argued that the horizontalsurfaceon whicha unit is laid constitutesits bed face, irrespective of what it might be called when laid in another attitude. However, the express purpose ofthe clause is to draw attention to the different attitudes in which units may be used and to point the need for tests to be performed in that attitude which relatesto the use of the unit in the masonry being designed. When reference is made in clauses 8.2, 8.3 and 8.4 to layingon a full bed of mortar attention is drawn (by a footnote)to the need to allowfor the effects of raking out a joint. Whether this is done prior to pointing or as a finished feature, the thickness of the wall used for calculating stresses and loads should take into account this reduction. Although the warning as stated refers only to frogged andperforated bricks it should be taken as applyingto all bricks and blocks.
A parallelmay be drawn with Codes or Schedules whichmay be 'deemed to satisfy' the requirementsofthe BuildingRegulations but whichdo not providenecessarily exclusive solutions to particular requirements. Reference to cellular bricks is not included. Normallythey will be laid on a full bed of mortar The prime constraint on the use ofalternative with their aperture lowermost and if so used methodsor materialsis that their suitability should be tested of course in that attitude. should bejudged on the basis of tests which are designed to representas far as possible the significant factors which would influence their performancein a real building.
The code containsspecific procedures in AppendixA for determining characteristic compressive and flexural strength as well as for testingmortars.
12
8.2 Bricks withfrogs Whileit would not normally be practicable or desirable to fill the cells ofa cellularbrick with mortar, the same is not necessarily true of frogged bricks. The most efficient use of such units in developing the maximumstrength possible in a wall requiresfulland proper bedding on mortar and the filling of anyfrogs in the bricks. In practice,it may not be possible to ensure that the lowerfrog ofa double-frogged brick is filled, and less onerous strength
requirements may make it acceptable to place single-frogged bricksfrog down and with the frog therefore only partially filled. Under these circumstances, strength tests accordingto BS 187 or 3921 should be performedon bricks with unfilled lower frogs.
8.3 Perforatedbricks 8.4 Hollow and cellular blocks The titles of these clausesemphasise the fact that the terms brick and block implyrelativeshapes and sizes of units without distinction of material. It just happensthat under current conditionsin Britain most bricks are clay or calcium silicate based and most blocks are cementbased. SimmsL G, Frog-upor frog-down brickworkcompared. The Builder, 191(5917) p. 329—31, 1956. Hodgkinson H R, The compressive strength ofbrickworktested in orthogonaldirections. B Ceram R A, Report to BDA.
9. Rate of laying Although the weight ofan excessive height of masonry may squeeze out fresh mortar there are other more serious effects which require a limitationto the rate oflaying. A higher wall is more vulnerable to minor disturbanceduring setting which can lead to a rounded profile to the hardenedmortar and reduced bond at the edges of the units. The importanceof these adverse effects will be magnified when eccentric vertical loads are supported or when the fiexural strength of masonry is to be relied upon. Installingcavity wall ties as both leaves are taken up together also has a stabilising advantagefor the two leaves. HailerP, Die technischen Eigenschaften von BacksteinMauerwerkfür Hochhauser. Schweizerische Bauzeitung,76(2) p. 411—419, 195, Also available as BRS Library Communication 70: The propertiesofloadbearingbrickworkin perforated firedbricks for multi-storeybuildings. Hailer P, Load capacity of brick masonry. Designing, engineeringand constructing with masonry products, Ed. F B Johnson Gulf Publishing Co, Houston, Texas, 1969.
10. Forming of chases and holes 11. Pallet slips These apparently minor modifications may be carried out relatively easily on site and without reference to anysupervisor. In many cases they will be admissible but in extreme cases may have a serious weakening effect on the strength of the
masonry. The designershould alwaysbe consultedbefore such modifications are made. Fisher K, The Effect of Chasingon the Compressive Strength of Brickwork. Proc 3rd mt Brick Masonry Conf. Ed. L Foertig and K Göbel Bonn Bundesverbandder Deutschen Ziegelindustrie,1975. Handbook to BS 5628.' Part I
12. Damp-proof courses Despitethe widespread use of damp-proofcourses in masonry elements, their structural properties have not been studiedwidely, nor do the BS specifications provide a structural performance requirement.There is some limited dataavailable to supplement that which maybe obtained from the manufacturers.Reference may also be made to BDA and BCRA who are obtaining experimental data. The principalfactors to be considered are (a) resistanceto squeezing out due to compressive loads, (b) abilityto resist shear stresses, and (c) adhesionto mortar so that fiexural stresses may be transmitted. Plowman J M & Smith W F, The selection ofdamp-proofcoursematerial for loadbearingstructures. Proc 2nd mt Brick Masonry Conf. Stoke-on-Trent 1970. Ed. West H W H and Speed K H BCeramRA 1971.
Damp-proofcourses. BuildingResearch Station Digest 77. HMSO, 1971.
13. Wall ties BS 1243 provides a specification for the geometry ofcertain configurations ofties and minimum strengthrequirementsfor a range of basic materialstogether with recommendations for achieving some resistance to corrosion. It does not providea structural or durabilityperformance specification as such.
Choice between the varioustypes of tie therefore requiresfirst an assessment of their structural performanceand that demandedby the particular designcircumstances. A major difficulty is that maximum load-sharingbetweenleaves ofa cavity wall requireshigh stiffness on the longitudinal axis ofthe ties, eg a vertical twist tie, but differential in-plane movements betweenleaves, particularlywhenthey are ofdifferent materials, require low fiexural stiffness, eg a double triangle tie. Clause 36.4.5 considers the requirement further.
It is clear that the necessary circumstances for
corrosion of zinc, namelyoxygen and water, may be present in the outer leafofa cavity wallfor significant periods. Any protection afforded by alkalinityofthe mortar will be lost due to carbonationin a few years. Therefore, serious considerationshouldbe givento the selection of ties of adequatedurability,particularlywhen a life of at least 60 years is required during whichthe minimum margin of safety is not reducedat all. Galvanised ties to BS 1243 may not be acceptable, particularlythose fabricatedfrom pre-galvanised wire. It is worth noting that they are not permitted by the London Building (Constructional)By-laws for use in buildings greater than three storeys in height.
De VekeyR C,
Corrosionof steel wallties: recognition,assessment and appropriateaction. BRE 1P28/79.
14. Cements
The references to cements have beenlimited to Portlandcement(ordinary and rapid-hardening), Portlandblast-furnacecement, sulphate-resisting Portland cementand masonry cement, which are the most relevantto mortars. Although BS4248 for Supersulphated cementis included in CP 121 it is used scarcely if at all nowfor mortar, cement to BS 4027 usuallyhavingadequate resistanceto sulphates. The low heat properties of BS 4248, along with low-heat cements tO BS 1370 and 4246, are not necessary for mortars. 15. Mortars
15.1 General
Identification of a particular mix proportion for a type of mortar is given now by the term mortar
'designation'.This term, already used in CP 121, is an attempt to encouragethe designerto assess the desiredcharacteristics for a mortar for a particular application,and not to assume that a higher cement content necessarily means a better mortar. Indeed,it is generally advisable to considerusing as weak a mortar as possible consistentwith adequate strengthanddurability. However, extremecare is needed to ensure that the proportion of sand is not exceeded, and that the correct amount ofcementis present. Since a wide range of particle sizes may be present in building sandswhich conformto BS 1200, the sand requiredby CP 121 for mortars, the compressive strength values for mortars in code Table I are essentially lower limits. It is possible that some sands conforming to BS 1200, and used in the proportions specified in code Table I, may notyieldmortars of the requiredstrength, although this shortcoming will be apparent only when site control ofmortar is beingused or when determining masonry strength by test (see code, Appendices A.l & A.2 respectively). A survey by CIRIA has shown that, in many areas, sandsconformingto BS 1200 are not available, but that other sands have produced apparentlysatisfactory results. The practice of usingsands which do not conformto the BS seems acceptable provided that the strength requirementscan be demonstratedto be met, for example, for a range of Scottishsands. It must be appreciatedthat the compressive strengthdata in code Table 2 are based on tests carried out on specimens built in mortars, primarilycement:Iime:sand, conforming to the designations in code Table I. 15.2 Ready mixedmortars Although there is not thought to be anything inherently wrong with the use of retarded readymixed mortars care must be taken to ensurethat they are used only during the allowable period of workabilityto avoidpremature setting. Due to the extended periodbeforefinal set the vulnerability to disturbanceis increased and there is a greater risk ofdeformedbed joints and reducedbond, as discussed under clause 9. Ragsdale L A & Birt J C, Buildingsands: availability,usageand compliance withspecification requirements. CIRIA Report 59, 1976.
14
Sinha B P, Strength of mortar for brickwork. Proc Inst Civ Engrs Part 1 v60 pp 655—662
1976.
Skeen J W, The strength of brickworkbuilt withplasticised (aerated) mortars. Trans Brit Cerarn Soc 62(8) 631 1963. Sneck T, Winter masonryconstruction. Proc 1st Canadian Masonry Conf, Calgary 1976.
16. Colouring agents
The recommendations ofthisclause should be followed closely to avoid significant reduction in strength of the mortar, particularlywhen using cement lime :sand mortars. Thomas K Coutie M G and Patenian J, The effectof pigmenton somepropertiesof mortar for brickwork. Proc 2nd Tnt Brick Masonry Conf. Stoke-on-Trent 1970. Ed West H W I-I and Speed KH B Ceram RA 1971.
17. Plasticisers The warningsacknowledge the wide range of compoundsavailable as mortar admixtures. Usually only small quantitiesare requiredso that the resultingchange in mortar properties is often very sensitive to the concentration.Control is particularlyimportant sinceexcess plasticiser may be to the bricklayer'simmediate advantageat the expense of an excessivelyporous mortar of reduced durability, reduced strength and reduced bond to the masonryunits. ConcreteAdmixtures:Use and Applications: Chapter6 'Mortar Plasticisers'. Ed Rixom M R. The Construction Press London 1977.
18. Frost inhibitors The extremely harmful effect of chloridesin accelerating the corrosion ofmetals cannot be emphasised too strongly. In any case, calcium chloride is not an effective frost inhibitor. Its action is to accelerate setting, during whichthe temperaturerises so that the risk of freezing is reduced. In practice,however, the masonryunits with which the mortar is in contact will be usually at a low temperature as well. Their thermalmass is so relatively large that it will swamp anyheating effects in the relatively thin mortar joints. Wrenn 1-1 & Butterworth B, A note on the effectof chlorideson the sulphate contentof bricks. Trans Brit Ceram Soc vol xiv p412 1949. Newman A J, Concretingand bricklayingin cold weather. National BuildingStudies Bulletin 3 HMSO
1964.
Publicationsof EngineeringDivision (Structural) BRS. BRS Library Bibliography195. 1966. Thomas K, Bricklayingunder winter conditions. BDA Special Publication 1971.
SECTION 3. DESIGN: OBJECTIVESAND GENERAL RECOMMENDATIONS 19. Basisof design The designerfamiliarwith CP 110 will be accustomedto the concept of the limit state approach which is applied now in this codeto the design ofmasonry members. Many structures contain concreteelements as well, so a welcome uniformityof approach is afforded. The basis of limit state designis that the designer shouldconsiderall the likely ways in which a structure or element could fail to performits requiredfunction and should then ensurethat there is an acceptable probabilitythat failure will not occur. The approach at once acknowledges the inherent variabilityof building materials, constructionprocesses and appliedloads, and gives the designerthe opportunityto take advantageof methodsor informationwhich improvehis control or knowledge of the variability.
The modes offailure are the so-called limitstates and should be considered in two groups: (I) ultimate limit states: compressive failure, tensilefailure, shear failure, flexural failure and (2) serviceability limit states: cracking, deflection, displacement.
In the case ofmasonry, permissible stresses have been relatednearly always to ultimate stressesso that the limit state approach may be regardedas
a more refined method with greater objectivity.
Although the serviceability limit state is often of importancein masonry structuresits control usuallylieswith detailingcovered by CP 121, and general layout, rather than by structural design. However, when masonry resists lateral loads by arching(clause 36.4.4) cracking usuallyoccursat a load very much lower than the ultimate load. In practice design is performed on individual elements ofa structure,taking account of interactions betweenadjacentparts. However, this proceduredoes not ensure necessarily that the overall structure cannot reacha limitstate, since at the larger scale there may exist mechanisms of behaviournot applicableto the elemental scale. Attention is drawn in clause 20 to these wider considerations. One ofthe key operationsin applyingthe limit state approach lies in assessing probabilities of reaching a particular limitstate, ofjudging their acceptability, and of incorporatingthem explicitly into a design procedure. Methodsofvarying sophistication are available. A three level classification has been adopted by the InternationalAssociationfor Bridge & Structural Engineering (IABSE) accordingto the type of approximationmade and the way in which reliability is defined.
the parameterswhich are based ideally on statistical data and representa certain probability of the particular value beingachieved (see for exampledefinitions 3.4 and 3.5, and below). These characteristicvalues are then modified bypartial safetyfactorswhich providefor a measureof further uncertainties existing in a real structure. Theoretically, knowingthe full statistical distributionof a parameter, it is possible to calculatea partial factor corresponding to a given probabilityof occurrence eg 10-3 or 10-4, ofan extremevalue. The partial factors so derived may be presentedas a series ofcurves(Figure 2) as functionsofthe coefficient ofvariation of the selected parameter.Clearly an appropriate factor couldbe chosen for every parameter so that in the design relationshipthe combinationof probabilitiesrepresentedby the various factors wouldyield the required probabilityof failure for the whole structure.The simplest possible exampleof this approach is shown in Figure 3 for the interactionoftwo parameterseg load, F andstrength,S. In practice even this apparently simple combinationofprobabilitiesto give an overall reliability is not straightforward(Beech). Taking into account the lack of detailed knowledge of the statistical variation ofall the parametersit is necessary to resort to a more subjective assessment ofvalues for partial factors (see clauses22 and 27). The factored characteristicvalues are called design values. The objects of design are then achieved usually by ensuringthat the design strengthof a member is not less than its design load. In the simplest terms this relationshipcan be representedfor each element by the inequality:
in which
Handbook to BS 5628: Part I
represents
Sk —
a partial safetyfactor
expressing uncertaintyin the value of the
characteristicload Fk and Ym represents a partial safetyfactor expressing uncertaintyin the value of the characteristicstrengthSk. This expression may be arranged readilyas Fk where P =-'c x ''m which is equivalentto the single Figure 2 Relationshipbetween safetyfactor and
coefficientofvariation ofone variablefor various probabilities offailure.
2 8
6 0 C)
4-
2
In the absence ofa full or adequate statistical knowledge of the parametersinvolvedin structural
design, a simplified (Level 1) approach has been used in BS 5628 based on apartialsafetyfactor format. This format uses characteristicvalues of
'
ifFk
V = probability offailure
L 0
0.12
0 14
0.16
_____________________
0.18
0.20
0.22
coefficient of variation of selected parameter
15
design condition
load F
strength S
F
x
=
Figure3 Simple design relationshipbetween two probabilisticvariables.
factor of safety incorporatedin the permissible stressapproach of CP 111. But whereas this factor existedonly implicitly in the permissible stresses which were quoted, the opportunity now existsto accommodate explicitly a range of factors relatedto current knowledge about loads and materialsandto accommodate other areas of ignorance.
As already defined in clauses 3.4 and 3.5 characteristic values are a means of defining extreme values likely to occur in populations of measurements. By common conventiona 5 limit has beenchosen and indicates that I in 20 of the values may lie above or below the characteristicvalue, dependingon whetheran upper or lowerlimit has been selected (Figure4). The characteristicvalue may be estimatedfrom the mean value by variousmethods depending on the number of measurements, their standard deviation(or as expressed by coefficient of variation)and the form ofthe statistical distribution of individual measurements about the mean. Detaileddiscussion for the derivationand accuracyofthe following relationshipsmay be found in statistical treatises. The relationships relevantto this code are stated here for convenience.
(a) 2 test results: in clauseA.2.7 the characteristic compressive strength fk may be calculated from the results of two wall tests to failure by the following: Fm
uYm
where Fm is the mean ofthe maximum loads carried by the two test panels,the other variables beingfunctionsofthe test walls. If the relationship in (b) below were applicablethe divisor 1.2 would imply a coefficient of variationfor the test results 16
lower characteristic
vaiueor measurements
vaIu,Jprobabilityofbeing exceeded is 95%
There are some cases in which design involves achieving an equilibriumof loads without involvingstrength of materialsas a prime factor. Examples are provided by free-standing walls with no allowable flexural strengthfor which failure occursby toppling or by the lateral strengthofwalls subject to significant axial loading. In these cases appropriate partial factors must be assessed for the restoringforces in addition to the disturbingloads.
of about l0%.
4
value,Jprobability of beingexceededis50% upper - characteristic vaiueJprobability of being exceeded is 5% mean
Figure 4 Characteristicvalues.
(b) 30 test results: most discussions of characteristicvalue assume that the population measuredmay be describedby the normal or Gaussiandistribution,which is symmetrical about the mean. In many cases thisassumptionis reasonableand fk =fm 1 .64s wherefm is the mean value ofthe sample, s is the standard deviation ofthe sample, and the constant 1.64 relatesto the 5% level of probability.For the same distributiondifferent constants would relate to different levels ofprobability.Characteristic compressive strength values given in code Table 2 havebeen derived from mean values on the basis of this expression. (c) 10 test results ofhigh variability: when the coefficient ofvariation is large, say or more, a normal distributionbecomesan increasingly poorfit to the spread of results, not least because it implies negative values which is nonsensefor the physical quantitiesunder considerationhere. A skew, positive only, distribution is required and one such is the log-normaldistribution. In the case of flexural strength tests, it has been shown by Beech to be a reasonablerepresentationand is scarcely more difficult to handle. The method of calculation is given in code AppendixA.3.3 and is similar to the usual calculation for standard deviationexcept that experimental values are replacedby their natural logarithms.The constant for obtaining characteristicvalue from mean value in terms of logarithmsbecomes 1.922.
l5
Turning in more detail again to the partial safety factors it is as well to be clear exactly what types of variability are included in the load (-'i-) and material ('m) factors.
y takes account of:
(a) possible unusual increases in load beyond those considered in deriving the characteristic load; for example, use of statistically inadequate data. (b) inaccurateassessment of effects ofloading, and unforeseen stress redistribution within the structure; the inclusion of thiselement may be contested on the grounds that the effects mentionedare also a functionof the material formingthe structureratherthan the loads on it. However, the balance of current opinion favours allowance for these effects in 'c. (c) the variations in dimensional accuracy achieved in construction; although statistical data on the accuracy which is achieved in practice is now available for some forms ofconstruction in BS 5606 its effect on structural reliability is not known so that it cannot be quantified separately. Some authorities also include 'the importance' of the limit state being considered, that is in relation
to the social or economic consequences associated with it. In the absence of any quantifiable data this aspect is normally ignored.
The factor 'rn takes account of: (a) possible difference between the strengthof masonry constructedunder site conditionsand that determined from specimens built andtested in the laboratory. (b) any other variation in the quality of the structure One of the important attributes of the partial factor format in limit state design is that as new data become available to improveknowledge of some aspect of materials,loads or behaviour, the appropriate partial factor may be reduced while leavingunchangedthose factors describing other aspects.In practice this flexibility does not exist yet to the extent desirable since, as enumerated above, both 't and Yrn includea mixture of possibly measurablefactors and inherently unknowableelements. As indicatedalready, no specific procedures are
given for examining serviceability limit states, such as a recommendationfor alternative values for the partial factors. Design considerationof these matters is less explicitly developed for masonry than, for example, for reinforced concrete.Crackingis the condition most usually to be avoided but under many forms of loading the onset of cracking is followed very soon by ultimate failure. The main exceptions are providedby combinedlateral load and high in-planeloads, and stresses induced by movements as opposed to applied loads. Such movements may be caused by thermal and moisturechanges in the masonry elements themselves, by differential movement between connected elements e.g. reinforcedconcreteframe and masonry panels,leaves ofa cavity wall of markedly differing properties, or by foundation movements. Althoughsome guidance for avoiding
such problemsmay be found in CP 121 and various guidance notes, the key to satisfactory Handbook to BS 5628: Part I
design for serviceability limit states lies in a correct appreciation of the possible behaviourof materialsand the provision ofappropriate details to accommodate movement withoutdeveloping loads for which the elements have not been designed. Aims of structuraldesign, IStruct London,1969. Cracking in buildings. BRS Digest 75, HMSO 1970. MacchiG, Safety considerations for a limit-statesdesign of brick masonry.
Proc 2nd mt Brick Masonry Conf. Ed West H W H and Speed K H Stoke-on-Trent BCeramRA 197!.
CP 110: 1972. The Structural Use of Concrete. British Standards Institution London.
Hendry A W, The lateral strengthofunreinforced brickwork. The Structural Engineer v 51 n2 1973. Cranston W B, Limit state designand its applicationto masonry structures. Symposiumon the Structural Use of Masonry IStructE London 1974. Burland J B & Wroth C P,
Allowable and differentialsettlementsofstructures including damageand soil-structureinteraction.
Review paper Confon Settlementof Structures Cambridge 1974 Pentech Press London. Beech D G, Someproblemsin the statistical calculationof safety factors. Proc 4th mt Brick Masonry Conf. Bruges 1976. Beech D G,
The conceptofcharacteristicstrength. 6th mt Symp on Loadbearing brickwork, London 1977. Proc Brit Ceram Soc n27 1978. BS 5606: 1978. Accuracyin building. British Standards Institution, London.
20. Stability Although the detailed procedures of limit state design have been introducedto masonry they still applyfor the most part to individual elements with whichmost ofthe code is concerned. This clause drawsattention to the vital need to considerthe overall behaviourofthe whole structure.it is a vital clause because some ofthe later detailed design recommendations rely on basic assumptions about overall behaviourandalsobecause there havebeen failuresof buildings due to lack of attention to andappreciation of total structural behaviour.
20.1 General considerations For a variety of reasons the building industry has turned to the large scale manufactureofelements, among the most noteworthybeing timber trussed rafters and precast concretefloor units. With their introduction,the erroneouspresumptionhas developed that the design ofcompleteroofs and floors need not be considered further, and that no attention need be given to the part that roofs and floors play in forming and stabilisingthe overall
structure. However, even though the component manufacturermay make recommendations about
17
the way in which his product should be included in a complete roofor floor, it is the overall designer who is responsible for theircorrect inclusion and for consideration oftheireffect on the whole structure.Theseaspectswill generally involve the provision of bracing, connections or additional reinforcement, on some aspectsof which guidance is given below. Masonryis a traditional material which lends itselfto layoutson plan which may have irregular outlines and a variety of internal walls. The traditional layout has become known as cellular planform and, due to the high degree of buttressingaffordedby intersecting walls, seems a desirable form ofconstruction. Changes in practice due to economicpressures. shortagesofcraftsmen and materials,changing standards for lighting, heating and appearance have lead to simpler planformswith fewer and lighter weight intersecting walls, and larger openings. The degree of redundancy afforded by cellular planforms has been erodedconsiderably with consequent uncertaintyabout the real effects on marginsof safety. Researchat the Building Research Establishment (BRE) is examining the interactionbetween componentsto explore in more detail their behaviourand to indicate the magnitude of any reserves of strength over and above those requiredto resist normal design
iiii
loads.
Figure 5 Comparisonofwall andfloor optionsfor simple crosswallconstruction
Such reserves ofstrength are a qualitative indicationof that attribute of a building which is impliedby the terms robustnessor sturdiness. These terms refer to the sensitivity of a structure, or parts of it, to abnormal effects not considered explicitly in design for normal loads. Such effects include faults ofdesign andconstructioneg
omission of connections or unexpected foundation
behaviour,and require an understandingof the use to whicha building will be put. The difficulty ofdefiningrobustness,particularlyfor masonry buildings of less than 5 storeys. is highlighted in Figure 5 (after Sutherland). The sequence of diagrams is self-explanatory and indicates how inappropriateit is to specify rigid standards for robustness or sturdiness. However, without the designerbeing continually reminded ofthese implicit requirements there is a real possibility that proper considerationmay go by default. The two paragraphs in the Code devised to embody these principlesbear repetition: 'Thedesigner responsiblefor the overall stabilityof the structureshould ensure the compatibility ofthe design and detailsofparts and components. There should be no doubt of this responsibilityfor overall stabilityu/ten some or all ofthedesign anddetails are not madeby tue sante designer. To ensure a robust andstable design it nil! he necessary to consider the layout ofstructureon plan, returnsat the ends of llalls, interaction betlt'een intersecting na/Is andthe interaction betneen masonry na/Is and the other parts oftile structure.' The draft for public comment published by BSI in 5 leaststurdy
most sturdy
0 0
)i) insitu 2-way rc (ii) composite precast (2-way)
(a) precast with lateral I
&longitudinal ties
•
-
E
(iv) timberboard & joist I with staggered lointsj Cv) precast planks with
nolateral ties& nocontinuityor tie bars at supports
least Sturdy
most sturdy
wall layout options
18
flooring options
1974 suggested alternative design procedures for vertically loaded walls depending on whether they were braced or unbraced,in parallel to CP 110. It was concludedthat for masonrywalls, which are essentially stiff and brittle, it was unwise to contemplatestructural forms for buildings in whichlateral movement or sidesway was permittedand that only braced structuresshould be recommended. This condition is a fundamental assumptionto the developmentofthe capacity reduction factor in AppendixB. It means effectivelythat form (a) in Figure Sin which resistanceto lateral movement is provided only by the flexural strengthof the walls is an unacceptable form of construction,even though adequateresistancemightbe demonstratedby calculation.Such a layout is too sensitive to adverseloads or displacements, and the code recommendation is again worth repeating: 'The design recommendationsin Section 4 assume that all the lateralforces acting on the nhole structure are resisted by walls in planes parallel to theseforces, or by suitable bracing.' The generaldiscussion on overall stability concludes with two more specific recommendations. The first states a required minimum resistance to overturning forcesfor the wholestructure, or any part of it, up to rooflevel. This resistance is stated in terms ofa uniformly
l.5
ofthe total applied horizontalload equal to characteristicdead load aboveany level. The method of determining the load is illustrated in Figure6 but it is required to be resisted only by 6
-4
-I O.O15G
—0--
in such a way that failure of a connection cannot lead to collapse of the whole building. 20.2 Accidentalforces The considerationof generalaspectsof stability and robustness has usuallyimplied provision of some degree of redundancyto ensurethat certain minimum standards are met for the structure in addition to those necessary for the design of individual elements on their own. Following the collapse at Ronan Point there was a growing beliefthat there wasa class ofextremeloading which should be considered in design and requirements were incorporated in Building Regulations for buildings of5 storeysor more. Typical examples ofthe loads envisaged are gas explosions and vehicle impactswhich have been shownto be the most common. Their chances of occurrence are very small andunpredictablefor an individual building but foreseeable and reasonably predictable, based on historical occurrence, for buildings as a whole. A philosophyhas developed that while it is not
generally economic or even possible to design structures to withstand totally the effects of likely or foreseeable extremeloads, it is possible to design structures to accommodatethe effects of such loads and so limit the spread of damage. So has arisenthe expression 'the extent of damage should not be disproportionateto its cause'. Here again it is difficult to set objective requirements. A given explosion which in a reinforcedconcrete framed structurewith infihl walls ofvarying strengthmight blow out only the lightestweight or weakest panel, might almostdemolisha detached brick house. Yetthe same brick walls at the base of a 4-storey building could well withstand the explosion. The general exhortationsgiven in this clause apply to all buildings although further more detailed recommendations are given in clause 37 for buildings which have to comply with the intentionsof regulationD 17 of the Building Regulations. The presumptionfor low-rise buildings (lessthan 5 storeys) is that proper
Figure 6 Application ofminimum lateral load (clause20.Ia)
attention by the designerto layout and bracingto resist normal design loads willprovide sufficient reserves of strength to accommodate a reasonable range of extreme loads.
the structural elements. This load is presentedin alternative form in clause22 as a minimum value for wind loading which is the commonhorizontal load. Design to resist normal wind loads will usuallysatisfy thisrequirementfor overall stability. The value of l.5% is the same as in CP 110 and although arbitrary there seems no reason to introduce a lower figure although several other countriesuse only 1 %.,
The most commoncause of failure during constructionofmasonry walls is lack of appreciation ofthe weakness of gablewalls subject to wind loading. Temporarypropping is often necessary to high gables andto ends of walls unbuttressedby returns. However, no specific documentaryguidance is available. Guidance on the designofdomesticaccommodation in loadbearingbrickworkand blockworktoavoid
The second recommendation focuses on connections. Since considerationofoverall behaviour will involve design of connections betweenmasonry and timber andconcrete structural elements, guidance is given in AppendixC. The forms given are based on generally acceptedgood practiceand may be used satisfactorily, often withoutfurther calculation. However, most failures are associatedwith shortcomings in connections and it must be considered good practice to structure a building Handbook to BS 5628: Pu/ 1
20.3 During construction
progressive collapse.
IStructE London 1969. Menzies B & GraingerG D, Report on the collapse ofthe sports hail at Rock Ferry Comprehensive School,Birkenhead. CP69/76 BRE 1976. Criteria for structural adequacyfor buildings. IStructE London 1976. Designguide for strappingand tying ofloadbearing brickworkin low-riseconstruction. SP 93 BCeramRA 1977.
J
19
The stability ofmasonry wallsin housingwithtimber roofs.
TRADAFebruary 1977. Mainstone R J Nicholson H G and Alexander S J,
Structural damagein buildings causedby gaseous explosions and other accidentalloadings1971-77. BRE 1978. Moore J F A, The stability of low-rise masonry construction. Symposiumon Stability oflow-risebuildings of hybrid construction, London 1978. IStructE. Sutherland R J M, Principlesfor ensuringstability. Symposiumon Stabilityof low-risebuildingsofhybrid construction, London 1978. IStructE.
21. Loads The statistical basis of the termcharacteristic value is again emphasised but for most types of load it has to be accepted that there is insufficient data to enable reliable statistical derivationsto be made at present.Thus the dead (Gk) and imposed (Qk) characteristic loads are taken as the loads given in CP 3 Chapter V: Part I. The characteristicwindload (Wk) is obtained from CP 3: Chapter V: Part 2. In CP 3 the wind is presentedin terms of a return periodfor the wind speed associated with various levels of probability,so that 'characteristic' is a more reasonableterm. It should be noted that this load is derived from the design wind speed in CP 3. It should not be confused with the design wind load which is the characteristicwind load multiplied by ','r (see clause 22).
In referring to CP 2004 for lateral earth pressure on foundation walls, care should be taken to make allowance for the difference in approach to safety factors betweenthe two Codes. 22. Design loads: partialsafetyfactor, y, The foursections(a)—(d)givethe combinationsof loadingwhich should be considered by the designer, section (d) applyingonly to extreme or accidental loading conditions. The loads given are design loads and comprisea number,the partial safety factor ", multiplied by the characteristicload. In some cases there are alternative values for the design load or partial safety factor. The values of for normal loads are shown in Table 1 which gives the value or values ofyt to be associatedwith dead, imposed and wind load for the threecombinationsoftheseloads which should be considered. Thesevalues follow CP 110 exceptthat in combinationwith imposedload CP 110 suggests a lower alternative valueof 1.0 Gk. In BS 5628 this valuehas been reduced to 0.9 Gkon the basis that if the principle offavourable or unfavourableload combinationsis accepted, Table 1. Partialsafety, for normalloads
f
Load combination
y, Partial factor to be appliedto load: Gk
Qk 1.6 — 1.2
Dead—imposed 0.9or 1.4 Dead+wind 0.9 or 1.4
Dead+imposed+
1.2
Wk
1.4*+ 1.2
wind
*Jf0.015 Gk isgreaterthan the design windload, 0.015 Gk should be used. + the wall may be removed without affecting the stability
If
ofthe structure in any way y 20
may be taken as 1.2.
together with uncertaintyabout actual load values,it is inadmissible to contemplatea partial factorofunity for normal loads. However,when considering accidental loadings the generallevel of uncertaintyis muchhigher and values of 0.95 and 1.05 representjust token differences from unity.
The lower values assigned to dead, imposedand wind loads whenacting in combinationreflect an assessment of the reduced probabilitythat extremevalues would occur simultaneously. One of the notes in Table 1 refers to the alternative valuesto be considered for design wind load. These values correspondto the nominal horizontalload for which a building should be checked to provide resistance to overturning(see clause 20.1). In the context ofthe wholebuilding this force is directlycomparable to wind loading and in effect ensures that a building is designed to resist a minimumwind load. It is mainlywhen considering longitudinalstabilityof narrow buildings that 0.015 Gk willbe the critical value of wind load. These load combinationsapply equally to individual walls and columns and in such cases 0.015 Gk as applied to the whole building should be distributedin the same way as wind loads would be through the building ie on the basis of relative stiffness, to determine the load on individualelements. Although all combinationsof loadingshould be examined to determinethat which is the most severe it will often be possible to select the most onerousconditionsbased on experience. Three particular conditionsof dead and imposed load may be considered. Firstly, cases such as freestandingwalls in which the weight of the wall is a majorifnot the only restoringforce to resist overturningmoments.Clearly, minimumvalues of vertical design load should apply andit should be taken as 0.9. Secondly the combination l.4Gk± 1.6 Qk will apply to internal walls to whichvertical load is applied only by a floor spanningto oneside ofthe wall. Thirdly, when floorsspan on to a wall loaded also from aboveit may be necessary to considera range of combinationsofdead and imposedload on each element. Although 1.4 Gk+ 1.6 Qk will give rise to the greatest total load on the wall, 0.9 Gk+ 1.6 Qk on a floor or from above may lead to a greater total eccentricity of a smaller load which may be a more onerouscondition for the wall(see Figure 7(a). Guidancebased on considerationof a wide range of possibilities is given in Chapter 3 of this handbook. A more onerouscombination still may arise ifQkis taken as zero on some elements. The code does not require this to be consideredand the number of combinationswould become impracticably large. Although CP 110 envisages this conditionfor a continuousframe the minimum partial safety factor on Gk is 1.0. The more logical use of0.9 Gk in BS 5628 to some extent removes the needto considerzero imposed load.
When considering dead and wind load acting together it is necessary to use 0.9 Gk in cases when net tensile stresses could occur, such as in top floor walls or lightweight structuresfor which
7
O.9Gk+ 1 6k
1.4G+ 16k
1.4G-+- 160k
4,
/
walls built with high strength bricks which suggest that earlier permissible stresses were perhaps too high. Equally some of the walls with low strength units, in which the mortar strength approachedor exceeded the unit strength, were considered to have been underrated previously. A further result was that the ratio ofwall strengthto unit strength seemed to be more continuouslyvariable so that the data were represented better by a smooth curve. This again explainsthe variations between
the new and earlierrecommendations.The
greatest total load
greatesttotal eccentricity
(a) deadand liveiced
n
tendencyto overturn 1.4Wkor0.01 SGk—Ø
signwithO.9Gk
with1.4Gk
sign (b) dead and wind
Figure 7Loadcombinations.
the ratio of wind load to dead load is relatively high. The contrastingcases are shown in Figure 7(b). The facility providedby the partial factor format to adjust the margin ofsafety for different parts of a structure is illustratedby a further alternative value of y for certain types ofelement. Freestandingwalls and laterallyloaded panel walls which may be removedwithoutaffecting the stabilityof the overall building in any way maybe designed for a dead and windload combinationof 1.4 Gk + 1.2Wk. Although the principle of considering varyingdegreesofreliability stands in its own right, the logic of the reduction was stimulatedby the comparison between the experimental results and the design procedure given in clause 36 and by the difficulty of justifyingthe design of panel walls of apparently acceptable size. The reduction thus rests on a calibration against current practice. 23. Characteristic compressivestrengthof masonry, fk
Normalmasonry Compressive strength of masonry, including that of the componentstructural units and mortar, has for long received the greatest attention in research and testing. Work has been necessary to increase the reliability ofearlier measurements and to examine the effects of changes in type of brick and block and mortar which have resulted from innovationand other changesin practice. Thereforethe revision of this codeof practice has taken account of the latest experimental datain addition to the need to presentthe compressive strengthin ultimateor characteristicterms. 23.1
As a result of this newdata and re-appraisalthere is not a simple correspondence between the values in BS 5628 and the basicpermissible stresses in CP 111. In fact the ratio ofstresses in codeTable 2a to the corresponding stresses in CP 111 ranges from 4.04to 5.24. However, the overallmean ratio is about 4.5 andfor unit strengths less than or equalto 50 N/mm2 the ratio is about 4.6, generally being higher for the lower unit strengths. These differences arise primarily because of newdata on Handbook to BS 5628: Part 1
relationshipbetween thesestress ratios, the safety factor implicitin CP 111 andthe partial safety factors in BS 5628 is discussed in clause 27. The averagingprocesses involved in reducinga large mass ofdata to simple relationships for general use inevitably producevalues whichfor particular units may be conservative. Ifundue disadvantageis felt to accrue it is permissible to carry out wall tests to determinecompressive strength. In some cases this procedureis essential (clause 23.1.4) and the test procedureis given in code AppendixA.2. It is worth remarkingat thisjuncture that despite investigationofa wide range ofshapesand sizes ofmasonry test specimens it is considered still in the UK that storey height wall testing gives the most realistic assessment of the likely performanceof masonry in actual buildings and that, using soundly based tabulated data, compressive strengthof masonry correlatesbestwith compressive strength of units and of mortar. The data given in code Table 2 relate to normal masonry, that is masonry in which the structural units are laid on their normal bed faces in the attitude in which their compressive strengthis usuallydetermined. Bondingis described only as normal which may be taken to implythat at least vertical joints must not be continuous.Clause 8 recognises that masonry units may be laid in other attitudes eg bricks laid on edge or rectangular section blocks laid flat, andthat the bedded area ofperforated bricks and hollowblocks is less than that of solid units. Clauses 23.2and 23.3 place conditionson the use of the values in codeTable 2. There are a number of reasons whythe compressive strength ie the mean strength of a sample tested accordingto the appropriate BS, has been retainedfor unit strength,ratherthan characteristicstrengthwhichmight have seemed more appropriate in a semi-probabilistic approach. Firstly, the relevantexisting standards
for determining and controlling compressive
strength specify mean values. Secondly, the characteristicvalueofa population is related directlyto the mean strengthfor a given coefficient ofvariation, which in the long run is sensibly constant. Within limits, too,the strength ofmasonry obtained for a given unit is not sensitive to smallvariation in unit strength. However, it is important to realise that although unit strength,mortar designationand the methodsoftheir determinationare not necessarily unique considerations,the values and methodsquoted in BS 5628 are those that relate specifically to the tabulated values ofmasonry strengthas determined generally from wall tests. Unilateral alteration of one parameter, such as the method of testingbricks, could invalidatethe tables in the absence of other correlations. 21
Code Table 2(a) appliesto masonry built with bricks ofstandard format complying with BS 3921, BS 187 or BS 1180and having a ratio of height to width of about 0.6. By implicationfrom clause 23.1.2 the values apply to walls 215 mm or greater in thickness. Code Table 2(b) is a repetition ofthe lower strengthrange of code Table 2(a) with the unit strengths altered to accommodate commonly produced concrete blocks. This table has been provided so that masonrystrengths for units having ratios of height to width between 0.6 and 2.0 may be obtained by interpolationwith code Tables 2(c) and 2(d)— see clauses 23.1.5
and 23.1.6.
