PART 5 STRUCTURAL LOADS AND DESIGN TABLE OF CONTENTS
SECTION
5.1 SCOPE 2 5.2 DEFINITIONS 2 5.3 DESIGN REQUIREMENTS ………………… 3 5.4 DESIGN LOADS AND EFFECTS …………… 6 5.5 LIMIT STATE DESIGN ………………………… 7 5.6 DEAD LOADS …………………………………….14 5.7 LIVE (IMPOSED) LOADS DUE TO USE AND OCCUPANCY .…14 5.8 DYNAMIC LOADING …………………………..19 5.9 EFFECTS OF WIND ………………………………..21
5.10 EFFECTS OF EARTHQUAKE …………………..58 APPENDIX A …………………………………………… …127
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PART 5 STRUCTURAL LOADS AND PROCEDURES 5.1 SCOPE 5.1.1 This section covers all dead loads and imposed loads which shall be sustained and transmitted by a building and certain structures without exceeding the stress limitations specified elsewhere in the Code. It applies to: (1) new buildings and new structures; (2) alterations and additions to existing buildings and structures; (3) existing constructions on change of use. 5.1.2 This part of the code does not cover (1) loads on roads and rail bridges; (2) loads on structures subject to internal pressure from contents,(e.g. bunkers silos and water tanks) which should be calculated individually; (3) loads due to machinery vibration, except those due to some gantry cranes; (4) loads due to lifts; (5) loads incidental to construction; (6) test loads. These loads are covered by specialized (proprietory) documents produced by manufacturers.
5.2 DEFINITIONS 5.2.1 Unless otherwise specified the following definitions shall apply for the purposes of this part of the Code. Dead Loads: The force due to the static weight of all permanent structural and non‐structural components of a building, such as walls, partitions, floors,
roofs, fixed service equipment and all other permanent construction. Live (Imposed) Loads: The load assumed to be produced by the intended occupancy or use including distributed, concentrated, impact, inertia forces but excluding wind and earthquake loads. Wind Loads: All loads due to the effect of wind, pressure or suction. 2
Earthquake Loads: All loads due to the effect of earthquake.
5.3 DESIGN REQUIREMENTS 5.3.1 (1) Buildings and their structural members including formwork and falsework shall be designed to have sufficient structural capacity to resist safely and effectively all loads and effects of loads and influences that may reasonably be expected, having regard to the expected service life of buildings. 5.3.1(2) All permanent and temporary structural members, including formwork and falsework of a building, shall be protected against loads exceeding the design loads during the construction period except when, as verified by analysis or test, temporary overloading of a structural member would result in no impairment of that member or any other member. In addition, precautions shall be taken during all stages of construction to ensure that the building is not damaged or distorted due to loads applied during construction. 5.3.2 Design Basis Buildings and their structural members shall be designed by one of the following methods: (1)
analysis based on well‐established principles of mechanics ;
(2) evaluation of a given full‐scale structure or a prototype by a loading test; (3) Studies of model analogues (modeling). 5.3.3 Deflections (1) Structural members shall be designed so that their deflections under expected service loads will be acceptable with regard to: (a)
the intended use of building or member;
(b)
possible damage to non‐structural members and materials;
(c)
possible damage to the structure itself and, where significant, the additional effects of loads acting on the deformed structure.
(2) Deflections listed in clause 5.3.3(1) shall be taken into account in all structures and structural members made of material susceptible to deflections, 3
deformations or changes in load distribution due to creep, shrinkage or other effects in the materials of which they are composed. (3) The lateral deflection of buildings due to design wind and gravity loads shall be checked to ensure that non‐structural elements, whose nature is known at the time the structural design is carried out, will not be damaged. Except as provided in Clause 5.3.3(4) and unless otherwise approved, the total drift per storey under design wind and gravity loads shall not exceed 1/500 of the storey height. (4) The deflection limits required in Clause 5.3.3(3) does not apply to industrial buildings or sheds if it is known by experience that greater movement is acceptable. 5.3.4 Vibrations of Floors (1) Special considerations shall be given to floor systems susceptible to vibration to ensure that such vibration is acceptable for the intended occupancy of the building. (2) Lateral Deflections of Tall Buildings: Unusually flexible buildings and buildings whose ratio of height to minimum effective width exceeds 4 to 1 shall be investigated for lateral vibrations under dynamic wind loading. Lateral accelerations of the building shall be checked to ensure that such accelerations are acceptable to the intended occupancy of the building. (3) Stability under Compressive stress: Provision shall be made to ensure adequate stability of a structure as a whole, and adequate lateral, torsional and local stability of all structural parts which may be subject to compressive stress. 5.3.5 Design drawings and Calculations (1) Structural drawings submitted with the application to build shall bear the signature of the designer. 4
(2) Drawings submitted with the application to build shall indicate in addition to those items specified elsewhere in other sections of Part 5, applicable to a specific material: (a) the name and address of persons responsible for the structural
design;
(b) the code or standard to which the design conforms; (c) the dimensions, location and size of all structural members in sufficient
detail to enable the design to be checked;
(d) sufficient detail to enable the loads due to materials of
construction incorporated in the building to be determined;
(e) all intended uses and occupancies; (f) all effects and loads, other than dead loads used in the design of
structural members.
(3) The calculations and analysis made in the design of the structural members, including parts and components of a building shall be available upon request for inspection by the authority having jurisdiction.
(4) Structural integrity: Buildings and structural systems shall provide such structural integrity, strength or other defenses that the hazards associated with progressive collapse due to local failure caused by severe overloads or abnormal events not specifically covered in this section are reduced to a level commensurate with good engineering practice.
5.3.6 Inspection of Construction (1)
Inspection of the construction of any building or part thereof shall be carried out by the designer, or by another suitably qualified person responsible to the designer, to ensure that the construction conforms with the design.
(2)
The designer or another suitably qualified person familiar with the design concept and responsible to the designer, shall review all shop drawings and other drawings relevant to the design to ensure conformance to the design.
(3)
Workmanship and Materials: Workmanship and materials shall be inspected and all reports of material tests shall be reviewed by the designer or another suitably qualified person responsible to the designer during the process of construction. 5
(4)
Off‐site inspections: Where a building or a component of a building is assembled off the building site, in a manner that it cannot be inspected on site, approved off‐site inspection shall be provided when required by the authority having jurisdiction to ensure compliance with this Code.
(5)
Inspection Reports: Copies of all inspection reports shall be made available by the designer upon request to the authority having jurisdiction.
5.4 DESIGN LOADS AND EFFECTS 5.4.1 (1) Except as provided for in Clause 5.4.2, the following characteristic loads, forces and effects shall be considered in the design of a building and its structural members and connections: GK – Dead load: Is the self‐weight of the structure and the weight of finishes, ceilings, services
and partitions (see BS 6399: Part 1, Loadings for buildings. Code of practice for dead and
imposed loads) and Appendix A.
QK–
Live (or Imposed or Variable) load: Due to intended use and occupancy (include loads due to movable partitions and vertical loads due to cranes) and rain (see BS 6399:Part1 and Table 5.6).
WK–
Wind load: Depends on the location, shape and dimension of the buildings (see BS 6399:
Part 2, Loadings for buildings: Code of practice for wind loads) and Section 5.9 of this Part.
En ‐ Nominal earth loads: Earth and hydrostatic pressure, surcharge, horizontal components of
static or inertia forces (see BS 8004: Code of practice for Foundations).
E – Earthquake load (See Section 5.10 of this Part) T – Contraction or expansion due to temperature changes, shrinkage, moisture changes, creep in component materials, movement due to differential settlement or combination thereof.
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5.4.2 (1) Where a building or structural member can be expected to be subjected to loads, forces or other effects not listed in Clause 5.4.1(1); such effects shall be taken into account in the design based on the most appropriate information available. (2) If it can be shown by engineering principles or if it is known from experience, that neglect of some or all the effects due to T do not affect the structural safety and serviceability, they need not be considered in the calculations. 5.4.3 Structural design shall be carried out in accordance with Section 5.5 ‘Limit State Design’.
5.5 LIMIT STATE DESIGN 5.5.1 (1) In this section the term Limit State means those conditions of a building structure in which the building ceases to fulfill the function or to satisfy the conditions for which it was designed. Limit State Design admits that a structure can become unsatisfactory in various ways, all of which need to be considered against defined limits of acceptability. By providing sufficient margins of safety against inherent variability in loading (actions), material properties, environmental conditions, design methods and construction practices, limit state design aims at giving an acceptable probability that the structure will perform satisfactorily during its intended working life. The limit states can be placed in two categories: (a) Ultimate limit states, which are those corresponding to maximum load‐carrying capacity and safety of people and the structure e.g. (i) Loss of equilibrium (overturning) of part or the whole of the structure when considered as a rigid body. (ii)
Rupture of critical sections of the structure.
(iii)
Transformation of structure into a mechanism.
(iv)
Failure through excessive deformation.
(v)
Deterioration arising out of fatigue effects.
(b) Serviceability limit states, which are related to the criteria governing normal use or 7
durability e.g. (i) Excessive deformations with respect to normal use of structure. (ii) Premature or excessive cracking. (iii) Undesirable damage (corrosion). (iv) Excessive displacement without loss of equilibrium. (v) Excessive vibrations. (vi) The comfort of people. (vii) The appearance of the structure. (2) Characteristic loads (GK, QK, WK, En, E, T ) means those loads defined in Clause 5.4.1. (3) Partial safety factors to the value of loads (γf), used in design in section 5.5.2 that takes account of the possibility of unfavourable deviations of the action values, uncertainties in modeling the effects of actions, and the significance of the particular limit state. (4) Partial safety factors to the values of material properties (γm) used in design. This makes allowances for sub‐standard materials or for the deterioration of materials during the life of the structure. (5) Action combination factor, ψ, which for imposed (variable) loads, are used in multiplying characteristic values to obtain representative values. The use of factors ψ reduce the design values of more than one variable load when they act together (see Table 5.3). (6) For imposed (variable) loads, under Eurocode (see 5.3): representative values = characteristic value x ψ (7) In most cases, the design value of an action ( load combination) can be expressed as: design value = representative value x γf
5.5.2 Methods of Limit State Design 5.5.2.1 Ghana, British System GS( BS 8110: Part 1)
5.5.2.1.1 Required Strength for Ultimate Limit State (1) The required strength R provided to resist dead load GK and imposed load QK shall be at least equal to: R = 1.4GK + 1.6QK ……… (5‐1) (2) In the design of a structure or member, if resistance to the structural effects of a specified wind load WK, must be included in the design the following combinations of GK, QK and WK shall be investigated in determining the greatest required strength R. 8
R = 1.2GK + 1.2QK + 1.2WK ……… (5‐2) where the cases of QK having its full value or being completely absent shall both be checked to determine the most severe condition using R = 0.9GK + 1.4WK ……… (5‐3) In any case, the strength of the member or structure shall not be less than required by Eq. (5‐1). (3) If resistance to specified earthquake loads or forces E must be included in the design, refer to Section 5.10 of this Part on Effects of Earthquake. (4) If lateral earth pressure H must be included in design the strength R shall be at least equal to 1.4GK + 1.6QK + 1.6H but where GK or QK reduce the effect of H (i.e. favourable), the corresponding coefficients shall be taken as 0.90 for GK and zero for QK i.e. the governing equations are: R = 1.4GK + 1.6QK + 1.6H R = 0.9GK + 1.6H R = 1.4GK + 1.6QK (6) For lateral loads F due to liquids, the provisions for Clause 5.5.2.1.1(4) shall apply, except that 1.4F shall be substituted for 1.6H. The vertical pressure of liquids shall be considered as dead load, with due regard to variation in liquid depth. (6) Where the structural effects of differential settlement, creep, shrinkage or temperature T may be significant the governing equation shall be R = 1.2GK + 1.2QK + 1.2T The above actions are summarized in Table 5.1 9
Table 5.1 – Load combinations for Ultimate Limit State Load
Load Type
Combination
Dead Load
Imposed Load
Earth and
Adverse Beneficial Adverse Beneficial
Wind
Water pressure
1.Dead and Imposed (and earth and water
1.4
1.0
1.6
0
1.4
‐
1.4
1.0
‐
‐
1.4
1.4
1.2
1.2
1.2
1.2
1.2
1.2
pressure) 2.Dead and Wind (and earth and water pressure) 3. Dead, Wind and Imposed (and earth and water pressure)
5.5.2.1.2 Values for a Serviceability Limit State A building and its structural components shall be checked for serviceability limit states as defined in Clause 5.5.1(b). Where more than one load contributes to the stress in the member the combination of loads shall be assumed to be: GK + ψ ((QK + (E or WK) + T)) Where ψ shall be equal to: (a) 1.0 when only one of the loads QK, (E or WK) and T act; (b) 0.70 when two of the loads QK, (E or WK) and T act; (c) 0.60 when all of the loads QK, (E or WK) and T act. 5.5.2.2 Eurocode System GS (BS EN 1990, 1991, 1992) One of the main differences between the Eurocodes and the British/Ghanaian system is the use of different partial safety factors and the option to refine/reduce load factors when different load cases are combined. 5.5.2.2.1 Required strength for Ultimate Limit State The design loads are obtained by multiplying the characteristic loads by the appropriate partial 10
safety factor, γf, from Table 5.2. When more than one imposed load (variable action) is present, the secondary imposed load may be reduced by the application of a combination factor, ψ0 (see Table 5.4). The basic load combination for the required strength at ultimate limit state for a typical building is: R = γGGK + γQQK1 + ΣγQψ0QKi where: QK1, QK2, QK3 etc. are the actions due to vertical imposed loads, wind load, snow etc., QK1 being the leading action for the situation considered. The ‘unfavourable’ and ‘favourable’ factors should be used so as to produce the most onerous condition. Generally, permanent actions from a single load source may be multiplied by either the ‘unfavourable’ or the ‘favourable’ factor.
Table 5.2 – Action Combinations for Ultimate Limit States ( BS EN 1990: Table NA.A1.2 (B)) Option
Permanent Actions
Variable Actions
Earth and
(Dead Loads)
( Imposed, Wind Loads)
Water*
Unfavourable
Favourable
Leading
Others( i > 1)
1
1.35GK
1.0GK
1.5QK,1
1.5Σψ0,iQK,i
1.35QK
2a
1.35GK
1.0GK
1.5ψ0,1QK,1
1.5Σψ0,iQK,i
1.35QK
2b
1.25GK
1.0GK
1.5QK,1
1.5Σψ0,iQK,i
1.35QK,i
*Note: If the water pressure calculated is the most unfavourable value that could occur during the life of the structure, a partial factor of 1.0 may be used.
Based on Table 5.2, a summary of Eurocode Partial Load Factors is given in Table 5.3 for the ultimate limit state. 11
Table 5.3 – Partial safety factors for loads at the ultimate limit state
Variable Actions Permanent Actions
Leading variable action
Accompanying variable
(GK)
(QK,1)
actions
Limit State
(a)Static equilibrium (b)Structural strength
(QK,I) Unfavourable
Favourable
Unfavourable
Favourable
Unfavourable
Favourable
1.10
0.90
1.50
0.00
1.50
0.00
1.35
1.00
1.50
0.00
1.50
0.00
1.35
1.15
1.50
0.00
1.50
0.00
1.35
0.00
1.35
0.00
1.35
0.00
(c)As an
alternative to (a) and (b) above to design for both situations with one set of calculations (d)Geotechni cal strength
5.5.2.2.2 Values for Serviceability Limit State The action (load) combination for checking the requirement at the serviceability limit state is generally of the form: GK + QK,1 + Σψ0,iQK,i Where, GK, QK,1 and QK,i are permanent action (dead load), leading variable action (imposed load) and other secondary variable actions ( where more than one imposed load contributes to the stresses) respectively. In the case of the secondary variable load(s), their effect(s) may be reduced by the application of the combination factors as given in Table 5.4. The corresponding load cases for the serviceability limit states are given in Table 5.5. 12
Table 5.4 – Combination reduction factors, ψ, for buildings Action
Ψ0
Ψ1
Ψ2
Domestic, residential area
0.7
0.5
0.3
Office area
0.7
0.5
0.3
Congregation areas
0.7
0.7
0.6
Shopping areas
0.7
0.7
0.6
Storage areas
1.0
0.9
0.8
0.7
0.7
0.6
0.7
0.5
0.3
Roofs
0.7
0.0
0.0
Wind loads
0.5
0.2
0.0
Temperature (non‐fire)
0.6
0.5
0.0
Traffic area Vehicle≤30kN Traffic area 30kN≤Vehicle≤160kN
Table 5.5 – Serviceability Load cases Design requirement
Action
Permanent(Dead
Variable (Imposed load)
Combinations
load) Actions
Actions
GK Function and
Leading QK,1
Others QK,i
Characteristic
1.0
1.0
Ψ0
Frequent
1.0
Ψ1
Ψ2
Appearance of the
Quasi‐
1.0
Ψ2
Ψ2
structure or element
permanent
damage to elements, including partitions and finishes User comfort, use of machinery, avoiding ponding of water
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5.6 DEAD LOADS 5.6.1 (1) Dead loads shall be calculated from unit weight given in Appendix A to this part or from materials not provided for in that Appendix as specified or agreed upon with the Authority having jurisdiction. (2) When partitions are shown in plans, their actual weights shall be included in the dead load. For all floors in which partition walls are or may be intended but are not located on the plans, the beams and the floor slabs where these are capable of effective lateral distribution of the load, shall be designed to carry in addition to other loads, a uniformly distributed load per square metre of not less than one third of the weight per metre run of the finished partitions, but not less than 1kN/m2 if the floor is used for office purposes.
