Corus Tubes library publication The contents of this publication are current, when republished it will be in the new Corus housestyle.
SHS Design to BS 5950 Part 1
DESIGN TO BS 5950 : PART 1: 1990 LIMIT STATE DESIGN OF TUBULAR STRUCTURES USING HOT FINISHED STRUCTURAL HOLLOW SECTIONS.
Preface This brochure has been produced to assist Structural Engineers and Designers who use Hot finished Structural Hollow Sections whose section properties comply with BS 4848 : Part 2 (Ref 1) and whose Steel qualities comply with EN 102 10-l (Ref 2) to design using the Limit State basis as covered by BS 5950 : Part 1 (Ref 3). It is important for designers to recognise that hollow sections, unlike their rolled open section counterparts, can be produced by a hot or cold forming process. The process of cold forming produces different mechanical properties in the section to that of hot forming and a reduction in the sectional properties used in design. Designers wishing to use cold formed hollow sections should design in accordance with the appropriate cold formed standard and with the sectional properties as given in BS 6363 (Ref 4). Further guidance is given in British Steels Tubes & Pipes publication TD369 - ‘Cold Formed Hollow Sections’. In addition to the information contained in this publication, further assistance and design guidance is given in companion British Steel Tubes & Pipes publications (references 16 to 21) and the Steel Construction Institute (references 8 to 15) publications as given in Appendix A. BRITISH STANDARDS INSTITUTION Extracts from British Standards are reproduced by permission of the British Standards Institution, 2 Park Street, London, W1 A 2BS from whom complete copies can be obtained. The information given is not intended in any way to replace that given in the Standards themselves to which reference should always be made. Where reference is made to specific clauses and tables throughout the text, these refer to BS 5950 : Part 1 : 1990 plus amendment No. 1.
Disclaimer Care has been taken to ensure that the contents of this publication are accurate, but British Steel plc and its subsidiary companies do not accept responsibility for errors or for information which is found to be misleading. Suggestions for or descriptions of the end use or application of products or methods of working are for information only and British Steel plc and its subsidiaries accept no liability in respect thereof. Before using products supplied or manufactured by British Steel plc the customer should satisfy himself of their suitability. If further assistance is required, British Steel plc within the operational limits of its research facilities may often be able to help.
Page
Contents
L .
1.0
INTRODUCTION
2
2.0 2.1 2.2 2.3 2.4 2.5 2.6
PROPERTIES OF MATERIALS AND SECTION PROPERTIES Structural Steel Physical properties of structural steel Hollow Section range Design Grade Design Strength py Section Classification
2 2 2 2 3 4 5
3.0 3.1 3.2 3.3
MEMBER DESIGN Members in tension Members in compression Members in bending
8 8 10 14
4.0 4.1 4.2 4.3
AXIALLY LOADED MEMBERS WITH MOMENTS Tension members Compression members Web bearing and buckling
17 17 18 19
5.0
MEMBERS IN TORSION
20
6.0
PURLINS AND SIDE RAILS
21
7.0 7.1 7.2
COLUMN BASES Empirical rules Effective area
22 22 22
8.0
DESIGN OF WELDED JOINTS
24
9.0
COMPOSITION CONSTRUCTION
24
10.0
FIRE RESISTANCE
24
APPENDIX A
REFERENCES
25
APPENDIX B
FORMULAE AND CONVERSION FACTORS
26
APPENDIX C
DESIGN EXAMPLES
29
BS 5950 Part 1 1.0 INTRODUCTION Limit State Design
2.0
The Limit State design approach for buildings and structures is based on BS 5950 : Part 1 code of practice for design in simple and continuous construction : hot rolled sections, and relates to the use of hot rolled steel sections and plates and hot finished Structural hollow sections.
1.1
Whilst the standard requires that all relevant limit states of strength, stability and serviceability should be considered this publication relates primarily to the limit state of strength. When considering the limit states of stability and serviceability due regard must be taken of the differing load factors and combinations that may apply.