Code Tables 2(c) and 2(d) refer to hollowblocks and solid concrete blocks respectively whose ratio of heightto width lies between 2.0 and 4.0 inclusive. It is important to note that these tables take account of the effect of the shape of a unit on its compressive strengthso that for shapes in this range no further modification factor has to be applied for normal masonry, unlikethe procedurein CP ill. The compressive strengthofthe basic material from which bricks or blocks are made may be considered as an intrinsic property of that material. However, when attempts are made to measurethat strength,differing apparent strengthsare obtained dependingon the shape of the test specimen used (see Figure 8). A squat, brick-shapedspecimen will have a much higherapparent strengththan a slender, blockshaped specimen fabricatedfrom the same material. The difference is due primarily to the restraint ofthe loading plattens of the testing machine which has a smaller effect in the middle region of the more slender specimen. In the absence of other factors the resultingmasonry strengthis independentof the shape of the units for the same basicmaterial. However in practice, taller units for a given width reducethe number of mortar joints in a given height so that the overall effect of unit shape on masonry strength is more complex. The detailedimplications of the factors involved have not been studied extensively but the overall effect is shown by the difference between code Tables 2(b)and 2(d). Slender units (aspect ratiobetween2.0 and4.0) of the same measuredie apparent, strengthas squat units (aspect ratio 0.6) of a different
:nits apparent relative strength higher
ratioof height to width
06
intrinsic (arbitrary)
lower
1.0
2.0
material can be seen to providewalls of double the strength. Conversely, however, because of the effect ofjoints, a squat unit cut from a slender unit might have double the strength of the slenderunit but might producemasonry of rather less than double the strength.
In codeTables 2(c) and 2(d) it can be seen that
lower strengthslenderunits can producemasonry of the samecharacteristicstrengthas the mean strengthofthe units, that is mean masonry strengthhigherthan mean unit strength. Although somewhat surprising at first sight, it is explained by several factors. At these low strengths, mortar strength is similar to unit strengthso that the masonryis more homogeneous. Also, the enhancement of unit strengthprovidedby confinement in the wallis relatively more important at these strengths. It is frequentlyfound that the strengthsdetermined for dry blocks are higherthan whenthe blocks are wet. BS 2028, 1364 requiresblocks to be tested wet, the mean strengthso determined beingused in code Tables 2(b), (c) and(d), but the walltests are carried out dry. Masonry constructedfrom slenderhollow blocks does not show the sameenhancement,see codeTable 2(c), because the constraintsofadjacentunitsareless effectivein preventing failure.
In all four tables it is permissible to interpolate
between values ofcharacteristicstrength for intermediatevalues of unit strength.This interpolationis facilitatedby code Figures 1(a), (b), (c) and (d). They also demonstrate graphically the point that the ratio of masonryto unit strengthdecreases as unit strengthincreases and also the relatively limited effect of mortar designationon masonry strength.The following clausesdescribe circumstances under which modifications shouldbe made to the tabulated values. 23.1.1 Walls or columns ofsmallplan area
The random variationof unit strengthabout the mean value is normally taken account of in the quoted value for masonry strength. However, in small samples ofmasonry there is an increased possibility that sufficient low strength units may be presentfor the strengthofa wall to be affected adversely. Although this effect is statisticaland could have been accommodated by a partial safety factor it is essentially a geometricaleffect on compressive strengthand has been retainedas a modification to masonry strengthin line with CF 111. In the absence ofadverseexperience with the previous reductionfactorthe maximum area of applicationhas been relaxed slightly but the progressive effect has been strengthened because walls ofvery small plan area are likely to be particularlysensitive to the effects ofslenderness
andeccentric loads.
walls numberof bedjoints
— 9
23.1.2 Narrowbrick walls Constructionof walls of width equal to or
— 5
— 2
Figure 8 Effect ofshapeofunits on compressive strength.
22
greater than the length of the units might appear to afford evengreater restraint to individual bricks so enhancingthe wall strength.In practice, however, compressive failure occurs predominantlyby the formation of vertical
cracks.Greater resistanceto theirdevelopment is affordedby the continuousbrick cross-section of a narrow (half brick) wallthan by a wider section which is weakened by the presence of more vertical mortar joints. Test results support the use of an enhancementfactor of 1.15 which may be applied to half brick walls made from British Standard bricks. AmendmentNo. 2 extendsthe enhancement to cavity walls. 23.1.3 Walls constructed in modular bricks Modular bricks 90mm wide x90mmhigh are
more slenderthan the standard format bricks which form the basis ofcode Table 2(a), so that taking account of the effect of shape as discussed abovea somewhat highermasonry strength should be expected. On the basis of limited enhancement ofthe experimental data a values in code Table 2(a) is suggested.When the masonry thickness equals the brick width the enhancement factor is 1.25, correspondingto the enhancementfor narrow bricks walls for modular applied in addition to the
l0
l5
bricks.
l0
23.1.4 Walls constructed ofwide bricks Following the discussion above on the effect of shape ofunit it is clear that such bricks are more squat than those covered by code Table 2(a) and requirespecialconsideration.Information is not generally available for this shape of unit but once obtained in accordance with AppendixA.2 no further testingis required for similarconditions of use; however, manymanufacturersofsuch bricks will have test data available for designers, and should be consulted. 23.1.5 Hollow block walls Code Table 2(b)is provided so that the strength of walls built ofhollow blocks intermediatein aspect ratio between 0.6 and 2.0 may be obtained by interpolationwith codeTable 2(c). it applies to clay andconcreteblocks whichcontain holes
or cavities.
It is important to bond the units in a pattern whichensuresthat the webs are aligned vertically. 23.1.6 Solid concrete block walls
Interpolationbetweencode Table 2(b) and Table 2(d)enables the strengthofwalls built of solid concrete blocks intermediatein aspect ratio between0.6 and 2.0 to be obtained. Concrete blocks in thiscase must be solid, having no perforationsor cavities, whetheror not they pass right through the block. This requirement is more restrictivethan the definition in BS 2028 which permits a solid block to have up to 25% voids. 23.1.7 Wallsofhollow concrete blocksfilled with in situ concrete If the block strengths are obtained by dividing the failing loads in tests by the actual crosssection of the concrete webs carryingthe load, contrary to the procedure requiredby BS 2028, 1364, a higher valueofstrength is obtained. This increase is an approximatemeasureof the effect Handbook to BS 5628: Part 1
of filling the cavities ofa block with concreteof strengthat least as high as the strength of the
blocks, as calculated by this modified, net area, method. This higher strengthmay be used in or, for interpolationbetween,codeTables 2(b) and 2(d).
23.1.8 Natural stone masonry No new data ofgeneral relevance are available for stone masonry and the recommendations follow those in CP 111. The clause recognises the reduced effect ofmortar joints on stone masonry strength whenthejoints are relatively widely spaced and are relatively thin as a result of careful preparationofthe mating surfaces. Any increase over the recommendations for characteristicstrengthfor solid concreteblocks must be based on the designer's experience and judgment or suitabletesting. 23.1.9 Random rubble masonry As noted under clause 3.20 random rubble is not covered strictly by the term'structural units'. Howeverthis recommendationrepeats that containedin CP 111 in the absence of any alternativeguidance. 23.2 Structuralunits laidother than on the normalbedface Clause 8.1 has indicatedalready that the strength is applicableonly to the directionin whichthe unit was tested. This clauseemphasisesthat the appropriate strengthshould be used in code Table 2. 23.3 Perforatedbricks andhollow blocks This clause notes that the strengthofunits which are not solid is determinedalso by dividing their failure load by the gross plan area ofthe unit. When hollow blocksare beddedon mortar strips along only the outer edgesload is transmitted only through these strips. The strengthofthe wall is affected and the valuedeterminedfrom code Table 2 should be reduced by the ratioof the bedded area to the net plan area of the block, taking into account the perforations,unlessthe block has been tested on two strips of mortar in accordancewith clause 3 1.2.4 of BS 3921. Davey N and Thomas F G, The structural use of brickwork. Proc iCE Struct. and BuildingPaperNo 24
1950.
Thomas F G, The Strength ofBrickwork. Structural Engineer v 31 n 2 1953pp 35—46. Concreteblocks: BRS publications. BRS Library Bibliography 164, 1956.
PrasanS Hendry A W and BradshawR E,
4
Crushingtests ofstorey heightpanels in thick. Proc Brit Ceram Soc July 1965 pp 67—80.
Simms L G, The strength ofwalls built in the laboratory with some types ofclay bricks and blocks. Proc Brit Ceram SocJuly 1965 pp 81—92.
23
West H W H Hodgkinson H R Beech D G and Davenport S T E, The performanceof walls built of wirecut bricks with and withoutperforations. Trans Brit Ceram Soc 67 421 1968. Reed J B and ClementsS W, The strength of concrete block walls, phase H: underuniaxialloading. C&CA Report 42.473 1972. Roberts J J,
A survey ofliteraturerelating to thepropertiesand use
ofconcreteblocks.
C&CAReport 42.467.
1972.
Fisher K, The effect of low strength bricks in high strength brickwork. Proc Brit Ceram Soc April 1973 pp 79—98. Beech D G and WestH \V H. The performanceof modular bricks in storey height salls. Proc Brit Ceram Soc April 1973 pp 25—38.
Roberts J J, A supplementary literature list relating to the properties
and use of concrete blocks.
C&CA Report42.495.1974.
24. Characteristic flexural strength ofmasonry, fkx CP suggests values for allowable tensile stressesin bendingto be used at the designer's discretion.Since that code excludes consideration ofwalls carryingonly self-weight and windloadit is unclear under what circumstances the discretionis to be exercised, other than to resist uplift, for example,due to wind suctionon roofs. Now, however, the inclusionof design informationfor such walls, defined as laterally
ill
loaded wall panels,is a major advance in the new code.
The designmethods given in 36.4(and 36.5 for free-standing walls) rely on a knowledge ofthe flexural strength of masonry. The word 'fiexural' is used deliberately to emphasise that this strengthparameter, although substantially tensileby nature, is based on data obtained from tests carried out in bending,or fiexure. Thus the samecaveat applies as beforeto using masonry in direct tension: it is left to the designer's discretion(see below). Attention has been drawn already to the two principaldirectionsof fiexural failure ofmasonry in the explanationof the term orthogonalratio. They are depictedin code Table 3 in whichthe failure surfaceis called a plane. For failure in the weakerdirection, along the bedding, this descriptionis reasonable.The nature ofthe failure surfacein the orthogonal directionis more complicated. Again as shown in the code, failure may cause a toothed or interlocking surface to develop in which fiexural tension develops across the perpends and rotational shear occurs in the bedjoints. However, when mortar and unit strengths are closerto each other, fiexural tensionmay develop across the whole sectioncausing a more or less plane fracture. 24
The values quoted representa significant amount of experimental data. Most of the testinghas been carried out by the British CeramicResearch Association,part of the programmebeingfunded by BRE. In the course of the work a range of parametersincluding water absorption,initial rate of suctionand unit fiexural strength were investigated for a possible correlationwith flexural strength of masonry. The most significant correlationfor clay bricks was obtained with water absorption andthe selection of three ranges takes optimum advantageof the overall spread of data (see Figure 9). For concreteblocks, unit compressive strength correlatedwell for the strongerdirectionbut in the weakerdirectionthere was general scatter but little correlationwith strengthof block or any other property. The test proceduredescribed in AppendixA.3 is basically that used by the British Ceramic ResearchAssociation.The specimen sizeand loading arrangementhave been determined from the need to incorporateas manyjoints as possible in the loaded region, the largest specimen conveniently movable in the laboratory and provision of as large a zone as possible with a uniform bendingmoment by limitationof the shear span ratio. Variousresearchworkers have used smaller specimens and different loading arrangementsbut by suitable transformationthe stresses at failure in the different tests may be compared with each other. Although no standardisedtest method has beenagreed yet, that proposed here represents an optimisationof the various constraints.An appraisal ofthe method is being carried out at BRE. Measurements of flexural strength are characterisedby a higher variabilitythan found for compressive strength. Calculation of the characteristic value takes this into account but when the coefficient ofvariation is high, say above l5°, the normal distribution becomes inappropriateand AppendixA.3 proposesthe use ofthe log-normaldistributionas discussed under section 19. Negligible error accrues from using a log-normal distribution when the standard deviationis small.
AppendixA.3 recognises variation in width of masonry but most of the experimentaldata refers to 102.5 mm bricks and 100 mm blocks. There are some indications that thicker wallettes may have lower strengthsbut the code draws no distinctions. Equally, the moisturecontent of units at the time of layinghas been considered of some relevance. The bricklayer may certainly wishto adjust the suctionof bricks by 'docking', as recommended for exampleby CP 121, to facilitatelaying. Although an improved bond may result, the flexural strength of wallettes built from a rangeofundockedbricks having high water absorptionexceeded the minimum values quoted in the code (ie, for waterabsorption over l2%). The contrast betweenthe permissible values quoted in CP 111 and the new values is marked. In the perpendiculardirection,for mortar designations higher than (iv), most characteristic
9
.
E E
z
undocked
0 docked
I
0) C a)
mortar:1:1/4:3 fature plane: perpendicular
U,
is
S S
.
U,
a)
S
.
•S I
undocked
•
•5
odocked
.1
S
0
. 0
•• 0
S
.
.
00
S
•'
0
•
.
mortar: 1:1/4:3 failure plane parallel
. 0 S
.
0
0
0
0
95%limit limit
0
1
0L
20
0
36
10
20
waterabsorption (0/)
E E
30
water absorption (%)
• undocked
z
0 docked
0) C a)
mortar 116 failure plane perpendicular
10 Cs
•
xa)
E E
••S.
•S
•undocked L
•
S S
S
••
0
S
.
S
•, • So
0
S
0
•
0
odocked
.
:
C
mortar:1:1:6 failure plane: parallel
S
0.
S.
. S
0.5
S
S
5 0
0
0
0
95% limit
0
0
10
waterabsorption (°)
Figure 9 Flexural strengthsand water absorption.
values of fkx are greater than before, except for lower strengthconcreteblocks which were excluded previously, anyway. However, generally only clay bricks with waterabsorption lower than l2% have strengths in the paralleldirection greater than before.In the design procedure described later it willbe seen that use is made of Handbook to BS 5628: Part 1
10
20
30
waterabsorption (%)
the higher(perpendicular)value of fkx in conjunctionwith the orthogonal ratio, not involving explicitly fkx in the parallel direction, other than for walls spanning in a vertical directiononly. The three explicit conditionsgoverning the use of flexural strength relate to direct tension, flexure at a damp proofcourse,and limitationof 25
9 (Cont.)
1.0r E
.
E E
odocked
C
mortar: 1:2:9 failureplane: perpendicular a)
2
failureplane:parallel
•
S
°•7r-
0.6k
S
SO S
.
I
. S ••0 S
,-
mortar: 1:2:9
'C
.
odocked
0.8: S
S
xa 3-
undocked
I
r C,
.
-
E
undocked
S.
S
I
.
C
0
0.3-
95'/limit
______ C
10
-
20
30
Figure 9Flexuralstrengthsand water absorption.
combined flexural and direct tensilestresses. It
is not generally acceptable to rely on masonryin direct tension but, under some circumstances it may be permissible, such as resistingwind uplift on roofs or accidental loads. The direct tensile stresses should be limited to halfthe flexural strengthsin codeTable 3. Sinha B P and Hendry A W. The tensilestrength of brickworkspecimens. BCeramRA TN 219. West H W H, The flexuralstrength ofclay masonry determined from wallette specimens. BCeramRA TN 247. Satti K M H and Hendry A W, The modulus ofrupture ofbrickwork. Proc 3rd tnt Brick Masonry Conf. Ed L Foertig & K Göbel Bonn Bundesverbandder Deutschen Ziegelindustrie 1975. Anderson C, Lateral loading tests on concreteblock walls. The Structural Engineer 54 n 7 239—246 1976. West H W H Hodgkinson H R and HaseltineB A, The resistanceofbrickworkto lateral loading: Part 1. The Structural Engineer v 55 n 10 1977.
f
25. Characteristic shear strengthofmasonry, There are several types ofshear failure of masonry. Vertical shear may occur, particularly at the junction of intersecting walls, in which masonry units bonding the walls together will suffer shear failure. Horizontal shear may occur alongbedding surfaces, particularlyat the level of damp-proofmembranes. However, unless the wall is particularlylong or the vertical load sufficiently high, failure by horizontal in-plane
0 95%limit
0.2b
0
10
water absorption 1%)
26
0
C
30
20
water absorption (%)
forces is more likely to occur by rotation ofthe wall, effectively tensileor peeling failure of the mortar joints. Once masonry is enclosed in some kind of bounding frame which offers restraint to the edges of the panel failurewill occurby diagonal shear. Both diagonaland horizontalshear resistanceare dependent on vertical stress in the masonry and the recommendations in the code relate to these conditions. if resistance to vertical shear is required it will be necessary to obtain experimental data.
The recommendationsdo not represent newdata but are a translation into limit state terms of the values given in CP 111: 1970, as amended in 1971, with the addition oflower values for mortar designation(iv). The amendment was based largelyon a reassessment ofexisting and additional experimental work. Furtherwork has providedthe addition for weakermortar. It may be observed here that the conventionfor subscriptshas lapsedas characteristicshear strengthmight have been expected to be denoted by fkv. The original relationshipin CP 111 waseffectively 0.1 *0.16 N/mm2. A global safety factor of 3.5, equal to -'c=l.4 multipliedby çmv=2.S (see clause 27.4) transformsthispermissible strengthto a characteristicultimate strengthof 0.35 --0.56 with a maximumof 0.5 x3.5=
g
g,
1.75 N/mm2
If, however, the shear strengthis requiredto resist wind load on a panel to which •'= 1.2 is applicable, the horizontal shear capacityis effectivelyincreased by 16% although the probabilityof failureis also increased. Care
should be taken to choosethe appropriate partial factorswhen determining design vertical load. The shear resistance of masonrywill be required usuallyto resist wind loading andload combinations(b) or (c) in clause 22 could apply for normal loads. But clearly case(b) is the more critical because the design dead load willbe lower and the design wind load higher.Normally, there will not be circumstances in which vertical imposed load can be includedin (see code AmendmentNo. 2).
g
Fox A,
A review ofthe literature on the racking strengthof brickwork.
BCerarnRATN 285.
L G, The shear strength of somestorey-heightbrickworkand blockworkwalls. Chartered Municipal Engineer 91(1) pp 87—91 1964. Sirnrns
PieperK and Trautsch W, Shear tests on walls. Proc 2nd mt Brick Masonry Conf. Stoke-on-Trent 1970. Ed West H W H and Speed K H BCeranRA 1971.
Grenley D G and Cattaneo L E, The effectofedgeloadon the racking strength of clay
masonry. Proc 2nd mt Brick Masonry Conf. Stoke-on-Trent 1970. Ed West H W H and Speed K H BCerarnRA
be independentofthe structural material and relate only to the applied loading regime. m must, of necessity, take account of the differing characteristics ofthe various structural materials. It may be helpfulto suggest an alternative frameworkwithin which to considerclause 27, since the relation to quality control recommended in clause27.1 does not apply to all values of (rn. Firstly, distinctionsmay be drawn between limit statesfor each material, ie, compressive and flexural failure (27.3) and shear failure (27.4), and finally account may be taken ofabnormal loading (27.3, 27.4 and 27.5). The requirements for quality control (27.2) have been omittedfrom thisframeworkdeliberately, not because their relevance andimportanceshould be minimised in anyway, but because they representessentially a separate set of conditions whichcould be applied to all aspectsofthe framework.However, because the compressive and flexural strengths of masonry are usuallythe most important strengthparameters,the question ofquality control has been applied only to them, and the clausebuilt up around this aspect. Improvementsin quality ofthese parametersare also likely to offer the best return to the designer in terms ofeconomyand lead to better quality of other properties.
27.2 Quality control 27.3 Valuesofyrnfor normalandaccidental loads 1971. 27.4 Values of Ymvfor shear loads Mainstone R J and Weeks G A, 27.5 Valuesofymfor use with ties The influenceofa bounding frame on the racking In CP 110, only single values are recommended stiffnesses and strengthsof brick walls. under normal loads for each type ofyrn, and Proc 2nd mt Brick Masonry Conf Stoke-on-Trent steel andconcretestrengths are the only relevant 1970. Ed West H W H and Speed K H BCeraniRA 1971. parameters.However, it could be considered that the differences between'designed'and 'prescribed' mixes are tantamount to two levels of quality Hatzinikolas M, control for concretestrength.In this code,the Shear behaviourofmasonrywalls subdivided by floorplates. flexibility presented by the partial factor format 1st Canadian Masonry Symp Calgary 1976. has been used as positive encouragementto the production of masonryof improved quality. The two most significant factors influencing the 26. Coefficientof friction compressive strength of masonryare the This value has been based on limited work but compressive strength ofunits and the manner in seemsto conformwith values given in other which the units are put together on site to form national codes for masonry structures. Its value the masonry. Thereforetwo types ofquality is identical to the slope of the shear strength/ conceived, based on control of vertical load relationshipin clause25 for masonry control are — control (clause 27.2.1) strength 'manufacturing' but with zero value in the absence ofverticalload. — and on control of workmanship and mortar — Ifa strong shear connection is requiredmasonry 'construction' control (clause 27.2.2). For each will offer greater resistance than can be provided of control 'normal' and 'special'categories type by friction of. for example, a concretefloor are defined. bearingon a wall. Conversely, beingweaker, such a joint may representthe critical limitstate under certain load combinations. The main use of The difficultiesin applyingthis approach have centredessentially on determining values for yrn frictionprobablyliesin design to resist accidental which, in relation to each other, are justified by damage. the differences achieved by the control methods, andwhich, in relation to overall safety, represent 27. Partial safetyfactorsfor materialstrengthm realistic levels of reliability. As indicatedabove 27.1 General under clause 19, it is difficult in practiceto Considerationof the valuesfor Ym, the partial establishanalytically partial factorswhich relate the overallreliability of a masonryelement to the safety factor for material strength, represents the essence oflimit state design, particularlyas variabilityofthe influences on it. Thus ?m has to to The effects covered be judged generally against established practice, applied masonry. possible an act of calibration,and the partition of Ym by yç have been considered under clause 19 and it has been shown that, ideally at least, -yr should between the combinationsofcategories of control Handbook to BS 5628: Part I 27
may be assessed analytically to judge relative values.
In translatingbasiccompressive stresses in CP 111
into characteristicvalues it was assumed that CP 111 embodieda safety factor of at least 5. This is the load factor recommended in CP 111 for tests on squat walls. As it related to basic stresseswhich were already tendingto lower limit values it was considered that 4.8 would be a reasonablefactor of safety in relation to characteristiccompressive values. Takinga typical partial safety factor for loads as 1.5 leads to a partial safety factor for materialsof 3.2. This value should representexisting practice which must in reality includea range ofconstructionin which quality control, particularlyofstructural units, is both better and worse than average. It was then envisaged that two categories of manufacturingcontrol could be established as equal marginsabove and belowthe nominal value of 3.2 Anynumbers must be construedas indicative of general argumentswhichalthough broadly correct cannot be exactlyso. In particular the value of overalldepends on the ratio of dead to live load whichwillvary. Retainingthese arguments,the value of 3.2 wasmodified to 3,3 (the mean of3.1 and 3.5), and the other categories ofcontrol related to it. When dead load predominates,;'f= 1.4 andthe overall factor of safety is 1.4 x 3.3 =4.6 which accords with the overall relationshipdiscussed in clause 23 betweenfk and basic stress in CP 111. In relation to the highestvalue of 'm=3.5, the other lower values of "rnrepresentajudgment of the improvements in strengthwhich may be attributed to improvedmanufacturingcontrol, vizan improvementof about 12%, by applying clause 27.2.1.2, and to improvedconstruction control, viz an improvement of about 25%, by applyingclause27.2.2.2. Both enhancements may be applied independently of each other ifjustified. For bricks, the use ofquality control schemes to demonstratethe attainmentofan 'acceptance' limit is often practisedalready by manufacturers. The aim ofa better guaranteeofstrength is sound because the average strength ofbricks is more important in determining masonry strengththan the individualor minimum strength.The reliability attached to the value of an 'acceptance' limit is reflected reasonablyin the 12% enhancement.Many manufacturersoperate suitable control schemes, and the Calcium Silicate Brick ManufacturersAssociationhas recommendedappropriate quality control proceduresto its members. It is to be expected that advantagewill be taken frequently "rn =3.1, as long as manufacturers provide the necessary information.It shouldbe understoodthat manufacturingcontrol implies a more reliable estimateof the strength of the bricks being produced,and does not imply that the manufacturingprocess itselfis being alteredso as to producea more reliable product. It is worth notingthat 'special categoryofmanufacturing control' should not be confused with 'special quality' bricks whichrefers to theirdurabilityas defined in BS 3921.
The enhancement affordedby special category 28
constructioncontrol must be acknowledgedto representa more subjective assessment of the benefits to be derived from improvedcontrol of site workmanship and mortar strength. It recognises the costs involvedin providingthe necessary supervision andtesting, and balances them against the economic advantagesto be gained from the enhancedstrength. Clearly, the applicationofthese procedures willbejustified only on major works, but factors which havebeen shown to have a significant effect on compressive strengthincludefailure to fill bedjoints, bed joints of excessive thickness and unfavourable curingconditions,the latteralso affecting bond (flexural) strength. Before examining other values for 'im it should be noted that the valuesgiven in code Table 4 are to be applied to flexural strengthfk as well as compressive strength fk. The data supportingthe effect of the quality control measureson flexural strength is not substantial. However, the design predictionsbased on clause 36.4using the lowest value Of';'rn=2.5 compare favourablywith the experimental strengths of laterally loaded panels. In view ofthe importanceof using the correct
value of fk appropriate to the water absorption, it is recommended, particularlywhen using reducedvalues "rn, that manufacturers' assurancesabout the value of water absorption should be obtained. In generalterms there is a loose correlationbetween the water absorption of clay bricks and their compressive strength,so that better assessment ofthe latter should ensure greater reliability of the former. With concrete blockwork,there is a broad correlation between the compressive strengthofblocks and the flexural strength of blocks, and betweenthe flexural strength of blocksand the flexural strengthof blockwork.Again, control of compressive strength willtend to better reliability of fkx, particularlyfor the perpendiculardirection used for most panel wall design. As there is no obvious correlationin the weaker parallel directionreduced values "rn should be consideredcarefully. Values of fkx in this directionare used for vertically spanning walls and, suitably reduced as recommended in clause 24.1, for resisting wind uplift forces. The option of testing masonryspecimens to obtain strength data, as an alternativeto using tabulated values,is encouraged throughout the code. Tabulatedvalues are ofmore general application and by incorporatinga widerrange of materialsare necessarily more conservative than informationobtained from and restrictedto only one material. This more specific dataoften implies the use of a higher characteristicvalue than tabulated, and in recognitionofthe improved informationa 10% reductionof the partial factors in codeTable 4 is permitted.An inseparable consequence ofthisallowance is that it is restrictedto the use of the circumstances of the test. The single partial factor for shear ofmasonry, 'mv, derivesfrom the global factor implicit in CP 111 and represents the relatively lower variabilityobtained in experiments on specimens. The valuefor ties represents an allowance for possibleshortcomings in the quality of installation including poor beddingand lack of normality to plane of wall.
Whenconsidering the effects of abnormal loads, about whose magnitude there is considerable uncertainty,the reductionin reliability by halving all the values assumed for m in the designfor normal loads is equivalent to increasing the probabilityof failure by something like two orders ofmagnitude.The exception to this reduction applies to the lateral strengthofaxially loaded walls and columns(36.8) for which m includedin the designprocedure is a general safety factor, not specifically related to material strength(see also discussion under clause 19). 1-lendry A W,
The effectof site factors on masonryperformance. Proc 1st Canadian Masonry Symp Calgary 1976. Reed
J B and
Clements S W,
The strength ofconcreteblockwalls. Phase Ill: effects of workmanship, mortar strengthand bond. C&CA Report 42.5 18 1977. Hendry A W,
A noteon the strength of brickworkin combined racking shearand compression. 6th mt Synip on I.oadbearing brickworkLondon 1977 Proc Brit Cerarn Soc n27 1978. Modelspecification for loadbearingclay brickwork. BCeramRA SP 56 1980.
SECTION4: DESIGN: DETAILED CONSIDERATIONS The code has providedin the first three sections a frameworkofbasic conditionswithin whichthe design of individual masonryelements has to be performed.Thus, within a discussion ofoverall structural performanceand of the philosophyof design to limit states, guidance has been given to enable the loadingregimes to be establishedand to assess the inherentstrengths of the available materials.The next stagein the design is to establishthe local constraintson elements as incorporatedin the structure so that design strengths or resistances may be establishedand equated to design loads or moments.This Section therefore suggests design procedures for the full rangeof combinations ofapplied verticaland horizontalloads, both normal to and in the plane of the wall, and suggests the degreesof restraint andresistancewhich may be providedby various other structural elementsor within the masonry itself to enhance the strengthof a simple unsupported masonry element.
AppendixC. It shouldbe noted that the slenderness ratio to be used in code Table 7 and AppendixB is based on whichever is the lesser of effective height and effective length. As the slenderness of an axially loaded member increases its load carryingcapacityreduces as its tendency towardsbucklingfailure increases. In order to avoid the possibility ofsudden buckling failure,without warning, a limiting slenderness ratio of 27 is adopted which is independentof the load to be carried andis simply a functionofthe geometry ofthe wall. The value is not derived analytically but based onjudgment and assessment ofexperimental tests on walls. The limitis the sameas that incorporatedin the 1971 amendment ofCP ill: Part 2: 1970 and represents a slight relaxationof the more stringentlimitswhich had beenintroduced earlier, althoughpart of the changewas duesimply to the reduction from nominal to actual thickness. At these high slenderness ratios the load carrying capacityis so reduced anyway that a practical limit would be placed on the usefulness of even more slender walls. The practical limitationson workmanshipand accuracyofconstruction inevitablewhen usingvery thin units (ie less than 90 mm) in buildings higher than two storeys (ie more than typicalhouses)lead to the limitationof slenderness ratio to 20.
28.2 Lateral support Clause 20 drew attention to the need to ensure that all masonry structuresare adequatelybraced both to resist horizontalloads and to prevent sidesway of walls, the liabilityto bucklingof whichwould otherwise be considerably increased. It is normally convenient to providethis resistanceby lateral supportswhichact either in a horizontalplane or a vertical plane. As far as the supported wall is concernedits interactionwith theseplanes is either a horizontalor a vertical line. This clause provides the strengthcriteria for lateral supports (28.2.1) and indicates the restraint providedby typicalforms ofconstruction to the supported wallor column(28.2.2 and 28.2.3).
28.2.1 Horizontalor vertical lateral supports The two load bearing requirements for lateral supports have been containedin CP 111 since its two earliestversions. Statement(a) that 'the simple static reactions to the total applied design horizontalforces at the line oflateral support' Therefore,the first five clauses28, 29, 30, 31 and shall be resistedis self-explanatory. Statement(b) 32 deal primarilywith aspects of vertical load derives from considerationofthe horizontal carryingcapacityofwalls togetherwith those forcesrequired to stabilise a wall out ofplumb by cases in which lateral load may be treated as an a nominal amount oftan-10.025 or 6 mm in a eccentricity of vertical load. The next threeclauses deal with types ofloading whichare generally less storey heightof2.5 m. Field measurements of the criticalbut nevertheless of significance: shear (33), accuracies achieved in constructionconfirm this assumption.These two requirements apply to concentratedloads (34) andcompositeaction with supportingbeams(35). The finalclause (36) individualwalls andcolumnsand their lateral supports.Whenwalls or other componentsare dealswith all other aspectsof walls subjected to to resist the total horizontalforces on provided lateral loads. the structure as opposed to individual elements Consideration ofslenderness ofwalls and columns the out ofplumbnessconsiderationmay be 28.1 Slenderness ratio ignoredon the basisthat it is cateredfor The definition of slenderness ratio given in clause separately. It is equally important to considerand 3 requiresthe determinationofeffective height, designthe connectionsbetweenwalls, supports length andthicknessof walls. Guidanceis given in and bracing, whetherfor elements or the whole clauses28.3 and28.4, the recommendations in the structure, to transmit the same loads as the former clausebeingbased on the conditionsof supportsetc have been designed to resist. In restraint discussed in 28.2and illustratedin other words, the possibility of overlooking Handbook to BS 5628: Part I 29
connectionsshould be carefullyavoided to ensure that they do notbecomethe weak link in the overall structural concept. In general terms, the greater the restraint applied to the edges of a masonry wall or column, the greater the load it can carry. Restraintmay be either resistanceto movement laterally ie normal to the plane of the wall, or resistanceto rotation of the edgesof the wall. Similar considerations apply to the ends of a column, but along both its horizontalaxes of symmetry. These conceptsof translational androtational stiffness are well established in structural analysis. It should be noted in particular that resistance to translation implies fundamentallya stiffness of support, although it may be convenient to interpret it in practiceas a force. Resistanceto rotation does not necessarily imply no rotation. When it is possible to take into account the relative stiffnesses of elements it may be possible to calculatedirectly the effective height or length of walls and columns without the needto use the guidance given in 28.2.2, 28.2.3 and 28.3. Based on experience, however, these clauses together with AppendixC show the restraint offered by various common forms ofconstructionfor which nominal values for effective dimensions may be used. Since the resistances afforded are only nominal, but adequate,forms ofidealised restraints they have been distinguished by the descriptions simple resistance' (cf translational restraint) and 'enhanced resistance' (cf rotational restraint). 28.2.2 Horizontallateralsupports The array of conditionsin this clause may be summarised as follows: (a) Simple resistanceis providedby all types of floors or roofs which abut walls as long as straps
are providedwhenrequired, as indicatedin AppendixC. Exceptionsto the need for straps are concretefloors abutting an internalwallon both sidesat the same level (code Figures 22, 23 and 24) and timber joists, in houses of not more than three storeys, provided that they are separated by not more than 1.2 m and bearingon not less than 90 mm of wall or are supported on typical joist hangers. As an alternative to straps for timber joists a stronger type ofjoist hanger,as illustratedin code Figures 13 and 14, may be used (code Figures 12 and 19). The recommendations on the spacingof straps and anchorsare contained in appendix C. The intervals should not exceed l.20m (page 31 of the code is incorrect) except in houses of not more than three storeys when they may be increased to 2m. (b) No types of floor or roofcan provide enhanced support unless they span across, or onto by at least 90 mm, their supportingwall. The applicationto timber floorsspanning from one side only is restricted to houses of not more than three storeys. In higher buildings enhanced resistancewill requirefloors of a greater stiffness than can be providedby timber. The exceptionsto the generalrequirementsthereforeapply to housingand connections to internal walls; examples are shown in Figure 10. The code of necessity refersto 'typical'joist hangers, meaning as commonlyavailable, because there is no relevantstandard. One of the main objectives of the design of hangerillustratedin code Figures 1 3 and 14 is to provide an improvedtensile 30
10
joist nailed or screwed to hanger
cfcodefigure11 (a) simple resistance in housing,N
3
(b) enhancedresistancein housing, N
3
joistsfirmlyfixedto
——-—intermediate
special hangers
_
____________
not exceeding
I
joistsfixed to typical
______________
hangers
p
2.Orn
cfcodefigure20 (c) simple resistance in housing, N
3
Figure 10 Horizontallateralsupportsnot requiringstraps.
connection to masonry.
It has been remarked already that the key feature for mobilising lateral support is an adequate
connection which introducesno additional flexibility or degreesoffreedominto the interface betweenwalls andlateral supports.Particular points to note are setting joist hangers tightly against the supported wall and securing thejoists firmly to the hangers, adequate packing between wall andjoists abutting it and adequatefilling betweenwall andprecast concreteunits if not tight against the wall. The design ofconnections usually requires closer attention when the floor units span in the direction parallel to the wall ie
abut the wall, as there will be no connection at all unlessdeliberatelyprovided. A particular difficulty to be considered in the detail is possible deflection of the floor. Although timber floors may be moreflexible than concrete,particularlyin housing,the abilityofconcretefloorsto span greater distancesconveniently mayalso incur
between a return wall bonded to the supported wall (enhancedresistance) and two walls tied together (simple resistance). Here again the recommendations are based more on experience than experimental quantification. Although not stated explicitly in clause 28.2.3.2, the length of return necessary to develop
A numberofgeneral points about AppendixC may be noted here for convenience. The suggested connections do not constitute necessarily the only forms of suitable connectionsfor lateral supports.They are based, however, on a widespread survey of current
less than ten times the thicknessof the wall it restrains. Although shear in the bed joints may be the limiting factor for both types ofrestraint, enhanced resistance involves a more complicated state ofrotational shear as well. Again, other forms of constructioneg columns, may be suitable (clause 28.2.3.3) providedthat theiradequacycan be justified. Although it may be possible to calculatethe simple resistance providedby an alternative form, the ability to resist rotation is likelyto be assessed subjectively.
increased deflection.
practice and therefore representa sound crosssection of perceived good practice. Nevertheless there has been little experimental investigation of the behaviourof connections either as components on their own, whereappropriate, or as parts of sub-assemblies comprising wall, connection andfloor or roof. The research programmeof BRE is planned to investigate this area which lacks quantification. When designing straps or anchors it is important to design adequatefixings between strap andfloor and between strap and wall. Mild steel will usuallybe suitable and a partial safety factor of = 1 .15 should be applied to the appropriate characteristicstrength. A more detailed discussion ofthe design ofanchors may be necessary but the metal should be corrosion resistant and the durabilityofgalvanised steel should be assessed if the straps or anchors are not likely to remain in a dry environment. Leaking flat roofs causingcorrosion may have serious structural consequences beyond that nf simple dampnesswithin the building. It is noted that the samedetails are generally applicableto roofs as well as floors even though the figures illustratethe latter. However, roofs may be subject to upliftforces as well and the need for ties to resist them must be considered. Guidanceis not given because it is not relevantto a roof's functionas a lateral support. A very common form of roofing is providedby trussed rafters which will be requiredusuallyto provide lateral support both to flank, ie front and back, and gable walls. In the case of gables, this support may be requiredat joist level as well as by the rafters to the verge. Similar considerationsapply to the design ofconnectionsbetween the end trussesand gable walls, as well as between trusses and wall plate, and wall plate and wall. Simple resistancemay be assumed. Guidanceon connections is also availabl&in the context of Schedule 7 of the Building Regulations. It should not be forgotten that in providinglateral support to gable walls almost certainlythe resistance to the applied loads will have to be transmittedto shear walls by diagonal bracing in the roof. 28.2.3 Vertical lateralsupports The same concept of simple and enhanced resistanceapplies to vertical lateral supports,that is buttressingwalls mayprovide resistance only to lateral movement or may in addition provide moment restraint at vertical edges ofa wall. The significance ofthese restraints is discussed in 28.3.2 but the distinction is made here primarily Handbook to BS 5628: Part I
reasonablemoment restraint should also be not
28.3 Effective height or length 28.3.1 Effective height The effective height is a measureofthe relative susceptibility of a wall or column to buckling failure based on classical Euler bucklingtheory. An effective height equal to the clear height (28.3.1.1(b)) of a member having lateral supports providingsimple resistance(28.2.2.1) corresponds to the length of a pin-endedEuler strut. The effect
ofrestraint at the ends is to restrict the rotation
and so increase the bucklingload. This load may be equated to the strengthof an effectively equivalent, shorter, pin-ended strut (Figure II).