5.7 LIVE (IMPOSED) LOADS DUE TO USE AND OCCUPANCY 5.7.1 The minimum live load to be provided for shall be as set out in the Clauses of this Part, or, where not covered by these Clauses, as specified or agreed upon with the Administering Authority. In all cases the live load or loads shall be so placed that in combination with dead load the maximum stresses are produced in the member or members being designed. 5.7.2 Floor Live Loads (1) The minimum floor live loads to be provided for shall be taken as being equal to an equivalent uniform static Load or concentrated load whichever produces greater stresses and shall be based on the intended use and occupancy as set out in Table 5.6 of this Clause. The concentrated loads applied over a specified area of a square with a 300mm side shall be located so as to cause maximum effects. Table 5.6 provides for normal effects of ordinary impact and acceleration but does not include any allowance for special concentrated loads. Special provision shall be made for moving loads other than those in garages for machinery and other concentrated loads as set out in Section 5.8. (2) The concentrated imposed load need not be considered where the floor slab is capable of effective lateral distribution of this load. 14
(3) All beams shall be designed to carry the distribution load appropriate to the uses to which they are to be put as given in Table 5.6. (4) Beams, ribs and joists spaced at not more than 1 metre centres may be designed as floor slabs. (5) Where in Table 5.6 no values are given for concentrated load, it may be assumed that the tabulated distributed load is adequate for design purposes. (6) Where an area of floor is intended for 2 or more occupancies at different times, the value to be used from Table 5.6 shall be the greatest value for any of the occupancies concerned. (7) When the occupancy of a building is changed the building shall conform to the requirements of this part of the Code for the new occupancy. 5.7.3 Reduction in Total Imposed Floor Loads (1) Except as provided for in 5.7.3(2) and 5.7.3(3), the reduction in assumed total imposed floor loads defined below may be taken in designing columns, piers, walls, their support and foundations. For purposes of 5.7.2(1) to 5.7.3(3), a roof may be regarded as a floor. Let, Le be the imposed load upon the roof and let L1, L2, L3 ‐‐‐ Ln be the respective imposed loads upon the floors numbered 1, 2, 3 ‐‐‐ n starting from the top of the building. For the design of the points of support the following imposed loads may be adopted: Supports under roof
LO
Supports under top floor (floor 1)
LO + L1
Supports under floor 2 LO + 0.95(L1+L2) Supports under floor 3 LO + 0.9 (L1+L2 + L3) Supports under floor 4 LO + 0.85 (L1+L2 + L3 + L4) Supports under floor n LO +
(L1+L2 + L3 ‐‐‐ Ln)
The coefficient (3+n)/2n is valid for n > 5 For factories and workshops designed for 5kN/m2 or more, the reductions shown above may be taken provided the loading assumed is not less than it would have been if all floors had been designed for 5kN/m2 with no reductions. 15
(2) Where a single span of a beam or girder supports not less than 46m2 of floor at one general level, the imposed load may, in the design of beam or girder, be reduced by 5% for each 46m2 supported, subject to a maximum reduction of 25%. This reduction or that given in 5.7.3(1), whichever is greater, may be taken into account in the design of columns or other type member supporting such a beam. (3) No reduction shall be made for any plant or machinery which is specifically allowed for or for buildings for storage purposes, warehouses, garages and those office areas which are used for storage and filing purposes. 5.7.4 Roof Live Loads other than Wind Loads or Rain Loads.
(1) Flat Roofs Flat roofs to which there is no direct access (except only such cases as is necessary for cleaning and repairs) shall withstand an imposed load of 0.25kN/m2 measured on plan or a load of 0.9kN concentrated on a square with 300mm side whichever produces the greater stress. (2) On flat floors where access (in addition to that necessary for cleaning and repair) is provided to the roof, allowance shall be made for an imposed load of 1.5kN/m2 measured on plan or a load of 1.8kN concentrated on a square with a 300mm side.
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Table 5.6 ‐ Uses and Loads Occupancy or Use
1.
Intensity of Distributed Loads (kN/m2)
Residential Multifamily house Private apartments Public rooms Corridors 2. Dwellings Not exceeding 2 storeys Exceeding 2 storeys 3. Hotels Guest rooms Public rooms Corridors serving public rooms Corridors above first floor
4.0 2.0 5.0 4.0
4.
5.0 5.0 2.5 3.5 2.0
Office buildings Areas (not including computer rooms) located in basement and first floor File, rooms in offices Floors above first floor Area with computing data processing and similar equipment Toilet rooms
5. Assembly areas with fixed seats including : Auditoria Churches Courtrooms Lecture halls Theatres and other areas with similar uses 6. Assembly areas without fixed seats including : Arenas Balconies Dance floors Dining areas Foyers and entrance hall Grandstands Reviewing stands Gymnasia Museums Stadia Stages and other areas with similar uses
1.5 2.0 2.0 5.0 5.0 4.0
Concentrated Load to be applied unless otherwise stated over any square with a 300‐mm side 2 (kN/m )
4.5 1.8 ‐ 4.5 1.4 1.8 1.8 4.5 4.5 4.5 4.5 4.5 2.7 4.5 ‐
4.0
‐
5.0
3.6
17
7. 8.
9.
Drill rooms and Drill halls 5.0 Garage for passenger cars unloaded buses and light trucks not exceeding 2500kg including driveways and ramps 2.5 All repair workshops for all types of vehicle and parking for To be determined but not less vehicles exceeding 2500kg gross weight including driveways than 5.0 and ramps Libraries Reading and study rooms without book storage Rooms with book storage (eg. Public lending libraries) Stack Rooms
9.0 9.0 To be determined but not less than 9.0
2.5 4.0 2.4 For each metre stack height with a minimum of 6.5
4.5 4.5 7.0
10. Schools and Colleges Classrooms Dormitories Gymnasia Kitchens Laboraties including equipment 11. Hospitals Bedrooms and Wards Laundries Toilet rooms Utility rooms X‐ray room and Operating theatres 12. Factories Light Medium Heavy
3.0 1.5 5.0 To be determined but not less than 3.0 To be determined but not less than 3.0
2.0 3.0 2.0 2.0 2.0 5.0 7.5 10.0
13. Warehouses General storage space in industrial and commercial buildings 10.0 (Note: For concentrated loads Pigeaud’s or Westergaard’s theory may be used)
2.7 1.8 3.6 4.5 4.5 1.8 4.5 ‐ 4.5 4.5 4.5 6.7 9.0 9.0
(3) Sloping Roofs up to angle of 65o to the horizontal shall withstand an imposed load of 0.25kN/m2 measured on plan or a vertical load of 0.9kN concentrated on a square with 300mm side whichever produces the greater stress.
18
(4) Curved Roofs
The imposed load on a curved roof shall be calculated by dividing the roof into not less than five equal segments and then by calculating the load on each, appropriate to its mean slope in accordance with 5.7.4(1) to 5.7.4(3).
(5) Roof coverings and purlins at a slope of less than 450 shall be capable of carrying a load of 0.9kN concentrated on any square with 125mm side.
5.8 DYNAMIC LOADING 5.8.1
Where loads arising from machinery, runways, cranes and other plant producing dynamic effects are supported by or communicated to the framework, allowance shall be made for these dynamic effects, including impact, by increasing the dead‐weight values by an adequate amount. In order to ensure economy in design, the appropriate dynamic increase for all members affected shall be ascertained as accurately as possible.
5.8.2 The minimum design load due to equipment, machinery on other objects or persons that may produce impact, is the total weight of equipment or machinery plus its maximum lifting capacity, or appropriate live load, multiplied by an appropriate factor listed in Table 5.7; except in cases where the actual multiplying factor has been supplied by the manufacturer or supplier of the equipment in which case this factor shall be used in lieu of those listed in Table 5.7. Where dynamic effects such as resonance and fatigue are likely to be important as a result of vibration of equipment or machinery, a dynamic analysis shall be carried out.
Table 5.7 ‐ Impact Loads Impact due to
Factor
Operation of motor driven cranes
1.25
Operation of hand driven cranes
1.10
Live loads on hanger supported floors and stairs
1.33
Supports for light machinery, shaft or motor driven
1.20
Supports for reciprocating machinery or power driven units
1.50
19
5.8.3 The minimum horizontal design loads on cranes runway rails are: (a) Lateral force which shall be: (i)
for power operated crane trolleys, 20% and for hand operated trolleys, 10% of the sum of the weights of the lifted loads and of the crane trolley excluding other parts of the crane;
(ii)
applied at the top of the rail, one‐half in each side of the runway, and
(iii)
considered acting in either direction normal to the runway rail.
(b) Longitudinal force which shall be: (i) 10 percent of the maximum wheel loads of the crane, and (ii) applied at the top of the rail. 5.8.4 (1) Loads on Railings The minimum design load applied horizontally at the top of a railing which guards a drop of more than 460mm shall be: (a) 5.8kN/m for exterior balconies of individual residential units and a concentrated load of 0.9kN applied concurrently; (b) 1.5kN/m for exits and stairs; (c) 2.2kN/m for assembly occupancies, except for grandstands and stadia; (d) 3.6kN/m for grandstands and stadia including ramps; (e) 4.4kN/m for vehicle guard rails for parking garages applied 530mm above
the roadway and minimum total load of (11kN) uniformly
distributed over
each vehicle space applied 530mm above the
roadway, and (f) O.6kN concentrated load applied at any point for industrial catwalks and other areas where crowding by many people is very improbable. (2) The minimum design load applied horizontally to panels under railings which guard a drop of more than 460mm shall be 1.0kN/m2.
(3) The minimum design load applied vertically at the top of a railing which guards a drop of more than 460mm shall be 1.5kN/m acting separately from the horizontal load provided in Clause 5.8.4(1).
(4) Grandstands and any building used for assembly purposes to accommodate large numbers of people at one time shall be designed to resist all inertia sway forces 20
produced by use and occupancy of the building or structure. The inertia force shall be not less than 0.30kN/m of seat parallel to each row of seats or 0.2kN/m of seat perpendicular to each row of seats.
5.9 EFFECTS OF WIND 5.9.1 Scope This Subsection deals with methods for calculating wind loads that should be taken into account when designing buildings, structures and components of buildings and structures. It does not apply to building or structures whose light weight, low frequency and 1ow damping properties make them susceptible to vibration. 5.9.2 Definitions Unless otherwise specified, the following definitions shall apply for the purposes of this Subsection. 1. Breadth: The dimension of the building normal to the direction of the wind. 2. Depth: The dimension of the building measured in the direction of wind. 3. Height: The height of a building above the ground adjoining that building. 4. Length: The greater horizontal dimension of a building above, the ground adjoining that building; or the length, between supports, of an individual structural member. 5. Width: The lesser horizontal dimension, of a building above the ground adjacent to that building, or the width of a structural member across the direction of the wind. 6. Height above ground: The dimension above general level of the ground to windward. 7. Element of Surface Area: The area of surface over which the pressure coefficient is taken to be constant. 8. Effective Frontal Area: The area normal to the direction of the wind or ‘shadow area’. 9. Dynamic Pressure of Wind: The free dynamic pressure resultant from the design wind speed. 10. Pressure Coefficient: The ratio of the pressure acting at a point on a 21
surface to the dynamic pressure of the incident wind. 11. Force Coefficient: A non‐dimensional coefficient such that the total wind force on a body is the product of the force co‐efficient multiplied by the dynamic pressure of the Incident wind and the appropriate area as defined in text. 12.
Topography: The nature of the earth’s surface as
influenced by the hill and valley configurations. 13. Ground Roughness: The nature of the earth’s surface as influenced by small‐scale obstruction such as trees and buildings (as distinct from topography) Note: Breadth and Depth of a building are to the direction of wind. Length and Width are dimensions related to the plan form.
5.9.3 Nomenclature A
=
element of surface
Ae
=
effective frontal area
b
=
breadth
Cf
=
force coefficient
Cfn
=
normal force coefficient
Cft
=
transverse force coefficient
1
Cf
=
frictional drag coefficient
Cp
=
pressure coefficient
Cpe
=
external pressure coefficient
Cpi
=
internal pressure coefficient
d
=
depth
D
=
diameter
F
=
force
Fn
=
normal force
Ft
=
transverse force
F1
=
frictional force
h
=
height
H
=
height above ground 22
j
=
width of member as indicated in diagram
ja
=
width of member across direction of wind
k
=
a constant
K
=
reduction factor
l
=
length
p
=
pressure on surface
Pe
=
external pressure
Pi
=
internal pressure
B
=
total load intensity
q
=
dynamic pressure of wind (stagnation pressure)
Re
=
Reynolds number
S1
=
topography factor
= ground roughness, building size and height above ground S2 factor S3
=
a statistical factor
V
=
basic wind speed
Vs
=
design wind speed
w
=
width of building
1
w
=
bay width in multi‐bay buildings
α
=
wind angle (from a given axis)
=
aerodynamic solidity ratio
ημ
=
shielding factor
v
=
kinematic viscosity
Ø
=
geometric solidity ratio
5.9.4 Procedure for calculating Wind Loads on Structures (1) The wind load on a structure should be calculated for: a) the structure as a whole; b) individual structural elements such as roofs and walls; c) individual cladding units and their fixings. (2) In the case of partially completed structures, the wind load will depend on the method and sequence of construction and may be critical. In calculating the temporary higher wind loads, the maximum design wind speed Vs may be assumed not to occur during the short construction period and a reduced 23
factor S3 used. It is recommended that the graphs of Fig.5.6 should not be extrapolated for periods less than two years. (3) The assessment of wind load should be made as follows: a)
The basic wind speed V appropriate to the area where the structure is to be erected is determined as specified in 5.9.5(2)
b)
The basic wind speed is multiplied by factors S1, S2 and S3 to give the design wind speed Vs (see 5.9.5(3)). Vs = V S1 S2 S3
c)
The design wind speed is converted to dynamic pressure q = kVS.2
Table 5.11 gives corresponding values of q and Vs d)
The design external pressure or suction at any point on the surface of the building is given by: p = Cpq A negative value of Cp indicates suction. The resultant load on an element or cladding depends on the algebraic difference of the external pressure or suction and the internal pressure or suction may be calculated from: F = (Cpe – Cpi)qA A negative value of F indicates that the resultant force is outwards. The total wind load on a structure may be obtained by a vectorial summation of the loads on all the surfaces.
e)
Where a value of force coefficient, Cf, is available, the total wind load on the building as a whole is more conveniently obtained from:
F = CfqAe
Pressure coefficients are given in Tables 5.14 and 5.20 for a range of building shapes. Force coefficients are given in Tables 5.21 to 5.25 for unclad structures. 24
5.9.5 Design Wind Speed, VS
(1) General: The design wind speed Vs should be calculated from Vs = VS1 S2 S3 The basic wind speed table is specified in 5.9.5(2) and the factors S1, S2, S3 in 5.9.5(3). (2) Basic Wind Speed: a) The basic wind velocity is the maximum 3‐second gust speed at a height of 10m above ground likely to be exceeded on the average not more
than once in 50years, in open country. The values are
shown by
isophleths (line of equal wind speed) on the map in Fig.
5.1. Table 5.8 gives basic wind speeds to be used in some major towns in Ghana. b) It should be assumed the wind may blow from any direction.
Table 5.8 ‐ Basic Wind Speed (in metres per second) for some major towns m/s
1. Accra
29
2. Takoradi
29
3. Kumasi
36
4. Tamale
34
5. Ada
34
6. Saltpond
29
7. Axim
29
8. Ho
9. Akuse
34
10. Kete – Krachi
38
11. Wenchi
38
12. Yendi
45
13. Wa
44
14. Navrongo
35
15. Bole
36
29
25
Fig. 5.1: Wind Speeds (m/sec)
26
(3) Wind Speed Factors
(a)Topography Factor, S1: The basic wind speed, V, takes account of the
general
level of site above sea level. This does not allow for local
topographic(orographic) features such as hills, valleys, cliff escarpments or
ridges, which can significantly affect the wind speed in their vicinity.