2.4 2.5
PROPERTIES OF MATERIALS AND SECTIONAL PROPERTIES
2.1 Structural Steel BS 5950 : Part 1 covers the design of structures fabricated from weldable structural steels in designated design grades to the appropriate product grade which for hot finished structural hollow sections are found in EN 10210-l (Ref 2). Other steels may be used provided due allowance is made for variation in properties, including ductility. EN 10210-l : 1993 contains the technical delivery requirements for Hot Finished Structural Hollow Sections, including British Steel Tubes dz Pipes two standard production grades of S275J2H and S355J2H. Tables in annex A and B detail the required chemical analysis, mechanical properties, testing and certification for hot finished SHS. For further details see TD 364 (Ref 17). Designers are recommended to consider the use of Grade S355 steels in structures. Design strengths for grade S355 are significantly higher than grade S275 steels at only a small extra cost, often resulting in more economical designs.
2.2
Physical Properties of Structural Steel The values of tensile strength and minimum yield strength specified in EN 102 lo- 1 for the two standard production grades of Hot Finished SHS are; Yield Strength Yield Strength N/mm2 N/mm2 (t 5 16mm) (16
Product Grade
Tensile Strength N/mm2 (3mm 5 t 5 65)
2.3 Hollow Section Range Structural Hollow Sections (SHS) comprise a range of circular hollow sections (HFCHS) and rectangular hollow sections - including squares (HFRHS).
2
3.1 2.4.4 2.4.4.3
BS 5950 Part 1
The range of Structural Hollow Sections manufactured by British Steel is generally in accordance with BS 4848, Hot Rolled Structural Steel Sections, Part 2 Hollow Sections. This standard gives dimensional and sectional properties and relates generally to the international standard IS0 657 Hot Rolled Steel Sections, Part 14 Hot Finished Structural Hollow Sections. The manufacturing range normally produced by British Steel is given in the leaflet TD 167 (Ref 16). Larger sizes of HFCHS, not detailed in that leaflet, may be obtained on application.
2.4 Design Grade To provide a transition path from the single U.K. standard of BS 4360 to the four European Standards for Structural Steel, BS 5950 : Part 1 Amendment 1 has introduced the term design grade. Reference to Table 2 of BS 5950 : Part 2 will show the relationship between the design grade and the appropriate product standard and grade which following the implementation of the European Standard for hot finished structural hollow sections is EN 10 2 10-l. Note: BS4360 is now withdrawn. The following table shows the appropriate product grade in EN 102 10-l for the BS 5950 design grade plus, for information purposes only, the previous product grades as given in BS4360 : 1990.
BS 5950 Design Grade
Current EN 10 210-l Product Grade
Previous BS 4360 : 1990 Product Grade
43c 43D 43EE
S 275 JOH S 275 J2H S 275 NLH
43c 43D 43EE
5oc 50D 50EE
S 355 JOH S 355 J2H S 355 NLH
5oc 50D 50EE
55c 55EE 55F
S 460 NLH
55c 55EE 55F
Note: The Standard production grades for Tubes & Pipes SHS is S275J2H and S355J2H, previously BS 4360 Grade 43D and 50D respectively.
3
BS 5950 Part 1 2.5 Design Strength py Throughout the design procedures the two factors of Design Strength (py) and Section Classification repeatedly occur. One or both will be required to be known in order to complete the design procedure. 3.1.1
The design strength pY is taken as equal to the specified minimum yield strength but not more than 0.84 of the minimum ultimate tensile strength from EN 10210-l. Based upon EN 10210-l the design strengths for different design grades of steel are given in BS 5950 Table 6 which for the range of SHS thicknesses are:
Table 6 (part)
Design strength py
Thickness (mm)
Design strength Py Nmm2)
43
5 16 > 16 540
275 265
50
1.16 > 16 1 4 0
355 345
55 *
5 16 > 16 1 2 5
460 440
Design Grade
*
Values have been shown for steel in grade 55 but the designer is advised to check availability before proceeding with its use.