That shorter length is equal to the length of the
restrained strut between its points of contraflexure. Full restraint ie no rotation at the Figure II Comparisonofeffective andactualheightsfor varionsend conditions. 11
r a)
t
.2
Q
a)
1.
wallwith
wallwith
simple resistance hei = h
enhanced resistance h0f = O.75h
wallwith fullrestraint
= he O.5h
column with no lateral support inonedirection hef = 2.Oh
rr.
(a) Constanteffectiveheight
(b) constant actual height
'a
i 31
ends ofa wall would providean effective length 0.5 the clear height of the wall. The factor 0.75 in 28.3.1.1(a) for walls restrained by one of the methodsdescribed in 28.2.2.2 is semi-empirical, based on experience and measurementof the behaviourof typical walls. Although it is not necessarily correct to make this global assumptionit will generally be conservative to do so. Theoreticaland experimental studies have shown that the actual effective height ofa wall may be strongly influenced by the level and position at which it occurs in a building. particularly one having more than two or three storeys. and by the pattern of loading. Thus some internal walls near the base of a high building ie having substantial precompression. may have significantly higher restraint with a factor of 0.6 being appropriate. More commonly, perhaps. walls will be contained betweenfloor and roofoffering enhanced and simple resistancerespectively. Then it may be appropriate to calculate an effective height between0.75 and 1 .0
Columns (28.3.1 .2) have been shown by experiment to have a somewhat lower strength for a given height than have walls, mainly due to lower in-plane restraint. The effect of slenderness on the strengthof a column is greater than for a comparablewall and an allowance for this is madeby increasing the effective heightto equal the clear height. It is assumed that columnswill be providedat both ends with only translational restraint. If restraint is lackingat the top in one direction the effective height is double the actual height (Figure 11). Vertical load bearing walls, of course, should not be unrestrainedin this way. The method of treatingcolumnsformedbetween openings in walls is described in 28.3.2.3 and represents a presentationof earlier recommendations more explicitly in line with the types oflateral support given in 28.2. The meaning is demonstratedin Figure 13. If the effective height ofthe wall equals its height ie simple lateral support. any brickwork above or belowthe openings adjacent to the column should be ignoredas its restrainingeffect is small. If
Figure 13 Effectiveheightofa column between openings. 13 enhanced lateral supports
-
simple lateral supports
h_Lh he = h
timberroof
Figure 14Effectiveheightofapier.
I h01
h2
he
14
= 1.0h1
= O.75h2
timberroof
*1Oh4
tiedto floor)
¶h4
h5
L—J 32
28.3.2 Effecth'e length Under some circumstances failure of a wall under vertical load may not follow the simple Euler bucklingmechanism. When the length of the wall is much shorter than the height and when the vertical edgesare restrained 'multiple buckling' occurs as if the wall is composed of a numberof approximately squarepanels each of height equal to the length ofthe wall. The effective strength is much greater due to the restraint and the enforced modeoffailure. The dimension controlling bucklingbecomeseffectively the length ofthe wall, or some function thereof. Determinationof the relevant length is related to the type of vertical lateral restraint as described in 28.2.3 and is illustratedin Figure 15. The assumptions behind this approach are based more on analogy with the bucklingbehaviourofthin steel sheets than on experimental tests on brickwork. However, it is
he O75h a25h, but c h
Figure 12 Effectiveheightsfor typical sections 12
enhanced lateral support is provided to the wall some measureof restraint is afforded by the adjacentbrickwork.The effective height is then determined by interpolationbetween 0.75 and 1.0 xfull height. by reference to the height of the taller opening. Clause 28.3.1.4 enablesthe slenderness of a pier to be determinedby treatingit as a column or as part ofthe wall. The conditionsare illustratedin Figure 14. The importanceof this consideration of effective dimensions ariseswhen additional load is carried by a pier by virtue of its reduced slenderness relative to that of the wall on its own. The pier is effectivelystocky in the plane ofthe wall. If its overall thickness is limited to 1.5 times the wall thickness, the effective height normal to the wall may be taken as that appropriate to a wall rather than a column.
hei5_ 1.0h5
waH
f
t5t H.
treatthis portionas wall of thickness t,
1
_____
assume Stocky inthis direction
treatthis portionascolumn of thickness and width b
buckling dueto vertical load
\
\
I I
I I
/ L
h
j
extent in 1964to cope with 'zig-zag' walls, which were irregular on plan but still essentially solid walls. However, these recommendations have not been included in BS 5628 for several reasons. Firstly, zig-zag walls, as such, are rarely used nowadays;secondlythere are more advantageous ways of stiffening walls, eg, diaphragm or cellular walls which contain voids and are therefore no longer 'solid'; and thirdly, althoughthe radius of gyrationcan be computedreadily for such sections, the failure mechanism is no longer clear. The effect of slenderness on load carrying capacitytherefore needsfurther examination. If such walls are used, it is recommended that the effective thicknessbe taken as the overall thickness of the wall, in the absence of experimental evidence suggesting greater freedom. 28.4.1 Walls andcolumns not stiffened by piers or
4+4
fr44
15
but ifh >> L andvertical
)))
edges simply supported, buckling occurs in shorter halfwaves
— )L) )
44 he=h
andsimilarly forother
minimum strength corresponds to h= K0 x L whereK0 is integer
4++
length controls instead of height
44
L
h01= L
combinations ofedge restraint
Figure 15 Effective length ofa wall.
relativelyrare for advantage to be taken of effective length in calculating slenderness. A typical example might be a lift shaft or stairwell in which all four walls buttress each other, or a short return wall supporting a substantially loaded lintel. An alternativeapproach is adopted in some countrieswhere a continuous function is used to define a factor modifying effective height dependingon the shape of the wall, and the degree ofvertical edge restraint. The allowances appear generous and, based on current
intersecting walls
The origin of the rule given for the effective thickness ofcavity walls is obscure, but is very nearly equivalent to adding the momentsof inertia of the two leaves. That is, the two leaves stiffen each other but do not act compositely. When the thicker leafexceeds twice the thickness of the inner leaf (which it might have done when cavityor 'hollow' walls were first devised) the effective thickness so calculated becomes less than that of the thickerleaf and should be ignored if the thicker leaf is the load-bearingleaf(also relevantto 29 and 32.2.3).
researchin the UK, it is not clear that they are
justified.
28.4 Effecth'e thickness For structural analysis in other materials, slenderness ratio is commonlydefined as the ratio of effective length to radius of gyration. However. for solid walls the actual thickness, which is equal to the radius ofgyration multiplied by \l2, was introducedby CP III: 1948 as the 'effective thickness' for calculating slenderness ratio. For timber, in fact, CP 112 provides alternative values for slenderness ratio based on both radius of gyration and effective thickness. The actual thicknesscould be modified to account for other arrangementsin plan (piers, intersecting and cavity walls) which could stiffen a wall and so increase its effective thickness. The concept of radius of gyrationwas reintroducedto a limited
284.2 Walls stiffened bypiers or intersecting fs'alls The data in code Table 5, based on limited work
at BRS, have remained unchangedsince the original publication of CP III. The effective
thickness is the thickness of an equivalent wall having the same moment of inertia as the wall with piers. The effect of changing the pier spacing and thickness is shown visually in Figure 16. The unity values in code Table 5 define the limits of applicationof the stiffness coefficient K. Whereas the effect of vertical lateral supports (28.2.3) is to alter the mode of failure ofthe wall (28.3.2), the effect of this limited degree ofstiffening is confined to an effective reduction of slenderness. but still with the sameeffective height. In the case
Figure 16 Stiffening due topiers.
16
L —
L, = — 20
10
L2
3r
I
/ I
2F
tp
L
I I I
= 20
•10
L1 = pier spacing, centretocentre L2 = pierwidth K = stiffness coefficient (code Table5)
2 K
L
= 10
1.o
4.4
tp
11•0
V
I. Handbook to BS 5628: Part 1
33
of bonded intersecting walls, it could be more
advantageousto considerthem as vertical lateral supports than as piers.
Timoshenko S and Woinowsky-Kreiger S, Theory ofplates and shells.
McGraw-HillNewYork
1959.
Timoshenko S and Gere J M.
Theoryofelastic stability. McGraw-HillNewYork 1961. Bradshaw R E and Hendry A W, Preliminary tests on storey heightcavity walls.
Designing,engineeringand constructing with Masonry Products. Ed Johnson F B, Gulf Publishing Co Houston Texas 1969. Milner R M and Thorogood R P, Accuracy ofloadbearingbrick constructionand its structural implications. Proc 2nd Tnt Brick Masonry Conf, Stoke-on-Trent 1970. Ed West H W H and Speed K H BCeramRA 1971.
Fisher K, The effectofwall ties on the compressive strength of cavity walls. Proc 2nd mt Brick Masonry Conf. Stoke-on-Trent 1970. Ed West I-I W H and Speed K H BCeramRA 1971.
Wood R H, Effectivelengths of columns in multi-storeybuildings. BRE CP 85, 74. Information Sheet No 1. Truss Plate Association May 1974. Curtin W G and Shaw G, Brick diaphragmwalls in tall single-storey buildings. Brick DevelopmentAssociation November 1977. Sawko F and Curtin W G, Effective thickness& structural efficiency ofcellular wallsand piers. Proc Inst Civ Engrs Part2 v 65 pp 893—898 1978. Fisher K and Haseltine B A. Compressive loading tests on diaphragmwalls. 5th Tnt Masonry Conf. Washington USA 1979.
29.1.2 Minimum thickness ofleaves This minimum is based on a considerationof the accuracy which is achievable for the plumb ofa single leaf. 29.1.3 Width ofcavity
The upper limit is a structural limit based on the ability of ties to be stiff enoughto transmit forces dueto buckling or windload. Wider cavities might be acceptable on the basis ofsuitable wall-tests. The lower limit is more a serviceability limit at which cleaning out the cavity becomes difficult. Mortardroppingsare likely to bridge the cavity and increase the passage ofwater to the innerleaf. 29.1.4 Spacingofties The spacingofties is the same as given in CP 121 and representstraditional practice over the last 60 years or so. Although not derived by calculation, the densityofties over the face area of a wall seems intuitively right, particularlywhen extra ties are placed around openings and at anglesor junctions with buttressingwalls. Tests have shown that, at the recommended spacings, the weakest tie specified by BS 1243 is adequateto transmit the bucklingresistance required in a vertically loaded wall. Other tests have suggested that even fewerties may serve this function.When lateral loads are to be shared between two leaves, the strengthrequired ofthe ties should be assessed (clause 36.4.5), although in many cases wire ties may be found to be adequate. However, the experimental data on widercavities is small and particular attention should be given to workmanshipand supervision to ensurethat the correct ties are installed at the correct spacings. 29.1.5 Embedment ofties
It is important that the minimumembedmentis achieved with the ties at right angles to the cavity to avoid significant reductionin either pullout strengthor bucklingstrength.
29.2 Externalcavity walls The differential vertical movements betweentwo leaves may be as much as 1 mm per metre height of wall, dueto temperature differences and to differing moistureregimes and responses. Since most of thesechangesare reversible and repetitive, the adverse effect on the anchorage strength ofties could be considerable. The effects are cumulative with increasing height ofwall so that, at three storeys, the differential movement at the top could be theoretically8 mm which would imposesevere strains on the beddingof ties. The relaxationto include four storeys is reallyto accommodatehousing whereexperience suggests, particularlyin Scotlandwherefour storey dwellings are relatively commonin cities, that the higherlimit does not causeproblems. In higherbuildings, masonrywalling will often be Various considerationslead to a determinationof built directlyoffa reinforced concrete slab. Ifthe the slenderness ratio of a wall, taking into account edge of the slab is not exposed but, for example, concealed by brick slips, particular attention its plan form and the type of edge restraint. should be given to achieving the accuracies of However, its strength arises basically from the stresses which can be resisted by the cross-section constructionand preparation ofsurfaces under load. Tn a cavity wall, the cross-section is necessary to achieve durable fixing of the slips. If the outer leaf of brickworkis builtoffa steel either that of a single leaf, or both leaves ifboth are loaded vertically (clause 32.2.3): it cannot be angle or similar support fixed to the floor slab, the gross plan area of the wall including the cavity. similar considerationsapply. In addition, the 29. Special types of wall Just as the message in clause 20 was to consider the overall behaviourof the structure as a function ofits component parts, so the message here, for compositewalls, is to considerthe interaction between the various materialsand their effect on the behaviourof the wall as a whole. Ifa number ofmaterials are designed to share the applied load, their interactionshould be assured by appropriate attention to detail. Conversely, elements not designed to accept particulartypes ofload should be isolated effectivelyfrom those that are. Althoughmost ofthese recommendations are practical detailsthey are often ofvital importanceto the structural performance. 29.! Cavity walls 29.1.1 General
34
corrosion resistance of the support and its fixings should be assured. The objective in limiting the height ofmasonry to 9 m is also to permit unrestrained movement vertically and care is necessary to provide adequatehorizontal movement joints in the design. It is essential to ensure that they are achieved in practice and not, for example, filled with mortar or other debris. Although again a matter ofdetailing,and covered by CP 121, it is important to considerthe need for vertical movement joints to accommodatehorizontalmovements. 29.3 Facedwalls The essential feature of a faced wall is that commonaction between the two compatible structural units is achieved by bonding, as in a solid wall composed offacingand common bricks. Ifthe connection is provided by ties, mortar or grout the wall should be designed as a cavity, double-leafor groutedcavity wall. 29.4 Veneeredwalls Even though no structural action may be attributed to a veneer, adequateprovision must be made for stabilising and securing the veneer to its supportingwall. 29.5 Double-leaf(collarjointed) walls 29.6 Groutedcavity walls The principalreason for using theseforms of wall is to achieve a fair-faced finish to both sides, ofa standard that could not be obtained normally from a single leaf wall due to unavoidable variations in the dimensions of bricks and blocks. In the absence of the cross-bonding inherent in a single leaf wall wider than a single unit, strict control of constructionaldetail is necessary to justify consideration structurallyas a single leaf wall. If the appropriate conditionsare not met, design as the more conservative cavity wall is permitted.
The conditionsare based on a limited numberof tests in which it wasshown that decreasing the stiffness and number of ties decreasedthe strength of the wall, and increasing the cavity width precipitatedfailure of the bond between the filling of the cavity and the bricks. The reference to flat metal ties arises because vertical twist ties will not sit in the bed joint properlywith such a narrow cavity as used in collar-jointed walls. The limitationson separation of the leaves for both types ofwall arise primarily from the characteristics ofthe infill material andthe practical aspects of placingit. The mortar is packed in as each layer of units is laid and derives its strengthfrom its limited thickness. Because of the difficulty ofachieving this with units more than about 75 mm high, the reduction is made to the quoted strengthsfor blockwork. As grout is essentially poured into the cavity, and may be placed and tamped in lifts of the order of0.5 m, a minimum width of cavityis required. -In theexperimental programme,the load was applied concentrically to both leaves, load being carried by the mortar or grout only by transfer through its interfacewith the bricks. The limitationon eccentricity wasnot tested experimentally andtherefore should be treated with respect. Handbook to BS 5628: Part 1
Beard R, The compressive strength of somegrouted cavity walls. Proc Brit Ceram Soc April 1973 pp 113—140.
30. Eccentricity in the plane of the wall 31. Eccentricity at right angles to the wall 32. WaIls andcolumns subjected to vertical loading In order to determinethe compressive strengthof a wall requiredto resist a specific load, or to determinethe vertical load bearingcapacityofa given wall, it is necessary to determinethe distribution of load on the wall, that is the effective eccentricity ofthe resultant vertical force. Distinction is drawn betweenvariation ofload intensity along the wall ie in its plane (clause 30) and acrossthe wall or column (clause 31). Along the length ofthe wall, the distribution will often be uniformunless the wall acts as a shear wallto resist, for example, windforces. In that case, the load combinations(b) or (c) in clause 22 are applicablei.e. I .4Gk+ 1 .4Wi or 1.2 (Gk+Wk+Qk) unless the uplift combination 0.9 Gk + 1.4 Wk is more onerous. Exceptional distributionsof vertical load may also occur(see clauses34 and 35). The horizontal forces may be transmitteddirectly to a single wall, eg, a spine wall, in whichcase the vertical forces induced in the wall may be calculated from considerationofsimple equilibrium, as long as adequate connections are providedeither along the vertical edge ofthe shear wall or by the floors along the horizontaledges. Whenthe horizontal forces are resisted by several walls, the sharing of the load must be deducedfrom the relative flexibilities ofthe floors and walls. If the floors can be considered as rigid diaphragms, it will be conservative to distributethe forces between the shear walls in proportion to theirstiffnesses on the assumptionthat theyalldeflect by the same amount
andthatadequateconnectionsare provided.Ifthe
layout ofwalls on plan is asymmetrical, the possibility of torsion of the buildingabout a vertical axis andfurther redistributionof forces may need to be considered. Ifthe floors are relatively flexible when considered as horizontal diaphragms, eg partiallyinterconnected precast units, the distribution of forcesbetweenwalls will be deducedfor each wall as ifin isolation. The desirability of calculating the effective height ofwalls from a knowledge ofthe relative stiffness of walls, columnsandfloors wasdiscussed in clause 28. Such analysis will take into account the effects of vertical and lateral loads and continuity atjunctions betweenwalls and floors. The resultingmomentsmay be expressed in terms of vertical load and effective eccentricities. However, it will not always be possible or appropriateto follow this procedureas the assumptions made maynot be in keeping with the sophisticationof the analysis. As an alternativeapproach, simplifying recommendations are madefor determining eccentricities in clause 31. They are describedin Figure 17. They represent approximationsfor commontypes of support or connection as envisaged in clause28.2.2 (horizontallateral support). 35
17
18 e1 positive
e1 positive
epositive it thiscondition applies calculat€ appropriate /3
e2 negative
conservative assumption
(a)floor or roofonone side
e2 = 0
assumed
condition
e2 positive
moreonerous condition
Figure 18 Combinationsofresultant eccentricities. eccentricities of opposite sense could carry more
c2 (b)floor both sides continuously —lost hanger
25mm
(c)joisthanger Figure 17Assumedfloor eccentricities.
In general, eccentricities might be expected at both top and bottom of a wall (see Figure 18). That at the top is dueto the combinedeffects of load from the structure above, from the effects of
horizontalforces, and from floor loads applied directlyto the top ofthe wall. The eccentricity at the bottom is determinedby the total load from above, and the degree of restraint afforded by the lateral support at that level. Following the argument shown in Figure 19 based on that used in CP 110 for a braced structure,code AppendixB assumesthat the eccentricity at the bottom will tend towards zero ie, the vertical load at that level, immediately above a lateral support, may be assumed to be axial. This assumptionis not intended to be conservative but a realistic assumptionof actual conditions. A wall bent in doublecurvature due to top and bottom 36
load, but a wall with both eccentricities in the same direction represents a more onerous condition.If such conditions were seen to prevail then the recommendations in clause 32 would not be applicable. In all cases of vertical loading(direct or induced by lateral loads), it is necessary to determinethe effects of these eccentricities on the ultimate strengthofthe most critical sections of a wall. The method ofdoing so is described in clause 32 based on the analysis given in AppendixB, although it may be said at oncethat other approachescould be acceptable. In CP lii, the effects of slenderness and eccentricity have been allowed for by a series ofstress reduction factors applied to the nominal basicstressfor the crosssection under consideration.These factors have been based on a considerable volume of experimental data obtained by BRS, initially on columns or piers, and then on walls, and more recently at BCRA, and also in the USA. As experience has been gained in usingthe factors, and as the experimental base has increased,the reductionfactors havebecomeless stringent. In reviewing this aspect of performancein the light of the limit state approach, an analytical basisfor determining the effects ofslenderness and eccentricity seemed appropriate. This basis is not a necessary consequence of limit state approach but has been verified, ofcourse, against experimental data. The approach used by CP 110 for plain concrete walls has been adopted. Tt is assumed that at ultimate failure the stress distribution in a wall at the critical section may be representedby a rectangular stress block and that, when significant, the effects of additional momentsinduced by lateral deflection of the wall under vertical loads are taken into account. Finally,the assumptionthat only braced vertical load-bearingmasonry walls should be built, or at least that the recommendations in the code apply only to such walls, leads as described above to the assumptionof zero eccentricity at the bottom of a wall.The modelsrepresenting these conditionsare shown in Figure 20 (stress block) and Figure 21 (deflection ofwall). Based on the deflections in the central region of the wall, the additional eccentricity dueto the effects ofslenderness ratios greater than 6 is given
19 -cracking here will causeeccentricity tomoveinwards upper loadN,assumed
toact centrally
floor load N2acting through third pointof bearing area
— N3acting on wallis resultant ofN,and N2
N3assumed
toact centrally here
influenceofcracking inslab
initialloading
safeassumptionsfordesign
Figure 19 Eccentricitiesin a braced structure.
r
byCatlL
1
h2j
'ef'
20
1
1, e,,
(Appendix B, \tef equation I). This function is plotted in Figure 22 to indicate its magnitude in relationto the eccentricity at the top, cx. The allowance is marginally more onerous than that given in CP 110, that is, a slightly larger deflection is assumed. However, for stocky walls and columns, the additionaleffect is ignored. From Figure 21 it is seen that the largest eccentricity occurs in the midheight region and, generally the total eccentricity, etr-:0.6ex (Appendix B, equation 2) because ex varies linearly from top to bottom of the wall. However, when ea is small the total calculated eccentricity at the top of a wall, cx, may be larger than et; design should be based then on this larger value, known as the 'design eccentricity', em. By relating the width and magnitude of the stress block to the design eccentricity (which includes the effects of structural and additional eccentricity), and to the characteristic compressive strengtha capaci1y ieduction fictor', may be deducedto yield directlythe load which a wall can carry. In CP Ill the use ofa stress reduction factor ofcourse requires a further calculation, based on an assumed stress distribution,to derive the load. The magnitude of the ultimate compressive stress is fk, or as a design stress
e
I
A
ii!±'but y,,
I
.
5jfoxe
y,
O.O5t 2e
t(i--)
Pigure 20 Siress blockunder ultimateconditions
21
ie
e, stocky wall e0 small
eadditional
O.6e
eccentricity
,
When the design eccentricity ie the larger of ex and et, is small, that is less than 0.05t its effects are negligible and the full section of the wall resists failure stressesthere is no reduction in capacityrequiredand = I. For larger values of em, the width of the stress block is t (i _--'). It is importantto distinguish clearly betweenem (a functionofcx) which is used to calculate the effects of eccentricity and slenderness, and cx which is used in code Table 7 as a design parameter. It should be noted also that hei in code Table 7 encompasses the lesser of effective length
or effective height.
Logically, the magnitude of the stress block at failure should also equal -—b- even when em is
greater than 0.05t. For convenience in design, however, it has been assumed that no further calculation should be necessary for applied eccentricities cx less than 0.05t. If a stress block of Handbook to BS 5628: Part I
(a) deflections
(b) maximum e1 at midheight region
(c) maximum at top
e
Figure 2/ Designeccentricity.
-s-were retained there would be an unreasonable
step reduction in 3 as cx exceeded 0.05t. By a smooth changeis increasingthe stress by / 2cm providedleading to a value of = 1.1 (Appendix B, equation 4). Values of calculated from this expression are given in codeTable 7. A comparisonbetween assuming a rectangular stress block and a triangular stress distribution, as suggested in CP Ill. is shown in Figure 23. It also illustrates the effect of not requiring. calculation for cx <0.05t. The key to the acceptability of this whole approach lies in correlationwith the experimental evidence. As the values of stand, they represent in many cases a considerable increase in allowable load capacitycomparedwith CP 111. A calibration exercise was carried out by Jenkins & Potter on behalf of the Building Research Establishment, with contributionsfrom the Cement and Concrete Association and the Property Services Agency of the Departmentof the Environment. The aim of
l0
1
37
22 e
1
oo(ç' _oo15] het2
-
O4h
jO.2h
-
JO.4h
h Figure 22 Additionaleccentricityv. slenderness ratio. a 0 a xa C) a
I
23 ,rectanguIar stress block, 11--k- and nochange
incapacityfor e
O.05tandstress block =
E
-o a
0 0
C
C)
0 0 C) C)
a E
Figure 24 Comparisonofcompressive loadcapacities.
eccentricity ÷ thickness,-
Figure 23 Comparison ofstress blocks with no slenderness effect.
the exercise wasto check that the proposednew code would not result in designs for the use of structural masonry which were significantly less safe than, or otherwise incompatible with, current practice.A major part ofthe calculationswas concernedwith the vertical load capacityof walls and columns ofvarious typical thicknesses and shapes. For each type of constructionnine combinationsof brick, block and mortar strength were considered under four combinationsofdead and live load with five slenderness ratios and four values of eccentricity. As a result, a number of alterationswere made to the draft code and recalculationcarried out where necessary. An overall comparison is affordedby the histogramin Figure24 wherethe Andividual calculated resultsare plotted on the basis ofthe ratio ofthe capacityallowed by CP Ill to that allowed by BS 5628. From an examinationofthe individual results which make up this composite picture, it is clear that for axial loads the two 38
codesgive broadly similar results. The divergence occursas eccentricity and slenderness increase. A direct comparison with CP Ill was made difficult by the different partial safety factors ascribedto dead andlive load. As the ratio of live to dead load is increased from zero to three BS 5628 becomes about lO° more onerous than CP Ill, all other conditionsbeing the same. Primarilyas a result of this thereare circumstances for most bricks and blocks which are slightly more onerous than before.Calculations were also performedfor the walls of a specific design of a two-storey house, an eight-storey cellular plan block and a nine-storey cross wall block. These results showed that, when using 'm=3.l for bricks, BS 5628 allowed bricks to be used of up to two classes lowerstrengththan when designed using CP 111. However, the major reason for the differences at eccentric loads lies in the assumptionof zero eccentricity at the bottom of a wall. The stress reduction factors have represented hitherto lower bounds to a mass of experimental results which for the most part have been derived from tests in which the eccentricities were applied at both top and bottom. In other words,they did not represent conditions comparableto those assumed now. By isolating and concentrating attention on the experimental data which do representthe assumed loading conditions Figure25 demonstratesthat the less conservative reduction factorsare justified. A small part of this data is derived from
tests at BRS but much ofit relates to tests in the USA on both bricks and blocks.
Lateral
supports: Horizontal 28.2.2 Vertical 28.2.3 Effective height of piers: 28.3.1 .4
Cavitywalls It must be made absolutelyclear that the thickness ofa wall or column referred to in 32.2.1 and 32.2.2 is the thickness ofa single leaf wall or of the loaded leaf of a cavity wall. Although 't' is defined in clause 4 as the overall thicknessthis does not apply in the context ofa cavity wall and is not used in codeFigure 2. The guidance given in clause 32.2.3 applies only to the case when both leaves support vertical load and the resultant is containedbetween the centroidsof the two leaves. When the resultant acts outsidethis central region the load may be assumed to be carried by one leaf
Effective thickness:
(two-thirdsrule) 28.4.2 (stiffening by piers or walls) 28.4.1
Loadedarea: one leaf 29.1.1 Limitations
on plan:
thickness 29.1.2
both leaves 32.2.3 cavitywidth 29.1.3 embedment 29.1 .5
Limitations
on face:
tie spacing 29.1 .4 height 29.2
only. WaIls subjected to shear forces The recommendations suggest that the design shear stress should be calculated on the
33. Since there are several clauses at variousjunctures in section 4 which refer to different aspectsof cavity walls it is convenient and desirable to list them togetherhere, excluding those relatingonly to lateral or accidental loads.
assumptionof a uniformdistribution over the horizontalcross-section ofthe wall resisting the horizontalload. If it should be moreappropriate
Figure 25 Experimentalbasisfor 3.
25
t
.
.
S
•
S
S
key
•e=O
S
S
S
S
S.
.
S
lO3results
. .
$
.
S
S S
slenderness ratio
key
0
•e=O.167t 33results
1. C
0 0
.
oe,=O.33t
. 0 a Q. a 0
S S
lOresults
• .
. S
•
S
4,. S..
O.167t
S
0
slenderness ratio
Handbook to BS 5628: Part 1
39
to assume an alternativedistribution, eg parabolic, it will be necessary to calculate the maximum shear stress and check that against the
design shear strength. The design shear stress will involve the appropriate partial safety factor from clause22. It is assumed that the walls have a simple rectangularplan and that no account is taken of intersecting walls. StaffordSmith B and Rahman K M K, The variatonof stressesin brickworkwallssubject to shearforces. Proc 3rd tnt Brick Masonry Conf. Ed L Foertig and K Gdbel Bonn Bundesverbandder Deutschen Ziegelindustrie 1975. 34. Concentrated loads: stresses underand close
to a bearing
The recommendations in CP Ill allow a 5O° increase in permissible stress, due to concentrated loads. However, the meaningof local' is left to the designer's discretion. Although experience has not found this allowance generally wanting, there are theoreticaland experimental groundsfor restricting the increase in some cases, and indeed for relaxing it in others. The new recommendations seek to define these conditionsso that a more realistic approach is adopted. When a small central area ofa pier is loaded, the capacityofthe pierhas been shown to increase several fold. The masonrybeneath the loaded area develops a state of triaxial stress which enhances its ultimate strengthcomparedwith a uniformly loaded pier. Similar enhancement occurswhen a load is applied to a short length of a wall, but other factorsthen become significant as well. The length to width ratio of the loaded area, the proportion of length and width of wall to which load is applied, and the proximityof the ends of the wall all need to be considered. The experimental data is not extensive and relates to full width bearings of various lengthsand positionson slenderwalls, and to central bearings as various proportions of the cross-section of square columns. Figure 26 (which reproducesFigure4 of the code, with annotations)attempts to presenta balancedassessment of the importance of the factors in terms of allowable increases in compressive strength in steps of 5O and lOO%. Figure 27 sets out a logical connection betweenthe various types of bearing on the basis ofthe effects of lengthto width ratio ofbearing area and ofthe ratio of bearing width to wall width. The starting point is bearing2.3 in Figure 26 in whichmore than half the width is loaded. A maximum allowable lengthof four times the width ofthe wallhas been assessed on the basisof the rate ofdissipationof vertical stress with depth beneath the bearingand the limited experimental data(unpublished). The allowable overstress of 5O% corresponds to current practice.As a rough guide the stress reduces by 5O° over a depth belowthe load equal to the length ofthe bearing. Whereasthisimplies significant reduction within a short distance below a shortbearing, beneath a long bearingthere will be a substantialzone of significantly increased stress within which failure of the wallwould occur.
25,
Figure 26 Bearingsfor concentrated loads.
local design strength
(b) bearingtype 2 distribution of stress under the spreader shouldbebasedon anacceptable elastic theory maximum stressshould not 21 exceed —--
(c) bearing type 3
27 bearing 2.3 increase length
L, length short W,width full
I
reduced end restraint
I, increase 5O%
bearing 1.4
bearing1.3
L, length medium
L, length short W, width full
W,widthfull
I, increase 25%
I, increase 25% increase length substantially; localised overstress
reduce width
bearing1.2
bearing 3
L, length long W, width < halt I, increase 25%
L, length long
increase length and restraint
bearing 1.1
W, width lull I, increase 100%
L, length medium
W,widthfull
I, increase 25%
decrease length
bearing2.1
bearing2.2
L. length medium
L, length short W, widthfull I, increase 50°o
W, width < half I, increase 500/0
Figure 27 Relations/zips between bearing types andlocal increases in stress.
In order to allow an increase in bearing length the overstress must be limited. Bearing I .4 in Figure 26 therefore allows an increase ofonly of
25
compressive strengthwhich provides a possible increase in total load of 25° compared with the shorter higher stress bearing. A similar allowance is permittedfor bearing 1 .2 in which the bearing width is less than half the width of the wall, but greater than 50 mm, a reasonable minimum bearing. There has been no experimental work on this type ofpartial bearingon masonry but limited tests on concrete suggest that the allowance is reasonable. Rupture occurs effectively by shear failure of the wedge of material beneath the bearing, modified by any restraint on movement of the loaded beam perpendicularto the wall. By restricting the length of this type of partial bearing, further restraint is gained from the ends ofthe failure zone andthe allowance of bearing 2.1 becomes feasible. The maximum length ofthis type of bearingis the same as that allowed for a full width bearing, 2.3.
25
50
type 3 (code Figure 4c). Then the overstress may be l00% since it applies over only a very short strip ofwall. Whereasit will be sufficient to assume a uniform stress beneath the concentrated load in most cases, the stress distributionbeneath a spreaderloaded at the end of a wallwill be distinctly non-uniformand the valueofthe maximumstress shouldbe considered. Although an elastic stress distributionis reasonably acceptable the presence of the vertical boundary means that numerical solutions will be the most practical in cases when standard solutions for rigid beamson elastic foundationsare not appropriate. It is worth noting the general similaritybetweena spreadersupportinga concentratedload at its end and the configuration obtained by inverting a compositewall-beam (see clause 35) supportinga uniformload and simply supported at each end. Each reactioncorresponds to an applied concentratedload. However, since a spreaderis of more restrictedlength than the supportingbeam the stressconcentrationwill be more severe. Althoughthe typical distribution illustratedin code Figure 5(b) appears to be out ofequilibrium with the appliedload, this obviously cannot be and local yielding ofthe masonry and fiexure of the spreaderwill occur. The illustrated distributionwas obtained from an experiment on
Tests with loads at or near the ends of walls confirm that when the bearing lengthis limited (to for the sake ofconvenience, 2t) only a overstress isjustifiable(bearing 1.3). This a spreader. arrangementis effectively 'half' type 2.3. When In most cases of spanning at right angles to the the failuremode is constrainedby the restraint wallthe distance ofthe bearingarea from the end offered by a beam spanningin the plane of the shouldexceed a minimum value as shown because wall, some enhancement is possible, either as an increase in bearinglength to 3t (type 1.1), or as an the increase in stress derives in part from the restraint at each side of the bearing. In addition, increase in overstress to (type 2.2, with maximum bearing length of 2t). In all these cases althoughit is convenient to assume a uniform stress distributionon a bearing surface, there will ofend loading, the width ofbearing should tend to be stress concentrationsbeneath the edges exceed half the width ofthe wall. of a relatively rigid beam or spreader.For a long Inothercases ofconcentratedloadingat the endsof bearing type 1.1 the contribution would be a wall, a spreadershould be used as in bearing negligible and the condition does not apply.
25
50
Handbook to BS 5628: Part
1
41
The discussion so far has assumed that only concentratedloads are acting. In practice,there will often be additional distributedloads and in suchcases the combinedstresses shouldbe checked against the appropriate allowable increases. Since the dissipation of stress, even at limited bearing lengths,occurs over a finite depth downthe wall it is possible that there will be a significant increase ofstress in the centralzone of maximum eccentricity in a slenderwall. The stresses should be checkedat a depth of0.4h using the appropriatecapacity reductionfactor and assuming that the stress disperseswithin planes at 45c to thehorizontalasshownin Figure5 in the code.
28
archingaction inwall
allowance forconcentrated
—
/ //
loadsinthiszone-------—-tyingactionofbeam
—lengthofcontact
I1
Attention has been drawn to minimumedge distances, but it should not be assumed that they can be applied on both sides of a bearing. This wouldlead to bearingareas as much as 75' of the cross-section of the wall for which no enhancement of strength can be justified. In fact, it is unwise for a bearingto exceed even of the cross-section of a wall if a 50° enhancement is required,particularlyifthe wall is very short.
Figure 28 Compositeaction within-planearching.
Bearing Stress Investigation:Report on Bearing Pressureson Brick Walls. Anon. Structural Engineer August 1938 pp 242—268.
Determinationof the relative stiffnesses ofbeam and wall can lead to an assessment ofthe contact length over which the increased stresses may be assumedto act. By relatingthis bearing area to the increases in local stress suggested by clause 34 and code Figure 4, the average concentrated stress near the ends ofthe beam may be checked. The stress concentrationspreadsout relatively quickly upwards from the beam so that the local effects of applied and additionaleccentricities may be ignored.Since the ultimate reserves of strength in a wall are used to some extent by the stress concentrations,the zones at the ends of the beams are likelyto offer the criticalconditions.
25
stiffness of the wall and the beam, there will be a
centralzone in which the masonryis not in contact with the top of a flexible beam. A check on deflection of the beam may be necessary, and also on shear near the supports.
Three principalconditionsdetermine the ability of the masonry to form an arch, althoughthereare further conditionsimposed on the supporting The calibrationexercise referredto before also included calculationofthe maximum concentrated beam which are not of immediate concern here. Firstly, it has been shownthat if the ratio of loadwhichcouldbecarriedon a 215mm brickwall height to length of the wall is less than 0.6 there is anda 200 mm block wall(unit strengths insufficient depth withinwhich an arch can 20.5 N/mm2and 7 N/mm2in mortar designation develop. Secondly, openings must not be placed iii) by a central padstone 400 >< 200mm wide and within the lines of thrust of the imaginary arch. wall. A by a beam spanning at right angles to the This aspect has not been studiedsufficiently to range of loadingconditions,eccentricities and enable precise limitationsto be set, but generally slenderness ratios was considered. On the whole BS 5628 gives lower capacitiesthan CP Ill, more an annulus centred on the midpoint of the beam (length L) with radii 0.25L and 0.6L should be so at axial than at eccentric loads. The limited imperforate. Finally, the increased stresses calculations suggest that usually the check at the level ofthe bearingwill control,ratherthan at 0.4h. imposedby the archingaction must not exceed the local compressive capacity of the masonry.
Hendry A W Bradshaw R E and Rutherford D J, Tests on cavity wallsand the effect ofconcentrated loads and joint thicknesson the strength of brickwork. CPTB Research Note v I n 2 1968.
35. Composite actionbetween walls and their supporting beams. The original work on the compositeaction of brick walls supported on reinforcedconcrete beamscomprisedexperimentaltests at BRS publishedin 1952. Since then there have been many analyticalstudies of the problemusing a variety of techniques, some leadingto methods suitable for design. More recently there has been further experimentalwork, including walls on steel beams.
Much of the interest has lain in studiesofthe bendingmoments,shear forces and tensile forces induced in the supportingbeam. Generally, the beam may be designed to support loads much smaller than caused by a uniformlydistributed load, because archingaction within the masonry concentratesthe vertical stresses near the ends of the beam (Figure28). Depending on the relative 42
Compositeaction of this type was originally investigated for the design of brick walls on beams supported by piledfoundationsfor low-rise housing.Subsequentwork extended the applicability to more heavily loaded walls, both cases permittingthe designer to achieve economies and more efficient designab initio. However,it is commonalso for compositeaction to be invokedwhen assessing the strengthof existing structuresas a result, for example, of damage or possible changes of loading. Under thesecircumstances, it is particularlyimportant to assess carefully the tying action ofthe beam. When the end ofa supported wall occurs at a
29
I>
relative magnitudes of lateral (H) andvertical(V) loads
a, C
H
a a a C, a •0
possibledesign method
V
H
capacity reduction tactor/3
V
vertical arching
C
a. C
Oa H
V
I,> a, C
a a a,
H
horizon
C
arching
Figure 29 Relations/zips between designmethodsfor
laterallyloaded walls.
corner of a building,there is no in-plane restraint to the arch other than affordedby the beam.