The factor S1 is a measure of the enhancement that occurs in wind speeds
over hills, cliffs and escarpments.
The effect of topography is to accelerate wind near the summit of hills or
crests of cliffs, escarpments or ridges and decelerate the wind in valleys or
near the foot of cliffs, steep escarpments or ridges.
Table 5.9 gives recommended values of S1
Table 5.9 ‐ Topography Factor S1 Topography
Description
Value of S1
category 1 2
All cases except in 2 and 3 below •
1.0
Very exposed hillslopes and crests where acceleration of
•
wind is known to occur.
1.1
Valleys shaped so that funneling of wind may occur.
•
Sites that are known to be abnormally windy due to some local influence.
3
Steep sided enclosed valleys, sheltered
0.9
from all winds. 27
(i)Effect of a Cliff or Escarpment on the Equivalent Height above ground.
The value of S1 in Table 5.9 can be explicitly calculated for the effect of a cliff or escarpment at a site. The effect of topography will be significant at a site when the upward slope (θ)
is greater than 3°( or 0.05 slope), and below that, the value of S1 may be taken
to be equal to 1.0. The value of S1 varies between 1.0 and 1.36 for slopes
greater than 3°.
The influence of the topographic feature is considered to extend 1.5Le upwind and 2.5Le downwind of the summit or crest of the feature, where Le is the effective horizontal length of the hill depending on the slope as indicated in Fig. 5.2. The values of Le for the various slopes are given in Table 5.10. If the zone downwind from the crest of the feature is relatively flat (θ < 3°) for a distance exceeding Le, then the feature should be treated as an escarpment. Otherwise, the feature must be treated as a hill or ridge. The topography factor is given by: S1 = 1+ C .s where C has values appropriate to the height H above mean ground level and the distance x from the summit or crest relative to the effective length Le as given in Table 5.11. The factor, s, is determined from Fig. 5.3 for cliffs and escarpments and Fig.5.4 for ridges and hills.
Table 5.11 – Variation of effective horizontal length of hill Le and factor C, with slope, θ Slope,θ
Effective horizontal length,
Factor, C
Le 3°< θ≤ 17 >17°
L
1.2(Z/L)
Z/0.3
0.36
Note: L is the actual length of the upwind slope in the wind direction, and Z is the effective height of the feature.
28
Fig. 5.2a: Topographical dimensions – General notations
29
Fig. 5.2: Topographical dimensions – (a) Hill and Ridge, (b) Cliff and Escarpment
30
31
Category 1 Category 2 Category 3
Fig. 5.5: Categories of Ground Roughness 32
(b) Ground Roughness, Building Size and Height above ground, Factor S2 The effect of wind on a building, structure or part thereof depends on
ground roughness variation of wind with height above ground and size of
building or component under consideration. The factor S2 takes account of the
influences on wind effect listed above.
(i) Ground Roughness
The ground roughness has been divided into three categories and buildings and their elements into three classes as follows: Ground Roughness 1: Open, level or nearly level country with no obstructions. Examples are most of the coastal region outside major urban and sub‐urban areas, air fields and areas surrounding the Volta Lake. Ground Roughness 2: Open country with few trees and houses. Examples are farmland and most of the areas of the North and Upper Regions outside major urban centres. Ground Roughness 3: Areas covered by large obstructions. Examples are forest areas, towns and their suburbs. Fig. 5.5 shows areas of the country outside major towns and suburbs where the different categories should be generally applicable. (ii)Cladding and Building size Natural winds are turbulent and continually fluctuating. There is evidence available that for buildings and components of buildings more susceptible to the action of wind, the 3‐second gust speed should be used in design while for other buildings a longer averaging time could be used. As a consequence of this, 3 classes have been selected. Class A: All units of cladding, glazing and roofing and their immediate fixings and individual
members of unclad structures.
Class B: All buildings and structures where neither the greatest horizontal dimension nor the
greatest vertical dimension exceeds 50m.
Class C: All buildings and structures whose greatest horizontal dimension or greatest vertical
dimension exceeds 50m.
The value of S2 for variation for wind speed with height above ground for various ground roughness categories and building size classes are given in Table 5.12. The height to be used for the 33
determination of S2 should be taken as the height from the mean ground level adjoining the building to the top of the building. Alternatively, the structure may be divided into convenient parts and wind load on each part calculated, using S2 factor that corresponds to the height above ground of the top of the part. The dynamic pressure should be assumed to act uniformly over the structure or part respectively. (c) Factor for building life, S3 The factor S3 takes into account the intended life‐span of the building or structure and the acceptable calculated risk. There is always an element of risk that a given design wind speed may be exceeded in a storm of exceptional violence. The greater the life‐span of the structure, the greater the risk. Fig. 5.6 shows values of S3 equivalent to a period of exposure of 50 years plotted against intended life span or design life in years. Normally, wind loads on completed structures and buildings should be calculated at S3 = 1 except for: (i)
temporary structures;
(ii)
structures where a longer period of exposure to wind may be required;
(iii)
structures where greater than normal safety is required.
The period of exposure should never be taken as less than 2 years. Example: Calculate the design speed for a tower 20m high, situated in a well wooded area ( roughness category 3) and for 100‐year probable life near an abrupt escarpment of height 35m. The tower is located around Ho. The crest of the escarpment is 10m effective distance from the plains. The tower is located on the downwind side, 5m from the crest. Tan θ = 10/35 = 0.2857, θ = 15.74 X = +5 Le = 10m H = 20m X/Le = +5/10 = +0.5 H/Le = 20/10 = 2 Basic wind speed for Ho, V = 29m/s ( Fig. 5.1, Table 5.8) S3 factor for 100 yr probable life with probability level of 0.63 = 1.05 (Fig. 5.6) S2 factor for 20m for a well –wooded area (ground roughness category 3)(Class B) = 0.90 (Fig. 5.5,Table 5.12) S1 factor for topography: For X/Le = +0.5 and H/Le = 2 ( Fig. 5.2); s factor from Fig. 5.3 is = 0.05 34
From Table 5.11, factor C = 1.2Z/Le = 1.2x20/10 = 2.4 → S1 = 1 + C x s = 1+ 0.05 x 2.4 = 1.12 →Design wind speed = Vs = V x S1 x S2 x S3 = 29 (1.12)(0.9)(1.05) = 30.7m/s
Note on Fig. 5.6 For example, using the graph for probability level 0.63 for a period of exposure equal to 100 years say, S3 = 1.05 i.e. there is the probability level of 0.63 that a speed which is 1.05 times the once in 50 years wind speed obtained from Fig. 5.1 will be exceeded at least once in 100 years.
5.9.6 Dynamic Pressure of the Wind Using the value of the design speed Vs obtained from section 5.9.5, the dynamic pressure of the wind q above atmospheric pressure may be calculated from
where: k = 0.613 in SI units( N/m and m/s)
Table 5.13 gives corresponding values of Vs and q. 35
Table 5.12 ‐ Ground Roughness, Building size and Height above ground, Factor S2 1. Open Country with no obstructions Class A B C
2. Open Country with few trees and houses Class A B C
3. Towns, Suburbs, Forest areas Class A B C
H (m) 3 or less
0.83
0.78
0.73
0.72
0.67
0.63
0.64
0.60
0.55
5
0.88
0.83
0.78
0.79
0.74
0.70
0.70
0.65
0.60
10
1.00
0.95
0.90
0.93
0.88
0.83
0.78
0.74
0.69
15
1.03
0.99
0.94
1.00
0.95
0.91
0.88
0.83
0.78
20
1.06
1.01
0.96
1.03
0.98
0.94
0.95
0.90
0.85
30
1.09
1.05
1.00
1.07
1.03
0.98
1.01
0.97
0.92
40
1.12
1.08
1.03
1.10
1.06
1.01
1.05
1.01
0.96
50
1.14
1.10
1.06
1.12
1.08
1.04
1.08
1.04
1.00
60
1.15
1.12
1.08
1.14
1.10
1.06
1.10
1.06
1.02
80
1.18
1.15
1.11
1.17
1.13
1.09
1.13
1.10
1.06
100
1.20
1.17
1.13
1.19
1.16
1.12
1.16
1.12
1.09
120
1.22
1.19
1.15
1.21
1.18
1.14
1.18
1.15
1.11
140
1.24
1.20
1.17
1.22
1.19
1.16
1.20
1.17
1.13
160
1.25
1.22
1.19
1.24
1.21
1.18
1.21
1.18
1.15
180
1.26
1.23
1.20
1.25
1.22
1.19
1.23
1.20
1.17
200
1.27
1.24
1.21
1.26
1.24
1.21
1.24
1.21
1.18
Table 5.13 ‐ Values of q in SI Units (N/m2) V s
(m/s)
0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10
61
74
88
104
120
138
157
177
199
221
20
245
270
297
324
353
383
414
447
481
516
30
552
589
628
668
709
751
794
839
885
932
40
981
1030
1080
1130
1190
1240
1300
1350
1410
1470
50
1530
1590
1660
1720
1790
1850
1920
1990
2060
2130
60
2210
2280
2360
2430
2510
2590
2670
2750
2830
2920
70
3000
(Note: To determine q for a speed of say 33 m/s look under 3 along the row corresponding to 30 which gives q = 668 N/m2).
36
5.9.7 Pressure Coefficients and Force Coefficients (1) General: The force on a building or structure or part thereof is obtained by multiplying the dynamic pressure by a coefficient that is dependent on the shape of the building or structure and by the area of the building or structure or part thereof. The two types of coefficients are: (a) pressure coefficient Cp which refers to a particular surface or part of building; (b) force coefficient Cf which refers to the building as a whole. The values of these coefficients are given in Tables 5.14 to 5.23. These tables may be used for other buildings of generally similar shape. (2) Pressure Coefficients: The average values given in the tables are for critical wind directions in one or more quadrants. In order to determine the maximum wind load on a building the total load should be calculated from each of the surfaces or parts of the surfaces of the building. Coefficients of local effects are also given. These are to be used in calculating loads for local areas but not for calculating the load on entire structural elements such as roof and walls. In such locations, the construction must be adequate to resist the local forces (additional nailing,
anchoring etc.). Furthermore, it should be noted that these local forces can act in a shaking manner and result in fatigue failures. The net design load due to wind on individual cladding and their fixings, roofs and walls should be the algebraic difference of the external pressure or suction and the design internal pressure or suction from: F = ( Cpe – Cpi ) qA Values of Cpe are given in Tables 5.14, 5.15, 5.16 and values of Cpi in section 5.9.7(3). (3) Internal Pressure Coefficient: It is normally difficult to estimate the internal pressure coefficient for a building as the coefficient depends on permeability through windows, ventilation louvres, leakage gaps around doors and windows and cladding. It is recommended that for wall and roof loading the internal pressure coefficient should be determined as follows:
37
(a) Where there is only negligible probability of dominant opening occurring during a severe should be taken as +0.2 or ‐0.3 whichever produces the greater effect on the
storm,
building or member concerned. should be taken as 7.5% of the value of
(b) Where a dominant opening is likely to occur,
outside the opening. (4) Force Coefficients: Force coefficients vary for the wind acting on different faces of a building or structure. In determining the critical load, the total wind load should be calculated for each wind direction . The total wind load on a particular building or structure is given by: F = Cf q Ae The direction of the force is specific in the table. Where the wind load is calculated by dividing the area into parts, the value of Cf applied to each part should be that for the building as a whole. (6) Frictional Drag: For certain types of buildings it is necessary to take into account a frictional drag in addition to the wind load calculated from 5.9.7(2) and 5.9.7(4). The frictional drag may be neglected for rectangular clad buildings where the ratio d/h or d/b is greater than 4. The frictional drag in the direction of the wind is given by the following: if h ≤ b, F’ = Cf’q b(d‐4h) + Cf’q 2h (d – 4h) or if h ≥ b, F’ = Cf’q b(d – 4b) + Cf’q 2h (d – 4h) The first term in each formula represents the drag on the roof and the second the drag on the walls.
= 0.01 for smooth surfaces without corrugations or ribs across the wind direction.
= 0.02 for surfaces with ribs across the wind direction.
0.
= 0.04 surfaces with ribs across the wind direction.
For other buildings the frictional drag will be indicated, where necessary, in tables of pressure coefficients and force coefficients. 38
Table 5.14: Pressure coefficient Cpe for walls of Rectangular clad buildings BUILDING
BUILDING ELEVATION
HEIGHT
PLAN
RATIO
RATIO
PLAN
WIND ANGLE
Cpe for surface A
Local Cpe
B
C
D
Ѳ° C
1
0
+0.7
‐0.2
‐0.5
‐0.5
90
‐0.5
‐0.5
+0.7
‐0.2
‐0.8
C
0
+0.7
‐.25
‐0.6
‐0.6
90
‐0.5
‐0.5
+0.7
‐0.1
0
+0.7
‐.25
‐0.6
‐0.6
90
‐0.6
‐0.6
+0.7
‐0.25
0
+0.7
‐0.3
‐0.7
‐0.7
90
‐ 0.5
‐0.5
+0.7
+0.1
0
+0.8
‐.25
‐0.8
‐0.8
90
‐0.8
‐0.8
+0.8
+0.25
0
+0.7
‐0.4
‐0.7
‐0.7
90
‐0.5
‐0.5
+0.8
‐0.1
0
+0.95
‐1.85
‐0.9
‐0.9
90
‐0.8
‐0.8
+0.85
‐0.85
0
+0.95
‐1.25
‐0.7
‐0.7
90
‐0.8
‐0.7
+0.95
‐1.25
0
+0.85
‐0.75
‐0.75
‐0.75
90
‐0.75
‐0.75
‐0.85
‐0.75
‐1.0
3/2
C
1
‐1.1
1/2
C
3/2
C
1
3/2
C
3/2
C
‐1.1
‐1.2
‐1.2
‐1.25
l/w = 3/2
h/w > 6
‐1.25
l/w = 1
‐1.25
l/w = 2
Note: h is the height to eaves or parapet, l is the greater horizontal dimension of a building and w is the lesser horizontal dimension of a building
39
Fig. 5.15: External pressure coefficients (Cpe) for Pitched roofs of rectangular clad buildings
40
41
Table 5.16: Pressure coefficient Cfe for monopitch Roofs of rectangular clad buildings with h/w < 2
42
Table 5.17: Force coefficients (Cf) for Rectangular clad (acting in the direction of the wind)
43
Table 5.18: Pressure coefficients (Cpe) for Pitched Roofs of Multi‐span buildings (all spans equal) with h ≤ w
44
Table 5.19: Pressure coefficients (Cpe) for Saw‐tooth Roofs of multi‐span buildings (all spans equal) with h ≤ w
45
Table 5.20: Pressure coefficients (Cp) for Canopy Roofs with 1/2 ≤ h/w < 1
46
Table 5.21: Force coefficient (Cf) for clad buildings of uniform section (acting in direction of wind)
47
Table 5.21 (cont.)
48
Table 5.21 (cont.)
49
Table 5.22: Pressure distribution around Cylindrical structures
For the purpose of calculating the wind forces that act in a way as to deform a cylindrical structure the values of Cpe in Table 5.22 may be used. They apply only in supercritical flow (i.e. they should only be used where D > 0.3m). They may be used for wind blowing normal to the axis of cylinders having their axis normal to the ground plane (i.e. chimneys, silos) and to cylinders having their axis 50
parallel with the ground plane (i.e. horizontal tanks) provided the clearance between the tank and the ground is not less than D. h is the height of a vertical cylinder or length of a horizontal cylinder. Where there is a free flow of air around both ends, h is to be taken as half the length when calculating h/D. Interpolation may be used for intermediate values of h/D. In the calculation of the load on the periphery of the cylinder, the value Cpi shall be taken into account. For open ended cylinders where h/D 0.3; Cpi may be taken as ‐0.8. For open ended cylinders where h/D 0.3; Cpi may be taken as ‐0.5
5.9.8 (1)
Force Coefficients for Unclad Structures General: This section applies to permanently unclad structures and structural frameworks while temporarily unclad. Structures that because of their size and the design wind velocity, are in the supercritical flow regime may need further calculation to ensure that the greatest loads do not occur at some wind speed below the maximum when the flow will be subcritical.
(2)
Force coefficients of individual members: The coefficients refer to members of infinite length. For members of finite length, the coefficients should be multiplied by a factor K that depends on the ratio l/ja, where l is the length of the member and ja is the width across the direction of the wind. Values of K are given in Table 5.23. Where any member abuts onto a plate or wall in such a way that free flow of air around that end of the member is prevented, the ratio l/ja should be doubled for the purpose of determining K. When both ends of a member are so obstructed, the ratio should be taken as infinity.