Note that currently rectangular hollow sections are limited to 20mm thick and circular hollow sections to 50mm thick. Thus in practice for sections up to and including 16mm thick, py = 275 N/mm2 (Design Grade 43) or 355 N/mm2 (Design Grade 50). For sections over 16mm and up to 40mm thick py = 265 and 345 respectively for Design Grades 43 and 50. However, this design strength will be reduced when, due to their size and thickness, sections are classified as slender (see section classification).
4
BS 5950 Part 1 2.6 Section Classification 3.5
The classification of a section gives an indication of its expected performance with particular reference to the elements of the cross section that are in compression due to bending or axial load. The majority of SHS members will tend to fail at ultimate load by compressive yielding in one or more elements of the cross section. However it is recognised that cross sections with slender elements may fail in compression by local buckling before reaching the full yield strength thus limiting the ultimate capacity of the section. The onset of local buckling will also be influenced by the level of axial stress. Thus if high yield steel is used (and the applied stress is greater) then the width to thickness ratio of elements must be within smaller limits to prevent local buckling. The Code places sections into four classifications namely plastic, compact, semi-compact and slender as follows: (illustrated diagramatically in Figure 1).
3.5.2
CLASS 1 PLASTIC (Can form plastic hinge with rotation capacity required for plastic design) CLASS 2 COMPACT (Can develop full plastic moment but with limited rotation capacity) CLASS 3 SEMI-COMPACT (Stress in extreme fibres can reach yield) CLASS 4 SLENDER (Design strength pY must be reduced to prevent local buckling)
3.6 Table 7
Figure 1 Section classification
5
BS 5950 Part 1 Class 1
Plastic:
Sections in which under bending a plastic hinge can form with sufficient rotation capacity to allow redistribution of moment within the structure. Stress will reach the full design strength pY in a rectangular stress block configuration which will be retained during rotation with no significant deformation of the cross section.
Class 2
Compact:
Sections in which under bending the full plastic moment can be developed but local buckling may prevent the development of a plastic hinge with sufficient rotation capacity to permit redistribution of moment. In this case elastic analysis of the frame should be used.
Class 3
Class 2
Semi-compact:
Sections in which under bending the stress at the extreme fibres can reach the design strength pY in a triangular stress block configuration but local buckling will prevent the development of the full plastic moment, and the moment capacity is therefore based upon the elastic modulus.
Class 4
Class 1
Class 3
Slender:
Sections in which local buckling will prevent the stress in the section from reaching the design strength pi and consequently a reduced value of design strength pyr must be used in calculating the bending capacity, which is based upon the elastic modulus, and the compression resistance.
Class 4
The classification of a section is determined by comparing the width to thickness ratio of each element of the section, or diameter to thickness ratio for a HFCHS, with the appropriate limiting values given in BS 5950 Table 7. These limiting values are scheduled for each classification and type of element and include a factor E (defined as (275/~y)O.~) which takes account of the steel grade of the section.
Table 7
The limiting values that apply to structural hollow sections are given in Table 7, part of which is reproduced on page 7. Elements that exceed the semi-compact limits of 39s for HFRHS or 80~~ for HFCHS are classified as slender.
Table 7
BS 5950 Part 1 Limiting width to thickness ratio for SHS
Class of section
Type of element
1. Plastic b
2. Compact b
I 26~
I 32~
3. Semi-compact b
I 39&
Internal element of compression flange
i
Web, with neutral axis at mid-depth
d I 79&
d
t
t
Web, generally
d<
79& t- 0.4 + 0.60~
d<9& t - OL
See Clause 3.5.4
Web, where whole section is subject to compression.
d I 39& t
d I 39& t
d 5 39s t
D
D I 80E2 t
Circular tube subject to moment or axial compression
0.5
D
t
and
t
I 40&2
T
I 98&
I 57E2
t
Table 7
d I 120&
t
a = 2y,
Notes to Table 7
d
Note that for HFRHS the element width is taken as the side wall length less 3 times the thickness as shown in Figure 2.