A further commoncircumstance investigated only
recently is the effect ofloads applieddirectly to the supportingbeam, as for example by floor joists spanningon to the beam. A modification to the design procedurefor a beam loaded only by a wall is possible. However, the stiffer beam requiredto resist the additionalapplied load increases the contact lengthwith the wall and so reduces the benefits of composite action. Wood R H, Studiesin compositeconstruction.Part I - The compositeaction of brick panel wallssupportedon reinforcedconcretebeams. National BuildingStudies, Research PaperNo 13, London HMSO 1952. Timoshenko
5,
Strength of Materials: Part 2. D van Nostrand Princeton 1957. Wood R H and Sinims L G, A tentativedesignmethod for the compositeaction of heavilyloaded brick panel walls supported on reinforcedconcretebeams. BRS CP 2669. Colbourne J R, Studiesin composite construction:an elastic analysis ofwall-beam structures. BRS CP 15/69. Burhouse P. Compositeaction between brick panel wallsand their supportingbeams. BRS CP 2/70. Riddington J R and Stafford Smith B, Compositemethodofdesign for heavily loaded wall-beam structures. Proc ICE Part 11978,64 137—151.
DaviesS R and Ahmed
A E,
An approximatemethodforanalysingcomposite wall/beams.
6th tnt Symp on loadbearing brickwork, London 1977, Proc Brit Ceram Soc n27 Dec 1978.
Handbook to BS 5628: Part 1
36. Wallssubjected to lateral load Specific recommendations for designing walls to withstandlateral load are one of the major new features ofthis code. They resultfrom a substantialvolume ofresearchdesigned to understandthe mechanisms involvedin masonry walls under the action of forcesnormal to their
plane. The work stemmedboth from a need to exploit the lateral strengthof masonry to the limit to cope with accidentalloading requirements and from uncertaintyabout the marginsofsafety existing in panel walls that were being built, particularlyfollowing the upwardrevisionof the magnitudeofextremewind loads. Thus the recommendations relate to panel walls with only edge restraint as well as to walls in which vertical or horizontalin-plane forcesare developed or applied.
The arrangementof sub-clauses follows broadly the same logical sequence adopted in clauses 28—32, that is: (1) supports and connections—
36.2; (2) limiting conditions—36.3; and (3) design procedures: (a) low in-planeforces— 36.4.2, 36.4.3 (panel walls) (b) high in-plane horizontalforces— 36.4.4 (horizontalarching) (c) high in-plane vertical forces— 36.8 (verticalarching) (d) free-standing— 36.5
(e) earth pressure— 36.6, 36.7 The relationshipbetween the variousapproaches is shown diagrammatically in Figure 29.
36.1 General The openingreference to the empirical guidance given in CP 121: Part 1 relates to the amendment no. 1, 1975, but the recommendations therein should be treated circumspectly. The amendment gives limiting sizes for laterally loaded panels with relatively little restrictionon their application. When applied to averagematerialsin conditions of medium exposure the recommendations are broadlyacceptable. However, if used at the extremeconditionspermittedby CP 121, the panel sizes are difficult tojustify using the recommendations of BS 5628. When CP 121 is next revised, it is to be expected that the 'rule of thumb' guidance will be modified so as to give conservative limitationsin relation to dimensions, calculated from BS 5628. 36.2 Supportsandcontinuity Because the degree ofedge restraint (translational or rotational, as in code clause 28) can alter the resistance ofa panel ofa given size andtype of masonryby nearly an order of magnitude,it is essential that the assumptionsmade in design reflect what can be achieved in practical construction.Although such a range of strengths representsan extreme case, an unjustified assumptionofcontinuityon one edge of a panel in place of simple support could, in reality, lead to a panel being 3O% weakerthan expected. As a generalrule, it maybe assumed that simple support only (ie no rotational restraint)exists at all but a freeedge, unless the masonry is bonded 43
30 E
-c 0) 4) -C
threeconditionsare plotted: 1. limitingratiosof for2wayspanning 2. limiting slenderness — horizontal andvertical 3. limiting areainrelation tothickness
t
some conclusions: 100mm, checkon 50t a) necessary in onlyonedirection b) 135mm,50tneednotbe considered fora2 inclause36.3 c)t0, 180mm,50t,neednotbe considered forb, in clause36.3
t0
L, length, m
Figure 30Limitingdimensions oflaterally loadedpanels.
itito return walls or is in intimate and permanent contact with the superincumbentfloor or roof. A good selection of practical conditionsare given in code Figures 6 and7. It may be possible to assess conditions in which less than full rotational restraint exists, but advantageis likely to be gained only for panels with a free top edge or one or both vertical edges free.
36.3 Limiting dimensions It is essential to treat the dimensions providedby this clause as checks to be carried out independentlyofthe strengthdesign procedures. They are not design calculations in themselves, but are akin to the limiting slenderness ratios for vertically loaded walls. They representa subjective assessment based on experience of extremepanel proportions, lengthH-thickness which did not combinedwith While the adequacy ofrotational restraint will be exist in CP 111.height±thickness, these there will be limits, Beyond assessed generally on the basis ofthe form of the a to errors ofdesign rapidly increasing sensitivity construction, it is possible, and necessary, to andconstruction,and sudden instabilitymay check by calculation the translational restraint, The form of the limiting dimensions for that is the shear, tensile or compressive strengthof occur. threeand four-sidedsupport allows restrictions the connections. The strengths of tied connections in onedimension to be traded against increases in (code Table 8 and, for compression, in the text the within an overallconstraint of 50 times other, clause 36.2) are based on limited tests on a range the effective thickness. of ties and anchors. Shear or frictionalrestraint nay be checked usingclauses 25, 26 and 33. It is convenient to representtheselimitsgraphically It is worth drawingparticular attention to the last and Figure 30 gives the envelopes of allowable heightsandlengthsfor walls ofeffective thickness paragraph of clause 36.2. It is essential to tie the of both leaves of a 100 mm, 135 mm (equivalent to a cavity wall with edges together adequately two 100mmleaves) and 190 mm. For typical cavity wall when, as is frequently the case, only one leafis connected to the supportingstructure. storey heightsof about 2.5 m the critical condition Knowledge of the strengths of ties is also needed limiting length is provided in most cases by the when checking the transferofload over the full general dimensional restriction of 50 tei, althpugh face ofthe two leaves, as well as locally at for the thicker walls with three-sided support condition(a) (2) may control. Figure 30 also supports.Although the strengths of ties in code Table 8 andclause 36.2 are stated in the context indicatesthe limits, derived from code Table 9, of connections, it is reasonableto assume that the beyond which only two-sidedsupport maybe relevantvalues apply also to cavity wall ties. assumed ie panel shapes to which the methodof 44
clause 36.4.2 is restricted. For taller panelsthe limitations of(a) (I) and (2) and (b) (1) and(2) usuallycontrol the length, but for thin walls with four supportededgesthe height may be limited by 50 tef. For thicknesses greater than 100 mm, limitationof one dimension by 50 tef will automaticallymeanthat the other dimension is alsoso limited. 36.4 Methods ofdesignfor laterallyloadedwall panels The developments leadingto the design methods proposed here havetaken place over little more than the last 10—15 years. The main lines of approach are distinguished by the part played by in-planeforces; it is convenient to follow that distinction here, dealingfirst with panel walls.
providedto resist thesedesign moments. In the presentcase, the momentsofresistancein orthogonaldirectionsare determined by the flexural propertiesofthe masonry and the design momentsinduced by a uniformload are proportionedin the two directionsaccordingto the orthogonal ratio ofstrengths,as shown at the head of codeTable 9. Therefore, equating moment and resistancein one direction automaticallysatisfies equilibrium in the orthogonaldirection. Figure31 Lateralloadexperimentaldataand predicted strength. 31 16T
15Much ofthe earliest attention to this problemwas 14 given in Scandinavia, particularlySweden. Based 13 on patterns ofcrackingobserved at failure in panels with foursides supported,applicationof z 12the yield-line theory developed for reinforced concreteslabs wasproposed. However, due to the a, 10— (0 apparent inapplicabilityof yield-line assumptions (0 a to a brittle material like masonry, this approach did notat first find support here. The use of elastic 7analysiswas exploredas well but the development or applicationof both methodswas hamperedby Ca, the lack of experimental data. During the E this has been a interveningyears, shortcoming xa, remedied to a substantialextent by a considerable key S three sidedwalls volume of laboratory testing at both full and reduced scale usingan increasing range ofbricks, 0 toursidedwalls blocks, mortars and boundary conditions. Although knowledge ofthe load-deformation behaviourand ultimate strengthof panel walls pressure, w,calculated bydesign method (kN/m2) has thus increased, a more fundamental understandingof the internalmechanisms by Figure32 Distributionofpanelbending moments. which the moment of resistanceofpanels is developed has not been obtained yet. 32
.
.
, Ca
Re-examination ofthe available analytical approacheshas swung in favour ofthe yield-line analogy,despite the continuinglack of rational justification.The approach finds favour because it enablesadvantageto be taken ofthe increased data on the orthogonalflexural strengthproperties ofa rangeoftypes of masonry. It is possibleto derivebendingmoment coefficients so that the ultimate strengthis realised simultaneously in the
orthogonal directions;appropriateaccount of boundary conditions may be taken as well. Nevertheless this approachcan be justified only on the basis ofcorrelationwith experimental data and not on more fundamentalgrounds.For this reason, the basis on which codeTable 9 has been derived is not stated explicitly. The only hint occurs in the suggestions in AppendixD for dealingwith openings or irregularly shaped panels. As a major exampleof thejustificationfor the design method recommended, Figure 31 shows the experimental results given by Haseltine, West and Tutt compared with the strength predictedby the design method. It is worth contrastingthe panel design method with the use of yield-line analysisfor reinforced concreteslabs. In the latter case, design moments are calculated usuallyfor two orthogonal directionsbased on the applied load andthe edge restraints on the slab. Reinforcement is then Handbook to BS 5628: Part 1
..
4
cx
cx
(a) panel supported onalledges(E—I)ortopedgetree (A—D)
(b) panel with one freevertical edge(J —L)
45
The proportioningofbendingmomentsin the two directionsis illustratedin Figure 32, (a) correspondingto the diagram at the head ofcode Table 9 and (b) representing the correct form of C-shapedpanel illustratedat J, K and L in the sametable. The orthogonal arrows in the centre ofthe diagramsdemonstratethat the ultimate momentsare in the ratio ofthe parallel to perpendicularvalues of flexural strength. Continuity exists at an edgewhen the full moment in the appropriate directioncan be resistedby the support. Masonryusuallyexhibits greater resistance to bendingin the horizontaldirection,about a vertical axis, so the bendingmoment coefficients are expressed in relation to the horizontal direction.The expression for moment applies only to a uniformly distributed load so that when local increases occur eg at corners of buildings, it is necessary to equate the resulting maximum moment to that producedby an equivalent uniform load, and to design for that equivalent load. The load has been expressed as a characteristicwind load as thisis the type of load which commonly will need to be considered, although occasionally design to resist bulk powdersor granular materialsmay arise. Due to the much lower flexural strengthwhen failure is parallel to the bed joints, there are certain types ofpanel which are more sensitive to the strengthin thisdirection. They are particularly panels with high ratios ofheight to length and with onevertical edge unsupported.In these cases, it will often be advantageousto takeaccount of the reduction in flexural stresses affordedby compressive stresses due to the self-weight ofthe masonryor by other vertical loads ofsimilar magnitude.For masonry of low flexural strength, a half-storey heightmay increase the effective characteristicstrengthin the parallel directionby as much as 5O°. When such an allowance is appropriate,the flexural strengthshould be modified before dividing by the flexural strength for the perpendiculardirectionto obtain a new valuefor the orthogonal ratio which should then be used in design to providean appropriate bendingmoment coefficient The original form of words in the code was intendedto emphasise that the modification to flexural strength should be made on a compatible basis, ie either as design stresses or as ultimate stresses. If fka and fkb are the fiexural strengths in the parallel and perpendiculardirections respectively, i=fka/fkbor =fka/'m±fkb/'m using design strengths. If gi is the designverticalstress, the modified orthogonalratio '(fka/'m*gd) or i'=(fka'm xgd)/fkb which corresponds to AmendmentNo. 2. It is worth noting that the numerator of t1i5 identical to the effective flexural strength given in clause 35.5.3 for a free-standing wall. should be determined using 'fO.9. Continuingthistemporary notation for the orthogonal strengths, fk in clause 36.4.3 for a panel is equivalent to fkb. However, when considering a vertically spanningwall with no restraint to its vertical edges only the weaker directioncontributes to the design moment of resistancewhich is then based on fka. A
g
46
contributionfrom vertical load is likely to be especially valuable in thiscase andfka may be modified in the mannerjust described. Although there may be restraints at top and bottom which will reduce the design moment belowthat applicableto a simply-supported panel, care should be taken to ensure that such restraintswill continue to act throughoutthe designlife ofthe panel. The suggested allowances for flanges when calculating section moduli of piers enable the piers to be designed as vertical lateral supports. The intervening wall maybe designedthen as a panel wall with three- or four-sidedsupport as appropriate.No distinction in flexural strengthis made between solid and hollow blocksso the gross plan section should be used for the latter when calculating the section modulus. Commenton clause 36.4.5 may be included here since it concerns only panel walls. During the early stages of experimentation, it seemed likely that separate recommendations would emerge for the useofwire ties and vertical twist ties.In the event, the difference appeared to be only one of degree. that is. it is reasonableto add together the momentsof resistanceof the two leaves of a cavity wall to determinethe overall resistance, as long as the ties are strong enough to transmit the necessary forces. Clearly, wire ties will reach their ultimate capacityat lower loads than the same pattern of vertical twist ties, but nevertheless they will be adequate for a wide range of uses especially in domestic construction wheretheir flexibility is necessary when brick and blockleaves are usedin conjunction. There is some concern that butterfly ties, due to their method of manufacture.may have insufficient axial stiffness to transmit adequate forces withouttoo much movement. While the concern appears to be reasonable,there is no evidence of problems in practicedue to this aspect of performanceand ofcourse experimental walls have incorporated typical manufactured ties. The adequacy ofthe ties should be checked using the values ofcode Table 8 and the guidance in clause 36.2. including the value of I 25 kN for double-triangleties, and 0.5 kN for butterfly ties. The recommendation to add the resistance ofthe leaves, although reinforced by experiment, is difficult tojustify analytically when the leaves comprisedissimilar materialsor havediffering edge constraints. Clearly, the forces in the ties will dependon the deflections of the walls, determinedin turn by their effective stiffnesses; and in general the two leaves will not develop theirultimate momentssimultaneously nor necessarily with identical fracture patterns. It is suggested that the applied horizontalforce is shared between the two leaves in proportion to their design momentsof resistance. For a given section modulus the resistanceis proportional to flexural strengthwhich in general terms is proportional to stiffness, so that the propositionis reasonable. Again, it is difficult to justify theoretically because the proposal, when stated analytically, involves in fact a circular argument. However, for a design procedure, the last paragraph of 36.4.5 may be adopted to derivefirst the tie forcesto be checked andthen to check the strengths of the two leaves separately.
33
L
()
idealised
lineof thrust
q
Figure 33 Horizontalarchingmechanism.
36.4.4 Arching
Turning nowto arching, the main experimental approach in justification of horizontalarching comprises tests on walls generally 2.7 m long and storeyheight built between massive abutments capableof resisting horizontalforces without significant displacement. The descriptionof the design methodcan be amplified most usefully by reference to Figure 33 which shows the lines of arch thrust which are assumed to develop within the wall at failure andthe effective bearing areas of these forces, Failure occursin the arching mode when sufficient shortening of the two halves of the arch has occurredfor the geometry to be overcome. It should be noted that when arching develops, that is when there is no possibility of in-plane movement ofthe ends of the wall, cracking mayoccur at a load substantially below that at which ultimate failure occurs. This condition ofcracking correspondsapproximately to failureofa panel wall having continuityover its vertical edges. Under conditionsoflimiting equilibrium, the applied lateral load, derived by taking moments for halfthe wallabout one end, is determinedby the horizontal in-plane thrust developedand its bearing areas, which in turn determines the 'arch rise' or momentarm ofthe thrust. At failure, local crushing, and therefore shortening,occurs at the crown and the abutments.Therefore,in the face of only limited attempts to measurethe thrusts directly, the thrust may be assumed to be determined by the compressive strength ofthe masonryfk. Due to the local nature of the stresses, a 50° increase may be assumed following the recommendations of clause 34, bearing in mindthat strictlyspeaking fk shouldbedetermined for the loadingdirectionparallel to the bed joints. It is likely that in practicethe bearing area will vary with the strength of brick which will determinethe extent of redistributionoflocal stresses. Nevertheless calculation of the area necessary to sustain the assumed concentrated stresses suggests that a bearing equal to a tenthof the wall thicknessis reasonable.The ultimate thrust is thus 1.5 fk (t/lO) per unit width (for a horizontally spanning wall, width in thisexpression means its height).
From consideration of momentsthe design uniform lateral load qiat = 8 < design thrust x moment arm of thrust ± (length)2. If the length/ thicknessratio is limited to 25 the deflection may be ignored,that is the correction to the arch is negligible. Substitutingthe appropriate expressions qiat
=8
13 fk
Handbookto BS 5628: Part 1
which reduces,within lO% conservatively, to . In view of the assumptions qiat = about local bearing areas and fk this approximation is sensible. qiat is ofcourse a design load so that to obtain a characteristicwind load, qiat should be dividedby an appropriate yt-, namely 1.2 for thistype of wall. It must be emphasised again that the thrust can develop only if the supports can provide the necessary restraint. In practicethere are likelyto be relatively few circumstances in whichfull advantagecan be taken ofthisform of action. In the absence ofanytests it is not recommendedto make any modification for self-weight or applied verticalload. Equally, there may be some panel walls in which in practice a degree ofarching may contribute to the lateral strengthbut design should be based on either completearching or only flexural strength(modified if appropriate).
t
\ /9t\ ± L2
i-j
36.5 Methodofdesignforfree-standing walls No guidanceis given in CP 111 for the design of thesewalls although their design as pure gravity structures straightforward,even if not necessarily economical. In addition to this drawbackthere has been some concern that guidance on wind loads for such walls leads to values whichare higher than experience suggests
s
to be reasonable. Nevertheless, in this context satisfactoryperformancehas meant simply that the overallfactor of safety has not fallen below
unity without necessarily implying correct design to a higher assumed margin of safety. Although thismatter has not been resolved yet the ability to take account of a reliable flexural strength enhancesthe availabledesign strengthofa freestandingwall. As a hiddenfactorit may explain the apparent stabilityof walls designed on the basis ofexperience rather than calculation. As suchwalls are usuallyexposed to the weather from both sides, the minimum mortar designation (iii) is given to accord with CP 121. A more cementitious mortar will often be desirable to increaseboth durabilityand flexural strength. Fromthe point of view of structural analysis,the designrelationshipsare elementary. However, they have been included for completeness and because of the previous absence of guidance. The designmoment is expressed in the form in which it will be used most commonlyie Wk for a wind load and Qk for a parapet load, although other types of load are equallyapplicable.The single symbol yt is used because with wind, imposed and dead load actingcombination'c' in clause22 applies. However, "t' on dead load should not be 1.2 but 0.9 as discussed below. In the absence of imposed load, yr on wind load will still be 1.2. The derivationofdesign momentof resistance recognises the importanceofdead load as a force tending to restore equilibrium. In all cases in which it appears,whetherin design dead load per unit areaor nw = (gd x t) design load per unit length, it is essential to use "c = 0.9 in the expression = "c x Gk. A restoringforce, as opposedto a disturbingforce, must be assumed to havea minimumvalue. When flexural strengthis invoked, appears as a
g
g
g
47
34
n
thedesign verticalload is resisted by arectangular stress blockof width tb
F*
h
on thepointoffailure by rotation about0, under theaction of the applied loadF, the stress block is limitedbythe designcompressive strength tk/y the moment of resistance about0 available to resistthe applied moment dueto Fis:
nwx_(i.tb)k
n
but = tb X
'b =
n
designmoment of resistance =
tb
n1
2
ny k
Figure 34 Designmomentofresistanceoffree-standi,ig wall withoutflexure.
modificationto fkx, as for panel walls in clauses 36.4.2 and 36.4.3. For practical walls this enhancement may be as much as 5O%. Ifno flexural strength can be relied upon stability derivesonly from equilibrium betweenwind, imposedloads and dead load. Assuming that failure occurs by tilting, as of a rigid body, about an edgeat a level at whichthe horizontal section is completely cracked, the designmoment of resistanceis simply 4nwt. A more sophisticated, and perhaps under some circumstances a slightly more realistic, assumptionis that local crushing occursin the vicinity of the edge over a depth Figure 35 Free-standingwalls— design momentof resistance.
determined by the compressive strength of the masonry. Assuming that the stress there is represented by a rectangularstress block, as in clause 32.2 and AppendixB for vertical eccentric load, reference to Figure 34 shows that the design moment ofresistanceshould be reduced to 1
/
flw —nw-—
Considering the effect of
n in parenthesis it
might be argued that it should embracea maximum ie 1 .6 x Gk, but different simultaneous values for ,'t' can hardly be entertained.Equally pedantically, the narrow width of the ultimate stress block might suggest an overstress allowance on fk. Whateveradjustment is made along these lines, the reduction in resistanceis proportional to the ratio of design dead load to design compressive strengthand will seldom make more than a few per cent difference except for particularlyhigh or dense walls or very low strength masonry. It should be appreciatedthat this approach recognises that the wallwillcrack, and probably rock, prior to failure by overturning.
g
A comparisonbetween the two approachesto moment of resistance is shown in Figure 35. It can be seen that increasingdead weight ie height of wall at constant thickness, provides a more rapidlyincreasingadvantageto toppling resistance than to flexural resistance, although again the practical implications of this would be significant only for relatively tall walls. It does suggest that any reduction offlexural strength during the life of a wall will not necessarily lead to failure althougha much reduced margin of safety may result.
35 E
z 0
C Ca
Ca Co
a,
215mm thick
0 C a, E
0 E C
0 a,
1
———
4Wmr
—
1100mm J thick
———
——
0 height,m
48
When there is a changein thickness ofa wall crackingmay occur at the level of the reduction. The stabilityofthe relevantupper parts of the wall should be checked therefore,as well as that ofthe whole wall. 36.6 Retaining walls Earthpressureis another type of loadingfor which statistical data is still not available. It may be assumedthat, in the absence of other data, the values derived from Civil Engineering Code of PracticeNo 2 representcharacteristicearth pressures. ifthey act as imposedloads, the partial safety factor should be taken as 1.6 (as in clause 22), but when earth pressureresists overturninga reduced value of0.9 is appropriate. In the case of gravity retainingwalls, 't- for dead load should be taken as 0.9 for resistance to overturning, but 1.4 for checking ground bearing pressures. If fiexure is to be relied upon, an appropriate value of "rn will need to be selected from clause 27. The code for earth retaining structuresuses both permissible stress and load factorapproachesto safety factors. In the latter case, whichis relevantto the failure of a gravity structure,an overall factor of safety between 1.5 and 2.0 is recommended, which is compatible with the above partial safety factors.Any pressure on the wall dueto ground water shouldbe consideredas an imposedload but with a reduced value of of 1.2 to allow for variation in the depth of water. However, the resultingdesign pressure should not exceed that due to water equal to the full height of the wall. Resistance of a retainingwallto sliding is less amenable to limit state analysis at presentand it is suggested that partial factors of unity are taken and that resistingforces should be at least double disturbingforces. 36.7 Foundation walls This type of wall is distinguished from a simple retainingwall by the presence ofvertical load, usuallya superstructure.The lateral characteristic loadingmay be derived as describedin clause 36.6 andthe combinedloadingbased on the partial safety factors in clause 22. The choice of design method between clauses 32 or 36 depends on the ratio of vertical to horizontalload and the uniformityofthe lateral load. 36.8 Design lateral strength ofaxially loaded walls
in-plane loads. As the vertical load increases, local crushing starts to occur and disruptionof the wall at failure becomesprogressively worse. Nevertheless, even under these conditions, derivationofthe ultimate lateral load from the arching mode of failure provides reasonable correlationwith experimental failure loads. An idealised model of the three-pin arch at failure is shown in Figure 36. As with horizontalarching, the testingand analysisrelateonly to uniform lateral loads and there is not an explicit way of adapting the method to take account of non-uniformloads. There are several end restraint andgeometrical conditionswhich haveto be satisfied for this method of analysis to bejustified, and a separate partial safety factor has been incorporated explicitly in the designexpression for qiat. Rather than introduce yet another value, "rn for compressive strength has been used even though, as indicatedabove, material propertieshave little influence on failure conditions.The presumption attendingthe choiceof a reduced value of Yrn for appropriatequality control is that all the relevant conditionsare controlledto a similarextent. The use of an unfactored characteristicload, for derivingn, is unusual but accommodated effectively by the presenceof m. Although "c, slightly less than unity, is introduced into the vertical load under accidential conditions,imposed load is includedas well as dead load ie 0.95 Gk + 0.35 Qk. It would be more logical perhaps to base n on 0.9 Gk for normal design purposes, but this method of designfinds its principal applicationwhen consideringdesignto resist accidentaldamage. Figure 36 Idealisedvertical arching.
36
andcolumns
Clause 32 has indicatedthe extent to which lateral loads may be treated as an effective eccentricity of vertical load when the latter is sufficientlyhigh. In the wake of Ronan Point there was interest in defining conditionsunder which masonry could withstandmuch higher lateral loads and experimental work centred on walls capable of developing vertical arching, not unlikethe horizontalarchingdescribedin clause 36.4.4. The main difference lies in the degreeofresistance which can be providedrealistically in the vertical plane of the wall, principally by the weight ofthe structureor possibly by verticalties. Whereas some estimatehad to be made of the arch thrust for horizontalarching, applied vertical loads may be calculated directlyin vertical arching.
Tests have shown that failure occurs by formation ofa three-pin arch with vertical movement of the Handbook to BS 5628: Part I
49
The factorsin code Table 10 are based on a limited amount of experimental work and to the extent that returns change the modeof failure from three-pin archingto yield-line type crackingthe large valuesshould be treated with reservation. Jones L L and Wood R H, Yield-line analysis ofslabs. Thomas & Hudson,Chatto & Windus London 1967. Anderson C and Bright N J,
Behaviour ofnon-loadbearingblock wallsunder windloading.
Concrete v 10, n 9, September 1976. HaseltineB A and Tutt J N. Brickwork retainingwalls. BDA 1977.
HaseltineB A West H W H and Tutt J N, The resistanceof brickworkto lateralloading:Part 2. The Structural Engineer v 55 n 10 1977. Moore J F A, HaseltineB A and HodgkinsonH R, Edge restraint provided by continuityofpanel walls. 5th mt Brick Masonry Conf, Washington USA 1979. Figure 37 Flow diagramfor designto resist accidental damage.
37
50
DAMAGE 37. Design: accidental damage. Becausethe recommendations in clause37 appear for the first time in a code of practice they are
presentedin considerabledetail. The specific guidance produced immediately after the collapse at Ronan Point related primarilyto concrete structuresand detailed recommendations were devised for CP 110 which was published in 1972. In 1969, general guidance for masonry structures was published by the Institution of Structural Engineers. Further detailed recommendations were made by the Brick Development Association and a substantialprogrammeof testinggaverise to the recommendations ofclause 36.8 as referred to in clause 37.1.1. Considerable experience evolved within the GLC andthiscombined informationhas formedthe basis ofclause 37. The general guidance in clause 37.1 is self-explanatory and is presentedin tabular form in codeTable 12. Use ofthisapproach to the design of structuresto resist accidental damage maybe clarified nevertheless by means ofthe flow diagram in Figure 37. The general preceptsfor design have been discussed in clause 20 which should be considered in conjunctionwith this section. The first question for all buildings is to establishthat theirlayout and method of constructionhave been arranged to providethe best resistanceto spread of damage. Although the codedoes not giveanydetailed guidance, the following features which specifically contribute to robustness,and are found in cellularconstruction,may be considered advantageous: avoidance of relatively thin or light-weight walls; limitationof floor spans; walls buttressedat both ends exceptfor occasional free ends to minor internalwalls; limitationof length of unbuttressedwall; and limitationof size of openings. There may be, ofcourse, other functional or architecturalrequirementswhich conflict with these featuresand the designer must establisha desirable balance.As an example of the extremedifferences possible, Figure 38 contrastscrosswall constructionwith a well buttressed cellular planform.The applicationof this philosophy,in commonto all buildings, is emphasised by the format ofcode Table 12. Over and above these somewhat general exhortations for robustness,specific recommendations are made for buildings offive storeys and above, in line with Building Regulations.
7
"....
SECTION 5 DESIGN : ACCIDENTAL
unprotected vertical elements removed without N.çausing9collap
yes
category2 option 2satisfied
The desirability of such a split has beenthe subject of much discussion. It is argued, on the one hand, that buildings belowfive storeys are sufficiently smallfor the spread of damageto be limited naturally to a reasonableextent by normal good design, and that the costofintroducing explicitly to Category I buildingsthe detailed recommendations for Category2 wouldbe unreasonable and of poorcost-effectiveness. On the other hand, it is arguedthat the division at 4—5 storeys is arbitrary, that the lack ofspecific guidance below 5-storeys placesunreasonable responsibility on the designer and that a reasonable minimum provision of robustness is not secured.
the need for anyfurther considerationof structural behaviour. In other words, it is assumed that improvedabilityto accommodatelocal damage of any kind willresult. To the extent that thisapproach is not related to anyspecific type of structure, it may be expected to be conservative, that is less economicto executealthough possibly more economical of design effort.
38
crosswallplan form
225mmcavitywall weight340 kg/rn2 170mm waIl
350 kg/rn2
_________102.5mm wall 210kg/rn2
Figure38 Comparisonbetween crosswalland cellularplan forms.
A numberofpoints are clear on both sidesofthe
argument. The taller the building the more significant the structural aspectsbecomeas part of the total cost, and introducingthe additional measuresgenerally becomes relatively easier and cheaper. The possibility ofextensive vertical progressive collapse is much greater in a taller building.In most cases, it is possible to design low-rise masonry buildings for normal loads in a manner whichwillprovide adequaterobustness. However, single-storey long span buildingsappear to form a class of buildings which may be particularlysensitive to abnormal events unless particular care is given by the designer to their structural behaviour,but nevertheless no special recommendations have been made. The possibility of extensive horizontalprogressive collapse, eg in
a crosswall building, should not be ignored.
Once the general conception andlayout of a building taller than four storeys have crystallised provisionally, it is necessary to examine the
preliminaryconclusionsin the light of the three options suggested in code Table 12. The details of the clausesrelatingto these options are considered below but first interactionbetweenthe requirementsofthe options andthe proposed layout may suggest alterationsto the layout more amenableto a particular option. In many circumstances Option 3 will be selected because it prescribes horizontal and vertical tyingwithout Handbook to BS 5628: Part I
Option 1 presents a more objective approach, sometimes known as the alternativepath method, in which each loadbearingelement is considered to be removedin turn, and the structurethen checked for its ability to accommodatethe loss. This more fundamentalapproach relies to a substantialextent on engineeringjudgement althoughguidanceis given in clause 37.5 andcode Table 11 for establishingrealistic structural elementsfor removal. The designer must still decide what forms of structural action may be invokedtojustify continued integrityand limitationof damage. In the light of previous arguments, it cannot be consideredgood practice to provide elements which are so vital to the structurethat their removalcannot be tolerated without unacceptablerisk to the restofthe structure.However, clause 37.1.1 gives guidance when these circumstances cannot be avoided or when removal ofa wall or column need not be considered, the basis ofloadingbeing that in Building Regulation D 17. In fact, Option I is essentially a restatementof that Regulation without specific limitationson the meaning of 'collapse'.Many engineers will preferthe freedom ofthis more independentapproach, especially when designing complex buildings. Perhaps the most commonly adopted solution willbe the recommendations ofOption 2. This option combines the specificprovisionsofOption 3 with regard to horizontalelements with the more general approach of alternativepaths of Option 1 for vertical elements. This option will find favour because buildings above 4 storeys will have concretefloors in whichit is relatively easy to accommodateany additional horizontalties, whereas vertical tyingmay present difficulties. Although no conditionsare specified to limit the application of the prescriptionsfor ties in Options 2 and 3 it is recommended that careful thought is given to the mode ofaction ofties. Only when it is clear that the spread of damage is likelyto be containedby the provisionofties and that the ties themselves are not likelyto have any adverseeffects, should oneofthese options be adopted. In case of doubt a systematic application ofthe principlesofOption 1 shouldbe adopted. The three key features ofthese options, namely horizontalties, vertical ties and load bearing elements, will be examined in more detail. 37.3 Horizontalties There are two main emergency actions expected offloorswhich can help to avoidthe spread of damage. Firstly, whena verticalloadbearing element is lost, the floor shouldbe able to bridge across the area ofincreased span, or in the case of loss of a corner wall, cantileverout, while still supporting the verticalstructure abovethe floor. The second requirementis that the floor should be 51
able to withstandthe debrisloading when collapse occurs from above. Both conditions envisage a floor developing two-wayspanning action, or at least beingable to span in either direction.In addition, the resultingdeflection must be sufficientlylimitedto avoid too extensive disruptionof walls above, particularly ifthe latter have limited ability to arch or span in their own plane. This clause is not specificallylimited to concretefloors, but although timber floors may achieve the necessary bridgingtheir deflection may be too large to limitdamage above. The questionof supportingdebris is important for the top floor. The coderecognises the impracticability of strengthening a lightweight roofto increaseits spanning ability,and thereby impliesthat the debris resultingfrom disruption of a roofwill fall to the floor below. Increased diaphragm action may be required as well to transmit lateral forces over greater distances to suitable shear elements.
Theserequirementscould arise naturallyfrom adoption of Option 1 andwould have to be satisfied by the designer in an appropriate way. Code Table 13 provides specific recommendations at A and B for solvingthisproblem. In doing so it follows closely the provisionsof CP 110 but expresses them in a tabular andmore graphic manner. However,these recommendations apply only abovefour storeys, not to all heightsas in CP 110, because normal robust constructionis considered to render them unnecessary for low-rise buildings. A particular implicationfor low-rise buildings is that pre-castconcrete floor units may not require additional tyingprovided that the units are adequatelytied to walls and have large enoughbearingson the walls (see clause 28.2.2 andAppendix C). Various types of ties are considered and the force to be resistedis related to a basic force, A pressureof 34 kN/m2 acting againsta typical storey height wall can be equated to equal horizontalforcesat the top and bottom of the wall of about 40 kN/m length ofwall. This is the derivationof the minimumvalue of F, but is
walls together, as might be the case in concrete panel construction,because unreinforced masonry walls would seldom be capable of resistingthe impliedmomentsimposedon them. Howeverit is essential that walls or columns should not fail prematurelyby loss of their horizontal connection at horizontallateral supports.Therefore,at C and D in code Table 13, strengths of such connections are given in relationto and the storey height. The normal practical method ofachieving this connection will be in horizontal shear or by friction. Again, the functionof this type oftying is not so muchto attach the walls together as to ensure the lateral restraint conditionsnecessary for developing the vertical load capacityof the walls. Whendesigning reinforcementfor horizontal tiesthecalculateddesigntieforceshouldbe divided by the characteristicstrengthof steel to derive the cross-sectional area required. No partial factors of safety are involved in this calculation. Steel already providedto resist normal loads may be considered for these ties, the stresses dueto the normal loads being ignored for this purposeonly. The completepattern of ties required is indicated
F
in Figure 39.
37.4 Vertical ties The horizontaltyingto ensure a minimum level of integrity of floors and roofs is relatively straightforward. However, the actions whichcan be providedor enhancedby vertical tyingare less obvious and perhapsless certain in their effectiveness.The following possibilities may be envisaged: (1) resistance to loss ofhorizontal lateral support to walls caused by uplift offloors subjected to explosive pressures;(2) maintenance ofvertical loads sufficient to permit vertical archingofwalls, as in clause 36.8; and (3) enhancement of interactionbetween wall and floor bridgingan area of local damage.
In all cases, the provision of vertical ties to
maintainthe relative positions betweensuperjacent floorscould be advantageous.In the first case, safeguardinglateral support is complementaryto horizontaltyingat C and D in codeTable 13 when a friction or shear connection is to be relied upon F the top or bottom of a wall. In the second case, also related to the numberof storeysin an attempt at lateral load resistance develops against the vertical to equalise the risk for all heightseven though the thrust, providednormallyby the dead weight of risk ofdamage may be related to the size of the structure. When explosive forces tend to building. Nevertheless, it is considered that no the dead nullify weight the necessary increase in is necessary above 10 storeys, partly because a generally stronger structure is a natural precompression could be providedby strain in the ties as long as their extensionis not sufficient for concomitantof a greater number of storeys. the wall to be pushed out. This type of action raises questions about the detailed responseof the The peripheraltie force is relatedonly to F, but structure because the tying resistancemust be the internaltie forces are also functionsof dead developed at the same time as the lateral load andimposedload and floor span based on develops on the wall, even though the dynamic typical upper limitsfor domestic construction. behaviourofwall andfloor may differ. In the The peripheralforce is specified primarilyto deal third casethe tying action could enable floors and with loss ofan externalwallimmediately below walls to act as a compositedeep beam of but it may serve to anchorthe internalties. considerablecapacity. Although the fixing requirementsfor the internal ties appear to include the possibilityoftheir The design requirement for vertical ties given in anchorageto the walls, it is doubtful whetherthis code Table 14 is based on the case of vertical can be achieved conveniently in masonry, except arching. Direct equation ofan accidentalpressure in conjunctionwith vertical ties (clause 37.4 and of 34 kN/m2to the expression for qiat in clause code Table 14) whichneed to be anchored 36.8 leads to the vertical force to be resistedby the ties, if ,'m is ignoredie, taken as unity instead vertically to floor slabs. It would not be right to interpret horizontalties as tying oppositemasonry of 1.05. The algebraicexpression is a total vertical
F
52
39
recommendedties vertical ties
= verticalwallties V= verticalcolumn ties
horizontal ties = internal transverse ties = internal longitudinal ties P = peripheral ties WE = externalwall ties = CE externacolumn ties
Figure 39 Full tying requirement.
force to be provided by ties at a convenient spacing, withina maximumof 5 m. The maximum force which would be required at this spacingis 1275 kN, comparedwith the minimum at 100 kN/m of 500 kN for whichabout 1200 mm2 of steel cross-section would be necessary. The minimumforce corresponds approximatelyto the minimumpercentagesteel requirement for vertical ties in plain concretewalls or the weight of a storey height wall.