51
Table 5.23 ‐ Values of Reduction Factor K for members of finite length and slenderness l/ja or l/D Circular cylinder, subcritical flow
2
5
10
20
40
50
100
∞
0.58
0.62
0.68
0.74
0.82
0.87
0.98
1.0
0.80
0.80
0.82
0.90
0.98
0.99
1.0
1.0
0.62
0.68
0.69
0.81
0.87
0.90
0.95
1.0
Circular cylinder, supercritical flow Flat plate perpendicular to wind
5.9.8(3)(a) Flat–sided members: The force coefficient in Table 5.24 are given for two mutually‐ perpendicular directions relative to a reference axis on the structural member. They are designated Cfn and Cft and give the forces normal and transverse, respectively, to the reference plane as will be apparent from the diagrams. Force coefficients are for wind normal to the longitudinal axis of the member. Normal force: F = Cfn qklj Transverse force: F = Cft qklj
(b) Circular sections: For circular sections, the force coefficients Cf, which are dependent upon values of DVs, are given in Table 5.25. The values of Cf given in this table are suitable for all surfaces of evenly distributed roughness of height less than 1/100 diameter i.e. for all normal surface finishes and for members of infinite length. Force, F = Cfqkld
52
Table 5.24: Force coefficients Cfn and Cft for individual structural members (flat sides) of infinite length
53
Table 5.25 ‐ Force Coefficients Cf for individual structural members of Circular Section and Infinte Length Flow regime Force coefficient Cf DVs 6m2/s
Subcritical flow
1.2
Re 4.1 x 105 DVs 12m2/s
6
4.1 x 105 Re 8.2 x 105
0.6
Supercritical flow
12
DVs 33m2/s
8.2 x 105 Re 22.6 x 105
0.7
DVs 33m2/s
0.8
Re 22.6 x 105
Reynolds number, Re > =
where: D is the diameter of the member Vs is the design wind speed, and v is the Kinematic viscosity of the air, which is 1.6 x 10‐5 m2/s at 15oC and standard
atmospheric pressure.
(c) Wires and cables: The force coefficients for wires and cables given in Table 5.26 are dependent upon values of DVs.
Table 5.26 ‐ Force Coefficients Cf for Wires and Cables (1/D >100) Flow Regime
Smooth
Moderately wire Fine
surface wire
(galvanized
stranded Thick
or cables
stranded
cables
painted) DVs 0.6m2/s
‐
‐
1.2
1.3
DVs 0.6m2/
‐
‐
0.9
1.1
DVs 6m2/s
1.2
1.2
‐
‐
DVs 6m2/s
0.5
0.7
‐
‐
54
(4) Single frames: In general, the most unfavourable wind load on a single frame occurs when the
wind is at right angles to the frame.
The wind load acting on a single frame should be taken as F = Cf q Ae where; Ae is the effective area of frame normal to the wind direction. The force coefficients for a single frame consisting of (a) flat‐sided members or (b) circular section members in which all the members of the frame have DVs value less or greater than 6m2/s are given in Table 5.27.
Table 5.27 ‐ Effective Force Coefficients Cf for Single Frames Solidity ratio Ø
Flat – sided members
0.1 0.2 0.3 0.4 0.5 0.75 1.0
1.9 1.8 1.7 1.7 1.6 1.6 2.0
Force coefficient Cf for: Circular Sections Subcritical flow Supercritical flow 2 DVs 6m2/s DVs 6m /s 1.2 1.2 1.2 1.1 1.1 1.5 2.0
0.7 0.8 0.8 0.8 1.4 1.4 2.0
The solidity ratio Ø is equal to the effective area of a frame normal to the wind direction divided by the area enclosed by the boundary of the frame normal to the wind direction. (5) Multiple frame structures: This section applies to structures having two or more parallel frames where the windward frame may have a shielding effect upon the frames to leeward. The wind load on the windward frame and any unsheltered parts of other frames should be calculated as in 5.9.8(3), but wind load on the parts of frames that are sheltered should be multiplied by a shielding factor n, which is dependent upon the solidity ratio of the windward frame, the type of member comprising the frame and the spacing ratio of the frames. The values of the shielding factor are given in Table 5.28. Where there are more than two frames of similar geometry and spacing, the wind load on the third and subsequent frames should be taken as equal to that on the second frame. 55
Table 5.28 ‐ Shielding Factor, n
Spacing Ratio
0.1
Up to 1.0
1.0
0.96
0.90
0.80
0.68
0.54
0.44
0.37
2.0
1.0
0.97
0.91
0.82
0.71
0.58
0.49
0.43
3.0
1.0
0.97
0.92
0.84
0.74
0.63
0.54
0.48
4.0
1.0
0.98
0.93
0.86
0.77
0.67
0.59
0.54
5.0
1.0
0.98
0.94
0.88
0.80
0.71
0.64
0.60
6.0 and over
1.0
0.99
0.95
0.90
0.83
0.75
0.69
0.66
Value of n for an aerodynamic solidity ratio of: 0.2
0.3
0.4
0.5
0.6
0.7
0.8 & over
The spacing ratio is equal to the distance, centre to centre, of the frames, beams or girders divided by the least overall dimension of the frame, beam or girder measured at right angles to the direction of the wind. Aerodynamic solidity ratio, = solidity ratio (Ø) x a constant where the constant is: 1.6 for flat‐sided members; 1.2 for circular sections in the subcritical range and for flat‐sided members in conjunctions
with such circular sections;
0.5 for circular sections in the supercritical range and for flat‐sided members in conjunction with circular sections. (6) Lattice Towers: (a) Lattice towers of square and equilateral triangular sections constitute special cases for which it is convenient to use overall force coefficient in the calculation of wind load. The wind load should be calculated for the condition when the wind blows against any face. The wind load acting in the direction of the wind should be taken as: F = Cf qAe The overall force coefficient Cf is given in Tables 5.29, 5.30 and 5.31. 56
Table 5.29 ‐ Overall Force Coefficient Cf for Towers composed of Flat‐sided members Solidity ratio
Force coefficient of for:
0.1
Square towers 3.8
Equilateral triangular towers 3.1
0.2
3.3
2.7
0.3
2.8
2.3
0.4
2.3
1.9
0.5
2.1
1.5
For square lattice towers the maximum load occurs when the wind blows on to a corner. It may be taken as 1.2 times the load for the face–on wind. For triangular lattice towers the wind load may be assumed to be constant for any
inclination of the wind to face. (b) Since it is only in very few cases with lattice towers composed of members of circular section that all the members of a lattice tower are entirely in either subcritical or supercritical flow, wind force calculations should be carried out as described in 5.9.8(4) for single frames, due account being taken of the shielding factors in 5.9.8(5).
When it can be shown that all the members of the tower are wholly in the same flow
regime the overall force coefficients Cf given in Tables 5.29 and 5.30 may be used.
Solidity ratio of a frame = Ø. For lattice steel towers, Ø typically varies between about 0.1 and
0.3
57
Table 5.30 ‐ Overall Force Coefficient Cf for Square Towers composed of Rounded Members
Solidity ratio of front face, Ø 0.05
Force coefficient Cf for: Supercritical flow Subcritical flow 2 DVs ≥ 62/s (45ft mile/h) DVs < 6m /s (45ft mile/h) onto face onto corner onto face onto corner 2.4 2.5 1.1 1.2
0.1
2.2
2.3
1.2
1.3
0.2
1.9
2.1
1.3
1.6
0.3
1.7
1.9
1.4
1.6
0.4
1.6
1.9
1.4
1.6
0.5
0.4
1.9
1.4
1.6
Table 5.31 ‐ Overall Force Coefficient Cf for Equilateral Triangular Towers composed of Rounded members
Solidity ratio of front face, Ø 0.05
Force coefficient of for: Supercritical flow Subcritical flow 2 DV≥ 62/s (45ft mile/h) DV < 6m /s(45ft mile/h) all wind directions all wind directions 1.8 0.8
0.1
1.7
0.8
0.2
1.6
1.1
0.3
1.5
1.1
0.4
1.5
1.1
0.5
1.4
1.2
58
5.10 EFFECTS OF EARTHQUAKES 5.10.1 SCOPE AND FIELD OF APPLICATION 5.10.1.1 This Code sets down minimum design requirements to be met when dealing with seismic situations i.e. situations in which the earthquake action is considered as a critical action in conjunction with other dead loads or live loads. It applies to: (1)
Reinforced and Prestressed concrete buildings for ordinary uses, having structural resisting systems belonging to one of three types defined below: (a) Frame System: A system in which both vertical loads and lateral forces are resisted by space frames. (b) Wall System: A system in which both vertical loads and lateral forces are resisted by structural walls either single or coupled. (c) Dual System: A system in which support for vertical load is essentially provided by a space frame. Resistance to lateral action is contributed to, in part, by the frame system and also in part by structural walls, isolated or coupled.
5.10.2 DEFINITIONS AND NOTATIONS Definitions Cross‐tie:
A continuous bar with a minimum diameter of 6mm, having a 1350 hook with a
ten‐diameter extension at one end, and a 900 hook with a six diameter extension at the other end. The hooks shall engage hoop bars and be secured to longitudinal bars. Hoop: A closed tie or continuously would tie with a minimum diameter of 6mm the ends of which have 1350 hooks with ten‐diameter extensions that encloses the longitudinal reinforcement. Boundary elements:
Portions along the edges of walls and diaphragms strengthened by
longitudinal and transverse reinforcement. Boundary elements do not necessarily require an increase of thickness of the wall or diaphragms. Edge openings within walls and diaphragms may also have to be provided with boundary elements.
59
Notations A = peak ground acceleration Ac = confined area measured to outside peripheral transverse reinforcement. Ag = gross sectional area of concrete Cd = design seismic coefficient Cg
= centre of mass
Ck
= centre of stiffness
E
= design seismic action (symbolic)
I
= importance factor
Mu,d =
ultimate moment of a concrete section, evaluated with factored values of concrete and steel strengths
M+u,d =
ultimate moment of a concrete section, evaluated with characteristic values of concrete and steel strengths.
Nd =
design axial force under the most unfavourable load combination including the seismic action.
K
= behaviour factor
S
= site coefficient
Si
= soil type index
Vcd
= shear force carried by concrete in beam or column sections
a = plan dimension of the building in the direction orthogonal to that of seismic action bw
= web width of a concrete section
h,b
= height and width of beams, major and minor sides in columns
h’, b’ = distance between reinforcement bars located at the ends of sides in and b, respectively, measured to outside the peripheral bars 60
d = distance from centre of stiffness and centre of gravity of the generic floor Sh = spacing of transverse reinforcement in beams, columns and walls. fcd = design concrete strength h = height of a floor lw = horizontal wall length hw
=
total height of a wall
hn
=
vertical distance between floors in walls
α
=
spectral amplification factor
β
=
parameter of the elastic response spectrum
γi
=
distribution factor
γn
=
over‐capacity factor
Δel
=
elastic interstorey drift under the seismic actions
ζ
=
ratio between maximum and minimum shear force at a beam end
Θ
=
deformability index
ξ
=
amplification factor for torsional effects
w
=
dynamic magnification factor
τRd
=
shear design stress of concrete
61
5.10.3 DESIGN CRITERIA 5.10.3.1 Reliability Differentiation Structures shall be classified under the following reliability levels: (1)
Class I: Buildings that are required to remain functional and to suffer reduced damage after a strong seismic attack (e.g. essential rescue facilities such as hospitals, fire and police stations, electricity stations etc. buildings with likely large number of occupants such as schools, audience or spectacle halls, etc).
(2)
Class II: Buildings not included in 5.10.3.1 (1)
(3)
The different reliability levels proper to each Class shall be obtained by amplifying the design action with a factor I, called importance factor.
5.10.3.2 Ductility Levels Structural systems covered by the Code may be designed to possess different ‘ductility’ levels according to the following classification: (1)
Ductility Level I (DL I) ‐ is that proper to structures proportioned in accordance to BS 8110 (1985) with additional requirements on detailing contained in 5.10.8. This ductility level, I is suitable for low rise buildings.
(2)
Ductility Level II (DL II)‐ for this level seismic provisions are to be adopted, enabling the structure to enter the inelastic range of response under repeated reversed loading, while avoiding premature brittle‐type failures.
(3)
Ductility Level III (DL III) ‐ special procedures for the evaluation of design action and for the proportioning and detailing of the elements are to be adopted to ensure the development of selected stable mechanisms associated with large energy dissipation capacities. DL III structures should be preferred whenever large uncertainties exist (e.g. Local amplification effects of difficult evaluation etc).
62
5.10.4 METHODS OF ASSESSMENT 5.10.4.1 Basic data 5.10.4.1.1 Material Characteristics 5.10.4.1.1 (1) Concrete
Normal concrete grades shall satisfy the following requirements (Table 5.10.4.1) Table 5.10.4.1 Ductility Level
Minimum Grades
DL I
C20
DL II
C20
DL III
C25
5.10.4.1.1(2) Steel (a)
DL I and DL II Structures The reinforcing steel is defined by its characteristic strength.
(b)
DL III Structures The following additional requirements shall be satisfied. (i)
It must be proven the steel used possesses adequate ductility under repeated reversed deformations.
(ii)
Steel grades with characteristic strengths higher than S400 (400N/mm2) shall not be used, unless it is demonstrated that the use of higher grades in special section arrangements does not affect unfavourably the ductility.
(iii)
The actual yield stress shall not exceed its normal values by more than 15%.
63
(iv) The ratio of the mean value of the ultimate strength to actual yield stress shall not be less than 1.25 for S220 and 1.15 for S400 (v)
Only high bond steel shall be used for flexural reinforcement, unless adequate provisions are taken to ensure bond and anchorage.
5.10.4.1.2 Material Safety Factor,
γm
Design values of strength for concrete and steel shall be obtained from their respective characteristic values by using the factors: Concrete γ c = 1.5 Steel γ s = 1.15 5.10.4.1.3 Structure Behaviour Factors (1)
The values of the behaviour factor K, defining the intensity of the design action (section 5.10.5.3) as a function of the structural type and of the selected ductility level, are given in Table 5.10.4.2 Table 5.10.4.2 DESIGN BEHAVIOUR FACTORS Ductility
Ductility
Ductility
Level I
Level II
Level III
Frame
2
3.5
5
Wall and Dual
2
3
4
Structural System
(2)
The values of K in Table 5.10.4.2 for wall and dual structures apply if, at least 50% of the lateral force in both directions is resisted by coupled walls.
(3)
If condition 5.10.4.1.3(2) is not satisfied, the K values for wall and dual structures shall be reduced by a factor of 0.7.
(4)
Ductility Level I is permitted only for Class II structures in areas of moderate seismicity.
64
(5)
Class I structures to be built in high seismicity areas shall be preferably designed for ductility level III. If appropriate, K values relative to DL II could be used in this case.
5.10.4.1.4 Design Load Combination The fundamental combination of load effects to be used for limit states verification (Section 5.10.7.4) is Sd = S (G + P + E + ∑ψi Qik) ... 5.10.4.1.1 where G =
all permanent loads at their normal value
P =
the long‐term prestressing force
E =
the design seismic action as defined in Sect .5.10.5.3.4
Qik =
fractile values of extreme distributions of all live loads whose duration of application is long enough for the probability of their joint occurrences with earthquake action to be considered.
ψ I =
factors required to change the fractile values Qik to the average values of Qik in their instantaneous distribution (See Table 5.10.4.3)
S = Site Co‐efficient Table 5.10.4.3: COMBINATION FACTOR ψ I FOR LIVE LOADS Live loads from persons and equipment Live loads from persons at places with likelihood of large number of occupants (halls)
0.3
0.5
Long term storage (warehouse, libraries)
0.9
Live loads on staircases and corridors
1.0
65
5.10.4.2 Structural analysis
5.10.4.2.1 Building Configuration A building shall be classified as regular when the following conditions are satisfied, regarding both plan and vertical configuration. (a) Plan Configuration (i)
The building has an approximately symmetrical plan configuration with respect to, at least two orthogonal directions along which the earthquake resisting elements are oriented. When re‐entrant corners are present, they do not exceed 25 percent of the building external dimension.
(ii)
At any storey the distance (measured in the direction orthogonal to that of the seismic action) between the centre of mass and that of the stiffness does not exceed l5% of the ‘resistance radius’ defined as the square root of the ratio of storey torsional and translation stiffnesses.
(b) Vertical Configuration (i)
The stiffness and mass properties are approximately uniform along the building height.
(ii)
In frame structures, the ratio between actual shear capacity (sum of shear forces contributed by all vertical elements at their design strengths) and design shear does not differ more than 20 percent, for any two storeys of the building.