Figure 3
HFRHS
b=B-3t d=D-3t
Figure 2 Dimensions of SHS
When members are subject to bending about one axis only the classification may be read directly from Steelwork Design Guide to BS 5950 : Part 1 (Ref 10);
7
3.0
BS 5950 Part 1 MEMBER DESIGN Design examples of members to BS 5950 : Part 1 can be found in reference 11 and Appendix C.
3.1
MEMBERS IN TENSION
3.1.1 Brittle Fracture BS 5950: Part 1 imposes maximum thickness limits for members subject to tensile stresses in service due to applied axial load or moment when brittle fracture is required to be considered. SHS supplied to EN 102 10-l grades have adequate notch toughness within the service temperature limits taken as -5 “C for internal conditions and -15 “C for external conditions except for sections greater than 30mm thick in design grade 50C.
2.4.4
When steel is subject to lower temperatures the charpy impact performance at the minimum service temperature should not be less than:
2.4.4.3
Table 4
y,t 710 K where K is determined from table 3 of BS 5950: Part 1.
3.1.2 Axially Loaded tension members
Table 3
4.6
The tension capacity, Pt of a member should be taken from: pt = Ae Py
4.6.1
where A, is the effective area of the section as determined from Clause 3.3.3. Eccentric connections When members are connected eccentric to the axis of the member the resulting moment has to be allowed for in accordance with Clause 4.8.2 (See Section 4.0, axially loaded members with moment).
4.6.2
Effective area at connections. The effective area, &, of each element of a member at a connection, where fastener holes occur may be taken as K, times its net area, but not more than its gross area, where for steels complying with BS 5950 design grades: K, = 1.2 for design grade 43 K, = 1.1 for design grade 50 K, = 1.0 for design grade 55
3.3.3
BS 5950 Part 1
In hollow section members with bolted flattened end connections, as in Figure 3, it is necessary to make allowance for fastener holes.
- 76.1 x 5 HFCHS with 2 holes 18mm diameter
Figure 3 The 76.1 x 5 circular hollow section (design Grade 43) member in Figure 3 has a gross cross section area of 11.2 cm (from Dimensions and Properties tables). In accordance with clauses 3.3.2 and 3.3.3 the effective area at the connection may be taken as K, times the net area, but not more than the gross area, where K, = 1.2 for design grade 43 steel. The effective area, 4, is therefore as follows:-
&
= = = = =
(gross area - area of holes) x K, (11.2 x 102) - (4 x 18 x 5) x 1.2 (1120 - 360) x 1.2 760 x 1.2 912 mm* 5 1120
Use effective area of 912 mm*
9
3.2 MEMBERS IN COMPRESSION 3.2.1 Compression resistance The compression resistance P, of a member is obtained from P, =AgPC where A, is the gross cross sectional area and pc is the compressive strength The compressive strength pc is obtained from the relevant strut curve and depends upon the slenderness l/r ( = h) and the design’strength py, or reduced design strength pyr in the case of slender sections. The design procedure as applied to hollow sections is given as follows:
3.2.2 Design procedure for hollow sections (1)
Select trial section and determine the value of the design strength py.
(2)
Determine whether or not the section is slender. For slender sections in order to prevent local buckling reduce the design strength as follows. For HFCHS obtain the reduced design strength pyr from the semi-compact limit of the circular tube in table 7. Thus from d/t s = 80 &2 and E = (275/~,)O.~ pyr = 80 x (275/ (d/t)) For HFRHS reduce the design strength py by the stress reduction factor for the internal element ot 31 compression flange in table 8: b -8 TE
(3)
Determine the effective length b
(4)
Calculate the slenderness ratio h = b/r
(5)
Select the relevant strut curve according to the section-shape and the axis of buckling. For hot rolled structural hollow sections strut curve a is always used.