40 i.1M
1:!:J Iength
37.5 Loadbearing elements The designer is requiredin usingOptions I and 2 to considerthe effect ofremovingindividual loadbearingelements. This in turn requires assessment of the most likelyextent oflocal structure whichcould fail under a range of accidentalloads. In order to helpthe designerand Handbook to BS 5628:Part 1
whereh = clearstoreyheight
minimum mass 340 kg/rn2 (including
finishes)-
(a) intersecting
orreturn walls
________________________
The steel may be distributedat intervals along a wall, but it willbe usuallymore convenient to concentrateit in pockets,where it may be also
better protectedagainstdamage andcorrosion. For a cavity wall, thismeansthe leafwhich carries the vertical load, usually the inner leaf. For a number ofreasons, it appears desirable that ties, even though provided in every storey, should not decontinuousbut should be anchored independently for each storey.The failure ofties in one storeyshould not prejudice their action in adjacentstoreys and certainlyshould not cause any spread ofdamage. A possible method of achieving this is by staggering the line of vertical ties in successive storeys.
minimum
______ max width 1 m
(b) stiffened section(strong point)pier
adequate thickness of Pier to resistbending, when spanning between floor slabs, under the action of accidental pressure on itsfacetogetherwith the reaction from the wall,which is assumed to failina yield-line mode
________ m mm
,—
average mass (allowing foropening) at least150 kg/mI (including finishes)
normal door
ng
,,
-—
,
,,, ,
not be in a'straight line,
but must in effect divide m mm
the bayintotwo compaments
-- _, ________________________ (c) substantial partition
Figure 40 Lateralsupports for Ioadbearingelements.
systematise the approach, code Table 11 defines the types of elements whichit shouldbe sufficient to consider. The extent of beams,columns,floors and roofs between supports is relatively clear, but the extent of vertical elements which might be lost is determinedeffectively by the adequacy of vertical lateral support or the presence of a free edge. Suitable supports are described in the clause at (a), (b) and (c) and are an extension to masonry of the similar requirements in CP 110.
wall is assessed;in type (b) the pier or stiffened section has to resist that pressureas well as the direct pressure on the pier itself; and in type (c) the pressureis assumed to be confinedto one side ofthe partition wall. 34 kN/m2is takenas the relevantpressurewith a typicalstorey height of 2.5 m, the resultant force being approximatedto a simple factored average value of F, being in the range 40-60 kN for Category2 buildings.
Examplesofthe three types envisaged are shown in Figure 40 together with a sketch showing the derivationof the forces to be resistedby the lateral restraints. In type (a) the pressureon the supported wallon each side ofthe buttressing
The BuildingRegulations1976. HMSO 1976.
54
F
KorffJ 0 A,
The overallappraisal ofbrickworkbuildings. BDA 1978. See also referencesto clause 20.
3
DESIGN
Chapter2has given the designer an insight intothe backgroundto the clausesof BS5628:Part 1, their scope andexplanationsof the contextsin which they are used. Chapter 4 containsexamples illustratingthe use of the various parts of the code by considering the detailed designoftwo loadbearingmasonrystructures.This chapter acts as a bridgebetween the two, bringingtogether the essential design formulaeand procedures explained in Chapter 2 andthen used in Chapter 4. The aim is to providea simple and concise reference section for the designer. The code clauseshave been arranged to followthe logical sequence of design procedures andthe same generalorder is followed here. DATA (code clauses 6-18)
As with other structural materialsthe datato be used in the design ofloadbearingmasonry buildings must first be defined. This data includes the structural form of the building,a statement of the basis ofdesign,the loads andforces to which the building will be subjected and the type and structural characteristics ofthe materialsto be used.
Thus: The structural units used should comply with the relevantBritish Standards,the principalof which are: BS 187 Calciumsilicate bricks BS 3921 Claybricks and blocks Concretebricks and fixing bricks BS 1180 Precastconcreteblocks BS 2028, 1364. be in accordance with Workmanshipshould CP 121: Part 1. Characteristicloads should be obtained from the appropriatepart ofthe loading code CP3, Chapter V, as follows: Dead loads Part 1 Imposed loads Part 1 Wind loads Part2 Design shouldbe in accordancewith BS 5628:
Part 1
Handbook to BS 5628: Part 1
DESIGNPROCEDURE Stability (code clause20)
Having set down the designdata, the next step is to considerthe overall stabilityof the building. Thefollowing itemsneedto begiven consideration: (1) Layout andstructuralform: (a) The provision of sufficient return walls and their distribution. (b) The interaction between the structural elements.
(2) Resistance to overturning forces: (a) Resistance providedby wall complexes acting as verticalcantilevers. (b) Resistance providedby shear walls (racking). (c) Resistance provided by suitable bracing. (3) The overturning force, which is the greater of: (a) The designwind loading on the building. (b) A uniformlydistributedhorizontalload equal to 1.5 % ofthe total characteristicdead load above anylevel, see Figure. 6, page 19. (4) Stabilitydesign: (a) The masonry must be designed to resist the appropriatecompressive loadingresultingfrom the designoverturningforces and the design vertical dead andimposedloads. (b) The stress at the windwardedge should be calculated. To avoid crackingno tension should be permitted andthe load distributionmay be assumed to be as in code Figure 3. However,in the ultimate limitstate, a certain amount of tensionmay be permitted at the discretionofthe designer as cracking is a serviceability limit state. See Figure 41. (c) A checkmust be made to ensurethat the characteristicshear strengthof the masonryis not exceeded.
(d) If the buildingbeing designed is 5 storeys high or over (category 2) it must be designed to resist accidentaldamage. Buildings under 5 storeys (category 1) requireno such additional consideration,beyond item 1 above.
Not only must the interactionbetweenthe structural elements, ie, the load path through the 55
tH
41
42
'1'
I
V12 //Zi, 4t
I
-f
41
wallelevation shearwall
r +
ultimate
ultimate limitstate
—
+
service
nocrack whereWand Mare theultimate verticalloadsand bendingmomentsrespectively on thewall and
andMarethecorresponding service W loadsand moments bending
Figure 41 Stress diagramsunder shear walls.
structureto the foundations,(1) (b) above, be considered, but also the connections betweenthe elements must be capable oftransmittingthe designforces. AppendixC is included in the code to assist the designer to satisfythis requirement.
Item 2(a) assumesthat walls bend as vertical cantilevers and the code suggests in clause 30 that the horizontalforcemay be shared between the shear walls in proportionto their flexural stiffnesses. The code does not comment on the contributionto the stiffnessesthat can be allowed for any fully bonded return walls perpendicularto the shear walls, but it seems reasonableto assume that the rules of codeclause 36.4.3 relatingto flange lengths may be adopted here; ie, the outstandinglength ofthe flange from the face of the wall for the purposesof calculating the stiffnesses of the shear walls may be taken as: (a) 4 >< thickness ofwallformingthe flange where the flange is continuous,see Figure43. Item4(a), design forcompressive strength, constitutesthe mainbody ofthedesignprocess for masonry buildings.
Theadditionalstabilityrequirements for buildings of 5 storeys or over, mentioned in item 4(d), are discussed on page 50 under the heading AccidentalDamage, Havingdecided how overturningforces will be resistedby the chosen structuralform, andhaving calculated the alternative overturningforces, it is necessary to consider items4(a), (b), and (c). It is desirable at this stage to calculatethe characteristicverticalloading for those walls on whichthe structure relies for stability,or at least on those walls which the designerconsiders will 56
Figure 42Length offlange whichmaybe considered when flange is unrestrained.
be critical. Thesecharacteristicloads can be presentedbest in tabular form keeping dead and imposed loads separate, to simplify the calculation of the design loads for the particular designcase being considered. The use ofthe limit state approach in the codepermits the degree of risk in a particular design case to be assessed by the use of different design load combinations. Design load combinations (codeclause 22) The design load is the sum ofthe characteristic loads (dead Gk; imposedQk; and wind Wk) multipliedby theirappropriate partial safety factor for loads, 't-. The code gives four combinationsof design loads containingthe appropriate numerical values of as follows: (a) Dead andimposed load: = 0.9Gk or I .4Gk design dead load
"
design imposed load = l.6Qk (b) Deadandwindload: design dead load = 0.9Gkor l.4Gk design wind load = l.4Wk or 0.Ol5Gk whichever is the larger.
In the particular caseoffreestandingwalls and
laterally loaded wall panels, whose removal would in no way affect the stabilityof the remaining structure, applied on the wind load
y
may be taken as 1.2. (c) Dead, imposed andwind load: = l.2Gk design dead load designimposedload = I .2Qk = l.2Wk or 0.Ol5Gk design windload whichever is the larger. (d) Accidental damage = 0.95Gk or l.O5Gk design dead load = 0.35Qk except that, in load design imposed the caseofbuildings used predominantlyfor storage,or wherethe imposedload is ofa permanentnature, l.O5Qkshould be used. = O.35Wk design wind load Combination(d) for accidental damage is considered later. Eachofthe different combinations must be considered in the design process and that producingthe most onerous loadingcondition used in the calculations. For a particular situation it may be obvious by inspection that one or more of the combinationswill notbe critical;for
Thecodedoesnotmakeclearwhetherthe alternativeyr values given for dead load should be used in conjunctionwith each other in the design ofa particular structural element. Nor does it implythat yr on imposedloads should everbe taken as zero, although this makesengineering sense in obtainingthe maximum eccentricity of load. It might, therefore,be assumed for a wall loaded from both sides that the code requiresthat the three cases shown in Figure 44 must always be considered: (i) giving the maximum vertical design load but minimumeccentricity, (ii) giving a high vertical design load combinedwith, when spansdiffer considerably, a large eccentricity and (iii) giving the minimumverticaldesign load but
43
shearwall
Figure 43 Length offlange whichmay be consideredwhen
flangeis continuous.
instance whenthe element
maximum eccentricity.
beingdesigned does
notcarry wind loading, combinations (b) and(c) need not be considered.
A mathematicalexercise has shown that only cases (i) and (ii) in Figure 44 need generally be
In order to check whethertension occursin a shear wall, combination(b) will be appropriate,
considered in design, since for (iii) to prove a worse case than (i) an unrealisticdisparity in the length ofthe two spans onto the wall would be required; unfortunatelya similar conclusion cannot be drawn for case (ii). The code does not
the designdead load beingtaken as equal to O.9Gk. Similarly the same combinationwill give the maximum design horizontalload for considerationof shear. When calculating the maximum compressive load on a masonryelement case(a), (b) or (c) may give the critical case. Combinations(b) and (c) are straightforward since in (c) no alterative values of 't are given and in (b) a designdead load of l.4Gk willgive the worstcase in compression. However, when using combination (a) the situation is more complicated.
require a case with zero imposedload to be considered. In the case of a wall or column loaded from aboveand one side it is only necessary to consider the maximum load condition shown in Figure45.
44 +
l.4Gkl + 1.60k,
'Jr
'I!
___L1___ l.4Gk2+ 1•60k2
'I!
l4Gk3+ 160k3
O.9G+1.6Q
U
Ir
(i)
I,
(ii)
l.4Gka+ 1.6Q
4
O.9Gk
1•60k1
___ Li___ O.9G+1.6Q
l.4Gk3+ 1.6Q
(iii)
Figure 44 Alternative casesfor loadcombination.
45
Figure 45 Loading condition to be consideredwhen wallor
____________________________________________________ columnloadfromone side only.
Handbook to BS 5628: Part 1
57
Compressive strength
(codeclauses 23, 28, 29, 30, 32, 34) Masonry is most efficient as a structural material when used in compression, and so a major part of the designofloadbearingmasonryis concerned with ensuring that the masonry has adequate compressive strength to carry its design vertical loads. The designcompressive strength ofthe masonry is related primarilyto the characteristic compressive strength ofthe masonry unit/mortar designationcombination,to the slenderness of the wall or column, and to the effective eccentricity ofloading.
The relationshipto be satisfied in design for compressive strength ofmasonry is: design compressive strengthofmasonry > design
46 any construction
floor or roof
I
(i)
(ii) widthof bearing
90or½wallthickness orinnerleafofcavity wall
compressive loading.
It is normal practice to use this relationshipto calculatethe characteristicstrength of masonry required for the structural element being considered. As this is the endresult ofthe design procedure, the other factorsgoverning the design compressive strength ofmasonry willbe dealt with beforeconsiderationofthe characteristic compressive strength. Slenderness ratio (codeclause 28) The slenderness ratio is defined in the codeas the ratio of the effective height or length (hef) to the effective thickness (tef)
(iii)
widthof bearing houses Only
90
3storeys
he
ie, — tef
Table 2 gives the effective heights and lengths of walls andeffective heights of columnsfor the alternativelateral support conditions.
Table2 Effective height/length ofwalls and columns Type ofIateral support Plane of Element
lateral
Simple
Enhanced
support
I.Oh
0.75h
Horizontal
1.0 I or 2.5 Ii
0.75 1 or 2.0
Vertical
length (between
Effective
I.Oh
0.75 h-4-
Horizontal
openings
height
Columns (general)
Effective
Walls
Effective
height Effective
Columns
in wall)
l
0.25h1 h*
h*
height in plane with lateral support
where:
h is verticaldistancebetween lateralsupports h1 is heightoftalleropening 1is length ofwall,centre to centre ofverticalsupports and is lengthofwall between verticalsupports and vertical
l free edge.
*In aplane withno lateralsupport the effectiveheight ofa column is taken as 2h
58
Figure 46 Enhancedresistance to lateralmovement (horizontallateralsupport).
Horizontal or verticallateral supports must be capableof transmittingthe sum ofthe simple static reactionfrom the applieddesign horizontal load and 2% of the total designcompressive load that the wall or column carries at the level of lateral support to the elements of construction whichprovide overall stability,ie the shear walls or bracing. The 2% requirementneed not be applied to the shear walls or bracingmembers themselves, since these are already designed to carry the appropriate proportion of 0.015 of the total characteristicdead load above the level of lateral support. AppendixC to the code gives details of connectionswhich may be considered to providea horizontallateral support with simple resistance to lateral movement. Enhanced resistance to lateral movement may be assumedin the cases shown in Figure 46. Simple resistanceto lateral movement for vertical lateral support may be assumed in the cases
shownin Figure 47.
Whilst the code saysthat the only requirement for enhancedresistanceis that the return or intersecting wall is properly bonded to the
47
49 l.ul_
.I
lot
e= Figure 49 Calculation ofeccentricity using moment
(i)
distribution method.
Table3 St?f/'ness coefficient,K,for walls stiffenedbypiers
—-1
t-
Ratio ofpier spacing Ratio— of pier thicknessto (centreto centre) actualthicknessofwall to which to pier width it is bonded 1 2 3 6 1.0 1.4 2.0 10 1.0 1.2 1.4 20 1.0 1.0 1.0
-
NOTE. Linear interpolationbetween the values given in the table ispermissible,but not extrapolation outsidethe limits given.
Figure 47 Simpleresistanceto lateralmovement (vertical lateralsupport).
supported wall, it is reasonableto assume that the samerestrictionson thickness andlength of returnwallas those for simple resistanceshould also be applied. The effective thickness of a wall or column is obtained from code Figure 2 modified if necessary by the coefficient K for walls thickenedby piers, obtained from code Table 5. Code Figure 2 and Table 5 are reproducedhere as Figure48 and Table 3 respectively.
When a wallis stiffened by intersectingwalls, such that the ratio ofthe distancecentre to centre of the intersecting walls to the thickness ofthe stiffened wall is less than 20, the stiffness ofthis wall may be modified by the coefficient, K; the pier thickness tp may be assumedto be 3 times the actualthicknessof the stiffened wallor leaf. Eccentricity at right angles to wall (code clause 31) The code suggests that preferablythe eccentricity should be calculated. The most obviousway of
doing this is to use the momentdistribution method. Usingthe conservative assumptionthat a pinjointexistsat the bottom of a masonrywall or column, the eccentricity of loadingbeing considered zero at this point (see code Appendix B), a moment may be calculatedat the top of the lower masonryelementandthiscan be equated to a load and eccentricity, as shown in Figure 49.
Figure 48 Effective thickness ofcolumnsand walls. Column
Single leafwall
Cavity wall
Walls stiffened bypiers Single leaf Cavity
Plan shapes
\Nt Effective thickness or b,
\jtP NH
'\\\\\N t
depending on direction of bending Handbook to BS 5628: Part 1
48
the greatest of (a) 2/3 (t1+t2)or or (b) t1 (c) t2
tx K
the greatest of
(a) 2/3 (t1+Kt2) or or (b) t1 (c) Kt2 where K is thestiffness coefficient from table 3
59
Similarly anyother analytical method may be
used to calculatethe design moment in the masonry wall or columnand hencethe effective eccentricity.
The codealso permits, at the discretionof the designer, the assumptionthat the loads act at one-thirdofthe depth of the bearing area from the loaded face ofthe wall, as shown in Figure 50(a). Figure 50 Notionaleccentricity;solid wall loadedfrom one side.
50
(a) solid wallloaded fromone side
Where auniformflooris continuousovera wall, a similarassumptionfortheeccentricities maybe made as shown in Figure 50(b). As mentioned above, the conservative assumptionshould be made that the eccentricity of loads from above is zero.
When calculating the eccentricity ofloading on a cavity wallwhich has both leaves loaded, the relative stiffness of the wall may be taken as the sum of the stiffnesses of the individual leaves. When only one leaf is loaded, it is reasonableto assume, provided wall ties are incorporated in accordance with the code, that the wall stiffness may be taken as two thirds the sum of the individual leafstiffnesses, or the stiffness ofthe loaded leafwhichever is greater. Correspondingto the simplified assumptionofthe load acting at one third the depth ofthe bearing area for a solid wall, the assumptionshown in Figure 51 may be used for externalcavity walls where both leaves are loadbearing.
(b) solidwall loaded frombothsides
In a cavity wall if the calculatedor assumed net eccentricity of the applied vertical load, represented by the eccentricity of the reactive force R in Figure 52(a) and (b), is between the centroidsofthe two leaves as shown, the leaves
may be designed as individual walls carryingthe statically equivalent loads W5 and W6 as shown in Figure 52(c). The benefit of the increase in stiffness ofeach leaf by virtue oftheirmutual connection is allowed for by using the slenderness ratio of the full cavity wall for the designofeach leaf.
Figure 51 Assumedeffectiveeccentricityofloading;cavity wall with both leaves loaded. 51
-
Design vertical load resistance (code clause 32.2) The tendency of a masonry wall or column to buckle increases with increasingslenderness ratio andeccentricity, and thus the load carrying capacity is reduced. This is allowed for in design by the application of a capacity reduction factor ç obtained from code Table 7. The value of 1 is relatedin codeTable 7 to the slenderness ratio andthe eccentricity at the top ofthe walland takes into account an additionaleccentricity due to the bucklingdeflection. The derivation of is given in code Appendix B.
i
The design vertical resistance ofa wall is given by: per unit length and ofacolumnby:
b t fk
is the thickness ofthe wall or column is the width ofthe column ym is the partial safety factor for material strength fk is the characteristiccompressive strength of the masonry
where: t
b
, ,'\
'(m is obtained from code Table 4, (Table4
below). Whilstnormalcategories of manufacturing 60
52
// / //
ii:i_ w6,
(b)
(c)
4-
neteccentricity ewithinceritroid ofleaves
2j
L
Re
=2(W6—W5)
statically equivalent loads,W5 and W6, ofW,W2W3W4in (a)& (b)
Figure 52 Eccentrically loadedcavity walls.
and constructioncontrol give a value of 3.5 for ym from codeTable4 it should be noted that an increasein loadbearingcapacityof approaching 30%can be made byensuringthat the requirements of the special categories of manufacturingand
Thus, the design vertical load resistancebecomes: (a) walls of small loaded plan area
= t(0.70+l.5A)fk Ym
columnsofless than 0.2 m2 loaded plan area
bt(0.70+l.5A)fk
construction control are achieved, leadingto a Ym value of 2.5.
Table4 Partialsafelyfactorsfor material
strength,
Ym
rn
Categoryof manufacturing control ofstructural units
Category of constructioncontrol Normal Special Special 2.5 Normal 2.8
Ym
(b) narrow walls = 3t1.lSfk-
3.1 3.5
The characteristiccompressive strengthof masonry, fk, is usuallythe end product ofthis part ofthedesignprocess, itscalculation confirming that either the masonryunits and mortar designationbeing proposedare adequate or enabling suitable units and mortar to be chosen. In certain circumstances however the value of fk is modified by factors as follows: (a) Walls and columns of smallplan area — Ifthe horizontal loaded cross-sectional area, A, of the wall or column is less than 0.2m2 then the value of fk must be multipliedby (0.70+l.5A) (b) Narrow brick walls — If a brick wall, or the loaded inner leaf of a brick cavity wall, is narrow ie, ofthicknessequal to the width of a standard format brick, the value of fk may be multiplied by 1.15 (c) Modular brickwalls — If a brick wall is built usingmodular bricks the value of fk may be multipliedby: (i) 1.25 ifthe wall is narrow or (ii) 1 .10 for other thicknesses Handbook to BS5628: Part I
per unit length
(c) walls in modular bricks:
t
(i) narrow walls l.25fk — —
per unit length
(ii) other thicknesses — —
tl.l0fk per unit length
When in (a) above, the wall or column is of cavity constructionand only one leafis vertically loaded, plan area 'A' should be takenas the area ofthe loaded leaf. It should be noted that the modification to fk in the formulae given in (a) may occurin combinationwith (b) or (c), should they also apply. Equatingthe above formulaeto the design vertical loads for the wall and column elements being considered enables the minimum values of fk to be calculated. From the value of fk obtained, the appropriate brick or block strengthand mortar designation can be selected from code Table 2 which is in four parts, reproducedhere as Tables 5, 6, 7 and 8. Table 5 is used when masonry is constructedwith standardformat bricks. Table 6 when the masonryis constructed with structural units with a ratio of height to least horizontaldimensionof0.6 (brick size). Table 7 when the masonry is constructedwith structural 61
units, other than solid blocks,with a ratio of height to least horizontaldimension of between 2.0 and 4.0 (most normal hollowclay or concrete blocks) and, finally, Table 8 when the masonryis constructedwith solid concreteblockswith a ratio of height to least horizontaldimension of 2.0 and 4.0 (most normal solid blocks). Table5 Characteristiccompressive strengthof masonryfk, in N/mm2,constructedwith standard format bricks Cornpressive stren gth of unit (N/mm2) designation 5 10 15 20 27.5 35 50 70
Mortar (i) (ii) (iii) (iv)
2.5 4.4 2.5 4.2 2.5 4.1 2.2 3.5
6.0 7.4 9.2 5.3 6.4 7.9 5.0 5.8 7.1
4.4 5.2 6.2
11.4 9.4 8.5 7.3
100
15.0 19.2 24.0 12.2 15.1 18.2 10.6 13.1 15.5 9.0 10.8 12.7
Table6 Characteristiccompressive strength of masonry,fk, in N/mm2, constructedwith blocks having a ratio ofheight to least horizontal dimension of0.6 Cornpressive stren gth ofuni t (Njmm2) designation 2.8 3.5 5.0 7.0 10 15 20 35 or
Mortar
greater (i) (ii) (iii)
(iv)
1.7 2.5 3.4 4.4 6.0 7.4 11.4 1.4 1.7 2.5 3.2 4.2 5.3 6.4 9.4 1.4 1.7 2.5 3.2 4.1 5.0 5.8 8.5 1.4 1.7 2.2 2.8 3.5 4.4 5.2 7.3 1.4
Table7 Characteristiccompressivestrengthof masonry,fk, in N/mm2, constructedwith hollow blockshaving a ratio ofheight to least horizontal dimension ofbetween 2.0 and4.0 Mortar Compressive strengthofunit (N/mm2) designation 2.8 3.5 5.0 7.0 10 15 20 35 or greater 5.7 6.1 6.8 7.5 11.4 2.8 3.5 5.0 (i) 2.8 3.5 5.0 5.5 5.7 6.1 6.5 9.4 (ii) 2.8 3.5 5.0 5.4 5.5 5.7 5.9 8.5 (iii) 2.8 3.5 4.4 4.8 4.9 5.1 5.3 7.3 (iv)
Table 8 Characteristiccompressive strength of masonry,fk,in N/mm2, constructedfrom solid concreteblocks having a ratio ofheight to least horizontaldimension ofbetween 2.0 and 4.0 Mortar Cornpressive strength ofunit (N/rn rn2) designation 2.8 3.5 5.0 7.0 10 (i)
(ii) (iii) (iv)
2.8 3.5 5.0 6.8 8.8 2.8 3.5 5.0 6.4 8.4 2.8 3.5 5.0 6.4 8.2 2.8 3.5 4.4 5.6 7.0
15
20
35 or greater
12.0 10.6 10.0 8.8
14.8 12.8 11.6 10.4
22.8 18.8 17.0 14.6
For units with height to least horizontal dimensionratios of between 0.6 and 2.0, fk is
obtained by interpolation between Table 6, and Table 7 or 8, whichever is appropriate. It should be noted that solid in the context of Table 8, means withoutcavitiesand not 'solid' to BS 2028/1364.
To simplify selection of brick class andmortar
designation when usingcode Table 2(a), the 62
Table is also shown in graphicalform as code Figure 1. AmendmentNo. 2 now gives codeTables 2(b), (c) and (d) in graphicalform as well.
It is usual to rationalisethe class or strengthof
masonry unit and mortar combinationrequiredin various parts of a particular building for reasons of economy, and to simplify construction,thus reducingthe risk of the wrong unit or mortar beingused in a particular situation. There are fourfurther design considerations whichmay affect the required value of fk and thereforethe choiceofunit strengthand mortar designation. They are as follows: concentratedloads shear strength walls subjected to lateral load and accidental damage, all ofwhich are considered in the following sections. Concentrated loads (codeclause 34)
To ensure that the chosen characteristic compressive strength ofthe masonry, fk, is adequateto cope with the local effects of concentratedloads due to beams,lintels or padstonesetc, the effect ofthe concentratedload, combinedwith stresses due to other loads, should be checked at the bearing and at a distance 0.4 h belowthe bearing, where h is the clear heightof the wall. The code permitsan increased local design bearing strength at the bearing, depending upon the type of bearing. It alsopermits the load to be dispersed at 450 through the masonry for the purpose ofchecking the design strength at 0.4 h belowthe bearing, at which level no increase is allowed. The bearing type applicableto the particular case can be chosen from code Figure4. Code Figure 4(a) representsthe limitingdimensionsofbearing area for which the local designbearing strength may be increased by 1.25. Bearings ofthistype may be designed for a local design strengthof 1.25 fk
If the bearingtype correspondsto the codetype
4(b), havinga more limited bearingarea, use may be made ofa higher local design strengthof 1.5 fk
When a spreaderbeam is incorporatedunder a concentratedload as in codebearing type4(c), the local design bearingstrength may be taken as 2.0 fk
The stress distribution under the spreadermust be based upon an acceptableelastic theory. The code does not giveanyguidance regardingthis, other than to indicate a possible shape of stress diagram in code Figure 5(b). Possible maximum design stressesmay be arrivedat using:
When considering shear the following relationship must be satisfied:
53
f
vh spreader diagram
Figure 53 Spreader beam:
A
mv
where
f
is the characteristicshear strengthwhich equals 0.35 +0.6gA N/mm2, up to a maximumof 1 .75 N/mm2, for mortar designations (i) (ii) or (iii)
or 0.l5+0.6gAN/mm2up to a maximumof 1.4 N/mm2, for mortar designation(iv).
Z approach.
gA is defined
54
spreader
stress diagram
Figure 54 Spreader beam: Timoshenko's approach.
WM
-+-
(a) the straightforward approach. This gives a stress diagram that implies that cracking would occur under the inner part of the spreader ifits lengthexceeds three times the distance from the line of action ofthe load to the end of the wall, as shown in Figure 53. The diagram would, ofcourse, be modified by any other uniformlydistributedloads acting on the wall form above.
as the designverticalload per unit area of wallcross section, due to the vertical dead andimposedloads calculated from the appropriateloading case. However, the appropriateloading case, giving the maximum design horizontal load, and hence shear load, togetherwith minimumvertical load willalways be load case (b), see page 57. No imposedload is included. Thus =0.9Gk If variesalong the length of a wall, its average value may be used to determinethe characteristic shear strength , beingcalculatedeither directly or by integratingthe load distribution diagram and dividing by the wall length.
g
g
mv is the partial safety factor for masonry strengthfor shear and is givenin the code as 2.5, providedthe mortar is not weakerthan designation(iv). Whenconsidering the effects of misuseor accidenta value of 1.25 may be used for mv.
Wallssubjected to lateral load (codeclauses 22, 24 and36) 36 of the code deals with the designof (b) Timoshenko'sanalysis for the bendingof bars Clause wall whichare subjected to lateral loading. panels on elasticfoundations.Strictlythismethod is Such is generally only necessary when design if the is of infinite applicableonly spreader length, either the lateral load is the predominantload on but it does result in a stress diagram (Figure 54) the and there is little vertical load other wall, that is similarto that shown in code Figure 5. than self-weight, or the wall has to resist accidentaldamage. The latter caseis dealt with When checking the effect of the concentratedload on page 68. at a distance of 0.4h belowthe bearing, see code Figure 5, the design compressive strengthshould The designer must first decidewhat restraint is be calculated in accordance with code clause32, offered to the panel by its supports and satisfy (pages 60 and97 in this book). himself that the supports are capable ofresisting the forces transmitted to them by the panel. Edge restraint will depend upon continuityover the support, the restraininginfluence of any Shear strength vertical loadingon the wall, the presenceand (codeclauses 25, 27.4 and33) type of dpc at the supports and the adequacy of Walls subjected to horizontalforces acting in their the connectionto the supports.Ifthe panel is to plane must be checkedfor shear strength.Shear in be designed as an arch, the strengthofthe abutmentsmust be adequate to develop the laterallyloaded walls is considered in the section with such walls. dealing in-plane forces. Code Figures 6 and 7 give some guidance on the assessment ofedge restraint. Fromthe designhorizontalforces obtained in the The adequacy ofthe ties can be checkedusing codeTable 8, reproducedbelow as Table 9, stabilityanalysis the shear stress, Vh in walls andthe characteristiccompressive strength, be calculated. The resistingoverturningmay shear load is assumed to act uniformlyover the given in the code, for double triangle and wire horizontalcross-sectional areaofthe 'web' ofthe butterfly ties in mortar designation(i), (ii) and wall. The area of any flanges is not included since (iii) of 1.25 kN and 0.5 kN respectively. The it can be shown analytically that the shear stress partial safety factor, m, to be applied to the distributionacross a sectionconcentratesthe strengthofwallties is 3.0, although thismay be halvedwhen considering misuse or accidental shear load on the web, as in steelwork and reinforcedconcrete design. damage. In cavitywalls especially it is necessary 63 Handbook to BS 5628: Part 1
Table9 Characteristicstrengths ofwallties usedaspanelsupports Characteristicstrengthsofties engaged in dovetailslots set in structural concrete Shear Tension kN kN
Type
Dovetail slot types ofties (a) Galvanized or stainless steel fishtail anchors 3 mm thick, 17 mm mm.width in 1.25 mm thick galvanized or stainless steel slot, 150mm long, set in structural concrete (b) Galvanized or stainless steel fishtail anchors 2 mm thick, 17 mm mm. width, in 2 mm thick galvanizedor stainless steel slots 150 mm long, set in structural concrete (c) Copper fishtail anchors 3 mm thick, 17 mm mm. width, in 1.25 mm copperslots, 150mm long, set in structural concrete
4.0
5.0
3.0
4.5
3.5 4.0 Characteristic loads in ties embeddedin
mortar Tension
Shear*
Mortar designations
Mortar
(i) and (ii)
(iii)
(iv)
designation (i), (ii) or (iii)
kN
kN
kN
kN
3.0
2.5
2.0
2.0
5.0
4.0
2.5
3.5
Zinc coated mild steel or bronze or stainlesssteel 5.0 *Applicable only to cases where shear exists between closely abutting surfaces tSeeBSl243: 1978
4.0
2.5
3.0
Cavity wall tiesl (a) Wire butterfly type:
Zinc coatedmild steelor stainless steel
(b) Vertical twist type:
Zinc coated mild steel or bronze or stainlesssteel
(c) Double triangle type:
to ensure that lateral forces can be transmitted to the supports if wall ties are beingrelied on for thispurpose. Limitingdimensions
(code clause 36.3) The codegives limiting dimensions for panels or walls subjected to lateral loadingfor mortar designations (i) to (iv) as follows:
(a) Panel supportedon threeedges: (1) two or more sides continuous: height>< length equal to 1 500tef2 or less (2) all other cases:
height x lengthequal to 1350tef2 or less
(b) Panel supported onfouredges: (1) three or more sides continuous: heightx length equal to 22SOtef2 or less (2) all other cases: heightx length equal to 2025tef2 or less (c) Panel simply supportedat top andbottom: Height equal to 4Otefor less
Method (a) The method does not allow for in-plane forces but does permit some allowance to be made for precompression dueto self-weight or applied vertical loads in suitablecircumstances. It also takes account ofthe difference in strengthof masonry in orthogonal directionsanddifferent edge support conditions.
To some extent the design process is by trial and error, since it is often necessary to assume a
masonry unit/mortar designationcombination and then to check the structural adequacyof that combination.
For bendingabout a vertical axis the design moment per unit height
=
L2
Wk
where:
'
is the bendingmoment coefficient is the partial safety factor for loads L is the horizontaldimension of the panel Wk is the characteristicwind load per unit c
area.
is obtained from codeTable 9 for the appropriate panel shape and edgeconditions.To obtain as (d) Freestanding itall well as knowledge of the geometry of the panel, to 1 or less 2tef Height equal the orthogonalratio of the masonry, p., must be known.This ratio is defined as the ratio of the In cases (a) and (b) no dimensionshouldexceed flexural strength of masonry when failure is 50 timesthe effective thickness tef. parallelto bedjointsto that when failure is perpendicularto the bedjoints. The characteristic fiexural strength of masonry, fkx, for the two Design oflaterally loaded wall panels orthogonal directionsis obtained from code (codeclause 36.4) Table 3, reproducedbelow as Table 10. For clay The code gives two approximatemethodsfor brickwork p. is sensibly constant at 0.35 so that designing a laterally loaded panel: prior assumptions ofbrick and mortar need not (a) as a panel in bendingsupported on a number be made; however, for concreteblockwork p. of sides. varies with block strength andan initial guess is (b) as an arch spanningbetweensuitable supports. necessary to obtain
,
.
64
Table10 Characteristicflexural strengthofmasonry,fkx, N/mm2 Plane offailure parallel to bed joints
Plane of failure perpendicularto bed joints
Mortardesignation
(i)
(ii) and (iii)
(iv)
(i)
(ii) and (iii)
(iv)
0.7 0.5
0.5
0.4
1.2
1.1
1.0
0.4
0.3
0.35 0.25
2.0 1.5
1.5
0.4
1.1
0.9
0.8 0.6
Clay bricks having a waterabsorption
7 l2 7 l2°,
less than between
and
over Calcium silicate bricks Concrete bricks Concrete blocks ofcompressi ye strength 2.8 in N/mm2: 3.5 7.0
0.2
0.3
0.9 0.9
*
0.3
0.4
10.5 14.0 and
0.45 0.60 0.75
0.20
0.25
0.90t
*
0.4 0.4 0.5
0.6
0.7f
over
* Values not atpresentavailable,pending
research.
tWhen used wit/iJiexural strengthin parallel direction,assume the orthogonalratio yr is obtained from code clause22, see page 56. Ifthe panel is non-loadbearingand is not designed to resist in-planewind forces yr may be taken as 1.2; ifhowever removalofthe panel would impair the stabilityof the structure 't must be taken as 1.4. The designmoment of resistance per unit height
=-z
where: fkx is the characteristicflexural strength, obtained
from code Table 3, for bendingabout a vertical axis ie in the column of codeTable 3 'Plane of failure perpendicularto the bedjoint'. is the partial safety factor for material strengthobtained from code Table 4. Z is the section modulus.
y
The code does not specificallystate that there is no need to check the bendingresistance in a two way spanning panel in other than the horizontal direction,because the derivationof the values given in the code makes allowance for the orthogonal ratio, and checking vertical bending will result in the same answeras checking horizontal bending. This can best be demonstrated algebraically: horizontal bending, fkx horiz X Z, vertical bending, fkx vert >< Z,
butfk vert = fkx horiz
=
WkL2
= Ic(WkL2
= 0.3.
Note that both equations(1) and (2) includethe horizontaldimension ofthe panel. Had they been written in terms ofthe vertical dimension, the value of wouldhave altered accordingly. The code permits anyverticalload whichacts to increase the flexural strength in the parallel directionto be used to enhance the lateral strengthof the panel. The bendingmoment coefficients in the code are derived on the basis that the ultimatefailure pattern in the panel is similar to fracture line failure patterns in reinforcedconcreteslabs. It is reasonable thereforeto assume that the strengthwill be enhanced only in panels with four sided support, or panels supported top and bottom and on one side, see Figure 55, but not in panels supported at the bottom and two sides, where the critical stress will occur at the top of the panel where there is no vertical load.
The vertical load increases the effective flexural strengthin the parallel direction,so modifying the orthogonalratio ofthe masonry and thus Figure 55 Wa//panelsfor whichorthogonal ratio maybe modified to allow for vertical load.
55
(1)
(2)
where fkx horiz is the flexural strengthin the perpendiculardirectionand fkx vert is the flexural strength in the parallel direction,seeTable 10 above Substituting in (2) for fk vert andcancelling results in equation (1). Handbook to BS 5628: Part 1
y.
supported edge
freeedge
65
reducingthe bendingmoment coefficient used to calculate the designbending moment. If is the designverticaldead load per unit area, to be taken as O.9Gk, the modified orthogonal ratio _fkx vert+Ymgd
g
56 lineofarchthrust
fkx horiz
The need for the Ym in the dead load term is explained on page 46. Ifthe verticalload is due to the self-weight of the wall itself only the weight of the upper half should be considered.
archrise =0.91 — deflection due10design laferalload
For laterallyloaded walls which span vertically, the code clause 36.4.1 suggests a design bending moment of: Wk yfh2 8
which may be modified ifthe top and bottom support conditionsjustify the assumptionof some endfixity. Earlierin the sameclauseit is permitted that fkx in the parallel directionmay be modified to allow for an increase in flexural strength due to self-weight and any vertical loading in a similarmanner to that discussed
above for panel walls. The designmoment of resistanceof the vertically spanningwallbecomes
xz (+gd) where fkx is the characteristicflexural in the paralleldirection.
Figure 56 Notionalthree-pinarch.