(iii)
In the case of a gradual setback along its height, the setback at any floor is not greater than l0% of the plan dimension in the direction of the setback. This clause need not be complied with if the setback occurs within the lower l5% of the total height of the building.
5.10.4.2.2 Application of Seismic Action (1)
Horizontal Action (i)
The seismic actions shall be applied to the building in the directions producing in each element the most unfavourable effect. 66
(ii)
In buildings having one axis of symmetry, the seismic action can be assumed as acting separately along this axis and its orthogonal direction
(2)
Vertical Action (i)
The vertical component of the seismic action shall be considered in the design of non‐vertical cantilevers and of prestressed beams.
5.10.4.2.3 Analytical Model (1)
The determination of the seismic effects on the structure shall be based on an idealized mathematical model which is adequate for representing the actual behaviours; the model shall also account for all non‐structural elements that can influence the response of the main resisting system.
(2)
For the purpose of the present code, the determination of the load effects due to design forces may be based on a linear elastic model of the structural system.
(3)
Regular buildings can be designed according to the simplified method of analysis (indicated as equivalent static analysis) described in 5.10.4.2.4 provided their height does not exceed 80m, and the fundamental period is shorter than 2 secs.
(4)
If conditions in 5.10.4.2.3.(3) are not satisfied or if the building is of irregular type, the dynamic method in 5.10.4.2.5 shall be applied.
5.10.4.2.4 Equivalent Static Analysis (1)
Horizontal Design Forces (a)
The design lateral force to be applied at each floor level in the direction being analysed, shall be given by: F = Cd .
γ i . W .... 5.10.4.2.1 i
where Cd = design seismic co‐efficient, equal in value to the design response spectrum, as given in Section 5.10.5.3.4
γ = i distribution factor, depending on the height of the floor, measured from the building base 67
Wi = total gravity load at floor i (b)
In cases where the period T is not calculated from methods of mechanics Cd shall be taken as:
1 ... 5.10.4.2.2 C = I . A . S .α . d
(c)
K
γi The distribution factor γi is given by the following expression
... 5.10.4.2.3 ∑W i γ i = hi
∑ W i hi
where hi is the height of floor i from the foundation level. (2)
Torsional Effects (a)
At each floor of the building, the lateral design force shall be assumed to be displaced from its nominal location at the distances e1 and e2 illustrated in Figure 5.10.4.1, which ever is most unfavourable for every member to be checked.
Fig. 5.10.4.1 ‐ Torsional Effects
(b)
The expressions for e1 and e2 are:
e1 = 0.5 d + 0.05 a
... 5.10.4.2.4
e2 = 0.05 a
... 5.10.4.2.5
68
(c)
The total shear force and torsional moment at the generic floor shall be distributed to the various resisting elements below that floor with due consideration of their relative stiffness as well as of the stiffness of the diaphragm.
(d)
Symmetrical Cases: When complete symmetry of stiffness and mass about one axis parallel to the direction of the seismic excitation exists, torsion effects can be accounted for by means of the following simplified procedure: (i)
the lateral design force shall be applied at the floor centre of gravity, to be distributed to the various elements as above;
(ii)
the actions in each of the elements shall be further multiplied by a factor ξ defined as:
ξ = 1 + 0.6
... 5.10.4.2.6 x
a
where x is the distance of the element from the floor centre of gravity, measured perpendicularly to the direction of seismic action. (3)
Second Order Effects (a)
Second‐order effects on storey shears and moments need not be considered when the following condition is satisfied at every floor:
Θ=
W . Δe l . K ≤ 0.10 V .h
where Θ = deformability index V = seismic design shear force acting across the storey considered ∆el = elastic interstorey drift due to design action K = behaviour factor h = floor height W = total gravity load above the considered storey
69
(b)
The deformability index, Θ shall not in any case exceed the value 0.20;
(c)
For 0.10 < Θ < 0.20 second order effects shall be accounted for by means of one of the statistical methods indicated in BS 8110 (1985).
5.10.4.2.5 Modal Analysis Procedure (1)
Modelling (a)
If the building can vibrate in two orthogonal directions without significant coupling, it can be analysed by means of two separate planar models, one for each orthogonal direction
(b)
The condition stated in 5.10.4.2.5(1) (a) shall be assumed to occur when 5.10.4.2.1(a) (ii) is satisfied.
(c)
When 5.10.4.2.1(a)(ii) is not satisfied the model shall account for the non‐ planar motion of the structure
(2)
Modes (a)
In the case of planar models, the analysis shall include for each of the two orthogonal axes at least the lowest three modes of vibration, or all modes of vibration with periods greater than 0.4 secs., whichever is greater.
(b)
For non‐planar models the analysis shall include for each direction of seismic action, at least four modes, two of them predominantly translational and two predominantly rotational, or all modes of vibration with periods greater than 0.4 secs., whichever is greater.
(c)
The mode considered shall be those with the greatest participation coefficients for the direction under consideration
(3)
Combination of Modal Responses
The response quantities (force, displacements etc) separately obtained for each mode under the effect of the design response spectrum given in Section 5.10 5.3.4 shall be combined to obtain their corresponding design values by taking the square root of the sum of the squares of modal values. 70
(4)
Torsional Effects (a)
At each floor of the building the mass contributing to inertia forces shall be assumed to be displaced from its nominal location by the amount "0.05a” whichever is more unfavourable for the element to be checked, ‘a’ being the dimension of the building in the direction orthogonal to that of the considered seismic action.
(b)
When the building is analysed by means of planar models (Clause 5.10.4.2.5 (1)), torsional effects can be accounted for by increasing the action effects due to the translational oscillations of the building by the factor ξ defined as:
ξ = 1 + 0.6 x/a where x is the distance of the planar element considered from the floor centre of gravity, measured perpendicular to the direction of the seismic action. (5)
Second ‐ order effects Clause 5.10.4.2.4 (3) applies.
71
5.10.5 SEISMIC ACTION 5.10.5.1 Seismic Zones For the application of this Code, a seismic risk map (Fig 5.10.5.1) has been used to discretize the area of Ghana into a number of zones. Within each zone the normalized ground acceleration is assigned a constant value as shown in Table 5.10.5.1.
Fig. 5.10.5.1 ‐ Seismic Risk Map Of Ghana 72
Table 5.10.5.1: DEFINITION OF SEISMIC ZONES Assigned Horizontal Design Ground Acceleration: A
Seismic Zone
(g units of gravity) 0
0
1
0.15
2
0.25
3
0.35
5.10.5.2 Characteristics of Seismic Actions (1)
For the purpose of the code, the ground motion shall be adequately described by means of: (a)
the peak ground acceleration Amax, treated as a random variable of known distribution;
(b)
one or more response spectra for horizontal motion, having a form appropriate for the area and firm soil conditions, normalized to Amax = 1 and probabilistically characterized;
(c)
one or more response spectra for vertical motion, scaled to 2/3 of the correspondence horizontal motion response spectra.
(2)
For particular zones, for instance, where geological evidence indicates the possibility of ‘near field’ type of shocks (for which the response spectrum concept is inadequate) or where there is extensive and deep soil layering (for which selective amplification can occur) the expected characteristics of ground motion shall be determined by special studies.
73
5.10.5.3
Design Seismic Action
5.10.5.3.1
Normalized Elastic Response Spectrum
For the purpose of this Code, the shape of the ‘standard’ (rocky or firm soil condition) elastic response spectrum normalized to a unit peak ground acceleration shall be idealized as shown in Fig. 1.4.2.
Fig. 5.10.5.2 ‐ Normalised Elastic Response Spectrum 5.10.5.3.2 Site Effects When more detailed knowledge of the effects of local soil conditions and on the characteristics of ground motions arriving at the site from possibly different sources is not available the procedure in Clause 5.10.5.3.2 (1) and (2), and 5.10.4.4.3 shall be applied. (1)
Soil Profile Types The effects of site conditions on building response shall be established based on the soil profile types defined as follows: i
SOIL PROFILE S1: Rock of any characteristic either shale‐like or crystalline (such material may be characterized by a shear wave velocity greater than 800mm/sec); or stiff soil conditions where the soil depth is less than 60m and the soil type overlying rock are stable deposits of sands gravel or stiffer clays. 74
ii
SOIL PROFILE S2: Deep cohesionless or stiff clay soil conditions, including sites where the soil depth exceeds 60m and the soil types overlying rock are stable deposits of sands, gravels or stiff clay.
iii
SOIL PROFILE S3:
Soft‐to‐medium stiff clays and sands, characterized by l0m or more of soft‐ medium stiff clay with or without intervening layers of sand and other cohesionless soils. In locations where soil properties are not known in sufficient detail to determine the soil profile type or where the profile does not fit any of the three types, soil profile S2 shall be used. (2) Site Co‐efficient The site co‐efficient S is used to modify the standard elastic response spectrum to account for the site condition. Its values are given in Table 5.10.5.2 Table 5.10.5.2: SITE COEFFICIENT Soil Coefficient
Soil Profile Type
S1
S2
S3
S
1.0
1.2
1.5
5.10.5.3.3 Site ‐ Dependant Normalized Elastic Response Spectrum The site‐dependant normalized elastic spectra for the three soil profiles are shown in Fig 5.10.5.3, their ordinates being defined as the smallest from the following expressions: R as = 1 + (α – 1). T/T1 R as = α for soil types S1, S2, S3 = 0.8α for soil S3 if A, as defined in Clause 5.10.5.3.4, is greater than 0.3g R as = S. α. ( T/T1)β 75
In case of lack of specific site‐related information the following can be assumed T1 = 0.12 secs T2 = 0.4 secs α
= 2.5 β = 2/3
However, for soil type S3 the value T1 = 0.25 secs. can be adopted. Spectra for vertical motions may be determined with sufficient accuracy by multiplying the ordinates of the spectra for horizontal motions by a factor of 2/3.
Fig 5.10.5.3 ‐ Site Dependent Normalized Elastic Spectra 5.10.5.3.4 Design Response Spectrum
The ordinates of design response spectrum are given by the smallest of the following expressions: R a (T)
1 = I . A .α . ( ) K
R a (T) = 0. 8 . I . A . α . (
R a (T) = I . A . α . S . (
1 ) K
for soil type S1, S2 and S3, or
for soil type S3 if A > 0.3g
T2 β 1 ) .( ) T K 76
Where: I
is the importance factor defined in Section 5.10.3.1(3) (see Table 5.10.5.3)
A is the peak ground acceleration to be adopted for the seismic zone of interest (% of g ‐ Table 5.10.5.1) S is the site coefficient as given in Table 5.10.5.2 K is the behaviour factor given in Table 5.10.4.1.3 In the case of lack of specific site‐related information α, β and T2 are assigned the following values: α = 2.5, β = 2/3, T2 = 0.4 secs. Table 5.10.5.3: IMPORTANCE FACTOR Class
Factor
I
1.4
II
1.0
5.10.6 DESIGN ACTIONS 5.10.6.1 General Structural elements shall be dimensioned and verified (see section 5.10.7) for design actions as defined in this section. 5.10.6.2 Ductility Level I: DL I DL I structures shall be dimensioned directly on the basis of the results of structural analysis, with a possible redistribution of action effects in accordance with BS.8110 (1985) 5.10.6.3 Ductility Level II: DL II (1) Elements subject to bending ( N d ≤ 0 . 1 . A g . f cd ) (a) Bending moments: 77
The design bending moments shall be those obtained from linear analysis of the structure for the load combination given by equation 5.10.4.1.1. Redistribution according to BS.8110 (1985) is permitted. (b) Shear Forces: (i)
The design shear forces shall be determined from the condition of static equilibrium of the element subjected to the relevant transverse load, if any, and a rational combination of the end moments.
(ii)
The end moments shall correspond to the design flexural strengths of the end actions based on actual reinforcement provided.
(iii)
The algebraic ratio between the maximum and minimum values of shear at each end section shall be denoted by ζ . The value of ζ should not be taken less than minus one (Fig. 5.10.6.1).
VA,d
(I)
B
A ζVA,d
(II) B
A
VA,d = VA,d + MA + M1B
ζVA,d = VA,d ‐ M1A + MB
L
L
Fig 5.10.6.1 - DESIGN SHEAR FORCES 78
(2) Elements Subject to bending and axial force ( N d > 0 . 1 (a)
Ag . f cd )
Axial forces and bending moments (i)
For regular structures, three storeys and higher, to which equivalent static analysis has been applied, the column moment due to lateral forces alone shall be multiplied by the dynamic amplification factor w as given by the following expressions: Planar Frames w = 0.6 T1 + 0.85 (1.3 < w < 1.8)
.... 5.10.6.1
.... 5.10.6.2
Spatial Frames w = 0.5 T1 + 1.10 (1.5 < w < 1.9)
where T1 is the fundamental period of the structure. (ii)
The values of the dynamic factor w given in 5.10.6.3(2)(a)(i) are applicable to storeys within the upper two‐thirds of the building height. Below this level a linear variation of w should be assumed: the value at first floor level should be taken as 1.3 and 1.5 for planar and spatial frame respectively (Fig 5.10.6.2).
Fig. 5.10.6.2 ‐ Values of Dynamic Factor at Various Floors
79
(iii)
Column moments in addition shall satisfy the condition on the relative strength between
columns and beams framing into a joint as specified in Clause 5.10.7.1(3). (b)
Shear Forces (i)
In evaluating the design shear forces from the condition of static equilibrium the design end moments shall be those producing maximum shear force obtained from analysis, modified if appropriate by the dynamic magnification factor.
(3)
Structural Walls (a)
The design actions shall be those obtained from a linear analysis of the building modified as appropriate in accordance with Clauses 5.10.6.3(1)(b) to 5.10.6.3(3)(c).
(b)
Redistribution
(i) The distribution of the total force to the various walls, as obtained from the elastic analysis may be modified provided the global equilibrium is maintained and the maximum value of the action in any wall is not reduced by more than 30% (ii)
In a coupled wall, the elastic shear force in the coupling beams can also be modified with a maximum reduction of 20% provided that corresponding increases in the shear capacities of beams at other floors are made.
(c)
Bending Moment Design Envelope The design moments along the height of the wall shall be those given by a linear envelope of the calculated moment diagram, vertically displaced by a distance equal to the horizontal length of the wall. (Fig. 5.10.6.3)
80
Fig5.10.6.3 ‐ BENDING MOMENT DESIGN ENVELOPE (d)
Earthquake Induced Axial Load in Coupled Walls
(i)
The design axial load in the walls due to the lateral action shall be computed using the shear strengths of the coupling beams above the section considered, calculated by using characteristic values of concrete and steel strength.
(ii)
The shear strength of the beams calculated in 5.10.6.3(3)(d)(i) shall be further amplified by a factor of 1.25
(e)
Dynamic Magnification Factors
(i)
Where the equivalent static analysis is adopted, the shear forces in the walls shall be magnified by the dynamic amplification factor w as given by the expression below for buildings up to 5 storeys high w = 0.1N + 0.9......... 1.5.3
where N is the number of storeys
(ii)
For walls taller than five storeys, w, shall be linearly increased up to the value of
w =1.8 for N = 15
81
5.10.6.4 Ductility Level III : DL III (1)
Elements subject to bending ( N d ≤ 0 . 1 . A g . f cd )
(a)
Bending moments: The design bending moments shall be those obtained from linear analysis of the structure. Redistribution according to BS 8110 (1985) is permitted.