If the length to thicknessratioexceeds 25,
allowance for the wall deflection must be made in the arch rise as follows:
rise=t—j—deflectiondueto design lateral load. The maximumdesign arch thrust per unit height assuming a solid masonry to support junction is: ym\IO
Assuming the wall deflection is smallenough to
be ignored,the designlateral strength,qiat, strength
This is the same designmoment ofresistanceas given in code clause 36.5.3 for freestandingwalls. The design moment of resistanceofcavity walls may be taken as the sum ofthe designmoments of resistance ofthe two leaves providedthat the wall ties used are capableof transmittingthe compressive forcesto which they are subjected. If the leaves have different orthogonal ratios, the design momentsshould be calculatedassuming that the lateral load is shared betweenthe leaves in proportion to their designmomentsof resistance.Further explanationofthe sharing of loads is given on page46. Thus it is first necessary to calculate the design moment of resistance (MR) ofeach leaf, as on page 65, and then apportion the design load betweenthe leaves as follows: designload on inner leaf M.R. inner leaf — —If kM.R. inner leaf+M.R. outerleaf load on outer leaf=yfWk—designload on design inner leaf. The design bendingmoment on each leafis calculatedusing the appropriatecoefficient cc from code Table 9 and comparedwith the design momentsofresistancealreadycalculated. Method (b) In certain circumstances, laterally loadedwalls may be designed assuming that an arch develops within the thickness of the wall. At the present time, in laterally loaded panelswith little vertical load, horizontalarching only may be considered although the code does give a method for designing walls archingvertically under axial load in clause36.8which is discussed on page 67. The assumedthree-pin arch is shown in Figure 56. 66
111<25 archrise= O.9t
fk Ym
(t\2 kL)
where: fk is the characteristiccompressive strength of the masonry,measuredin the directionin which the bricks are used (see codeclause 23.2). 'Cm is the partial safety factor for materials.
It is, ofcourse, necessary for the supportsto be able to withstandthe arch thrust. Freestanding walls
(codeclause 36.5) Freestandingwalls may be designedeither as verticalcantilevers or as panels spanningbetween piers or other abutments to code clause 36.4. The piers or abutments must then be designed to resist the panel reaction.
If a freestanding cantileverwall is subjected to
horizontalforces dueto the characteristicwind load, Wk, and a characteristic imposedload, Qk, as shown in Figure 57, then the design bending moment on the wallis given by:
Wkyf +QkyfhL Figure 57Freestandingwalls.
57
y, the partial safety factor for loads is taken as 1.2 for freestandingwalls.
(
58
The design moment ofresistanceis given by: + x
gi)
where: fkx is the characteristicflexural strength
the designverticaldead load per unit area gZ isisthe section modulus. The value offk to be used will be that taken from codeTable 3 for the plane offailure parallel to the bed joints. Ifthe wallincorporatesa damp proofcourse,which has beenproved by test to transmit tension,the value of fkx used willbe based on the value at the dpc, but not more than the appropriatemasonryvalue. Ifthe dpccannot transmit tension,only the self-weight ofthe wall can be used to resist overturning. The design vertical dead load must be taken as 0.9 Gkand the section modulusmay be calculatedto allowfor anystiffening effect the wall geometry may give, eg curved or zig-zag in plan. When the designercannot relyuponthe flexural strength ofthe wall, eg because ofthe type ofdpc used, the design moment of resistance per unit length
flw[ 2
[t
nwym
fk
where:
t is the wall thickness
flw is the designverticalload per unit lengthof
wall(taken as 0.9 Gk) fk is the characteristiccompressive strength of masonry.
This formula is based upon the assumptionof a rectangular stress block at the leeward edgeofthe wall as shown in Figure 34, andconsequently the wall is assumed to be cracked. The derivationof the formula is also shownin the figure.
M
e1
e
=
+e
Figure 58 Resultanteccentricityofverticallyloaded walls carrying lateralloads.
relatively high design vertical load is required. This limits the applicationofthismethod.
el =
M
+e
where:
M is the designmoment dueto the wind force W is the design vertical load e is the eccentricity of W ci is the resultant eccentricity ofW.
(b) by calculating the design lateral strengthof the wallor columnqiat,, assuming the vertical load, n, resists the arch thrust in the wall or columndueto the lateral load, using the relationship qiat
,
8tn
ii2 Ym
where:
t is the actual thickness ofthe wallor column h is the clear height ofthe wallor column.
Design lateral strengthofaxially loaded walls and columns. (code clause 36.8) The code permitsthe designerto deal with the design ofaxially loaded walls and columnsin
two ways: (a) by adjustingthe eccentricity ofthe design verticalload to includethe effect of the bending moment due to the lateral load, see Figure 58, and then designing the wall for compressive strengthusingthe capacityreductionfactor as usual. Whenthismethod is used, the design verticalload is that appropriateto the loading case being considered, usually0.9 Gk, although 'ii on the wind force maybe taken as 1.2 rather than 1.4 ifremoval ofthe wall willnot impair the stabilityof the building. In order to keep the resultant eccentricity to a reasonablevalue (the largesteccentricity for which values of 1 are given in code Table 7 is 0.3t, although 3 for eccentricities greater than 0.3t may be calculated in accordancewith code AppendixB), a Handbook to BS 5628: Part 1
To use this approach the ratio-i must not exceed 25 in the case ofnarrow brick walls or 20 in other cases.
Normally,n is based on the appropriatedesign dead load, but when considering the possible effects ofmisuse or accidentit shouldbe taken as 0.95 Gk. The designload must produce a
minimum stress of 0.1 N/mm2.
The form ofconstructionofthe floors or membersabove andbelow the wallor column must provideadequatelateral support and resistanceto rotation of the top andbottom of the memberfor its full width. This effectively limits the floor constructionto reinforced concrete. Any damp proofcourse etc, in the wall or column must be able to transmit the relevant horizontalforces. Where the wall or column has return walls, as shown in Figure 59, the value ofqiat may be multiplied by the factor k from code Table 10 67
59 4
//
[N
h=
h— clear height
of wall V
1/
t1I1i1I q
11111111111 q
Ia!
Figure 59 Distributionoflateralloads on wall panel between supports.
reproducedbelow as Table 11. The returns must be capable of resisting the horizontalreactions transmitted to them. Table 11 Factork Numberof Value ofk returns
L
0.75
1.0
2.0
3.0
1
1.6
4.0
1.5 3.0
1.1
2
1.0 1.2
1.5
Accidentaldamage (code clauses22 and32) Category2 buildings ie those of5 storeys and abovemust, in addition to satisfying the code requirementsfor Category 1 buildingsfor stabilityand robustness,also be designed to cope with the possible effects of accidental damage. The code recommends that thisis dealt with by making an assessment of the residual stability and spread of damagefollowing the removal of a loadbearingelement, or alternativelythat provision is made within the structure for verticalor horizontaltying or both. Three design options are given in the code for satisfying these requirementsas follows: Option I: All vertical andhorizontal loadbearing elements, as defined in code Table 11, must be proved removable,one at a time, withoutcausing collapse, unless they are protected members. Option 2: Horizontalperipheral, internal and columnor wall ties must be providedin 68
/
/\
clear height ofwat
accordancewith code Table 13, see Figure 39. All verticalelements must be proved removable unless they are protected members. Option 3. Horizontal ties must be provided as for option 2 and vertical ties must be providedin accordance with code Table 14. Option 1 is the most satisfactorysince the actual behaviourof the building is considered under accidental loading. Load case (d) on page 56 is used in checking that the loadbearingmembers are removable. Engineering judgement is required to decide upon the structural effect of the removal of loadbearing elements.
It is necessary only to prove vertical loadbearing elements removable in the top few storeysofa
buildingas such elements will usuallybe protected below. A protected element is one that can withstand, together with its essential supports, an accidental design load of 34 kN/m2 applied in any direction.For vertical masonry elements this can be checked using the clause 36.8 equation: 8tn see qiat —j--——page 67. ' (m
It should be noted that the axial load per unit length, n, should be calculatedfor load case (d) page56 andTm should be taken as 1.05. Option 2 willoften be used for loadbearing masonry buildings since horizontal ties can be
accommodated easily in the reinforced concrete slabs normally used in masonry structuresof 5 storeys and over. The design procedurefor provingthe vertical loadbearingelements removable or protected is the same as for
option 1. Option 3 is unlikely to be used often for loadbearingmasonry buildings since the vertical tie requirement involves the inclusion of continuousties from rooflevel to a level at which the relevantmembers are protectedor to foundation level, and the simplest way of providingthese is as reinforced concretecolumns. Also, the minimum thickness ofa solid wall or the loadbearingleaf of a cavitywall is 150mm. These constraintswill not usually be acceptable in loadbearingmasonry structures.
In options 2 and 3, peripheral horizontalties must be designed to resist a basic horizontal force, F, equal to 60 kN or 20+4N2 whichever
is less, where N is the numberofstoreys including ground floor and basement.Internal ties must be designed for a forceof F or Ft(Gk+Qk) L 7.5
whichever is greater, where L2 is the lesser ofthe distance between the centres of the vertical loadbearingmembers, in the directionof the tie, or 5 times the clear storey height. If the tie being considered is perpendicularto the span ofa one-way spanning slab, it need only be designed to resist F. External column or externalwall tie connectionsmust be designed to resist 2Ff, or timesthe clear storeyheight divided by 2.5.
F
Vertical ties must be designed for a force of: or 100kN/m length of wall or ()2r column whichever is the greater.
where: A is the horizontalcross-section area in mm2 of the column or wall, including piers, or the loadbearingleafofan externalcavitywall. ha is the clear height of a column or wall. t is the thickness of the column or wall.
The required locations of theseties are shown diagrammatically in Figure 39. The exact locations and fixing requirements are given in code Tables 13 and 14.
Handbook to BS 5628: Part 1
69
Page blank in original
DESIGN EXAMPLES
The following chapter contains two worked examples whichattempt to coveras many as possibleof the design aspectsof BS 5628 Part 1. Where different forms ofconstructionmight be used or where different methods ofanalysiscould be applied, examples of such design have been incorporated by the device of parallel calculations. The parallel calculations are printed in colour so that they may be distinguished easily from the main example calculations. The examples are crossreferenced in the left-hand margin to the relevantclause numbers in the code ofpractice. Reference is also made to Chapter 3 of this handbook. The first example is for the design ofa multi-storeyloadbearingbrick structure. The buildingis seven storeys high and has cavity brickworkexternal walls and one brick thick internal structural walls. The roofand floor slabsare in reinforced concrete. The layout of the structural walls falls somewhere between a crosswall arrangementwith substantialreturn walls, and a fully cellular arrangementand repeatsat each level so ensuring a stable and robust structure.Overturningforces on the building are resistedby the brick walls. The example illustrates designfor stability, design for axial andeccentric compressive loads, design lateral strength of axially loaded walls and designfor accidentaldamage. The secondexample is for the design ofa three storey, end of terrace, house in structuralmasonry. The houses ofthe remainderofthe terrace are only two storeys in height. The house has a trussed rafter main roofand a jack rafter pitched roofwhere the building steps back at second floor level. The front externalwall to the secondfloor is carried on a reinforcedconcretebeam which is supported on one leaf ofthe party cavity wall, an internalloadbearingwalland the inner leaf ofthe externalcavity wall. This building illustrates the design of structural blockwork, design for concentratedloads and the design of laterallyloaded wall panels.
In both examples the partial safetyfactor for material strength,Ym, has been taken generally as 3.5 ie assuming normal category of both manufacturingandconstructioncontrol. The effect ofvarying the value Of"m is shown in the parallelcalculations.
Two further example calculations which could not sensibly be a part of Examples 1 and 2 are given at the end of the chapter for the design of masonry walls stiffened by piers and for laterally loaded masonry infill panels to framed structures. EXAMPLE1
Seven-storey loadhearing brickwork block offlats A typical plan ofandcross-section through the building are shown infigure60. The external cavity walls are 280 mmthick with a 25 mminsulating lining within the cavity. Both leaves are ofbrickwork. The internal loadbearing walls are 215 mm brickwork.
29.2
Thefloors androofare 150 mmreinforced concrete slabs spanning between the internal andexternalwalls andbearing on the innerleafofthe externalcavity walls. Thefloor slab is extended outwards at the thirdandsixth floor levels to support the outerleaf, andthe externalwalls are restrainedatgroundfloor level. The storeyheightis 2600mm. The buildingis locatedon the outskirts ofBristol.
Handbook to BS 5628: Part 1
71
Loading Characteristic loads
Roofload:
Dead loads, Gk, 75 mm lightweight screed 150 mm rc slab
1.0 kN/m2 3.6 kN/m2 0.4 kN/m2
felt, chippings, services, etc
5.0 kN/m2 Imposed load, Qk, Floor load: Dead load. Gk, 50 mm screed 150 mm rc slab partitions services
1.5 kN/m2
1.2 kN/m2 3.6 kN/m2 2.0 kN/m2 0.1 kN/m2
6.9 kN/m2 2.0 kN/m2
Imposed load, Qk, Self-weight of walls, Gk: External walls 102.5 mm outer leaf 102.5 mm inner leaf, plastered one side
2.25 kN/rn2 2.50 kN/m2 4.75 kN/m2
280 mm cavitywalls, plastered one side Internal walls 215 mm structural walls plastered both sides
5.0 kN/m2
The value for the live load, Qk, on the floors is taken here as 2.0 kN/m2, a figure referred to in the Building Regulations. It is more usual for this load to be taken as 1.5 kN/m2. as given in CP 3: Chapter V: Part 1: 1967. Whatevervalue is used, the design method remainsthe same. Wind loading (from CP 3: Chapter V: Part 2: 1972) Assumedbasic wind speed=43 rn/s Wind speed factors:
5=1.0
S2 =0.88 usingground roughness category (3) class B, height of building= 18.2 m. S3 1.0 =43.0x 1.0 >0.88 x 1.0 =37.8 rn/s Design wind speed, vs.
=
Therefore,dynamic wind pressure, q,=
l
0613 '37 82
=0.875 kN/m2
Characteristic vertical loads on walls Only the most heavily loaded walls will be designed. These walls are numbered 1, 2,
3 and 4 in Figure 60. The characteristicloads on the walls from each floor and the roofare as follows: Wall 1 (inner leafonly) Span ofslab —2=1.83 m Load from roof: dead load, Gk, =5.0 x 1.83= 9.2 kN/m imposed load, Qk, =l.5x1.83= 2.7 kN/m Load from one floor: dead load, Gk, =6.9 x 1.83= 12.6 kN/m imposed load, Qk, =2.0 x 1.83= 3.7 kN/m Wall self-weight per storey height =2.5 x2.45= 6.1 kN/m Wall 2 (inner leafonly) Length ofwall=l.2 m, width ofslab carried=2.25 m, span of slab—2 as wall 1. Load from roof:
x-= kN/m =1.5 x 1.83 xf= 5.2 kN/m
dead load, Gk, =5.0 x 1.83 imposed load, Qk,
17.2
Load from one floor: dead load, Gk, =6.9 x 1.83 xj=23.7 kN/m imposedload, Qk, =2.Ox 1.83 Wall self-weight per storey height, inner leaf only =2.5 x2.45
x1-= 6.9 kN/m =
6.1
kN/m
60
18670
key oadbearingwalls
—fIoor span
Figure 60 Details ofsevenstorey loadbearingmasonrybuilding.
Wall 3
Length of wall=2.125 m, width of slab carried=2.545 m, total span of slab±2=3.665 m dead load, Gk, =5.0 >< 3.665 x
=22.0 kN/m
imposed load, Qk, =1.5 x 3.665 x
= 6.6 kN/m
Load from one floor: dead load, Gk, =6.9 x3.665 x
=3O.3 kN/m
Load from roof:
imposed load, Qk, =2.0 x 3.665>< Wall self-weight per storey height =5.0 x2.45 Handbook to BS 5628: Part 1
8.8
kN/m
=12.3 kN/m 73
Wall 4 (total load) Width ofslab carried=1.7 m, total span of slab —2 as for wall 3. Load from roof: dead load, Gk, =5.0 x 3.665x 1.7 =31.2 kN imposedload, Qk, = 1.5 x 3.665 x 1.7 = 9.4 kN Load from one floor: dead load, Gk, =6.9 x 3.665x 1.7=43.0 kN imposedload, Qk, =2.0 x 3.665 x 1.7=12.5 kN Wall self-weight per storey height =5.0 x2.45 xO.8= 9.8 kN
Total characteristicloads at each level are tabulated in Table 12 , the imposedloads have been reduced in accordancewith CP3: Ch. V: Part 1: 1967 — Table 2. Walls 1 to 4 will first be checked to ensure that the part of the coderequirements for overallstabilityrelatingto resistance to horizontalforces is satisfied. Stresses derivedfrom thisanalysiswillthen be used to designthese walls for compressive strength. Table 12 Characteristicloads on walls (kNJm) Wall 3
WaIl 2*
Wall 1*
Wall 4
Levelof Gk
Qk
Gk
Qk
Gk
Qk
Gk
Qk
9.2
2.7
17.2
5.2
22.0
6.6
31.2
9.4
27.9
5.8
47.0
10.9
64.6
13.9
84.0
19.7
5thfloorslab underside of
46.6
8.1
76.8
15.2
107.2
19.4
136.8
27.5
4th floor slab underside of 3rd floor slab underside of 2nd floor slab undersideof 1st floor slab just above ground floor
65.3
9.7
106.6
18.1
149.8
23.1
189.6
32.8
84.0
10.5
136.4
19.7
192.4
25.1
242.4
35.7
102.7
12.7
166.2
23.8
235.0
30.4
295.2
43.2
121.4
15.0
196.0
27.9
277.6
35.7
348.0
50.7
127.5
15.0
202.1
27.9
289.9
35.7
357.8
50.7
loading underside of roof slab
underside of 6th floor slab underside of
slab
*The tabulatedcharacteristic loads for walls I and 2 assume the inner leafof the wall is loadbearing and include the self-weightofthe inner leafonly. The outer leaf is assumed to carry its own weight.
The characteristicloads tabulated in Table 12 are the loads at the underside ofeach roofor floor slab (except for that just abovethe ground floor slab). Thus the characteristicdead load at the undersideofthe 4th floor slab of wall 3 is as follows:
roof load Gk = 4th, 5th and6th floor loads Gk =3 x 30.3 self-weight of wall (3 storeys) =3 >< 12.3
= 22.0 kN/m = =
90.9 kN/m 36.9 kN/m
characteristic dead load at underside of 4th floor= 149.8kN/m Similarly the characteristicimposed load at underside ofthe 4th floor slab of wall 3: = 6.6 kN/m roofload Qk
4th, 5th and 6th floor loads Qk
=
30% imposedload reduction
= —9.9 kN/m kN/m
characteristicimposedload at undersideof4th floor
= 23.1 kN/rn
26.4 kN/m
33.0
20.
3.4
Stability
The structuremust be capableof resistinghorizontalloads due to: 1. Characteristicwind pressure 2. l.5% of the total characteristicdead load above any level considered as a uniformlydistributedhorizontalload 3. Accidental forces Characteristic T%'ind loading (CF 3: Chapter V: Part 2, Table 10) Force coefficients, Cf:
In directionA (Figure 61): 74
61
___________________ 1
62
1
3 —
3 —
5 wind direction
I
6
A
7
b=18.67m
d = 18.67m
1
L
=15.175m
J I = 18.20m
63 Figure61 Wallsresistinghorizontalforcesin direction'A'. Figure 62 Wallsresistinghorizontalforces in direction'B'.
1.4Wk or0.015Gk h
Figure 63 Overallstability —overturningdue to horizontal forces.
building elevation design overturning moment dueto horizontal forces isthegreater of: 1.4Wkx
oro.015G,X
±
18.67
1 23 15.175 18.67 — 1.23 15.175 18.20 0.97 18.67
w
b d h b ThereforeCf = 1.0 The dynamicwind pressure, q,=0.875 kN/m2, see page 72. Thereforethe total characteristicwind load in directionA, Wk
= 0.875 x 18.2 x 1.0 x 18.67 = 298 kN
In direction B (Figure 62): 1.23
b
d
—
15.175 — 0.81 18.67
h 18.2 1.2 b 15.175 ThereforeCc = 0.95 The total characteristic wind load in directionB,
= 0.875x15.175x0.95x18.2 = 230kN Characteristic dead load ,Gk, ofwhole building at groundlevel = Wk
Total plan length ofexternalwall 47.5 m Total plan length ofinternalwall = 78.0 m = 3870kN Walls: 7 x4.75 x2.45 x47.5 = 6700kN 7 x 5.0 x2.45 x 78.0 = l4lOkN Roof: 5.0x15.l75x18.670 Floors: 6x6.9xl5.175xl8.670 =ll700kN 23680 kN
Handbook to BS 5628: Part 1
75
Design loading Design horizontal load is the greater of 1.4 Wk or 0.015 Gk. = 355kN 0.Ol5Gk =0.015x23680 In directionA, 1.4 Wk = 1.4 x298 = 417 kN Hence, designhorizontalload is based on wind loading. Indirection B, 1.4 Wk = 1.4 x230 = 322 kN Hence, design horizontal load is 0.015 Gk.
22(b)
Direction A Havingestablished that the design horizontalload is 1.4 Wk, it is convenient to revert to characteristicloadingat this stage. The characteristicoverturningmoment due to wind loading, see Figure 63
=
x
298
l2 = 2720 kN/m.
Following normal loadbearingdesign procedure,this moment is shared betweenthe walls shown in Figures 64 to 68 in proportion to their stiffness, ie, their momentsof inertia,as all the walls have the same height. The characteristicshear force and bendingmoment on each wall are tabulated in
Table 13.
Table13 Bending moments andshearforces due to characteristicloading in direction 'A'. Moment
ofinertia, Wall no. No. off
1, of
each wall (mi)
5
4 4 2
0.273 3.720
6
1
1.968
1
3
ofinertia,
I
Shear Totalshear B. moment Total B. force V force Vt on moment on each each wall M (kNm) (kN) wall (kN) (kNm)
1
M
(m4)
7.700
0.0849
1.092
0.0120
7.440 1.968 4.480 22.680
0.1640 0.0868 0.0988
1.925
2 2.240 Summation
7
Total moment
25.3
101
3.6
14
48.9
98 26 59 298
25.9 29.4 —
—
230.9 32.6
924
446.0
892 236 537 2720
131
236.1
-
268.7
66
64 note infigures4to8flangelengths havebeenlimitedto4t
H
1075..
(clause 36.4.3.)
215 5657
102.5-
2692
L-1
3067.5 NA
_1075,
NA
-_____________
4j.OIi
1800
I
_______
-
750 215
3450
1= 1.925m4
65
102.5
2125 215
NA
215—'
I
96741260
I= 0.273m4 Note. Infigures 64 to 68flange lengthshave been limited to 4t (clause 36.4.3) Figure 64 Wall 7 Figure65 Wall 3 Figure66 Wall 5 Figure67 Wall6
76
I=3.720m4
67 102.5—h
—-
H 215
3610 NA
iiiLi
—215
I i_i
2141.5
I = 1.968m4
* 1075
Table14 Stressesat bottom ofwalls due to characteristicloading in direction 'A'. Stress at extremefibre*(N/mm2)
Wall no.
Y minimum I
0.37
3 5
±0.15 0.24 ±0.26 ±0.30
6 7
Y maximum
NA
n
215
±0.32
0.I2 ±0.24 ±0.21 ±0.30
*stress= Mw
M
68 I
2500
2500
1= 2.240m'
Figure68 Wall 7
I
where and are obtainedfrom Table13 and y minimumandy maximumare obtainedfrom Figuresl64 to 68 (distancesfrom neutralaxisto extremefibre).
Stresses due to design vertical andhorizontal loads The load caseto be considered is Dead and Wind load so that the partial safety factor, yr, =0.9 on deadloads and 1.4 on wind loads. 0.9 x 5.0 x 2.6 x7 Stress due to design self-weight ofwall only= =0.38 N/mm2 1 0 x215 Stress dueto designwind loading (yrxstress from Table 14): Wall 1=1.4xO.37=0.52 N/mm2 Wall 7 =1.4 x 0.30=0.42 N/mm2 By inspection the stress due to design wind loading in the other walls is exceeded by the design self-weight stress. It can be seen that only a small amount of dead load from the floor slabs on these walls will prevent any residualtension occurringin walls I and 7. Design dead load from roof and floor slabsrequired to prevent residualtension in wall I
22(b)
= (0.52—0.38) 102.5 x 1000 =14.4kN/m 1000
Now, from page72, characteristic dead load from roofslab andone floor slab =9.2+12.6=21.8kN/m Thereforedesign dead load =0.9 x21.8= 19.6 kN. This exceeds 14.4 kN/m and there will thereforebe no residual tensionunder wall 1. Design dead load from roof and floor slab requiredto prevent residual tension in wall 7 = (0.42—0.38) 102.5 x 1000 =4.1 kN/m 1000
From page 72 characteristicdead load ofroof=5.0 kN/m2 Thereforedesign dead load=0.9x5.0=4.5 kN/m2and only 1.0 m width of roof slab is requiredto prevent residual tension.Actual width ofroofslab carried by wall 7 is 3.45 m. 33.
Shear — direction A
30.
The shear force is distributedbetween the walls in proportion to their stiffness in Table 13. As only walls I to 4 in Figure 60 willbe fullydesigned, walls 5, 6 and 7 will be checked here as follows:
The plan area ofeach wallto be considered as resisting shear is that area of the wall that forms the webofthe section. The shear stress in each wall is given in Table 15, see Chapter 3 page 63. Table 15 Shear stress in walls 5, 6 & 7 due to design loads. Characteristic Area of wall Wall no. shearforce, V, resistingshear, (kN) A, (m2) 5 6 7
48.9
1.79
25.9 29.4
0.84 1.07
Shear stress due to design loadsvh, * (N/mm 2) 0.038 0.043 0.038
l.4V *Vh
33. 25.
27.4
Design shear strengthof masonry= (my wherecharacteristicshear strengthf=0.35+0.6 g&
and mv=2.5
Handbook to BS 5628: Part 1
77
The constant component of the design shear strength 0.35 =----=0.l4
N/mm2 This exceeds the stresses due to designloads in Table 15 and is therefore satisfactory. The increase in shear strength from dead load is not needed. Direction B (seepage 75) The design overturningmoment, Figure 63
=355x—--=3230 kNm.
This moment is shared equallybetweenthe two wall complexes made up of walls 5, 8 and 2, as shownin Figure 69. The design bendingmomentper wallcomplex =3230x0.5=1615 kNm. Therefore, stressesdueto thisdesign bendingmoment = My as for directionA, page 77. 1615x4.415 16l5x3.017
±l5317x 103or ±l53l7x103
= +0.47 N/mm2or +0.32 N/mm2 Stressdue to
design vertical andhorizontal loads
The load case to be considered is dead and wind load when the partial safety factor, y,=0.9 on the dead load. Therefore,stress due to design self-weight ofwall only =0.38 N/mm2as for directionA, page 77. It can be seen that the self-weight stresswillonly be exceeded near the wall 2 end of the wall complex. Using the same method as shown for direction A on page79, it can be shownthat the dead load from the floorsis more than sufficient to prevent anyresidualtension. Shear — directionB The horizontaldesign shear force per wall complex is: kN. This force is resisted by the walls in whose plane it acts, ie, the walls parallelto directionB in Figure 69. 178 x l0 Design shear stress, vh=2lS(3767+2x3880)
33.
=l78
=0.07 N/mm2
69
1035 215
102.5
4
3450
4415.5
2485
215
860i 215
1= 15.317m4
78
Figure 69 WaIlcomplexmade upofwalls2, 5 and8, see Figure 60(2 no.)
Thereforeminimumcharacteristic shear strengthrequired 25.
mv Vh =2.5 xO.07=0.175N/mm2
The characteristicshear strength of masonry, f,
=0.35+0.6g& N/mm2 exceeds the requiredcharacteristicshear strength even without the self-weight component0.6gA and is therefore satisfactory. Characteristic compressivestrength ofbrick required at ground floor of walls 1 to 4, see Figure 60 The critical section ofa wall for design for compressive strengthis 0.4 h belowthe level of applicationof the load, where h is the storey height. For simplicity, the design loads in this example includethe full self-weight of the storey height of wall under consideration,rather, than just 0.4 ofit.
22. 22(a)
22(b)
22(c)
WaIl 1 Characteristicdead load, Gk, = 127.5 kN/m, from Table 12. Characteristicimposed load, Qk,= 15.0 kN/m, from Table 12. = +0.37 N/mm2or +0.32N/mm2, from Characteristicwind stress Table 14. Design loads
Consider 1 m length of wall. Load case(a), dead and imposedload: Design dead load =ycGk=l.4x 127.5=179 kN/m Design imposed load ='fQk=l.6 x 15.0= 24 kN/m Therefore,design vertical load =203 kN/m Load case (b), dead and windload: Design dead load='fGk=l.4x 127.5 103=179kN/m Design wind load="fWk=l.4xO.37 x 102.5 x —= 53 kN/m 10 =232 Therefore,design vertical load kN/m Load case (c), dead, imposedandwind load: =153 kN/m Design dead load =yfGk=1.2x 127.5 = Design imposedload Qk =1.2 x 15.0 1O 18 kN/m Design windload =yfWk=l.2 xO.37 x 102.5 x—3= 45 kN/m 10 =216 Therefore, designverticalload kN/m
=f
28.
28.2.2 28.3.1
28.4
Slenderness considerations Enhancedlateral resistance is providedby the in situ concreteslab bearing on the inner leafofthe wall. = 0.75 x2450 Effective height, her, = 1840 mm Effective thickness, tef, 0.67 (2 x 102.5) = 137 mm
=
=
hef
=
1840 137
=
28.1
Slenderness ratio
31.
Eccentricity at right angles to the wall (see Figure 70) Loading (See page 72) Design loads:
Wi: l.4Gkl 1.6 Qkl
W2: l.4Gk2 1.6 Qk2
tef
13.4
= l.4x12.6 = 17.6 kN/m = 1.6 x3.7 = 5.9 kN/m 23.5 kN/m = 1.4(121.4—12.6) = kN/m = 1.6 (15.0—3.7) = 152.0 18.0 kN/m
170.0 kN/m Takingmomentsabout centre line ofinner leaf:
(170.0+23.5)ex
=
Therefore,ex
= 23.5xt 6x193.5
= 0.02 t
23.5x
Hence,from codeTable 7, capacityreductionfactor, 1, = 0.9 A largereccentricity could, perhaps, be obtained by considering the loading case: W2 = 0.9 Gkl + 1.6 QkI Wi = l.4Gk2 + 1.6Qk2 However, virtuallyalways, the effect of the decrease in the vertical load outweighs the effect of any increase in eccentricity on the design stress, as shown in the chapter on design, and, therefore, this latter loading caseneed not usuallybe considered,but see page 57. Handbook to BS 5628: Part 1
79
32.2.1 23.1.2
Design vertical resistance ofwall 1 As the thickness of the inner leaf of wall I is equal to the width of a standard format brick, the value of fk may be multiplied by 1.15. Therefore,the design vertical resistance ofwall 1
= t(l.15fk) = 0.9x102.5x1.l5fk=30.3fk Ym 3.5 70
at rig/it angles to wall I.
__________________________________________________________ Figure 70 Eccentricity
27.3
The partial safety factor for material strength,m, is taken as 3.5 from code Table 4, as both the category of manufacturingand constructioncontrol are assumed in this case to be normal. Design verticalload =232kN/m (load case (b)). Therefore,minimumcharacteristiccompressive strength,fk, required
232x 10
10=
N/mm2 =30.3 x From code Figure 1, class 4 bricks in mortar designation(ii),or class 5 bricks in mortar designation(iii) may be used.
32.2.1
Parallel calculation If it is possible to obtain both special control of manufactureof the masonry units and ofconstruction,a considerable reduction in the strengthof the unit required can be made by the modification øf Yrn from 3.5 to 2.5: Design 'erticalresistance ofwall I =0.9 > 102.5x l.l5fk =42.4fk 2.5 Design vertical load =232 kNm Therefore,fk required
232x l0
=
5.5N/mm2 42.4x103 Thus, from code Table 1. a class 3 brick in mortar designation (iii) may be used, instead of the class 4 brick required for Ym=3.S 33.
80
Horizontalshearforceinplane ofwall1 Characteristicshear load due to wind on wall =25.5 kN, from Table 13. Characteristic dead load = 127.5 kN, from Table 12. Loadingcase(b) gives the most severe conditions,ie, no imposed vertical load. Design wind load =1.4 x Wk Design dead load =0.9 x Gk
Therefore,design shear stress, Vh, = 1.4 x25.5 x lO 5759x 102.5
=0.061 N/mm2
Characteristicshear strength ofmasonry, f, =0.35 +0.6 for walls in mortar designation (i), (ii) or (iii). Design vertical load per unit area, g,
25.
g
= 0.9 x 127.5 x 10 =1.12N/mm2 102.5x1000 Therefore,f=0.35+0.6 x 1.12
= 1.02 N/mm2
The partial safety factor for shear loads, mv, 2.5*. Therefore,the design shear resistanceof the wall
27.4 33.
mv
N/mm2
2.5
This exceeds the design shear stress, vii, and is therefore satisfactory. *No alternative valuesfor Imvare given in the code, except ii'hen considering the effects ofaccidental damage. Parallel calculation The code statesthat the eccentricity of loading on a wall should preferablybe calculated. The following calculation illustrates onemethod ofdoing this. It also illustrates some of the assumptions made by the code in its treatment of eccentricity (see code AppendixB and chapter 2 page 36 . This calculationalso considers the case whereboth leaves of the cavity wall are !oadbearing.
31.
The calculation procedureifonly the innerleaf is loaded, is similarexcept that the relative stiffness ofthe masonryis based on two thirds ofthe sum ofthe stiffnesses of the two leafs or the stiffness of the inner leaf alone, whichever is greater, see chapter 3, page 60. Assume both leaves ofthe external wall are loadbearing(ie, floor and roof slabs bear fully on both leaves) at all floors. Consider wall 1 Design loads — groundfloor level The criticalload case is, as before,load case (b): dead and wind, see page 79.
22. 32.2.3
In order to apportion the total vertical load between the two leaves of the wall, it is necessary to determine the eccentricity of loading at first floor level. One method of calculating the eccentricity is by the momentdistribution method, assuming rigid joints between the masonry andthe floor slab, see Figure 7!.
71
2525
L 3665
—,
Figure 71 JdealisedfrarneJr
calculation
ofeccentricity.
Design dead load = 1.4 x 6.9 =9.7 kN/m2 Fixed end moments
SPanABFMAB
wL2
9.7x3.6972 12
=—ll.l kNm/m FMBA =—FMAB
=+ll.1 kNm/m
Similarly, span BC & CD
Handbook to BS 5628: Part 1
FMBC
=FMCD=—97x3.6652
FMCB
= —10.8 kNm/m —FMc =FMc +10.8 kNm/m 81
StUlnesses Assume: Young's modulus for concrete Young's modulus for brickwork Relative stiffness,
=25,000N/mm2
=
El
8,750 N/mm2 (from modularratios given in CP 111. Part 2, 1970for 27.5-34.5 MN/rn2 bricks)
kAB=kBc=—--- -=25,000+
l000xl50 12
=1.92x109 El
=1.92+ 10x0.5 =0.96+ 10
kcD=
=0.75 875O+2x _________
3E1
kAE=J k BF=
=0.46xl0 El
_______ CG =0.75+8750+ =2.15x109
2525
12
Distributionfactors The vertical design load at a point immediately above the point of lateral support, ie. the floor slab, is considered axial. Therefore,the wall is considered pinned at this level. = 1.92 +l.92<'l0 Joint A: factor for span AB 1O 0.46+ 109=0.81 =0.19 Thereforefactor for column AE = 1.0 —0.81 Joint B: factor for span BA =factor for span BC
31.
1.92.<
10
+ 1.92+ l0+2.l5 +109=0.32 =0.36 Thereforefactor for column BF = 1.0=2 +0.32
l.92+l0
= 1,92+ lO 0.96 + lO+2.15 +109=0.38 Joint C: factor for span CB =0.19 factorfor span CD =0.38 <0.5 Thereforefactor for column CG=l.0—0.38-—0.l9 =0.43 Aloinent distribution (BendingmomentskNm/m width)
A AE
AB
BA
B BF
0.32
0.36
C
BC
CB
CG
0.38
0.43
CD
Distribution
factor
0.19
F.NI. Distribution+2.2 Carryover Distribution Carryover Distribution—0.1 +2.3
0,81 —11.1
+11.1
— 0.1
—0.1
4.5 1.4
—1.7
—
+14.1
—1.8
—12.3
+
+ 8.9...
0.7 + 0.6 — —
2.3
0.32 —10.8 — 0.1
1.4-.....,
+10.8
— 0.7
+
0.3 +10.4
+0.3
+0.3
72 iO2.5
75
-
,1O25,
'4-10.5
280
_______
Figure 72 Calculateddesign eccentricity Wall 1
82
0,19 —10.8
+
0.1 —10.7
Design vertical loads at underside of first floor (see Figure 72)
Wi:
Characteristic dead load from inner leafand floors =121.4 kN/m (Table 12) = 35.1 kN/m Self-weight of outer leaf=2.25 x2.6x6 156.5 kN/m Design load, W1,=I.4 x 156.5 =219.1 kN/m =2,3 kNm/m from moment distributionabove, at A Design bending moment
Thereforedesign eccentricity
2 3 x 106
=2191 >< 1O
=10.5 mm, see Figure 72 Statically equivalent load on outer leaf, taking momentsabout R (Figure 72): R0 =219.1
x.12=97 kN/m and R =219.1 —97 = 122.1 kN/m Addingthe self-weight of brickworkbetween ground and first floors: Total design vertical load on outer leaf =97+2.25 x2.6 x 1.4 = 105.2 kN/m Total design vertical load on inner leaf = 122.1 +2.5x2.45x 1.4=130.7 kN/m Design ii'ind loads — groundfloor level As both leaves of wall I are now loadbearing,the momentof inertia ofthe wall is increased, and it will attracta higher proportion of the wind moment than originally. However, thisis more than offsetby the increase in wall area, resulting in slightly lowerwind stresses than before.Calculations similarto those on page 77 show that the maximum stressdueto characteristicwind loading =0.27 N/mm2. Hence,stress due to design wind loading= 1.4 x0.27=0.38 N/mm2. Design ofinner leaf(noii axiallyloaded) ==130.7+0.38x102.5 Design vertical load = 169.9 kN/m = 13.4, from page 79 Slenderness ratio Hence for axial load, [ =0.90 t fk* vertical resistance = 1 Design
(m
0.9 >< 102.5 xfk 3.5
Therefore,equating design load and design resistance and solving: 3.5 x 169.9 x l0 fk=09 x 102.5 x 10006.4 N/mmFrom code Figure I, class 3 bricks in mortar designation (ii), or class 4 bricks in mortar designation (iii), may be used. * The narroii it'a/lftzctor, 1.15, should not be appliedto tile loaded inner leafofa Cavity wall whereboth leaves are loaded.
Design of the outer leaf follows the same procedure.
22(a)
Wall 2 = 202.1 kN/m from Table 12 Characteristicdead load Gk Characteristicimposedload Qk = 27.9 kN/m from Table 12 Design bendingstress due to horizontal loads, = 0.47 N/mm2, see page78. Load case(a) dead and imposedload yr = 1.4 (dead load) and 1.6 (imposed load) Design vertical load = 1.4 x202.1+1.6 x 27.9 =328 kN/m
22(b)
Load case (b) dead and wind load yr = 1.4 (dead load) and 0.015 (dead load*) 103 Design verticalload = 1.4 x202.1 +0.47x 102.5 x-1--= 331 kN/m
22(c)
Load case (c) dead, imposedand wind load yr = 1.2 (dead load and imposed load) and0.015 (dead load*) 10 = 324 Design vertical load = 1.2 x 202.1+ 1.2 x27.9+0.47 x 102.5 kN/m * 0,015 Gk exceeds 1.4 Wk andalso therefore 1.2 Wk andis usedas the design horizontal load (seepage 19).
XJ
Handbook to BS 5628: Part 1
83
28. 28.2.2 28.3.2 28.3.1
Slenderness considerations Enhanced lateral resistance is providedby wall 8 bonded to wall 2, and by slab bearing on the inner leaf of the wall. Effective length, hef,
= 2 x493 = 986 mm
Effective height, hef,
= 0.75 x2450 = 1840 mm
ie 2 x distancebetweena freeedge and a support (wall 8) Thereforeuse the lesser of thesevalues ie 986 mm.
28.4
Effective thickness, tef,
=
28.1
Slenderness ratio =
= 7.2
31.
Eccentricity at right angles to the wall Assume ex = 0.02t as wall 1 since calculation would be similarto that on page 79, evenifgiving a slightly different answer. Hence,from code Table 7, capacityreduction factor, 1, = 1 .0
23.1.1
Horizontal loaded cross-sectional area ofwall, A*
137 mm, as waIl 1.
= 1200x 102.5 = 0.123 m2, ie, less than 0.2 m2. 106
23.1.2 32.2.1
Thereforethe characteristiccompressive strengthof the masonry, fk, must be multiplied by the factor: (0.7-i-1.5A) = (0.7+1.5 xO.123) = 0.88. As the thickness of the inner leaf of wall2 is equal to the width of a standard format brick, the value of fk may also be multipliedby 1.15. Design vertical resistance ofwall2 (0.88 x 1.15 fk) — 1.0 x 102.5xO.88 x Ll5 fk 3.5
= 29.6 fk kN/m, assuming Ym = 3.5, as for wall 1. Design vertical load = 331 kN/m (load case (b)). Therefore,minimum characteristiccompressive strength,fk, required 331 >< l0 = = 29.6x 10 11.2 Nmm2. From code Figure 1, class 7 bricks in mortar designation(ii), or class 10 bricks in mortar designation(iii) may be used. 33.
As wall 2 is not being used to resist wind forces in its plane, there is no need to considerits shear strength. *Jt may be argued that it is not necessary to apply the area reduction factor to this as there is an internalii'aIlfully bonded into it; hoii'ever, strict interpretation of the code does require its application. It is usual to rationalisethe strengths of brickworkrequired in a structure, in order to simplify constructionand for reasons ofeconomy. In thisbuilding,wall 2 is the most heavily stressed, and so the strengthof brick requiredfor thiswall mightbe used throughout the ground floor. The strengthofbrick requiredwill be less in the upper storeys, and calculations would be done at each level until the class of brick requiredwas less than that ofthe loweststrengthbrickeconomically available. For example, considerthe characteristic strengthof brickworkrequired for wall 2 just above third floor level: Characteristicdead load, Gk,=l06.6+6.1=112.7kN/m, from Table 12 = 18.1 kN/m, from Table 12 Characteristicimposedload, Qk,
20.
Stability Design moment at third floor in direction B is based on 0.015 Gk.
Gk at third floor= (3870+6700)+14l0-- x 11700 = 13300 kN (loads from page75). Therefore0.015 Gk=200 kN, and the designmoment=200x =1040 kNm. 1040 Thus, the designmomentpercomplex (Figure69)=—— =520 kNm. 84
The maximumdesignbendingstress in wall 2 My 520x4.4l5x106 l53l7x106
= +0.150 N/mm2
22.
Load case (a) dead and imposedload: Design vertical load = 1.4 x 112.7+ 1.6 x 18.1 =187 kN/m. Load case (b) dead and wind load: Design verticalload =1.4 x 112.7+0.150 x 102.5 x
=173kN/m. Load case(c) dead, imposed and wind load: Design vertical load=l.2xl 12.7+1.2 x 18.1 +0.150 x 102.5
=172kN/m. Thus case (a) is the critical case.
x 10
28. 28.1
Slenderness considerations Slenderness ratio=7.2, as for ground floor.
31.
Eccentricity at right angles to the wall For simplicity, assume eccentricity, ex, =0.02 t, as for the ground floor. Hence 3= 1.0 from code Table 7.
Area reductionfactor, as before,=0.88. 32.2.1
Design vertical resistanceofwall2 3
t (0.88x 1.15 fk)
296 fk kN/m
Therefore, the minimumcharacteristicstrength, fk, required 187 x =6.3 N/mm2 =29.6x 10
l0
From code Figure 1, a class 3 brick in mortar designation(ii) may be used, or a class 4 brick in mortar designation (iii). The same brick may also be used for the other brickworkat this level, and above if required. Wall 3
=
Characteristic dead load, Ok, 289.9 kN/m, from Table 12 =35.7 kN/m, Characteristic imposed load, Qk, from Table 12 Stress dueto characteristicwindload=+0.15 N/mm2or +0.12 N/mm2, from
Table 14.
22(a)
22(b)
Load case(a) dead and imposedload:
yi= 1.4 (dead load) and 1.6 (imposed load). Design vertical load = 1.4 x 289.9+ 1.6 x 35.7
=463 kN/m. Load case (b) dead and wind load: yr= 1.4 (dead load) and 1.4 (wind load). Design vertical load=l.4 x289.9+l.4 xO.l5 x215
0
1
=450 kN/m. 22(c)
Load case(c) dead, imposedand wind load: yr= 1.2 (dead, imposed andwind load). Design vertical load=1.2 x289.9+1.2 x35.7+l.2 xO.15 x215x
l0
=430kN/m. 28.2.2 28.3.1 28.4
Slenderness considerations Enhancedlateral resistance as wall I (see page79). Effective height, hef, 0.75 x2450 = 1840mm. Effective thickness, tef =215 mm.
28.1
Slenderness ratio
28.
=-
=8.55.
Eccentricity atright angles to the wall ex=0, as wall is symmetrically loaded, but see page 57 for discussion of the effect of varyingloading on each side ofinternal wall. Hence,from code Table 7, capacityreduction factor, 3, =0.99. Handbook to BS 5628: Part 1 85
31.
32.2.1
Design vertical resistance ofwall 3
tfk
0.99x215xfk 3.5
=60.8fk kN/m, assuming m3.S as for wall 1.
Design vertical load =463 kN/m (load case (a)). Thereforeminimumcharacteristiccompressive strength,fk, required 463 x103 =60.8x 10=7.6 N/mm2. From code Figure 1, class 4 bricks in mortar designation(i), or class 5 bricks in mortar designation(iii) maybe used. 33.
Horizontalshearforceinplane ofwall Characteristicshear load dueto wind on wall =3.6 kN, from Table 13. Characteristicdead load =289.9 kN, from Table 12. Loadingcase(b) gives the most severe conditions Design windload= 1.4 xWk Design dead load =0.9 x Gk
1.4x3.6x l0
Therefore,design shear stress, Vh,= 2227 > 215
=0.0 10 N/mm2. 25.
Characteristicshear strengthof masonry, f, =0.35+0.6 for walls in mortar designation (i), (ii)or (iii). 0.9 x289.9 x 10 Designvertical load per unit area, gb., = 215
g
=1.22N/mm2.
00
Therefore,f,=0.35+0.6x 1.22
=1.08 N/mm2.
27.4
The partial safety factor for shear loads, mv,=2.5. Therefore,the design shear resistanceofthe wall
=-=!=0.43 N/mm2. mv 2.5
This exceeds the design shear stress, vt, and is therefore satisfactory. 31.
Parallel calculation In the design of wall 3, the eccentricity at right angles to the wall is zero, as the loading is symmetrical from each side. Had the spans on each side of the wall differed greatly and were the Qk on one side to be taken as zero, a further load case might have had to be considered. However, accordingto the code, the imposed load, Qk, is only taken as zero in the dead +wind load combination.The calculation below shows what would happen if Qk was taken as zero on the short span side, following the method for wall 3, see Figure 73.
73
FJ
WIOTAL
e Figure 73 Loadingcase wit/i zero live loadon one span.
86
Loading(see page 73)
= 13.6kN/m = 1.4 x 30.3 x 0.5 + 1.6 x8.8 xO.5 = 28.2 kN/m
W2=0.9x30.3x0.5 W3
Therefore,W1 =463—2 x28.2
=406.6 kN/m 448.4 kN/m
Taking momentsabout the centre line: 448.4 ex=(28.2—13.6)
23.1.2
Therefore,e=2.33 mm=0.01 t Thus, from codeTable 7, the load may be considered axial and the criticaldesign case will still be full load on both spans. If, for example, wall 3 had been made equal in thickness to the width of the bricks, ie, a narrow brick wall, and the bricks were of standard format, then its design would be modified as follows:
28.4
Slenderness considerations Effective height, hef, 0.75 >(2450 = 1840, as before. Effective thickness, tef, = 102.5 mm.
28.1
Slenderness ratio
28. 28.3.1
=
= 18.0 31. 32.2.1 23.1.2
Eccentricity at right angles to the vall cx =0. From code Table 7, capacityreduction factor,
,
0.77
Design vertical resistanceofwall As the wall is narrow, the characteristiccompressive strength,fk, may be multiplied by 1.15. Thus, design vertical resistance x 1.15 fk 0.77 x 102.5 x 1.15 fk
t
3.5
=25.9 fk. Design vertical
=402.8 kN/m.
load=l.4 (289.9 —2.5 x l7.2)+1.6x35.7
402.8 x 10 Therefore, minimum fk required= 25.9 = 15.6 N/mm2 From code Figure 1, a class 8 brick in mortar designation (i), or a class 11 brick in mortar designation (ii), could be used. These are higherclasses than might normally be used, but if the special category of manufacturingand constructioncontrol can be achieved (see page 61), fk becomes 15.6 11.1 N/mm2 and, from code Figure 1.
l0
x--=
a class 5 brick in mortar designation (i) can be used. Wall 4 Characteristicdead load, Gk, =357.8 kN, from Table 12. Characteristicimposed load, Qk, =50.7kN, from Table12. As wall4 is notrequired to resist horizontalforces, only load case(a) need be considered. 22(a)
3.7
28.
28.3.1.2 28.4.1
28.1
Load case (a) dead and imposedload: vf= 1.4 (deadload) and 1.6 (imposed load) Designverticalload= 1.4 x 357.8+1.6 x 50.7 =582kN. The walllength (800mm) is less than 4 timesits thickness (215mm), andhence the wall must be considered as a columnfor designpurposes. Slenderness considerations
Lateral support is providedby the concreteslab in both directions. Effective height, hef, 2600 mm. Effective thickness, tef, = 215 mm. = 12.1 Slenderness ratio
Handbook to BS 5628: Part 1
=
87
31.
Eccentricity at right angles to the wall ex =0, as the wall is symmetrically loaded, but see page 57 for discussion of the effect of varying loading from each side of internal walls. Hence from code Table 7, capacityreductionfactor, ,=0.93.
23.1.1
Horizontal loadedcross-sectional area ofwall, A, 800 x2l5 106
=0.172 m2 Therefore,the characteristiccompressive strengthof the masonrymust be multiplied by the factor: (0.7+l.5A)=(0.7+l.5 xO.172) =0.96 32.2.1
Design vertical resistance ofwall 4
btx0.96fk 0.93x0.8x2l5x0.96fk 3.5
=43.9 fi kN, assuming ;'m=3.5, as wall 1. Design vertical load
=582kN
Therefore minimum characteristic compressive strength,fk, required
582x 10
43.9x l0
= 13.3 N/mm2 From code Figure 1, class 7 bricks in mortar designation (i) may be used. 37.
Design: Accidental damage The example building falls into Category2, having five storeys or more, thus the additional detailed recommendations in codeclause37 for the limitation of accidental damagemust be met over andabove the recommendations in code clause 20.2 for the preservationof structural integrity.
Three options are listed in code Table 12 for these additionalrecommendations, one of which must be adopted. Option 1 is the full engineering option and requiresthe designerto prove that all vertical and horizontal elements are removable one at a time, without causing collapse unlessthe memberbeing considered is protected. A protected memberis one that is able to withstand, together with its essential supports, its reduceddesign loads (see clause 22(d)), and an accidental load of34 kN/m2, applied in any direction.
Option 3 is the 'soft' option which lays down rules for horizontalties and vertical ties. Compliance with these rules removes the need for further considerationof residual stabilityor spread ofdamage.
Table 12 Table 13
Table 13
88
Option 2 combines the horizontaltie requirements of Option 3 andthe need to prove the verticalelements removable, unless protectedas in Option 1. Option 2 willbe used, in this example withoutconsiderationofthe horizontalelements, as these are not the subject ofthis handbook. Option 2 Horizontalties Basic horizontal tie force, F=60 kN or 20-1-4N whichever is less where N is the number of storeys (including ground andbasement): 20—4N=20+4x7=48 kN This is less than 6OkN, therefore use F=48 kN Peripheral,internal andexternalwall ties are requiredat each floor level and roof level, as shown in Figure 74. They may be provided by using the reinforcement required for the floor androofslabs. The internalties may be spread over the full width ofthe building or concentratedat maximum 6.Om centres. The peripheral ties must be placed within 1 .2m of the edge of the floor or roof. Internal ties must all be fully anchoredto the perimeterties. The tie connection to masonry external walls may be based on shear strength or friction at the wall/slab interface,but not on both. Design tie forces: (using formulae given in code Table 13)
Peripheralties: designtie force = F =48 kN. internal ties: design tie force = F (Gk--Qk) x
or F, whichever is the greater.
74
75_ N\ N
(externaldesign tieforce)
Figure 75 Tying to external masonry walls.
76 a
Cd
b
e
—t———----—peripheraItieswithin
1 .2m of edgeof slab -.--•—-i—--internal tiesdistributed uniformly throughout slab width,typical tiesonly shown ineachdirection
Figure 74 Typical floor planshowingperipheral and inter/ia!ties to comply withoption 2and3 requirementsfor horizontal tying.
F (Gk+Qk)
h
Figure 76 Wallson line A
48 (6.9 +2.0)
La
3.67
75
7.5
=42 kN. Therefore,use F=48 kN. Tiesto externalwalls: designtie force =
(—)F
kp
=
x48
()
F1 or 2
F, whichever is the lesser.
=47 kN/m. This is less than 2Ff, therefore design tie force=47 kN/m, see Figure 75. Tying connections to externalwalls are requiredalong all external loadbearing walls. Check shear strengthof masonryto concreteconnection. Design shear stress
=0.23N/mm2. 27.4
Minimumdesign shear strength 0.35 Imv
Ymvmay be reduced
Table 12
x 103 at masonry/concrete interface = 2><47 102 )00
to 1.25 whenconsideringthe effects ofaccidents.
Therefore,minimumdesignshear strength= =0.28 N/mm2. This exceeds 0.23 N/mm2, and externalwalltie requirementsare thereforesatisfied. Vertical ties (these requirements tt'ould also apply to option 1, hadit been chosen) Vertical elements must be provedremovable,one at a time, withoutcausingcollapse, unless they are protected (see page 68). In the lowerstoreys, the vertical members can be shownto be protected; the upper storey membersmust be shownto be removable.
Walls on line A (fromfigure 60). Partitions h and k in Figure 76 are substantialpartitions having a weight ofnot less than 150 kg/rn2, and walls g and 1 have a length withoutopenings of not less than the clear height of the wall between horizontallateral supportsdividedby 2, = 1250 mm, thus they maybe assumed to providelateral support to the wall element provided that the edge strip of the slab above is designedto span from left to right onto walls g to h toj etc., any one of walls a to f can be removed. Handbook to BS 5628: Part 1 89 37.5
The edge strip of slab at each floor level must be designed to carry one storey height of brickwork,plus the floor loading with the reducedpartial safety factors permitted in CP 110. The load on the edge strip of the slab can be reducedby designing the whole slab panel to span betweeng andj, andj and I. Ifwalls g and I had been less than 1250 mm long a smallreinforcedconcretecolumn would needto be introduced at thejunction ofwalls g and a and also fand 1. The columnwould then be designed as a protectedmember, ie to carry 34 kN/m2 in anydirectionon both itselfand the walls it supports. Walls on line B (from Figure60)
37.1.1
77
__ a
____________________
II
bi
C
de
ig 1=1
f
________________
h
H
I
H0 Iflm II ________________________________________________
Figure 77 Wallson line B
Wallsj and o in Figure 77 have a lengthwithout openings greater than 1250 mm and walls k, n, p and q are substantialpartitions as before; again, the removal ofany one of walls a to h is treated in a similarmanner to the walls on line A. Walls on line C (from Figure 60) 78 h
c
b
I
I
I
I
d
Figure 78 Wallson line C
f
Walls and in Figure78 have a length, withoutopenings, greater than 1250 mm, andwalls g andh are substantialpartitions, as before, so again the removal of any one of the walls a to e is treatedin a similar mannerto the walls on line A. 37.1.1
22.
36.8 37.1.1
j
Protectedwalls For walls to be considered as protected,they must be capable of resisting an accidental design load of 34 kN/m2. Considerwall 3 at underside of4th floor. Design loads (Characteristic loads takenfrom Table 12) Load case (d) code clause 22, = 142.3kN/m designdead load = -(fGk=0.95 x 149.8 load designimposed (no imposedload reduction) = 'cfQk=0.35 (3 x8.8+6.6) = 11.6 kN/m 153.9 kN/m The design lateral strengthof the wall, qiat, 8tn where ?m== 1.05 (codeclause 37.1.1) jj—, n fm _8 xO.2l5 x 153.9 — 2.452xl.05
=42kN/m2 (>34 kN/m2) height thickness
2450 215
=11.4(<20).
Hence,wall 3 is capableofresistingthe accidental design load of 34 kN/m2below 4th floor level, and can therefore be considered as a protectedmemberbelow this level. It is thus only necessary to consider its removal above the 4th floor. A similarcheckcan be made for the other vertical elements. Design of external walls subjected to lateral loading Assuming that wind forces on the windows of the buildingare not transferredto the adjacent brickwork,ie that frames are full storey height andspan top to bottom, only waIl 1 (Figure 60) at top floor level need be designed to resist lateral wind loads. Below the top storeythere will be, by inspection,sufficient precompression on the walls to resist windforces. Also by inspectionother walls at top floor level are smallenough to resist wind forces. The wall is simply supported top andbottom andfull continuityexistsat the sides, ie around the corner ofthe building and over the internalpartition which is block bonded into the inner leaf, see Figure 79. 90
79
75block internal non-Ioadbearing r
2450 4200
L 4200
waIl 1: seefigure60 ______________________________________________ Figure 79Laterally loaded wall.
36.3
Limiting dimensions
For a panel supported on four sideswith less than three sides continuous,the height x lengthofthe panel must be less than or equal to 2025 x W2:
teiO.67(2 x 102.5) = 137.3 mm Therefore2025 x 137.32 = 38.17 >< 106 mm2
= 10.29x106mm2
hxL=2450x4200
This is less than 2025 X tt-2 and thereforesatisfactory. No wall dimension mayexceed50 x tef = 50 x 137.3=6865 mm. Wall length = 4200 mm, therefore the wall satisfies the limitingdimensionclause. Wind loading
Dynamicwind pressure,q,=0.875 kN/m2 (see page 72). Pressurecoefficients Buildingdimension ratios: 18.2 — 18.67 — height — — — 1 2 length — — — width 15.175 width 15.175 1 23 Width ofbuilding affected by local pressure = 0.25 x 15.175=3.8 m. Therefore,from CP3: Chapter V: part 2 Table 7,
'
local Cpe =
1.1
= —0.3 or +0.2 Thereforemaximum Cpe-Cpi = —1.3 Cpi
Thereforecharacteristicwind load, Wk,
= 1.3 x0.875 = 1.14 kN/m2
= 1.6 kN/m2 Designwind load, yfWk=l.4x 1.14 is taken as 1.4 as the wallcontributes to the overallstabilityofthe building.
y 24.
Characteristic flexural strength Both leaves ofthe wallare assumed to be ofclay bricks, having a water absorption ofover 12%, in mortar designation(i). Thus, from cQde Table 3, the characteristic flexural strengths, fkx, of the masonry are 0.4 N/mm2and 1.1 N/mm2in the two orthogonaldirections.
36.4.2
The roofload is carried on the inner leaf, andthisload togetherwith the self-weight ofthe top halfofthe inner leafacts to increase its fiexural strengthin the parallel* direction.Similarly, the self-weight of the top half of the outer leafacts to increase its flexural strengthin the parallel direction. As both leaves havethe samemoment ofresistancein the perpendicular** direction, being ofthe same materials,the appliedhorizontal force must be shared equally between them. For this reason, it is necessary only to check the strength ofthe outer leaf, since if it is satisfactory, the inner leaf, with the greater verticalload, will automatically be so. Design vertical dead load dueto self-weight oftop half of outer leaf =0.9 x 1.2 x 2.25 = 2.4 kN/m run, note yjis taken as 0.9. Stress due to designvertical load 2.4 x l0 =102.5 x iooo = 0.023 N/mm2
36.4.5
*
Bending in the 'parallel' direction refers to bending about an axisparallel to the plane ofthebedjoint. **Bendingin the 'perpendicular' direction refersto bending about an axis perpendicular to theplane ofthe bedjoint. Handbook to BS5628: Part 1
91
Thereforethe modified orthogonalratio, ., 0.44-0.023 x3.5 0.48 1.1 36.4.2
1.1
0.44.
Design momentin panel: The bendingmoment coefficient,
;
for the panel shape shown in Figure 79, for an ratio of from code Table 9G is 0.025. Thus, the design bending orthogonal 0.44, moment on the outer leaf in the perpendiculardirection
= W (f 36.4.5
L2=0.025
1.4xl.14
x4.22=0.35 kNm/m.
The design moment ofresistanceofeach leaf in the perpendiculardirection 1.1 l000xlO2.52 1 fk
rn35>
6
x=0.55kNm/m.
This exceeds the design bendingmoment and is therefore satisfactory. Parallel calculation Alternative approach to designfor lateral load— effectiveeccentricity
80 20=46.7mm
_____________________________________________________________
Figine 80 E//eciiieeccenrl'icitg.
The code assumesin AppendixB that the total design eccentricity of vertical loading is usuallya maximumin the mid-height region of the wall. Therefore,considering the bendingmoment dueto lateral wind forces at mid-height ofthe wall to beWkL2 the design bendingmoment 1
8
6x262
=l.35kNm/m. The code does not give anyguidance as to how this moment should be shared by the leaves in thiscase, but from engineeringprinciplesit would be appropriate to share it in proportion to the stiffness ofthe two leaves. In this instance, the leaves are of the samestiffness and, therefore, each has to resist half the moment. 8
22(c)
Consider wall I, loading case 1.4Gk, l.4Wk: The roofdesignverticalload
= 1 .4Gk=1.4 x 9.2 = 12.9 kN.
31.
This is considered to act at an eccentricity of46.7mm (see Figure 80). Taking momentsabout the centre line of the outer leaf, the staticallyequivalentaxial load, W, on the inner leaf 12.9 x 135.45 177.5
=9.8 kN.
Therefore,W0= 12.9 —9.8 =3.1 kN. Considerthe outer leaf:
moment on wall
bending . Effective eccentricity dueto lateral load = design design axial vertical load —
= 3.1
x 106 <
l0
=218 mm=2.12t.
This is obviously unacceptable, and there is no point in proceedingwith this approach. It can be seen that, in order to reduce the effective eccentricity to a 92
t
sensible figure (0.499 recurringx being the theoretical maximum), a considerable increase in the vertical load on the outer leafis required. For thisreason, this method is rarely a practicalalternativefor the design of laterally loaded wall panels with little vertical load. Evenwhen the vertical load is larger, panels are more conveniently designed using the vertical arching approach given in code clause 36.8.
EXAMPLE2
Three-storey end ofterrace house 81
groundfloor plan
82
j
first floorplan Figure 82 Firstfloor plan.
key cavitywall
=
internal loadbearing wall
83
non-Ioadbearing partition
Figure 81 Groundfloor plan. dual pitchtrussed rafter roofover
ridgeline span of
roof
san
of roof
2nd floorplan
Figure 83 2ndfloor plan.
Floorplans andcross sections ofan end ofterrace three storeyhouse are shown in Figures 81 to 87. The external cavity walls are 280 mm thick with afacing brick outer leaf, a 100 mmlightweight block innerleaf, andcavityinsulation. Theparty wallis a 280 mm cavity brick wallandthe internalload bearing partitions are either 100 mm blockwork or 102.5mm brickwork. Thefloor construction is timberboarding on timberjoists eithersupportedonjoist hangers or builtinto the masonry. The roofconstruction is tiles and battenson timber trussed rafters supported on wallplates on the inner leafofthefront andrear walls.
Handbook to BS 5628: Part 1
93
84
= 2400
igure 84 Elevation on wall1.
85
rc beam
480 long x 225deep concretepadstone
= 2400
Figure 85Elevation on walls 2 and3.
86
—z
'igure86 Elevationon wall4. 87 100
2025
2Tr825T
Figure 87Elevationon wall5. Handbook to BS 5628: Part 1
1800
1275 250
95
It is assumed that the roofis adequately bracedto act as a rigiddiaphragm to resist
horizontal loads,andthat the floors and roofare adequatelyfixedto the masonry with connections capable ofproviding at least simple resistance to lateralmovement, in accordance with Appendix C to BS5628:Part 1: 1978. Loading
FromCP 3: Chapter V: Part 1: 1972
2.1
Characteristic loads
Roofload (on plan) Dead loads, Gk: tiles felt and battens trussed rafters
0.58 kN/m2
0.12kN/m2 0.25 kN/m2 0.15 kN/m2 1.10kN/m2 0.75 kN/m2
ceiling
Imposed load, Qk: Floor load Dead loads, Gk: boarding floor joists ceiling
partitions (lightweight)
0.12 kN/m2 0.13 kN/m2 0.15 kN/m2 0.50 kN/m2 0.90 kN/m2 1.50 kN/m2
Imposed load, Qk:
Self-ii'eightofi%alls, Gk 102.5 mm brick outer leaf 2.25 kN/m2 External wall: 100 mm lightweight block 1.15 kN/m2 plastered one side ___________ 280 mm cavity wall 3.40kN/m2 plastered one side with Party wall: cavitywall 102.5mm brick leaves 5.00 kN/m2 plasteredboth sides Internal partition walls: 100 mm lightweight block 1.40 kN/m2 plasteredboth sides 102.5 mm brick 2.75 kN/m2 plastered both sides Wind loading (from CP 3: Chapter V: Part 2: 1972) Assume basic wind speed = 40 m/s, andwind speed factors:
= 1.0 S2 = 0.74 using ground roughness category (3) class B, Si
S3
of building = height 1.0
9.75 m to ridge
Therefore,design wind speed, V, = 40.0 x 1.0 x0.74x 1.0= 29.6 rn/s 0.613 x29.62 = 0.537 kN/m2 Therefore,dynamic windpressure,q, = l0 Design of walls for vertical load
Wallsnumbered 1 to 5 on plan in Figure 81 will be designed. Wall 1, 280 mm cavity party wall An elevationon the wall is shown in Figure 84. The critical sections for design are x-x, y-y and z-z. Whilstthe critical section for design ofa uniformlyloaded wall is usually0.4h belowthe level oflateral restraint, for simplicity, sectionz-z will be designed here, allowance being made for the additionalself-weight of the wall, see page 100 for further explanation. Sectionx-x (580 mm long) underpadstone Characteristic loading
Load on rc beam: = roofGk Qk
1.1 x8.6x0.5
= 0.75 x8.6x0.5
wall self-weight = 3.4 x 2.2 beam self-weight = 24 x0.4 x0.28
Gk (dead load)
Qk (imposed load)
= 4.7 kN/m = 7.5kN/m =_________ 2.7kN/m
= 3.2 kN/m ________ _____
14.9 kN/m
96
3.2 kN/m
Load from 2nd floor: = 0.9 x3.25 xO.5 = 1.5 kN/m floor Gk = l.5x3.25x0.5 Qk loads on one leaf only ofthe party wall, Considering total load at section x-x: = 14.9 x 3.25 ><0.5 =24.2 kN rc beam Ok = 3.2x3.25x0.5 Qk = 1.5 xO.15 = 0.2 kN 2ndfloor Gk Qk
wall self-weight
=2.4x0.15
= 5.OxO.5x3.OxO.58=
4.4kN 28.8kN
= 2.4kN/m
= 5.2kN =0.4kN _____
5.6kN
Design loading at x-x
1.4Gk =1.4x28.8=40.3 kN
l.6Qk =1.6x5.6
=
9.OkN
49.3kN Stress due to design load = 49.3 x103
x580°83 N/mm2.
102.5
34.
The padstonebearing conforms to bearingtype 1 (code Figure 4). The narrow wall factor, 1.15, is not applied to fk here, because code clause 23.1.2 refers specificallyto the loaded inner leaf ofcavity walls, andshould not be used when both leaves are loaded. 1.25fk
Therefore,the design strength = Assumingnormal manufacturingand constructioncontrol, from code Table 4
=3.5
Hence,
1.25 fk
must be greater than 0.83 N/mm2.
Therefore,minimumfk required =
0.83 x3.5 1.25
= 2.32 N/mm2.
Section y-y(2200mmlong) 0.4hbelow underside ofrc beam Characteristic loading
rc beam Gk Qk 2nd floor Gk Qk wall self-weight
= 24.3 x =
1.0
'<22
= assectionx-x = as section x-x = 5.0 x 0.5 x 3.96
Gk (deadload) =11.OkN/m
= 1.5 kN/m =
9.9 kN/m
22.4 kN/m
Qk (imposed load)
= 2.4 kN/m
= 2.4 kN/m ________
4.8 kN/m
Design loading aty-y 1.4 Gk =1.4 x22.4 31.4 kN/m
= 1.6Qk=1.6x4.8 = 7.7kN/m 39.1 kN/m 28. 28.2.2.1
Slenderness considerations Simple resistanceto lateral movement is provided by timberjoist hangers in
28.3.1
Effective height, hef, Effective thickness, tef,
28.4 28.1
accordancewith codeFigure 13 to the right ofthe rc beam, as viewedin Figure 84; andby the straps in accordancewith codeFigure 18 to the left ofthe rc beam.
= 2400 mm = 0.67 (2X 102.5)
= 137mm Thereforeslenderness ratio = 2400 137 = 17.5
Eccentricity at right angles to the wall, see Figure 88 The reinforcedconcretebeam is ofsufficient stiffness andshortenough span to enable its reaction on the wallto be considered as an axial load. The second floor loading is applied25 mm from the face ofthe wall, ie, 102.5x 0.5 +25=76.3 mm eccentricity. Handbook to BS 5628: Part 1 97 31.
Two loadingcases will be checked, as follows: (a) minimumaxial load, 0.9Gk2+ 1.6Qk2+maximum floor load, 1.4GkI +1.6Qkl (b) maximum axial load, l.4Gk2+1.6Qk2+maximumfloor load, l.4GkI+1.6Qkl (a) loadingfor maximum eccentricity: WI=1.4Gkl+1.6Qkl =1.4 x 1.5+1.6 x2.4 =5.94kN/m. W2=0.9Gk2+1.6 Qk2 =0.9 (22.4—1.5)+1.6 (4.8—2.4) =22.65 kN/m. Taking momentsaboutthe centre line: 5.94x76.3=(22.65+5.94) ex 453.2 15.9 mm Therefore,
=0.15 t
e=—=
The slenderness ratio = 17.5 Therefore,by interpolation,from code Table 7, capacityreductionfactor, 3,=0.65 88
76.3 w2
At W -- W2
e Figure 88 Wall 1— 2ndfloor eccentricity.
________________________________________________
32.2.1
Design verticalresistanceofwall tfk 0.65x102.Sfk 3.5
= 19.0 fk
Designverticalload =Wi +W2=5.94 +22.65 =28.59 kN/m 28.59 Therefore,minimum fk required
=jjj
=1.50 N/mm2
(b) Loadingfor maximumaxial load: WI =5.94kN/m (as for case (a)) W2= 1.4 Gk2+1.6 Qk2
=1.4 (22.4—1.5)+1.6(4.8—2.4)
=33.1 kN/m Taking momentsabout the centre line: 5.94x 76.3 =(33.1 +5.94) ex 453.2
e=-=
32.2.1
11.6 mm Therefore, =0.11 t. The slenderness ratio(as for case(a))=17.5. Therefore,by interpolation,from code Table 7, 1, =0.71. Design verticalresistance of wall 3tfk 0.7lx102.5fk 3.5
=20.8 fk Designverticalload=Wi+W2 =5.94+33.1 =39.04 kN/m 39.04x 10 Therefore,minimumfk required=208>< 10
= 1.88 N/mm2
98
Section z-z (5200mmlong) 1stfloor level Characteristic loading
= 24.2x 1.0 52 5.2 = x 1.0
rcbeamGk Qk
= 4.7kN/m
5.2
= assectionx-x
2nd floor Gk
Gk (deadload)
=
l.5kN/m = as section x-x Qk = as 2nd floor 1st floor Gk = 1.5kN/m = as2nd floor Qk wall self-weight = 5.0 x0.5 x(3.96 +2.6)= 16.4 kN/m 24.1 kN/m
Design loading at z-z
Qk(imposedload)
= 1.OkN/m = 2.4 kN/m
= 2.4kN/m 5.8 kN/m
1.4 Gk=l.4x24.1 =33.74 kN/m 9.28 kN/m
1.6 Qk=1.6x5.8
=
43.02 kN/m 28. 28.1
Slenderness considerations 2400 Slenderness ratio
=17.5, as before. 31.
Eccentricity at right angles to wall, see Figure 89 As above, the floor loading is applied 25 mm from the face of the wall. The axial load is nowgreater than previously considered. Therefore, it is only necessary to considerthe load case with the maximumaxial load.
Loadingfor maximumaxial load: WI =5.94 kN/m, as for section y-y
W2l.4 Gk2+l.6Qk2
=1.4 (24.1 —1.5)+l.6 (5.8—2.4) =37.08 kN/m
89
N N \ Figure 89 Wall 1 — 1stfloor eccentricity.
Taking momentsabout wallcentre line: 5.94x76.3 =(37.08+5.94) ex. 453.2 Therefore,ex= 43.02 = 10.5 mm =0.1 t. The slenderness ratio= 17.5. Therefore,by interpolation,from codeTable 7, $,=0.72. 32.2.1
Design verticalresistance ofwall
3tfk 0.72x102.Sfk
m
3.5
=21.1 fk Designvertical load=Wi+W2=5.94+37.08 =43.02 kN/m. 43.02x l0 Therefore,minimumfk required=21 1 >< 10
=2.04N/mm2.
Handbook to BS 5628: Fart /
99
Thus, section x-x is the critical section, and the minimum characteristiccompressive strengthof brickwork,fk, requiredis 2.32 N/mm2. From code Figure 1, class 2 bricks in anymortar designationmaybe used.
,
In the abovedesignat section z-z, the capacityreduction factor, is based upon the design eccentricity at 0.4h below z-z (see Chapter 2, page 37). This is conservative as the beam load wouldbe spread over a greater length of wall at thislevel. Appendix B to the code can be used to derive the capacityreduction factor, ç3, at z-z if required as follows: At z-z, cx = 10.5 mm, additionaleccentricity, ea, =0 (see Chapter 2, page 37). Therefore,design eccentricity, em, = 10.5 mm. From equation 4, AppendixB to the code, capacityreductionfactor
=1.l (1_20f)=0.87 32.2.1
Design vertical resistanceofwall
tfk m
0.87x102.5fk 3.5
==25.Sfk
Design vertical load, as before,
=43.02 kN/m.
43.02x 10 Therefore,minimumfk required= 25.5 >< 1O 1.69 N/mm2,comparedto 2.04 N/mm2whenusing code Table 7 to obtain
.
Wall 2, 102.5 mmthick brickwork An elevationofthe wallis shown in Figure 85. The critical sections for design are sections x-x, y-y and betweenground and first floor. Section x-x(480 mmlong) underpadstone Characteristic loading
rc beam (as wall 1) Gk=14.9 x3.25
Ok (deadload) =48.5 kN
Qk== 3.2x3.25
2ndfloorGk=0.9x1.8x0.5x4.25x0.5= l.7kN Qk=l.5x1.8x0.5x4.25x0.5 _____
50.2kN
Design loading at x-x 1.4 Gk=l.4x50.2=70.3 kN
Qk (imposed load)
=l0.5kN
= 2.9kN 13.4kN
1.6 Qk=l.6x13.4=21.4kN
91.7 kN
Stress due to designload
91.7x103 =102.5 x480 =1.87 N/mm2.
34.
23.1.2
The padstonebearing conforms to bearingtype I (code Table 4), and as the wall is narrow, ie, its thicknessis equal to the width of a standard format brick, fk can be multipliedby 1.15. 1.25 (1.15 fk) Therefore,the design strength= Assuming Ym3.S, 1.25 (1.15 fk)
must be greater than 1.87 N/mm2. Therefore,minimumfk required = 4.55 N/mm2.
Parallelcalculations If the rc beam had beenlocated at the end ofthe wall, the padstone (spreader) would have been of bearingtype 3 as in code Figure 4(c). Maximum stress under spreader due to design loads (See Chapter 3, page 62, for discussion of the following methods of analysis) (a) Using Timoshenko'sanalysis for the bendingof bars on elastic foundations (Strengthof materials— Part 2): Assumedesign load, P,=91.7 kN acts at end of spreader, see Figure 90. Select length of spreader as 1000 mm.
Moment of inertiaof spreader,I,
= 0.102 xO.2253 =9.7 x
l0
m3.
Assume modulus of elasticity for concrete, E, =25 x 106 kN/m2. Assume modulus of elasticity for brickwork,Eb, =900fk =10x106 kN/m2
Modulusof foundation, k,=A SEb = 0.102x1 xlOxlO6 =4.1 x105
2.5
where:
A=area under unit length of spreader. S =unit deflection L =height of wall. k maybedefined as a constantdenotingthe reactionper unit length, whenthe deflection is equalto unity. P Deflection beneath the
Whereconstant
=2.55.
load=23 E
.
* =(4-I) =(
x 10-5)
Therefore,deflection beneath the load 91.7
10
2 x2.55 x 25 x 106 x9.7 x =0.0011 m. Reaction per unit Iength=kxdeflection=4.1 x 10 xO.001l =451 kN/m.
451x l0
Therefore,maximum stress =1000 102 =4.42 N/mm2. *Note must not be confused with the capacityreduction factor in the code. 90
91
spreader beam
225
140 102 5mm wall
Figure 90 Stress distribution uiider spreader bean,,after Tin,oshenko.
3x140=420 Figure 91 Stress distribution underspreader beam, triangular stress block.