(b)
Shear Forces:
(i) The design shear forces shall be determined from the conditions of equilibrium of the element subjected to the relevant transverse loads, if any, and to a rational adverse combination of end moments, as specified in 5.10.6.4(1)(b)(iii) (ii) The end moments shall correspond to the design flexural strengths of the end sections based on actual reinforcement provided, multiplied by the factor γ n = 1.25 (iii) The algebraic ratio between the maximum and minimum values of shear force at a section shall be denoted by ζ . For the purposes to follow, the value of ζ should not be taken smaller than minus one.(Fig 5.10.6.4)
A VA,d (1) B VA,d = VA,d + MA + M1B
L
A ζVA,d (11)
ζVA,d = VA,d ‐ M1A + MB
B
L
Fig 5.10.6.4 DESIGN SHEAR FORCES 82
(2)
Elements subject to bending and axial force ( Nd > 0 .1. Ag . f cd )
(a)
Axial forces and bending moments
(i) The axial forces and bending moments to be used for column design shall be determined from a linear analysis of structures, eventually redistributed according to BS 8110 (1985). (ii)For regular structures, three storeys and higher, to which equivalent static analysis has been applied, the column moment due to the lateral forces alone, shall be multiplied by the dynamic magnification factor, w, as given by the following expressions: Planar frames:
w = 0.6 T + 0.85 1
(1.3 ≤ w ≤ 1.8 )
5.10.6.4
5.10.6.5
Spatial frames:
(1.5 ≤ w ≤ 1.9 )
w = 0.5 T 1 + 1.10
where T1, is the fundamental period of the structures. (iii)
The values of the dynamic factor, w as given in 5.10.6.4(2)(a)(ii) are applicable to storeys within the upper two‐thirds of the building height. Below this level a linear variation of, w, should be assumed; the value at first floor level should be taken as 1.3 and 1.5 for planar and spatial frames respectively. (Fig 5.10.6.5)
83
Fig. 5.10.6.5 ‐ Values of Dynamic Factor (iv)
Column moments shall satisfy the condition on the relative strength between columns and beams framing into a joint (see 5.10.7.1 (3))
(b)
Shear forces
(i) In evaluating the design shear forces from the conditions of static equilibrium the design end moments shall be the most adverse ones as obtained from the analysis of the structure. (ii) The end moments as calculated above shall be further amplified, if appropriate by the dynamic magnification factors, and by the γ n factor: γ n = 1.10 (3)
Beam ‐ Column Joints
(a)
The design actions shall be those induced in the joint when the design ultimate moments of the beam or beams multiplied by a factor γn, equal to 1.25 are developed, except in cases when hinges are permitted to form in the columns (see Clause 5.10.7.1 (3)) The axial force in the column shall be the minimum corresponding to the design seismic actions.
84
(b)
Horizontal Shear Force (Vjh)
(i)
Interior Joint (see Fig. 5.10.6.6) The shear force Vjh across a typical interior joint without prestressing may be calculated from:
V jh = γ n ( As1 + As2 ) f yd - V col
........
5.10.6.6
where
Vcol =2 l1 .M1 + l2 M2 / ( lc + l’c) ......... 5.10.6.7 l1n l2n with
l1, l2 = centre to centre span of adjacent beams l1n ,l2n = clear spans of adjacent beams lc, l'c = centre to centre upper and lower column heights M1, M2 = design end moments of beams multiplied by γ n = 1.25 for spans l1 and l2
respectively.
As1, A s2 = top and bottom steel in beam
85
Fig. 5.10.6.6 Design Shear Actions at Beam – Column Joints (ii)
External joints For external joints equation 1.5.6 still applies while equation 5.10.6.7becomes
V col
⎛ l = 2 ⎜⎜ 1 . M ⎝ l 1n
1
⎞ ⎟⎟ / ⎠
( l c + l ′c )
5.10.6.8
(c) Vertical Shear Force (Vjv) The vertical shear force may be approximately as follows: V
jv
= V
jh
.
bb hc
5.10.6.9
where bb = depth of beam hc = width of column 86
(d)
When two non co‐planar frames have common joints, verification of these joints may be considered in each direction separately.
(4)
Structural Walls (a)
The design actions shall be those obtained from a linear analysis of the building modified as appropriate in accordance with clause 5.10.6.4(b) ‐ (f)
(b)
Redistribution
(i)
The distribution of the total force to the various walls, as obtained from the
elastic analysis, may be subsequently modified, provided the global equilibrium is maintained and the maximum value of the action in any wall is not reduced by more than 30% (ii)
In a coupled wall, the elastic shear forces in the coupling beams can also be modified with a maximum reduction of 20% provided corresponding increases in the shear capacities of beams at other floors are made
(c)
Bending Moment Design Envelope The design moments along the height of the wall shall be those given by a linear envelope of the calculated moment diagram, vertically displaced by a distance equal to the horizontal length of the wall. (Fig5.10.6.7)
87
Fig5.10.6.7 BENDING MOMENT DESIGN ENVELOPE (d) Earthquake induced Axial Load in Coupled Walls The design axial load in the walls due to the lateral action shall be computed using the shear strengths of the coupling beams above the section considered which should be calculated from the characteristic values of concrete and steel strength. The shear strength of the beams thus calculated shall be further amplified by a factor of 1.25 (e)
Dynamic Magnification Factor Where the equivalent static analysis has been adopted, the shear forces in the walls shall be increased by the dynamic amplification factors w as given by the expression below, for buildings up to 5 storeys high: w = 0.1 N + 0.9
5.10.6.10
where N is the number of storeys. 88
For walls taller than 5 storeys w shall be linearly increased up to the value of w = 1.8 for N = 15 (f)
Shear Forces
(i)
The design shear forces in walls shall be compatible with the actual flexural strength that can possibly be developed at the base of the walls
(ii)
The design shear forces shall be obtained by multiplying the shear forces due to the Code loading by the following γ n factor,
γ
+
n
u, d = M M d
5.10.6.11
where Md is the design moment obtained from the analysis, and M+u,d is the flexural strength of the section on the basis of actual reinforcement provided calculated by using the characteristic values of concrete and steel strengths. In evaluating the flexural strength of the base section the appropriate axial load shall also be considered. (iii)
The factor γ n need not be taken greater than 4
89
5.10.7 DIMENSIONING AND VERIFICATION 5.10.7.1 (1)
Linear Elements (General) Design Strengths The design strengths of the structural elements in bending, bending with axial force, shear and torsion shall be evaluated in accordance with BS 8110 except as modified by this Section 5.10.7
(2) Limiting Axial Load The design axial compression load under the most severe load combination including seismic action shall not exceed the following limit
0.5 A g . f
ck
(3) Beam ‐ Column Strength Ratio (a)Except for cases where hinge formation in column is permitted (see 5.10.7.1 (3) (b) (iii) at any beam ‐ column joint the sum of the absolute values of the design ultimate moments of the columns (under the most unfavourable value of the axial force) shall not be less than the sum of the absolute values of the design ultimate moments of the beams framing into the joint (Fig.5.10.7.1)
Fig.5.10.7.1 ‐ Beam – Column Strength Ratio 90
(b)
DL III Structure (i)
For columns of DL III Structures, the design bending moments shall account for possible increase in strength of the beams framing into the joint.
(ii)
Unless otherwise justified, the global strength increase can be assumed as: γn = 1.15
5.10.7.1
and is applicable to all storeys, including column bases in the first storey. (iii)
Development of plastic hinges in columns and of columns hinge mechanism (i.e. exemption from the prescription on beam – column ratio) is permitted in the following cases:‐ ‐
for frames having four or more columns, hinging is permitted to occur in one column for every three others remaining elastic.
‐
column hinge mechanisms are permitted in single and two –storey buildings and in the top storey of multi‐storey building.
(4)
Resistance to Shear (a)
Contribution of Concrete The magnitude of the term Vcd, expressing design resistance contributed by concrete shall be taken as follows: (i)
When Nd ≤ 0.1 Ag fcd , Vcd shall be assumed to be zero in all regions where stirrup‐ties are required in accordance with Clause 5.10.8.2.3 (with the exception of Case (c))
(ii)
When Nd > 0.1 Ag fcd , Vcd shall be computed by the expression Vcd = 2τRd bw d β1
5.10.7.2
where the values of τRd are given in Table 1.6.1 as functions of concrete grades and β 1 is given by 5.10.7.4 91
M β 1 = 1+ o ≤ 2
Md
5.10.7.3
where Mo and Md are decompression moment and design moment respectively. Mo shall be computed by the expression Mo = Nd h/2
5.10.7.4
Table 5.10.7.1: DESIGN CONCRETE SHEAR STRESS
Concrete grade
τRd (Mpa)
25
30
35
0.30
0.34
0.38
(b)
Transverse Reinforcement
(I)
Nd ≤ 0.1 Ag fcd (i).
ζ > 0.
The resistance to shear provided by the reinforcement: Vwd shall be given by
Vwd = 0.87 h Asw . fyk
5.10.7.5
s . γs
where, h is the effective depth, Asw the individual cross‐sectional area of a mat of transverse reinforcement, and
92
s
the spacing of the mats of transverse reinforcement measured parallel to the axis of the beam.
(ii)
ζ< 0. For Vsd not exceeding the limit value, VRd1 where
VRd1 = 3( 2 + ζ ) τRd .bw . d
5.10.7.6
same requirement as in( i) above applies. ‐
For Vsd exceeding the limit value VRd2 where
VRd2 = 6( 2 + ζ ) τRd .bw . d
5.10.7.7
the entire shear shall be resisted by diagonal reinforcement across the web, that is, steel bars inclined in two directions shall equilibrate with their compression and tension components the shear forces of opposite sign Vsd and ζ.Vsd occurring at the section. ‐
For VRd1 < Vsd < VRd2 one half of the maximum shear force shall be carried by doubly diagonal bars, the other half by transverse reinforcement.
(II)
Nd > 0.1 Ag fcd The resistance to shear shall be checked as for Case (I) (i)
5.10.7.2 Beam ‐ Column Joints (DL III only) (1)
Horizontal Joint Shear
(a)
Nominal Horizontal Shear Stress
(i) The nominal horizontal shear stress in the joint as given by the following expression
τ
jh
=
V
jh
5.10.7.8
b j hc
shall not exceed the value 20 τRd 93
(ii) The effective joint width bj shall be taken as: ‐ when ( bc > bw )
or
either bj = bc
bj = bw + 0.5hc
whichever is smaller
(Fig. 5.10.7.2)
‐ when bc < bw
either bj = bw
bj = bc + 0.5hc
or
5.10.7.9
5.10.7.10
whichever is smaller
Fig.5.10.7.2 ‐ Effective Joint Width and Effective Joint Areas (b)
Shear Force carried by Concrete The value of shear force carried by the concrete strut Vch shall be assumed zero except for the following: (i)
When minimum average compression stress σ cm on gross concrete area of the column above the joint including prestress where applicable, exceeds 0.1 fck 94
V ch = (2 τ Rd
( σ cm - 0.1 f ck ) ) b j h c
(ii)
When beams are prestressed through the joint: Vch = 0.7 Pcs
5.10.7.11
5.10.7.12
where Pcs is the permanent force in the prestressing steel that is located within the central third of the beam depth. (iii)
When the design precludes the formation of any beam plastic hinge at the joint, or when all beams at the joint are detailed so that the critical section of the plastic hinge is located at a distance from the column face not less than hb, or for external joints where flexural steel is anchored outside the column core in a beam stub.
Vch = A’s . Vjh 1 + Nd
5.10.7.13
As 2 0.4Agfck
where the ratio A's/As of the compression to the tension longitudinal beam reinforcement shall not be taken larger than 1.0. When the axial column load results in tensile stresses over the gross concrete area exceeding 0.2 f ck the entire joint shear shall be resisted by reinforcement. For axial tension smaller than this limit, the value of Vch may be linearly interpolated between zero and the value given by equation 5.10.7.13 with Nd taken as zero. (iv) When parts Aa1 and Aa2 of the column tensile reinforcement and As1 and As2 of the adjacent beams are bent vertically and anchored in the tensile face of the column
V ch = Aa
f yk
γs
5.10.7.14
where Aa is the smaller of Aa1 and Aa2. 95
The values of Vch obtained from equations (5.10.7.11, 5.10.7.12, 5.10.7.14) may be added where applicable. (See Fig 5.10.7.3)
Fig. 5.10.7.3 ‐Shear Force carried by Concrete (c)
Horizontal Shear Reinforcement
(i)
The horizontal shear reinforcement shall be capable of carrying the design joint shear force: Vsh = Vjh ‐ Vch
5.10.7.15
across a corner‐to‐corner potential failure plane. The effective total area of the horizontal reinforcement that crosses the critical diagonal plane and is situated within the effective joint width bj shall not be less than:
V sh f yk / γ s
A jh =
5.10.7.16
(ii)
Horizontal sets of stirrup ties shall be distributed as uniformly as practicable between layers of the top and bottom beam reinforcement.
(2)
Vertical Joint Shear
(a)
The vertical shear reinforcement shall be able to resist a vertical shear force
96
Vsv = Vjv – Vcv
5.10.7.18
5.10.7.18
where the value Vcv shall be determined from Vcv = A’sc . Vj 0.6 + Nd
Asc Agfck where A'sc and Asc are the areas of longitudinal compression and tension reinforcement in columns respectively, with the following exceptions: (i)
Where axial load results in tensile stress over the column section, the value of Vcv shall be linearly interpolated between the value of Vcv given by equation (5.10.7.18) with Nd taken as zero when the axial tension over the gross concrete area is 0.2 fck;
(ii)
Where plastic hinges are expected to form in the column above or below a joint, part of the primary seismic energy dissipating mechanism, Vcv shall be assumed to be zero for any value of the axial load on the column.
(b)
The required area of vertical joint shear reinforcement within the effective joint width bj shall be determined from:
A jv =
f (c)
V yk
sv
/ γ
s
5.10.7.19
The vertical joint shear reinforcement shall consist of intermediate column bars placed in the plane of bending between corner bars, or of vertical stirrup ties or special vertical bars, placed in the column and adequately anchored to transmit the required tensile forces within the joint.
(d)
The spacing of vertical joint reinforcement in each plane of any beam framing into a joint shall not exceed 200mm, and in no case, shall there be, less than one intermediate bar in each side of the column in that plane.
97
(3)
Eccentric Beam ‐ Column Joints All design provisions of this section apply except that in case of an eccentricity of a beam relative to the column into which it frames, as measured by the distance between the geometric centre lines of the two members, the effective joint width bj shall not be taken as larger than: 0.5( bw + bc + 0.5hc) – e 5.10.7.20
5.10.7.3 Structural Walls (1)
General The design strengths of walls and coupling beams shall be evaluated as for linear elements (Section 5.10.7.1) except as modified by provisions in section 1.6.3
(2)
Resistance to Shear
(a)
Maximum Allowable Shear Stress The maximum nominal design shear stress in a wall section, evaluated by means of the expression τd = Vd / Ag
5.10.7.21
where Vd is the design force computed in accordance with Clauses5.10.6.3 (3) or 5.10.6.4 (4) shall not exceed the following limit τd ≤ 10τRd
5.10.7.22
(b)
Contribution of Concrete to Shear Strength
(i)
In the potential plastic zone, as defined in Clause 5.10.8.5.3(2), the contribution of concrete to shear resistance is assumed to be zero, unless the minimum axial load produces an average compression stress over the gross concrete area of the wall equal at least to:
0.1 fcd. 5.10.7.23 98
In which case the shear contributed by concrete shall be computed by:
τcd = 2.5 τRd .β1
5.10.7.24
(ii)
Outside the potential hinge zone, and when the average compressive stress is less than 0.1 fcd, the shear stress contributed by concrete shall be taken as:
τcd = 2 τRd
5.10.7.25
while in case the average stress is greater than 0.1 fcd the value is taken as:
τcd = 2.5 τRd .β1
(c)
Web Reinforcement
5.10.7.26
Horizontal bars fully anchored at the extremities of the wall section, shall be provided in the amount:
ρv = Ah = τd ‐ τcd
5.10.7.27
5.10.7.28
b.sv fyd while the vertical reinforcement ratio shall be:
ρv = Av = τd ‐ τcd ‐ Nd / Ag
b.sh fyd The vertical shear reinforcement can be assumed to fully contribute to the required flexural strength. (3)
Coupling Beams
(a)
Symmetrical flexural reinforcement, (ρ = ρ'), shall be adopted in case of usual arrangement.
(b)
Design for flexure and shear shall be carried out as for ordinary beams unless the following limits are exceeded τd ≥ 6.τRd
ρ = l√ (8fck) / (4.h.fyk), (fck, fyk in Mpa)
5.10.7.289
99
(ρ = longitudinal reinforcement ratio, top or bottom) in which case all flexural and shear actions shall be resisted by diagonal reinforcement in both directions. 5.10.7.4 Verifications (1)
Collapse Verification
(a)
For the purpose of the present code, a structure shall be deemed to satisfy the safety requirement against collapse if the following conditions are met (i)
the strength and stability verifications are satisfied;
(ii)
the elements are dimensioned and detailed in accordance with rules given in Sections 5.10.7 and 5.10.8 relative to the appropriate structural type and intended ductility level.
(2)
Strength Verification The following condition must be satisfied for every element: Sd ≤ Rd
5.10.7.30
where Sd is the design load effect on the element considered, evaluated according to Section 5.10.6. Rd is the design strength of the same element, evaluated according to Section 5.10.7 (3)
Stability Verification The stability verification shall be considered satisfied if: (i)
the deformability index Θ formula 5.10.4.2.7 is less than 0.1,
(ii)
for 0.1 < Θ < 0.2, the second order effects are calculated and added to the design forces.
(iii)
the stability verification cannot be satisfied if
Θ > 0.20. 100
(4)
Serviceability Verification
(a)
The elastic drift, Δel resulting from the application of the horizontal forces specified in 5.10.4.2.4 or from the dynamic procedure in 5.10.4.2.5, shall at any storey satisfy the condition:
Δ el ≤
0.010 .h K
5.10.7.31
where h is the clear height of the floor. (b)
For Class II buildings, the indicated limits may be increased by 50% if it can be demonstrated that the finishes adopted are not brittle ‐ type and can accommodate without significant damage to those limits.
(c)
When the limits in (a) and (b) are exceeded, separation of the non‐structural elements is required, of an amount adequate for permitting an inter storey drift equal at least to:
Δ = 0.35 Δ el . K
5.10.7.32
5.10.7.33
to take place without restraint. (d)
In no case shall inter‐storey drift Δel exceed the limit :
Δ max = (5)
0.025 .h K
Maximum Expected Displacements The maximum expected displacements of the building shall be obtained by multiplying the displacements produced by the system of horizontal forces specified in 5.10.4.2.4 or those obtained from dynamic analysis as in 5.10.4.2.5 by the appropriate values of the behaviour factor K. 101
5.10.8 DETAILING, EXECUTION, USE 5.10.8.1 General When no explicit distinction is made, the provisions in this section apply to both DL II and DL III structures. Provisions applicable to DL I structures are always explicitly stated. 5.10.8.2 Elements Subject to Bending ( N d ≤ 0 . 1 . A g . f cd ) 5.10.8.2.1 Geometrical Constraints DL II and DL III Structures Unless special proofs for exemption are given, the following dimensional limitations shall be satisfied (i)
The width shall not be less than 200mm or more than the width of the supporting column, plus lengths, on each side of this member not exceeding one fourth of the depth of the column cross section.
(ii)
The ratio b/h shall not be less than 0.25
(iii)
The ratio l/h shall not be less than 4 (This requirement does not apply to coupling beams in wall structures, Clause 5.10.7.3(3).(Fig 5.10.8.1)
(iv)
The eccentricity of any beam relative to the columns into which if frames as measured by the distance between geometrical centre lines of the two members shall not exceed 1/4 bc (Fig5.10.8.2)
102
Fig. 5.10.8.1
Fig. 5.10.8.2 (a)
Maximum eccentricity of beams
(b)
Example of bad structural layout for this and analogous cases, if they cannot be avoided, special detailing shall be provided to ensure continuity with ductile behaviour.
103
5.10.8.2.2 Longitudinal Reinforcement (1)
DL II and DL III Structures
(a)
At any section of the member the tensile reinforcement ratio for top or the bottom reinforcement shall not be less than:
ρ min =
1.4 f yk
( f
yk
i n Mpa )
5.10.8.1
5.10.8.2
nor greater than
ρ max =
7 f yk
with ρ min and ρ max referred to the gross concrete area, Ag. (b)
At least two 12mm bars shall be provided both top and bottom throughout the length of the members.
(c)
Within any potential plastic hinge region, the compression reinforcement ratio ρ' shall not be less than one half of the tension reinforcement ratio at the same section.
(d)
At least one quarter of the larger of the top reinforcement required at either end of the member shall be continued throughout its length.
(e)
In T and L beams built integrally with slabs, the effective reinforcement to be considered near column faces in addition to all longitudinal bars placed within the web width of beam, shall be as follows: (i)
At interior columns when a transverse beam of similar dimensions frames into the column, all reinforcement within that part of the slab which extends a distance 4 times the slab thickness from each side of the column. (Fig 5.10.8.3a)
104
(ii)
At interior columns where no transverse beam exists all reinforcement within that part of the slab which extends a distance of 2.5 times the thickness of the slab from each side of the column. (Fig 5.10.8.3b)
(iii)
At exterior columns where a transverse beam of similar dimensions frames into column and where the beam reinforcement is to be anchored all reinforcement
within that part of the slab which extends a distance of twice the slab thickness from each side of the column. (Fig5.10.8.3c) (iv)
At exterior columns where no transverse beam exists, all reinforcement within the width of the column. (Fig.5.10.8.3d)
Fig. 5.10.8.3 ‐ Areas of Effective Reinforcement (v)
In all cases, at least 75% of the reinforcement in each face providing the required flexural capacity, must pass through or be anchored in the column core.
105
(2)
DL I Structures Clause5.10.8.2.2. (1) (a) only needs to be satisfied.
5.10.8.2.3 Minimum Transverse Reinforcement (1)
Transverse reinforcement as specified in this section shall be provided unless a larger amount is required to resist shear (section 5.10.7.1.(4) ) . Portions of the beams to be considered as ‘critical’ regions are: (a)
Twice the member depth, measured from the face of the supporting column, or beam, towards midspan at both ends of the beam.
(2)
(b)
Twice the member depth on both sides of a section where yielding may occur.
(c)
Wherever compression reinforcement is required.
DL II Structures In the critical regions as defined in 5.10.8.2.3 (1), stirrup ties of not less than 6mm diameter shall be provided, with maximum spacings not exceeding the smaller of: (a)
h/4
(b)
eight times the minimum diameter of the longitudinal bars
(c)
24 times the diameter of the hoop bars
(d)
200mm
The first hoop shall be located not more distant than 50mm from the face of the supporting member. 106
(3)
DL III Structures In the critical regions as defined in 5.10.8.2.3 (1) stirrup ties of not less than 6mm diameter shall be provided, with maximum spacing not exceeding the smaller of: (a)
h/4
(b)
six times the diameter of the longitudinal bars
(c)
150 mm
The minimum area of one leg of the transverse reinforcement shall be:
As, min =
ΣAb =
∑ Ab . f yk 16 f ykt
S 100 .
5.10.8.3
Sum of the areas of longitudinal bars at the section considered to be restrained by the transverse leg
fyk = yield strength of longitudinal bars fykt = yield strength of stirrups S =
spacing of stirrups in mm
The first hoop shall be located not more than 50mm from the face of the supporting member. (Fig 5.10.8.4)
Fig. 5.10.8.4 Regions and Spacing of Transverse Reinforcement 107
5.10.8.3 Elements Subject to Bending and Axial Force ( N d > 0 . 1 . A g . f cd ) 5.10.8.3.1 General Corner columns should be detailed according to DL III requirements. 5.10.8.3.2 Geometric Constraints (1)
DL II Structures
(a)
The minimum cross ‐ sectional dimension shall not be less than 250mm
(b)
The ratio l/b shall not exceed 25
(2)
DL III Structures
(a)
The minimum cross‐section shall not be less than 300mm
(b)
The ratio l/b shall not exceed the value of 16 for columns having moments of opposite sign at the two extremities; 10 for cantilever columns.
5.10.8.3.3 Longitudinal Reinforcement (1)
General (a)
The reinforcement ratio shall not be less than 0.01 or larger than 0.06 including the region of lap splices.
(b)
For S400 steel, the reinforcement ratio outside the splices shall not be greater than 0.045.
(c) (2)
The bars shall not be spaced further apart between centres than 200mm.
DL I Structures The provisions in 5.10.8.3.3 (1) apply to DL I Structures.
108
5.10.8.3.4 Transverse Reinforcement (1)
General
(a)
A basic amount of reinforcement shall be provided all over the height of the column while special reinforcement shall be placed in the column critical regions defined in Clause 5.10.8.3.4 (2)
(b)
The amount of reinforcement required by 5.10.8.3.4 shall be provided unless a larger amount is required to resist shear according to Clause 5.10.7.1 (4)
(2)
Column Critical Regions
(a)
For usual cases, critical regions are considered to be the regions at each end of a column above and below connections over a length from the faces of the connection of not less than the larger of: (i)
the longer column cross‐section dimension in the case of a rectangular cross‐section, or the diameter of the section in case of a circular column.
(ii)
one‐sixth of the clear height of the column
(iii)
450mm
(b)
When a masonry infill wall is in contact with one or both of the two opposite sides of the column, over the whole height or part of it, the entire column height shall be considered as a critical region.(Fig 5.10.8.5a)
109
Fig. 5.10.8.5 ‐ Solutions to be avoided (c)
In case of columns with part of their height restrained due to a connection with a wall the free part of the column shall be considered as a critical region.
(3) DL II Structures (A)
Critical Regions (a)
Special transverse reinforcement having a minimum diameter of 8mm in the form of spiral or hoop reinforcement shall be provided.
(b)
Cross ties to restrain longitudinal bars not directly held by hoops shall be used in accordance with BS 8110
(c)
The maximum spacing between spirals or hoops shall not exceed the smaller of: (i)
eight times the minimum diameter of the longitudinal bars
(ii)
one half the least cross‐sectional dimension of the section
(iii)
200 mm
110
(d)
The transverse reinforcement in the amount specified above shall be continued throughout the length of the beam ‐ column joint.
(B)
Non‐critical regions The minimum transverse reinforcement in non‐critical regions shall be in accordance with Table 5.10.8.1
Table 5.10.8.1: TRANSVERSE REINFORCEMENT ‐ DL II Critical Region lc = max (h, l/6, 450 mm) Spacing
Critical Region Sh = min (8φ L, 1/2b, 200mm)
Elsewhere Sh = mm (12φL, b, 300mm)
(See Fig. 5.10.8.6) (4)
DL III Structures
(A)
Definition (a)
The volumetric ratio is the ratio of volume of spiral or hoop reinforcement to total volume of concrete core ( out ‐to‐out of bars) within the spacing, Sh
(b)
The volumetric ratio ρs for rectangular sections is defined as
ρs =Ash / Sh . h’
5.10.8.4
where Ash is the total area of hoop bars and supplementary cross ties in each of the principal directions of cross section, Sh is the spacing and h' is the distance between centres of outer bars.
111
Fig. 5.10.8.6 ‐ Special Transverse Reinforcement. Critical Region and Spacing (B)
Critical Regions (a)
The volumetric ratio of transverse reinforcement (spiral or hoops) shall not be less than the greater of
ρ s = λ1 .
f ck f yk
5.10.8.5
112
ρ
s
⎛ Ag ⎞ f = λ2 ⎜ - 1⎟ ⎝ Ac ⎠ f
where, Ag = Ac =
ck
yk
5.10.8.6
gross sectional area confined area of concrete and the values of λ1 and λ2 are given in Table 5.10.8.2 as functions of the reduced axial force ratio Nd / Ac fck
Table 5.10.8.2: VALUES OF λ1 AND λ2
Nd /Ac .fck
0.10
0.20
0.30
0.40
0.50
λ1
0.05
0.06
0.07
0.08
0.09
0.22
0.26
0.30
0.34
λ2 0.l8 (b)
The minimum diameter of spiral or hoops shall be 8mm.
(c)
The maximum spacing between spirals or hoops shall not exceed the smaller of:
(d)
(i)
six times the minimum diameter of longitudinal bars;
(ii)
one fourth of the smallest lateral dimension of the section
(iii)
l50 mm
Each longitudinal reinforcement bar or bundle of bars shall be laterally supported by the corner of a hoop having an included angle of not more than 135o or by a supplementary cross tie except that the following bars are exempted from this requirement:
113
(i)
bars or bundles of bars which lie between two bars supported by the same hoop where the distance between the laterally supported bars or bundles of bars does not exceed 200mm between centres.
(ii)
inner layers of reinforcing bars within the concrete core centred more than 75mm from the inner face of hoops.
(e) The yield force of the hoop bar or supplementary tie shall be at least one‐sixteenth of the yield force of the bar or bars it is to restrain including the contribution from the bar or bars exempted under 5.10.8.3.4 (4)(B)(d)(i) (f) Each end of a supplementary tie shall engage either a longitudinal bar or the peripheral hoop besides a longitudinal bar with a bent of at least 1350 and an extension beyond the bent of at least 10 tie bar diameters. Supplementary ties and legs of hoops shall not be spaced transversely more than either 200mm or one‐quarter of the column section dimension perpendicular to the direction of the transverse steel. (Fig. 5.10.8.7).
114
hoop
supplementary
cross ties
hoop
(a) Single hoop plus two
(b) Single hoop plus two
supplementary crossties bent
supplementary cross ties
round longitudinal bars
bent round hoop
(c) Two overlapping hoops
(d) Two overlapping hoops not preferred detail
preferred detail
(e) Three overlapping hoops
(f) Four overlapping hoops
Fig. 5.10.8.7 ‐ Typical details using overlapping hoops 115
(C)
Non‐critical regions The requirements relative to the critical regions of DL II columns apply (see Table 1.7.3).
Table 5.10.8.3 TRANSVERSE REINFORCEMENT
DUCTILITY LEVEL III Critical Region lc = max (h, l/6, 450mm) (Fig. 5.10.8.6) Spacing
Critical Region Sh = min (6φL, 1/4b, 150mm)
Elsewhere Sh = min (8φL, 1/2b , 200 mm)
5.10.8.4 Beam ‐ Column Joints 5.10.8.4.1 Confinement (1)
DL I and DL II Structures The horizontal transverse confinement reinforcement in beam ‐ column joints shall not be less than that required for the columns.
(2)
DL III Structures (a)
The horizontal transverse confinement reinforcement in beam ‐ column joints shall not be less than that required for the columns with the exception of joints connecting beams at all four column faces that are designed according to Clause 5.10.7.2(1)(b)(ii) or (iii) in which case the transverse joint reinforcement may be reduced to one half of that required for the columns, but in no case shall the stirrup tie spacing in the joint core exceed ten times the diameter of the column bar, or 200 mm, whichever is less.
(b)
When the width of the column is larger than the effective joint width specified in in Clause 5.10.7.2(1)(a), all flexural reinforcement in the column that is required to interact with the narrow beam shall be placed within the effective joint area, bj.hc. 116
Additional longitudinal column reinforcement shall be placed outside this effective area. 5.10.8.5 Structural Walls 5.10.8.5.1 Geometrical Constraints (1)
General (i)
Wall thickness shall not be less than 150 mm.
(ii)
Openings in the walls not regularly arranged to form coupled walls shall be preferably avoided, unless their influence on the behaviour, of the wall under seismic action is either insignificant or accounted for by rational analysis
(2)
DL III Structures In addition to the requirements in 5.10.8.5.1 (1) ‐ DL III structures shall also satisfy the following. (a)
the height (hw) to width (lw ) ratio shall not be less than 2;
(b)
the local thickness of a wall shall not be less than hn/10 (hn is storey height) wherever the maximum compressive strain exceeds the value εcu /3, unless (i)
the distance of the critical fibre (ie where εcu = εcu /3 ) from the wall edge is smaller than 2b or 0.2 lw,
(ii)
the distance of the critical fibre from a transverse wall, or from a flange the width of which is at least hn/5 is smaller than 3b (see Figs. 5.10.8.8 – 5.10.8.9)
117
Fig. 5.10.8.8 ‐ Minimum Width Requirements
Fig. 5.10.8.9 ‐ Exemptions from Clause 1.7.5.1 on Minimum Wall Width
Fig. 5.10.8.10 ‐ Definition of Vertical Reinforcement Ratio 118
5.10.8.5.2 (a)
Longitudinal Reinforcement
The vertical reinforcement ratio in any part of the section shall not be less than 0.25% or greater than 4% (see Fig. 5.10.8.10).
(b)
At least two orthogonal grids of reinforcement shall be used one near each side of the wall
(c)
The diameter of the bars used in any part of a wall shall not exceed b/10
(d)
The maximum spacing between bars shall be 300mm except where the section is required to be confined, in which case the spacing shall not exceed 200 mm.
(e)
Curtailing: Vertical flexural reinforcement shall be curtailed in accordance with the bending moment envelope, allowing for the development lengths of the curtailed bars.
(f)
Splicing: Splicing of the vertical reinforcement in potential areas of yielding (See 5.10.8.5.3(1)) shall be avoided whenever possible. In no case shall more than one third of such reinforcement be spliced in those areas. Special care shall be taken for splicing of the main (flexural) vertical bars. The splices should be staggered in the longitudinal direction at least twice the spliced length.
(g)
Construction joints: The ratio of vertical reinforcement crossing a construction joint shall be such as to provide for the transfer of the entire shear capacity of concrete and is given by the expression: ρv = (1.3 fctm – 0.7 Nd/Ag) / fyk > 0.0025
5.10.8.7
ρv = Ast / b . lw
where:
with Ast = total vertical wall reinforcement, including that in boundary elements provided to resist flexure. Ag
is the gross area of the effective wall section including boundary elements.
Nd
is the minimum compression force in the wall. Tension shall be taken as negative.
119
5.10.8.5.3 Transverse Reinforcement (1)
General The requirement for minimum reinforcement ratio, maximum diameter and maximum spacing, shall be as for longitudinal reinforcement (Clause 5.10.8.5.2)
(2)
Zones with special transverse reinforcement
(a) The zones of walls requiring special reinforcement as specified in (b) below are defined as follows: (i)
in the vertical direction, they shall extend from the base over the probable plastic hinge length, which for the purpose is assumed to be the greater of; the length ( lw) or 1/6 of the height (hw) of the wall.