(b) Using triangularstressblock: Assumedesign load, W,=9l.7 kN, acts at centre line ofwall, see Figure 91. Length of stress block=3 x 140 =420 mm. (padstoneneed not exceed 420 mm in length; if it does, theoreticallytensionoccurs under the padstone.) Therefore,maximum stress = = 2 x91.7 >< 10 =4.28 N/mm2. 420x 102
Handbook to BS 5628: Part 1
101
Section y-y (1215mmlong) 0.4hbelow underside ofrc beam Characteristic loading Gk (dead load) Qk (imposed load)
rc beam Gk
=41.3 kN/m
1.215 13.4
=l1.OkN/m
Qk
wall self-weight= 2.75 xO.96= 2.6 kN/m
_________
l1.OkN/m
43.9kN/m Design loading at y-y
1.4Gk=1.4x43.9=61.5kN/m 1.6 Qk=l.6 x 11.0=17.6_kN/m 79.1
28. 28.2.2.1 28.3.1.1
28.4 28.1
kN/m
considerations Simple resistance to lateral movementis provided by one intermediatestrap as shown in code AppendixC, Figure 21, betweenthe rc beam andthe externalwall. Effective height, hef =2400 mm. =actual thickness Effective thickness = 102.5 mm 2400 ratio Therefore,slenderness Slenderness
=— =
23.4
31.
Eccentricity at right angles to the wall The wall is symmetrically loaded, therefore e=0 By interpolationfrom code Table 7, 1, =0.56
23.1.2
Design vertical resistance of wall, (including narrol% brick wallfactor) t(l.lsftc) —0.56 x 102.5 x 1.15 fk 3.5
=18.9 fk Designverticalload =79.1 kN/m. 79.lx 10 Therefore,minimum fk required=18.9 >< 10 =4.19 N/mm2 Ground tofirstfloor (2700mmlong) For the cavity wallsection, the vertical load is carried on the inner leafonly. Characteristic loading
rc beam Gk Qk
Gk(dead load) Qk (imposed load)
50.2
=18.6 kN/m
2.70
=
13:4
Firstfloor Gk=0.9 x 3.25 +0.9 x 1.8 xO.5 x4.25 xO.5 Qk=1.5 x3.25
x=
x
+1.5 x 1.8 x0.5 x4.25 xO.5 Wall self-weight (full height of wall)=2.75 x 5.2
5.0 kN/m
3.6 kN/m
= 6.0 kN/m = 14.3 kN/m 36.5kN/m
________ ll.OkN/m
Design loading
1.4Gk=l.4x36.5=51.1 kN/m 1.6 Qk=1.6x11.0=17.6kN/m 68.7 kN/m
28.
Slenderness considerations
28.4
Timberjoists spanningonto the wall from both sides provideenhancedresistanceto lateral movement. =0.75 X 2400 Effective height,hef, =1800mm =102.5 mm, as at y-y. Effective thickness
28.1
Therefore,slenderness ratio
28.2.2.2 28.3.1.1
= 17.6 102
31.
Eccentricityat right angles to the wall e=0, as at y-y. The designloading and slenderness ratio at this level are lowerthan at y-y, andthe eccentricity is the same. Therefore,by inspection, the required fk is less than the 4.19 N/mm2at y-y. The wall will be designed for the maximum value offk required, ie, 4.19 N/mm2. Using standard format bricks, from code Figure 1, class 2 bricks in any of the mortar designations (i) to (iii) may be used.
Wall 3, 100 mmthick solid concreteblockwork The critical section for design is from ground to first floor (see Figure 85). Characteristic loading
Ok(deadload) Qk (imposed load)
Floors Gk=2 x 0.9 x 3.25
+2x0.9xl.8x0.5x4.25x0.5x=7.2kN/m
Qk=2 x 1.5 x3.25 +2 x 1.5 x 1.8 xO.5 x4.25 xO.5 wall self-weight=l.4 x2.6x3
=10.9 kN/m
=12.OkN/m
18.1 kN/m
Design loading 1.4 Gk=1.4 x 18.1 =25.3 kN/m 1.6 Qk=1.6 x 12.0=19.2 kN/m
________ 12.0 kN/m
44.5 kN/m 28. 28.2.2.2 28.3.1.1 28.4
Slenderness considerations Timberjoists spanning onto the wall from both sides provideenhanced resistance to lateral movement. Effective height, hef,=0.75 x2400 =1800 mm Effective thickness=actual thickness=lOO mm
28.1
Therefore,slenderness ratio=
31.
Eccentricityat right angles to the wall The wall is symmetrically loaded, thereforeex=0
32.2.1
1800
=18
Fromcode Table 7,3=0.77
Design vertical resistanceofwall
tfk
0.77xlOOxfk
Ym
3.5
=22.Ofk
Design vertical load =44.5 kN/m 44.5 x103 =2.02 N/mm2 Therefore,fk
required=220 Using 215 mm high x440mm long solid concreteblocks (ratio ofheight to least <
horizontaldimension=215:lOO=2.15),from code Table 2(d), a block with a unit compressive strength of 2.8 N/mm2in any mortar designationmay be used. Wall 4, 280 mmcavity externalwall, with 102.5mm facing brick outerleaf & 100 mm lightweight solid concrete blockwork inner leaf The critical sections for design of the inner, loadbearing,leaf are sections x-x, y-y, and z-z(see Figure 86). Section x-x(730 mmlong) underpadstone Characteristic loading
rcbeamGk Qk
=14.9x3.25x0.5 =3.2x3.25x0.5
wall self-weight=say,1.5 xO.73 x3.0
Gk (dead load)
=24.2kN
=
2.5 kN
26.7 kN
Qk(imposedload)
=5.2kN _____ 5.2 kN
Design loading at x-x 1.4 Gk=1.4 x26.7=37.4kN
l.6Qk=l.6x5.2 = 8.3kN 45.7kN 45.7x 10 Stress due to design load = =0.63 N/mm2.
<730
Handbook to BS 5628: Part 1
103
Length of padstone,730 mm, exceeds 6 xwall thickness (code Figure 4) and, therefore, no increased local stress is permissible. which must be greater than 0.63 N/mm2. Design strengthof wall Therefore,minimumfk required =0.63 x3.5 =2.21 N/mm2, assuming m=3.S
=
Section y-y(2200mmlong) 0.4h belowunderside ofrc beam Characteristic loading
Gk (deadload)
rcbeamGk
=—
Qk
22 wallself-weight =say, 1.15 x 3.5
Qk(imposedload)
=11.OkN/m
=2.4kN/m
=
4.0 kN/m
15.0 kN/m
Design loading aty-y 1.4 Gk=l.4 x 15.0=21.0kN/m
________
2.4 kN/m
l.6Qk=l.6x2.4 = 3.8kN/m 24.8kN/m
28. 28.2.2.1 28.3.1.1 28.4 28.1
Slenderness considerations Simple resistance to lateral movement is provided as for wall 1 (see page 97). Effective height,hef,=2400 mm. Effective thickness, tef, =0.67 (100 +102.5) =136 mm. 2400 Therefore, slenderness ratio
= 17.6. 31.
Eccentricity at right angles to the wall The reinforcedconcretebeam is of sufficient stiffness and short enough span to enable its reaction on the wallto be considered as an axial load. As the staircase is adjacent to one side ofthe beam, the only other load to be consideredis the wall self-weight which is axial. Thereforethe eccentricity, ex,=0. By interpolation from code Table 7, =0.78.
,
32.2.1
Design vertical resistanceofwall 3tfk 0.78x100fk 3.5 Ym
=22.3fk. Design vertical load=24.8 kN/m 24.8xlO3 Therefore,minimumfk required=22 3 < lO
=1.11 N/mm2.
Section z-z, groundtofirstfloor Characteristic loading
rc beam Gk
24.2
=
Qk 1st floor Gk =0.9 x3.25xO.5 =1.5 x3.25xO.5 Qk wall self-weight say, 1.15 x7
=
Design loading 1.4 Gk=l.4x 17.5=24.5 kN/m
l.6Qk=l.6x4.l
Gk (deadload)
=
7.9 kN/m
= 1.5 kN/m =
8.1 kN/m 17.5 kN/m
= 6.6kN/m 31.1 kN/m
28. 28.1 104
Qk(imposedload)
Slenderness considerations Slenderness ratio= 17.6, as sectiony-y.
=l.7kN/m =2.4 kN/m ________ 4.1 kN/m
31.
Eccentricity at right angks to the wall, see Figure92. It was explained in chapter 3, andhas been shown in thisexample(page 98), that
the load combinationgiving the maximum design load is usuallythe critical one. Therefore,only this casewillbe considered. Loading
W1= l.4Gi1 =l.4x1.5= 2.1 kN/m + 1.6 Qk1 =1.6 x2.4= 3.8 kN/m 5.9 kN/m =25.2 kN/m W2=31.1—5.9 W1+W2=31.1 kN/m Takingmomentsaboutthe wallcentre line: 5.9 x75=31.le 442.5 =
Thereforeex=-j-1--1- 14.2mm =0.14 t. By interpolationfrom code Table 7, (3, =0.66.
Figure 92 Wall 4— 1st floor eccentricity.
32.2.1
Designverticalresistanceofwall (3tfk 0.59x100xfk rn = 18.9 fk.
3.5
Designvertical load =31.1 kN/m. 31.lx lO Therefore,minimum fk required=189
= 1.65 N/mm2.
The wall will be designed for the maximum value offk required,ie, 2.21 N/mm2. Using 215 mm high x440 mm long solid concreteblocks (ratio of heightto least horizontaldimension 215: 100=2.15), from codeTable 2(d), blockswith a unit compressive strength of 2.8 N/mm2in any mortar designation may be used. Wall 5, 280 mmcavityexternalwall with 102.5 mmfacing brickouter leaf and 100 mm lightweight solid concrete blockwork inner leaf The critical section for the design of the inner, loadbearing,leafis sectionx-x (see Figure 87). Characteristic loading
Rooflintolsa and b: roofGk=1.1 x6.l xO.5 Qk=0.75 x6.1 xO.5 self-weight of lintol, say
Floor level lintolsC:
self-weight ofwall over = 1.15 x 1.1 glazing =0.5 x 1.25 self-weight of lintol, say Handbook to BS 5628: Part 1
Gk (dead load)
= = = = =
3.4kN/m l.OkN/m 4.4 kN/m
Qk (imposed load)
=2.3 kN/m
____ 2.3
kN/m
l.3kN/m 0.6kN/m l.OkN/m 2.9 kN/m 105
Floor level lintol d: Self-weight ofwall over= 1.15 x 3.7 self-weight oflintol, say
= 4.3 kN/m = _________ l.OkN/m 5.3 kN/m
Total characteristicload at section x-x
lintolsaandb Gk=4.4 x3.825x0.5 Qk=2.3 >3.825 xO.5
= 8.4kN = 5.9kN = 4.8kN
Gk=2.9 x2.025x0.5x2 Gk=5.3 xl.8 xO.5 Gk=1.1 x6.l xO.5 xO.675= 2.3 kN Qk=0.75 x6.l xO.5 xO.675 = 6.1 kN wall self-weight Gk=l.15 xO.675 x2.6 x3 27.5 kN lintols c lintol d roof
28. 28.2.3.2
28.3.2
=4.4 kN =1.5 kN ______ 5.9 kN
Slenderness considerations It is assumed that the central loadbearingpartition wallat right angles to wall 5 is properlybonded to the inner, loadbearing,leaf of wall 5, thus providinga vertical support with enhanced resistance to lateral movement.As wall 5 is not an isolated vertical loadbearingmember, it will be considered as a wall for design purposes. The section of wall under considerationis x-x in Figure 87, therefore the slenderness ratio will be based on effective length. The effective length of the wall, hef2.0x400=800mm. = 136 mm. Effective thickness, tef,=0.67 (100+ 102.5)
Therefore,slenderness ratio
=
31.
Eccentricityat right angles to the wall No eccentricity ofloading need be considered in this direction as the roofand lintol loads are axial.
30.
Eccentricity in the plane ofthe wall Whilst wind forces have been assumed to producenegligible eccentricity on the walls in this direction, an eccentric load is introducedby the loads from the concrete
lintols spanning onto wall 5.
Design loading at section x-x,see figure 93 W1=2.9 x2.025 xO.5x 1.4= 4.1 kN W2=5.3xl.8x0.5x1.4 = 6.7kN 10.8 kN Total design vertical load: =38.5 kN 1.4 Gk=l.4x27.5 = 9.4kN l.6Qk=l.6x5.9 47.9kN kN. Therefore,W3=47.9—10.8=37.1 It is assumed that the lintols butt over the centre line of the wall, or are continuous, and the positionsofW1 andW2 havebeen assessed from code clause31. Taking momentsabout the centre line ofthe wall: 47.9 e=(6.7—4.l) Therefore,e= 12.2 mm=0.Ol8L
x-
Figure93 WaIl5 — eccentricity at x — x. 106
W M 47.9x103 47.9x103x12.2x6 Design stress =A+=675 < 100 + 100 x6752 =0.710+0.077 N/mm2 =0.79 or 0.63 N/mm2 load unit Design per length=79 kN/m Therefore,by interpolationfrom codeTable 7, 32.2.1
,=
1.0
Design vertical resistanceofwall Horizontal loaded cross-sectional area of wall, A,
= 675x 100 =0.068m2 106
Therefore,the characteristiccompressive strengthof the masonrymust be multiplied by the factor: (0.7+ 1.5A)=(0.7 + 1.5 x0.068)=0.8, and the design vertical resistanceofwall 5
x 100 xO.8 fk 1t0.8fk1.0 —
—
3.5
=22.9fk, assuming Ym=3.S Therefore,minimumfk required
=3.45 N/mm2
Using 215 mm high x440 mm long solid concrete blocks (height to least horizontal dimensionalratio 215:100=2.15), from code Table 2(d), blocks with a unit compressive strength of 3.5 N/mm2in any mortar designation may be used. Design of walls for lateral loading The worst wall from a lateral load point of view is the gable wallas it has no precompression from the roof.
The gable wall is tied back to the trussed rafter roofstructureat eaves andceiling levels in accordancewith code AppendixC and the roof is adequatelybracedto transmit the forcesfrom these ties to the longitudinalwalls ofthe structure.
94
95
j
A LI =======H LI P== = === = H
IL ——
r11
3850
2600
0.68 L
3850
Figure95 Edge supportconditions— WallA.
E
Figure94 Elevation ofgable wall.
ConsiderWall A, Figure 94:
The wallis simply supportedtop and bottom. Where the masonry is continuous around the cornerofthe building, a continuousedge may be assumed. Whilst the wall is continuouspast an internalpartition at the other end, it will be considered as simply supported as there is a windowopening close to the partition over the lower part ofthe wall(Figure 95). 36.3
Limiting dimensions
For a panel supported on foursides with less than three sides continuous,the height x length ofthe panel must be less than or equal to 2025 tef. tef0.67 (102.5+100) =136.0 mm Therefore,2025 x 136.02 =37.5 x 106 mm2 hxL=2600x3850 =10.OxlO6mm2 thisis less than 2O25tet2andtherefore satisfactory. The maximumwall dimension must not exceed SOtef =50 x 136.0=6800 mm. Wall length=3850 mm, thereforethe wall satisfies the limiting dimensionsclause.
Handbook to BS 5628: Part 1
107
Wind loading
Dynamicwind pressure,q, =0.537 kN/m (see page96). Pressurecoefficients Assume length of terrace is 28.0 m and averageheight is 7.8 m. Building dimension ratios: height 7.8 0 91 length 28.0 — width 8.6 'width 8.6 3 26 Therefore,from CP 3: Chapter V: Part 2, Table 7, maximum Cpe = +0.7 maximum CPL = —0.3 or
+0.2. Therefore,maximumCpe
= +0.7 (0.3) = + 1.0 local C= —1.1 = maximum local —1.1 —0.2 = —1.3 Therefore, Cpe —Cp1
22(b)
The local pressureacts over a quarter of the width of the building =0.25 x8.6=2.15m. For the purposesof this example, it will be assumed that the local pressure(suction) acts over the full width ofthe wall being designed. Therefore,characteristicwind load, Wk, = 1.3 x0.537=0.7 kN/m2. =0.98 kN/m2. Design wind load, yfWk,=l.4 xO.7 yt is taken as 1.4 as the wall contributesto the overall stabilityofthe structure.
24.
Characteristic flexural strength
Outer leaf Assume the outer leaf is of clay bricks, with a water absorption of between 7% and 12, in mortar designation (iii). Thus, from code Table 3, the characteristic fiexural strength, fkx, of the brickworkis 0.4 N/mm2and 1.1 N/mm2in the two orthogonal directions. 36.4.5
The verticalload due to the self-weight of the top half and gable sectionofthe outer leafacts so as to increase its flexural strengthin the parallel direction. Design vertical dead load dueto self-weight ofthe top halfand gable of outer leaf =0.9 x 2.3 ><2.25=4.66 kN/m (note yt is taken as 0.9). Stress due to design vertical load
4.66x 10 = 102.5 x i000o•o4s N/mm2
Therefore,the modified orthogonalratio, i, 0.4+0.045 x3.5 — —0.51
1.1
Inner leaf The inner leaf is oflightweight solid concreteblockworkin mortar designation(iii). The blockshave a unit compressive strengthof 3.5 N/mm2. Thus, from codeTable 3, the characteristicflexural strengthsare 0.25 N/mm2 and 0.45 N/mm2. As for the outer leaf, the self-weight of the wallacts to modifythe orthogonalratio. Design vertical dead load dueto self-weight oftop half andgable of inner leaf =0.9 x2.3 >< 1.15 =2.38 kN/m Stress due to design vertical load = 2.38x103 100x 1000
=0.024 N/mm2
Thereforethe modified orthogonal ratio,
+
0.25 0.024 x 3.5 0.45
,
0.74
Because the orthogonal ratios of the leaves differ, it is necessary to calculate the design momentsofresistance ofeach leaf, in order to apportion the applied
36.4.5
horizontalforcebetweenthem. Design momentsof resistance: The design moment ofresistance ofthe outer leaf (o)in the perpendiculardirection, see page 65.
fko
1.1
=—Z0=-x
=0.55kNm/m.
1000x102.52
6
1
Xm6
The design moment ofresistance ofthe inner leaf()in the perpendiculardirection, see page65. fkxi
0.45 1000x1002
=0.21 kNm/m 108
6
1
X06
Thus, the load taken by the outer leaf =0 55+0.21 xO.98=0.71kN/m2 and by the innerleaf =0.98 —0.71 =0.27 kN/m2 moment coefficients: Bending Outer leaf, from code Table 9F for L=°68 and =0.51 =0.033
Inner leaf, from codeTable 9F for
-=0.68 and =0.74
=0.027 Design bending moments: Design bendingmoment on outer leafin the perpendiculardirection =s. Wko yf L2=0.033xO.71 x3.852 (Note 0.71 =Wko -rf)
36.4.2
=0.35 kNm/m
This is less than the designmoment ofresistanceofthe outer leaf andis therefore satisfactory.
Designbendingmoment on the inner leafin the perpendiculardirection =c Wk1 ycL2=0.027xO.27 x3.852 (note0.27=Wkr if) =0.108 kNm/m This is less than the design moment ofresistanceofthe inner leafand is therefore satisfactory.
The remaininggable walls are satisfactoryeither because oftheir short span or, for the lowerpanels,the vertical load from above. The walls to the back elevation ofthe building contain substantial openings, and whilst the code deals in general terms with laterally loadedwalls with openingsin AppendixD, it gives little guidance on the design of thesewalls,exceptfor recommending the sub-division of the wallinto smallersub-panels. EXAMPLE3 Design of Piers
Consider a single storey warehouse buildingconsisting ofa sheetedroofsupportedby shallowpitchedsteel trusses whichare in turn supportedon loadbearing masonry piers. The buildingis 4.0 m high to eaves level andthe trusses,whichare at 3.6 m centres, span 20 m. The masonrypiers are in clay brickwork andare bonded into the brickwork inner leafofa cavity wall whichformsthe external wallofthe building.
Theroofdeck acts as a deep girder to transferthe windforces on theside walls back to thegable walls. Design ofa typicalpier:
\
96
\
oftruss
\\\\
N
fl '\ \N N ji5___ H
\\\
oftruss I
285
327.5
L.
3.6m
___________________________ -
Characteristic loading
Figure 96Plan detail — wall withpiers.
Roofload: Dead load 1.75 kN/m2 G= Imposed load Qk=0.75 kN/m2 Windpressure Wk=O.5 kN/m2 Wind uplift Wk=O.32kN/m2 Pier design
Assumea pier size of 327.5 mm by 215 mm, as shown in Figure 96.
Handbook to BS 5628: Part 1
109
Designfor vertical load Loadingcase(a):design loadper pier =1.4 Gk=l.4x 1.75 Designdead load
x
Design imposedload=1.6 Qk=1.6 xO.75 x 28.3.1.4
x3.6=
88.2 kN
x 3.6= 43.2kN
131.4kN Thickness of pier 327.5_3 2 Thickness of inner leaf of cavitywall 102.5 This is greater than 1.5, and thereforethe pier should be treated as a columnin the plane at right angles to the wall.
28.4.1
Slenderness considerations The slenderness ratio ofthe pier need be consideredonly in oneplane, as the wall restrainsthe pier againstbucklingin the plane ofthe wall. Had the thickness ratio beenless than 1.5, the pier could have been considered as a wallfor effective height purposes. =4000 mm Effective heightofpier = 327.5 mm Effective thickness of pier
28.1
Therefore,slenderness ratio
28.
28.3.1.2
= =
327.5 12.2
31.
Eccentricity at right angles to the wall The truss fixing to the padstoneon top ofthe pier is arranged to provideaxial loadingon the pier.
32.2.1
Design verticalload resistance ofpier For a slenderness ratio of 12.2 and axial loading, from code Table 7 the capacity
reductionfactor, 27.3
,=
0.92
Assuming normal categories of manufacturingandconstructioncontrol, the partial safety factorfor material strength, Im, 3.5, from code Table 4. Design verticalload resistance
=
—
b tfk Ym
—
0.92x215 x327.5 fk 3.5
=18.5fkxlO3N 23.1.1
Ifthe pier is correctlybonded into the inner leafofthe cavity wall, it is unreasonable to applythe factor for columnsof small plan area to the characteristiccompressive strength,fk, ofthemasonry. if, however, anydoubt existsas to the efficiencyofthe bonding, the factor should be applied— as is done here, by way of example: Area of pier=0.3275x 0.215=0.07m2. Therefore, fk should be multipliedby 0.7+1.5xO.07=0.8, andthe design vertical load resistancebecomes: 14.8 fk x N. 18.5 xO.8 fk x Therefore,equatingdesign load and design resistance: 131.4x l0 minimum fk required=
l0
l0=
=8.9 N/mm2.
14.8 >< lO
From code Figure 1, a class 4 brick in mortar designation (i) may be used. Designfor lateralload Loading case (b) Assume net design dead load, allowing for uplift, (0.9 Ok — 1.4 Wk (uplift)) = 1.125 kN/m2.
x3.6=40.5 kN Design dead load on pier=l.125 = 0.7 kN/m2(suction) Design wind load = 1.4 Wk= 1.4 x0.5 = 2.52 kN/m, x 3.6 Design wind load on pier =0.7 wall for that the assuming simplicity cavity spanshorizontallybetweenpiers. 36.4.2
Design moment on piers, assumingsimple support top and bottom
2.52x4.02
=5.04kNm
If necessary, a moment at the base ofthe wall due to the self-weight of the pier may 36.4.3
110
be used to reducethe design moment on the pier. Designmoment ofresistanceof pier: In assessing the section modulusof a pier, the outstandinglength ofthe flanges may be takenas 6 timesthe thicknessofthe inner leaf, see Figure 97.
97 _____
6t
61
tfL 1NA
.
= 12.8 x 1O°mm4
Zmin = 5.5 x 106mm3 Zmax = 13.6 x 106mm3 ___________________________________________________
Figure 97 Sectionpropertiesofpier.
Assumingthat the bricks used have a water absorption greater than 12% and that mortar designation(i) is used the characteristicflexural strengthof the masonryin the parallel directionis 0.4 N/mm2from codeTable 3. 40.5 x103 Stressdueto designvertical load=327.5 x215°58 N/mm2 Thereforedesignmoment ofresistanceof pier x = /0.4 x 5.5 106 =3.82kNm, whichis unsatisfactory.
'
—+0.58)
Neither allowingfor the self-weight ofthe top half ofthe pier, nor using a brick with a lower water absorptionwill improvethe moment of resistance of the pier sufficiently, thereforeits size must be increased. Trya 327.5 mm square pier I =18.OxlO8mm4 Z min=8.03 x 106 mm3 Thereforedesignmoment ofresistanceof pier /0.4 8.03x106 X
106
=5.6kNm
This exceeds the design moment, 5.04 kNm. andis therefore satisfactory. Because of the increase in pier size to resist wind loading, a reduced minimum characteristiccompressive strengthof brick, fk, may be calculated ifdesired,using the load casegiving the greatest value offk. EXAMPLE4 Laterallyloaded wallpanel Consider a single-storey steelframe buildingon the outskirts ofManchester. The structureis clad with masonry in theform ofa 265 mm thick cavity wall. The outer leafis ofa clayfacing brick,andthe innerleafofa 100 mmthick lightweight unitcompressivestrength.Both leaves are builtin aggregate block of3.5 mortar designation(iii) andpass outside the columns. Thecolumns are at 4.0 m centres, and the panels are 3.0 m high to the underside ofthe independentlysupported clerestorey windows. The masonry is adequately tied to the steel columns. It is assumed that theframeis bracedindependentlyofthe claddingfor overallstability. Expansion joints are provided in the cladding at the corners ofthe structure andat every 12 m. Design the cladding to resist windforces. The critical panel is the endpanel which will be subjected to local wind pressure. Windpressure(from CP 3: Chapter V, Part 2) Basic wind speed for Manchester, say, 46 rn/s. Design windspeed factors, S1 and S3 = 1.0 S2=0.70 (ground roughness category (3), class A, height ofbuilding =5.0 m).
Therefore,design windpressure,Vs, =46.0x 1.0 x0.70x 1.0
=32.2 rn/s
0.613 x 32.22
and dynamicwind pressure,q,= =0.64kN/m2.
of Assume height building width
lO
1
<2
3 length of . building >—but<4
and width 2 and that there are no dominant openings, the local coefficient ofwind pressure,external,Cpe = —1.0
internal, Cpj = +0.2. Therefore,total local coefficient of wind pressure
CpeCpj
—l
(+0.2)
—1.2.
The characteristiclocal suctionwind load, Wk, =1.2 xO.64=0.77 kN/rn2 Handbook to BS 5628: Part 1
111
22(b)
The designwind load =-çfWk. As the removal of the panel would not affectthe stabilityof the building, -'f maybe taken as 1.2. Design wind load=l.2 xO.77=0.92 kN/m2
24.
Characteristic flexural strength From codeTable 3, assuming the use of a clay brickwith a water absorption of less than 7 for the outer leaf, the orthogonalcharacteristicflexural strengths, fk, are 0.5 N/mm2and 1.5 N/mm2. The correspondingfkx values for the inner leafare 0.25 0.5 N/mm2 and0.45 N/mm2. These values give an orthogonal ratio, p, of-i—- =0.33 for 0.25 the outer leaf and =0.56 for the inner leaf.
98
h
aspect ratioof panel —
= L
4.0
= 0.75
Figure 98Panel edgesupport conditions.
The panel is considered simply supported at the corner of the building and continuityat its other endprovidesfixity. The bottom is considered simply supportedand the top edge free. Thus, the panel is as shown in Figure 98. 36.3
Limiting panel dimensions The panel is case (a) (2), ie, supported on three edges with less than two edges continuous.Therefore,height >< length must not exceed 1350ter2, and the maximum panel dimensionmust not exceed 50 tef tef=O.67 (102.5 -F100)= 136 mm. 1350x 1362 Therefore, 1350tef2 = 106
=25.0m2
and 50 tr=5O x 136 =6800mm Now, heightx length=3.0 x 4.0= 12.0 m2, which is less than 25.0m2 and is therefore satisfactory. The maximum panel dimension is 4000 mm, and thisis less than 6800 and again satisfactory. 36.4.3
Design moment ofresistance oflaterally loaded ii'all
=! Ym
Section modulus, outer leaf
x l000x102.52= x = Section modulus, inner leaf 1.75
106
mm3/m
=x1000x1002 =l.67x106mm3/m
Therefore,design moment of resistance of outer leaf, using the fkx value for the plane of failureperpendicularto bed joints, see Figure 1, 1.5 x 1.75 x 106 =0.75kNm/m and the design moment of resistanceof the inner leaf =0.45 >< 1.67 x 106 =0.21 kNm/m Note that there is no needto considerbendingabout the plane of failure parallel to the bed joints, since the code method of design for two-wayspanning panels automatically deals with this, ie, ifthe panel is satisfactoryin the perpendicularto bed joint failurecase, it will also be satisfactoryin the parallel to bed joint failure case. 36.4.5
The design momentson each leaf may be calculated assuming that the applied horizontalforce is shared between the two leaves in proportion to theirdesign momentsofresistance. Therefore:
proportion of design wind load taken by the outer leaf 0.75+0.2l xO.92=0.72 kN/m2 112
andthe proportion taken by the inner leaf =0.92 —0.72=0.20kN/m2 36.4.2
Design bending moments
The designbendingmoment on a laterallyloaded wall
yfWk L2. From codeTable 9, case B, for the outer leafthe bendingmoment,; =0.060 for orthogonalratio of0.33and aspect ratio, of0.75, L' for the inner leaf, the bendingmoment coefficient, c' =0.054 for orthogonal ratio of0.56 andaspect ratio of0.75. Design bending moment on outer leaf =0.060 xO.72 x4.02=0.69 kNm/m. This is less than the moment of resistance of thisleaf, and is therefore satisfactory. Design bending moment on inner leaf =0.054 xO.20 x4.02=0.17 kNm/m. This is less than the moment of resistanceofthis leaf, andis therefore satisfactory.
Handbook to BS 5628. Part 1
113
Page blank in original
INDEX
Consecutive page numbers eg, 24, 25, 26 represent separate references, whereas 24—26represents continuous discussion. Accidental damage designfor 7, 19, 20, 27, 43, 49, 50-54, 55, 56, 68—9,88—90 category ofbuilding 9, 50, 55, 68, 88 tying 49, 51—53, 68—9, 88—9 valuesofYm 26,29, 49, 52, 89 Arching 42, 43, 47, 49, 52, 66 Bending momentcoefficients 46, 64, 91—2, 109, 113 Blocks cellular concrete 12 compressive strength 12, 21, 22, 28, 62, 103, 105, 107, 108, 111 flexural strength 24, 28 hollowclay 12 hollowconcrete 12, 21, 23,46 laying 12, 13, 23 shape 22, 23, 61—2 Blockwork characteristic compressive strength 21—23, 35, 61—2, 103, 105 characteristicflexural strength 24, 25, 26, 28, 64—7 Bricks cellular 12 compressivestrength 12, 21, 22, 28, 62, 79, 80, 83, 84, 85, 86, 87, 110 frogged 12 laying 12, 13,21,23
modular 23, 61
perforated12, 21 shape 22, 23, 61—2 standardformat 22, 23 Brickwork characteristic compressivestrength 21—23, 61—2, 79, 80, 83, 84, 85, 86, 87, 110 characteristicflexuralstrength 24, 25, 26, 28, 64—7 BritishStandards, reference to BS 187 9, 12, 22, 55 CP3 9, 20, 55 BSJI8O 9,22,55 CPIIO 7,9, 11, 15, 19,20,27,36,37,50,52,54
BSJ200 9,14 BS 1243 9, 13, 34 CPIJI 7—8, 9, 16, 21, 22, 23, 24, 26, 28, 29, 33, 36, 37, 38, 40, 42, 44 BS2028 9,22,23,55,62 BS 3921 9, 12, 22, 23, 28, 55 CPI2J 9, 12, 14, 17, 24, 34, 35, 43, 47, 55 BS4027 9,14 CPJI2 33 BS5390 9, 12 CP2004 9,20 BS 5606 17 Amendment No 2 to BS 5628 23, 27, 46, 62 Building regulations
7, 12, 13, 19, 31, 50, 51
Calibration 21, 27, 37,42 Capacity reduction factor 37—39, 60—1, 80, 83, 84, 85, 86, 87, 88, 98, 99, 100, 101,102, 103, 104, 105,107, 110 Cement 14, 14 Characteristic load general 14, 16, 56 deadload 20, 28, 35, 47,48, 49, 55, 72—4, 96—7, 99 imposedload 20, 35, 47, 49, 55, 72—4, 96—7, 99 windload 20, 35,43, 46, 47, 55, 72—4, 91, 108 Characteristic strength ofmasonry general 10, 14, 15, 16 compressive 16, 21—23, 27, 28, 47, 48, 58, 60, 62 flexural 13, 16,24—26,27,28,45,46,47,48, 64—7, 91, 108—9, 112 shear 26, 27, 31, 35,55, 63, 79, 81 Handbook to BS 5628: Part 1
115
Chases 10 Columns betweenopenings 32 cavity 39 definition 10 lateralstrength (axially loaded) 29, 49,67 smallplan area 22 verticalload capacity 35—39 Composite action 42—43, 52 Concentrated loads 40—42, 47, 62—3, 100—! Concrete elements 15, 17, 19, 27, 30, 31, 34, 35, 36, 45, 50, 52, 53, 71, 87, 89, 100, 102,103—4 CPJJO 11, 15, 19, 27, 36, 50, 52, 54,90 Connections general 17—19, 29, 30, 31, 35, 43, 44, 55
shear 27, 44, 52, 89 Construction control 14, 17, 27, 28, 29, 34, 35 Damp proof courses 13,25,26
Design accidental damage 7, 19, 20, 27, 43, 49, 50—54, 55, 56, 68—9, 88—90 free-standing walls 16, 21, 24, 47—49, 55, 66—7 general 15, 29
laterallyloadedpanels 45—50, 63—69 probability (reliability) 15, 16, 20, 21, 27, 56 Design load 10, 15, 16, 20, 35—39, 56—7, 67, 76—9, 81—3, 97 Design strength 15, 37, 46—50, 58, 60—69, 77—83, 84, 85, 87, 88, 98, 99—100, 102, 103, 104, 105, 107, 110 Durability 13, 14, 28, 31, 34, 35, 52 Eccentricity inplane ofwall 35, 106 atrightangles to wall 13, 35—38, 42, 57, 59—60,79, 85, 87, 88, 97, 99, 102, 103, 104, 105, 106, 110 Effectiveheight columns 31 definition 10
evaluation 29, 30—33, 35 piers 32, 33 Effectivelength definition
10
evaluation 29, 32, 33 Effectivethickness definition 10
evaluation 29, 33, 59 Foundations 20, 42,49, 55
Friction 27, 44, 52 Initialrate ofsuction 24 Lateral support connections29, 58 definition 10, 29, 30 horizontal 29—32, 35, 36, 43, 44, 54, 58, 84, 90,97, 102, 103,107 vertical 29—31, 33, 43, 44,46, 47, 58, 84, 90, 107 Layingunits 12, 13 Limiting dimensions ofpanels 44—5, 64, 91, 107, 112 Limitstates design 7, 15, 36, 49, 56 serviceability(cracking, deflection) 15, 17, 31,47 ultimate 15, 29, 31, 34 Manufacturing control 27, 28 Mortar admixtures 14 designation 14, 21, 26, 62 joints 12, 22, 23, 24,28, 35 rate oflaying 13 ready mixed 14 strength 14, 21, 28 testing 12, 14
116
Openings 32, 42, 45, 50, 90, 107,109 Orthogonalratio 10, 24, 25, 45, 46, 65—6,91, 108,112—3
Palletslips 13 Panels(laterallyloaded) definition 10, 24, 43 design 21, 28, 43—50, 63—9, 90—3, 111 irregular shape 45, 90, 107,109 limitingdimensions 44—45, 64, 91, 107,109 Partialsafety factor design (general) 15, 16, 17, 20, 21, 26, 27, 28 load (yj-) 15—17, 20, 28, 35, 38,49, 56—7 material (ym) 1517, 20, 28, 49, 52 quality control 27, 28, 80 valuesfor yj 20,21, 26, 47, 56-7, 112 valuesfor Ym (compressive and flexural) 27,28, 29, 60—61, 71 valuesfor Ym (wall ties) 27,28, 29, 63 valuesfor Ymv 26, 27,28, 29,40, 63 Piers 32, 33, 40, 46, 54, 59, 109 Quality achieving 9, 12, 13, 15, 17, 19, 29, 44, 49 constructioncontrol 14, 17, 27, 28, 29, 34, 35, 60—61, 80 manufacturingcontrol 27, 28, 60—61, 80 Referencessee individual clauses in Chapter2
Shearforce 31, 35, 39—40, 44, 56, 76—9, 80—1, 86 Slenderness ofunits 22—23 ratio ofwalls 29, 32, 33, 34, 36, 37, 38,44, 58, 79, 84, 85, 87, 97, 99, 102,103, 104, 106, 110 Stability accidentalforces 7, 19, 26, 27, 29, 43, 88, 90 bracing 18—19,29, 36, 111 during construction 19 general 17—19,29,46—47, 55, 74 layout 18—19,50, 51, 55, 56, 71 minimum lateralload 19,20, 55, 76 overturning 16, 18—19,48, 49, 55, 56, 71, 84—5 support conditions 29, 30 Steel 27, 31, 34,42, 52, 53, 88, 102, 109,111 Stress bearing 40, 41,42, 47 caused by movement 17, 34, 36 distribution (block) 36, 37, 39, 40,41,42,48,62—3, 100—1 permissible 7, 15, 16, 21,27, 40 reductionfactors 36, 37, 38 tensile 20, 24, 25, 55, 57, 101 ultimate 7, 15, 34, 37 Testing compressive strength 12, 14, 16, 21, 23 12, 16, 24, 28 mortar 12, 14
tiexuralstrength
Ties horizontal 42, 50—52, 68—9, 88 vertical 49, 50—54, 68—9, 89 wallsee wall ties Timber 17, 19, 30, 31, 52, 93, 97, 103, 107 Walls axially loaded(lateralstrength) 17, 29, 49, 67—8, 90 bracing 18, 19, 29, 36 cavity defi,iiiion
11
eccentric loading 35, 39, 60, 103,105 external 34, 103,105 general 13, 23, 34, 35, 39, 53, 66 doubleleaf 11,35
faced 11,35
foundation 20,42, 49 freestanding 16, 21, 24, 47, 56, 66—7 groutedcavity 11, 35 irregularonplan 33 hollowblock 12, 21, 23 hollowblockfilled with concrete 23
Handbook to BS 5628: Part 1
117
lateralloads 7, 17, 43—50, 90—3, 107 ,nodular brick 23,61 narrowbrick 22—23, 61, 80, 84, 87, 100, 102 naturalstone 23 perforated brick 12, 21, 23 random rubble 23 retaining 49 solid concreteblock 103, 105 shearfarces 31, 35, 39—40,44, 56, 76—9, 80—1, 86 sn,allplanarea 22, 61, 84, 88, 110 strength ratio to unit strength 21 veneered 11, 35 wide brick 23
Wallties characteristic strength 34 durability 13 embedment 28, 34 partial safety factor (ym) 27, 28 spacing 34, 35 specification 13 stiffness 13,34 use in panels 34, 44, 46, 63—4, 66
Waterabsorption 24,28, 91, 108, 110
118
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