(ii)
in the plan section whenever the computed concrete strain exceeds the value:
εcu/3. The strain profile over the section shall correspond to development of its flexural strength, under the maximum design axial compression force occurring for a load combination including the seismic action (Fig. 5.10.8.11) E
Fig. 5.10.8.11
120
(b)
The amount of special transverse reinforcement to be provided is a function of the computed depth of the neutral axis: x in the base section of the wall, and of the selected ductility level as follows: (i)
DL II Structures The critical neutral axis depth, computed for the most adverse, design bending moment, d, is given by:
χ = 0.2
( M +u ,d ) . lw M d
when: χ ≤ χ ‐
5.10.8.8
Transverse reinforcement shall satisfy the minimum requirements set forth in Clause 5.10.8.5.3. Cross ties to restrain longitudinal bars shall be used in accordance with BS 8110 (1985)
χ > χ ‐
Transverse reinforcement shall satisfy the requirements of Clause 5.10.8.3.4(3) (Ductility Level II columns in critical regions).
(ii)
DL III Structures The critical neutral axis depth, computed for the most adverse bending moment Md, is given by:
χ = 0.1
( M +u ,d ) . lw Md
5.10.8.9
when:
χ ≤ χ ‐ Transverse reinforcement shall satisfy requirements of Clause 5.10.8.3.4(4) (DL III columns in non‐critical regions).
χ > χ ‐ Transverse reinforcement volumetric ratio shall not be less than the greater of: 121
ρ s = λ1 .
f ck
f yk
5.10.8.10
or
ρ
λ
=
s
2
⎛ A ⎜⎜ ⎝ A
g c
⎞ f - 1 ⎟⎟ ⎠ f
ck yk
5.10.8.11
where the values of λ1 and λ2 are given in the following Table 5.10.8.4 as functions of neutral axis depth ratio. TABLE 5.10.8.4 VALUES OF λ1 AND λ2 IN EQUATIONS 5.10.8.10 AND 5.10.8.11 x /lw
0.1
0.2
0. 3
0.4
0.50
0.60
0.70
λ 1
0.07
0.08
0.09
0.105
0.115
0.125
0.135
λ 2
0.18
0.205
0.23
0.26
0.285
0.31
0.34
The volumetric ratio is defined as
ρ = A’sh
where h1 =
5.10.8.12
Sh h1 dimension of wall concrete core measured perpendicular to the direction of hoop bars to outside of peripheral hoops
A’sh = total steel area of hoop bars and supplementary cross ties in direction under consideration, with spacing Sh 5.10.8.5.4 Coupling Beams (a)
The diagonal reinforcement in each direction shall be enclosed by rectangular stirrups, hoops or spirals in accordance with Clause 5.10.8.3.4(4), however their spacing or pitch shall not exceed l00mm.
122
(b)
Minimum thickness for diagonally reinforced beams shall be 200 mm. The anchorage length of diagonal reinforcement in the adjacent wall be increased by 50% of the lengths prescribed in BS 8110 (1985) (Fig. 5.10.8.12).
Fig. 5.10.8.12 5.10.8.6
Anchorage and Splicing of Reinforcement
5.10.8.6.1
General
In addition to the rules of BS 8110 the following requirements shall be satisfied in order to ensure reliable behaviour during cyclic loading reversals caused by seismic action: (a)
All reinforcement bars should be considered to be in insufficient bond conditions except when anchorage is made in regions confined by means of special transverse reinforcement where good bond condition can be assumed.
(b)
All bars should be able to develop their maximum strength (γn) fyk when a plastic hinge is formed.
5.10.8.6.2 Flexural Members: Anchorage of Longitudinal Reinforcement (a)
Flexural members framing into opposite sides of a column shall have top and bottom reinforcement provided at ends of members continuous through the column where possible.
(b)
When top or bottom reinforcement cannot be continuous through the column due to the variations in flexural members cross section, and in exterior columns, the reinforcement shall be anchored within the beam column connection in accordance with the following: (i)
Reinforcement shall be extended to the far face of the confined region and anchored to develop its yield strength.
123
(ii)
Every bar shall terminate with a standard 90‐degree hook or equivalent anchorage device, as near as practicably possible to the far face of the column core. Top bars should be bent down and bottom bars bent up.
(iii)
Development length of beam reinforcement shall be computed beginning at a distance of 10 φ from the near face column.
(c)
For DL III Structures when beams frame into opposite sides of a column, the maximum diameter of the longitudinal beam bars which are continuous through the column should not exceed the following fractions of the column depth (parallel to the bar) in Table 5.10.8.5
Table 5.10.8.5 Steel grade
Fraction of hc
S220 smooth
1/35
S220 deformed
1/20
S400 deformed
1/30
5.10.8.6.3 (a)
Columns: Anchorage of Longitudinal Reinforcement
The maximum diameter of longitudinal column bars which are continuous through a joint shall not exceed the following fractions of maximum depth of the beams framing into the column.(Table 5.10.8.6) Table 5.10.8.6 Steel Grade
Fraction of hb
S220 smooth
1/25
S220 deformed
1/15
S220 deformed
1/25
124
When hinges are permitted to form in columns the values indicated in Clause 5.10.8.6.2 shall be applied. (b)
The anchorage of a column bar into an inter‐section beam shall be made by a horizontal 90‐ degree standard hook or equivalent device, as near the far face of the beam as practically possible. The direction of the horizontal leg of the standard hook must always be towards the core of the joint.
(c)
When columns terminate at joints at the top of frames or at joints between columns and foundation members, the anchorage of the longitudinal column bars into the joint region shall be assumed to begin at a distance equal to one half of the depth of the beam, or 10φ, whichever is less from the face at which the column bar enters the beam. (Fig 5.10.8.13)
Fig 5.10.8.13 5.10.8.6.4 Splices of Longitudinal Reinforcement (a)
Splices are not permitted within beam‐column joints or within potential plastic hinge regions.
(b)
If it can be shown that plastic hinge cannot develop, splices are permitted in the end sections of columns, provided that transverse reinforcement spaced vertically no further than 6 bar diameters, is present.
125
(c)
Stirrup‐ties shall be provided over the length of all lap splices of reinforcement in beams and columns. The maximum spacing of the stirrup‐ties shall not exceed 10 times the diameter of the bar being spliced. For DL III structures the maximum spacing shall also not exceed 150 mm.
(d)
Welded splices or approved mechanical connections conforming with BS 8110 (1985) may be used, provided that not more than alternate bars in each layer of longitudinal reinforcement are spliced at a section, and the distance between splices of adjacent bars is 600 mm or more measured along the longitudinal axis of the frame component.
5.10.8.6.5 Anchorage and Splicing of Transverse Reinforcement (a)
Transverse hoop reinforcement shall be anchored by at least a 135o bent around a longitudinal bar with a minimum extension at the face end of 10 bar diameters. Alternatively, the ends of the hoops can be spliced by welds capable of developing the full strength of the bar.
(b)
Transverse reinforcement shall not be lap‐spliced in cover concrete with beam –column joints or within potential plastic hinge regions. Deformed bars shall be used for lap splices.
(c)
When the anchorage for a spiral terminates with a 135o bend around a longitudinal bar, the extension beyond the bend shall be at least 10 spiral bar diameters.
126
APPENDIX A SCHEDULE OF UNIT WEIGHT OF BUILDING MATERIALS Weights of concrete
Table 1A
Aggregate or type Expanded clay or shale ‐ditto ‐ structural Vermiculite (expanded mica) No‐fines (gravel) Cellular (aerated or gas concrete) Cellular structural
con struction with concrete products
Reinforced concrete
Lightweights concrete
L i g h t w e ig h ts c o n c r e t e
Non‐reinforced plain or mass concrete
Concrete block and brick walls Other products
Normal weight Aggregate: limestone gravel broken brick other crushed stone Nominal weight Reinforcement: 1% 2% 4% Solid slabs – Thickness (floors, walls, 75mm etc.) 100mm 150mm 250mm 300mm Ribbed slabs 125mm 150mm 225mm 300mm Compressive strength N/mm2 5.6 to 8.4 13.8 to 34.5 0.5 to 3.5 ‐ 1.4 10.3 to 15.5
Sandcrete block: solid Lightweight aggregates: solid Brickwork (nominal) Paving slabs (flags) 50mm thick Roofing tiles: plain inter‐locking
kN/m3 22.6 21.2 to 23.6 22.0 to 23.6 19.6(av) 22.8 to 24.4 23.6 22.6 to 24.2 23.1 to 24.7 24.0 to 25.6 KN/m2 1.80 2.40 3.60 6.00 7.20 2.00 2.15 2.75 3.35 kN/ m3 9.4 to 11.8 13.4 to 18.1 3.9 to 11.0 15.7 to 18.9 3.9 (min.) 14.1 to 15.7 kN/ m3 17.3 13.2 21.7 kN/m2 1.15 0.6 to 0.9 0.6
To convert values in kN to values in kg. multiply by 102
127
Weights of constructional materials Concrete Brickwork etc.
Miscellaneous Materials
Table 2A N/m2
Clay floor tiles
575
See Table 1A KN/m3
Damp‐proof course
48
Tarmacadam
22.6
N/m2 mm per
Macadam (waterbound)
25.1
thickness
Vermiculite3 (aggregate)
0.8
Felt (insulating)
1.9
Terracotta
20.8
Paving slabs. (stone)
26.4
Glass
26.7
Granite sets
28.3
Cork: granular
1.2
Asphalt
22.6
:compressed
3.8
Rubber paving
15.1
Polyvinylchloride
19(av)
Glass‐fibre (forms)
1.9
Chipboard Plywood Fibreboard Wood‐wool Plasterboard Water boarding Gedu nohor Guarea (cedrata) Guarea (thomsonii) Idigbo Ilomba Iroko Mahogany, African Makore Okwen Opepe Ptergygota Sapele Stervulia, Brown Sterculia, yellow Utile
N/m2 per mm 7.5 6.1 2.8 5.7 9.4 3.8 Density at 12% moisture constant 3 KN/m 4.7 to 6.1 4.7 to 6.1 4.7 to 6.1 4.7 to 6.1 4.7 to 6.1 6.3 to 7.7 4.7 to 6.1 4.7 to 6.1 4.7 to 6.1 6.3 to 7.7 6.3 to 7.7 4.7 to 6.1 6.3 to 7.7 6.3 to 7.7 6.3 to 7.7
Timber
Abura Afara or limba African walnut Afromosia Afzelia Agba Albizzia (A.ferruginea) Alstonia Antiaris Avodire Ayan Canarium, African Celtis Dahoma Danta Ekki Esia Mansonia Mubura Miangori Obeche Odoko Ogea Okan
density at 12% moisture content 4.7 to 6.1 4.7 to 6.1 4.7 to 6.1 6.3 to 7.7 7.9 to 10.2 4.7 to 6.1 6.3 to 7.7 3.1 3.1 4.7 to 6.1 6.3 to 7.7 3.1 3.1 4.7 to 6.1 6.3 to 7.7 4.7 to 6.1 6.3 to 7.7 6.3 to 7.7 6.3 to 7.7 10.2 7.9 to 10.2 4.7 to 6.1 6.3 to 7.7 4.7 to 6.1 3.1 to 4.6 4.7 to 6.1 4.7 to 6.1 7.9 to 10.2
128
Natural stone (solid)
Granite
25.1 to 28.7
Stone rubble (packed)
22.0
Sandstone
22.0 to 23.6
Quarry waste
14.1
slate
28.3
Hardcore (consolidated)
18.9
All‐in aggregate
19.6
iron: cast
70.7
Structural steel work
Net weight of member +
wrought
75.4
Riveted
steel (see also below)
77.0
copper: cast
85.6
: wrought
87.7
Brass
83.3
Welded
Bronze
87.7
Aluminum
27.2
Rolled sections: beams
Lead
111.0
:stanchions
Zinc (rolled)
70.0
g/mm2
Plate‐web girders
per metre
Steel bars
7.85
Roof trusses
10% for cleats, rivets bolts etc +1
1 1 % to 2 % 4 2
for welds etc + 2
1 % for 2
caps and bases) + 10% for rivets or welds, stiffeners etc. See Table 3A
Steel stairs: industrial
N/m
Type in wide
820
Steel tube:
50mm in bore
45 to 60
Gas piping: 20mm
18
129
Weight of roofs
Material
Table 3A
Weight per m2 of slope of roof (N/m2)
claddnin g
Net including normal laps and fastenings
Aluminum sheet corrugated 18. S.W.G Aluminum sheet, corrugated 20 S.W.G Aluminum sheet corrugated 22. S.W.G Aluminum sheet corrugated 24. S.W.G Aluminum sheet, flat 18 S.W.G Aluminum sheet, flat 20 S.W.G Aluminum sheet, flat 22 S.W.G Aluminum sheet, flat 24 S.W.G Asbestos cement sheets, corrugated 6mm thick Asbestos cement sheets, flat 5mm thick Asbestos cement sheets, flat 6mm thick Asbestos cement sheets, flat 10mm thick Asbestos cement sheets, flat 12mm thick Copper sheeting 16 S.W.G Copper sheeting 18 S.W.G Copper sheeting 20 S.W.G Copper sheeting 22 S.W.G Copper sheeting 24 S.W.G Roofing felt, 3‐ply Roofing felt, 2‐ply Roofing felt, 1.ply Shingles (excluding battens) Steel sheet, galvanized, corrugated 18GB Steel sheet, galvanized, corrugated 20GB Steel sheet, galvanized, corrugated 22GB Steel sheet, galvanized, corrugated 24GB Steel sheet, galvanized, corrugated 26GB Steel sheet, galvanized, corrugated 28GB Steel sheet, galvanized, flat 18GB Steel sheet, galvanized, flat 20GB Steel sheet, galvanized, flat 22GB Steel sheet, galvanized, flat 24GB Steel sheet, galvanized, flat 26GB
37.8 28.7 22.0 17.2 33.5 24.9 19.6 15.3 135 80 110 170 220 145 110 80 65 50 25 20 15 110 90 70 55 45 35 100 80 60 50 40
47.9 38.3 28.7 23.9 160 120 135 105 90 70 55 45
130
Table 3A (cont’d)
Steel sheet, galvanized, flat 28BG
Cladding
Thatching, 300mm nominal thickness :dry
30
:wet
410
Roofing, burnt clay Marseilles type
530
(excluding battens)
430
Tiles, roofing, burnt clay Etruscna type
(excluding battens)
570
Tiles, roofing, burnt clay, Broseley type
(excluding battens)
670
Tiles, roofing, burnt clay, Italian type
(excluding battens)
720
Reinforced concrete slabs, concrete tiles etc.
See Table 1A
Spacing of trusses 2
Approximate weights of steel roof trusses in N/m of Roof trusses
plan area of roof
Span of trusses
3.0m
4.5m
7.5m
95
72
9m
120
72
12m
132
84
15m
144
108
18m
203
144
25m
239
168
131
Solid and packed ma terials
Li quids and semi -liquids
Weights of stored materials
Tables 4A
Acids: acetic
KN/m3
KN/m3
nitric
10.4
Mineral oils: naptha
7.4
sulphuric
15.1
Paraffin (kerosene)
7.9
alcohol (commercial)
18.1
Petrol(gasoline)
6.9
ammonia
7.9
Petroleum oil
8.6
beer: in bulk
8.8
Pulp (wood)
7.1
bottled (in cases)
10.0
Slurry: cement
14.1
in barrels
4.6
Clay
11.9
benzene, benzol
5.5
Sewage
9.7 to 11.8
bitumen (prepared)
8.6
Tar, pitch
11.8
methylated spirit
13.7
Turpentine
8.5
linseed oil milk
8.2
Water: fresh
9.81
8.8
Sea –water
10.05
10.2
Wine: in bulk
9.7
Bottled (in cases)
5.8
Lime (slated) dry 5.5 wet 17.3 9.4 to 10.2 Paper (packed) 2.4 to 5.5 Waste(pressed) 7.1 Salt: dry 6.3 Loose 1.7 Sawdust 9.0 Slag: basic 8.8 Crushed 10.7 Foamed 7.1 Sugar (loose) 9.4 Tea (in chests) To convert values in kN to values in kg. multiply by 102 Brewery’s grains (wet) Bricks (stacked) Clinker Cotton (in bales) Flour: in bulk In sacks Hops (in sacks) Ice Bottled goods (in cases) Eggs in bulk Meat Tinned goods (in cases)
5.5 14.9 9.4 5.5 9.4 14.1 2.4 17.3 9.4 to 14.1 6.3 7.9 4.4
132