(6)
Obtain the compressive strength pc from strut table 27a for the appropriate values of design strength py (or pyr) and slenderness h (= L/r)
(7)
Calculate the compression resistance P, = A, pc Slender sections Slender sections under compression will fail by local buckling before the stress in the section reaches the full design strength py. Local buckling is avoided by reducing the design strength pyr as described above. Problematically, on occasion it will be found that pyr is less that the lowest value of py (= 225 N/mm2) tabulated in table 27 and in such cases the compressive strength pc must be calculated according to Appendix Cl and C2. Note that since no HFCHS section in the current range is slender, the reduced value of pY will only apply to a limited range of HFRHS. Generally speaking it is the thinner wall sections of side length 200 and above that need to be checked. Section clarification for members subject to bending is given in published form (see Appendix A reference 9).
10
BS 5950 Part 1
3.2.3 Effective length of struts The effective length L of a compression member should be determined from its actual length L centre to centre of restraint in the relevant plane as given in table 24 of BS 5950: Part 1. The effective length factors from Table 24 are given below and are shown diagrammatically in Figure 4 as follows:
.! 2.0
Figure 4 Nominal effective length, L, for a strut.
7.2.4 Effective length, L
Conditions of restraint at ends (in plane under consideration) Effectively held in position at both ends
Restrained in direction at both ends
0.7L
Partially restrained in direction at both ends
0.85L
Restrained in direction at one end
OML
NOT restrained in direction at either end
l.OL
One end
Other end
Effectively held in position and restrained in direction
Not held in position
Effectively restrained in direction
1.2L
Partially restrained in direction
1.5L
NOT restrained in direction
2.OL
Table 24
11
BS 5950 Part 1 3.2.4 Lateral restraint Lateral restraint to compression members should have sufficient strength and stiffness to inhibit movement of the restrained point in position and direction as appropriate.
4.7.1.2
Compression chord members forming part of a lattice beam, girder or roof truss may require one or more lateral restraint within the span, these intermediate lateral restraints should be capable of resisting a total force of not less than 2.5% of the maximum factored force in the compression chord, divided between the intermediate lateral restraints in proportion to their spacing. All intermediate lateral restraints should be either connected to an appropriate system of bracing capable of transferring the restraint forces to the beam, girder or trusses, effective points of support, or else connected to an independent robust part of the structure capable of fulfilling a similar function. Where two or more parallel members require lateral restraint at intervals, it is not adequate merely to connect the members together such that they become mutually dependent. Where three or more intermediate lateral restraints are provided, each intermediate lateral restraint should be capable of resisting a force of not less than 1% of the maximum factored force in the compression chord.
4.3.2.2
In this case, the bracing system should be capable of resisting the greater of the effects of: (a) the 1% restraint force considered as acting at only one point at a time; (b) the restraint forces described in 4.3.2.1 Where more than three parallel members share the same system of restraints, the combined lateral restraint force should be taken as the sum of the three largest lateral restraint forces required for each individual restrained member, as determined in accordance with 4.3.2:1 and 4.3.2.2.
4.3.2.3
3.2.5 Maximum Slenderness The value of the slenderness ratio h (= L&) should not exceed the following:
4.7.3.2
60
for members resisting loads other than wind loads
180
09
for members resisting self weight and wind loads only
250
@I
for any member normally acting as a tie but subject to reversal of stress resulting from action of wind
I I
Members whose slenderness exceeds 180 should be checked for self weight deflection. If this exceeds length/1000 the effect of bending should be taken into account in design.
12
BS 5950 Part 1 3.3 MEMBERS IN BENDING 3.3.1 General conditions All members in bending should be checked to take account of the following:
4.2
a)
At critical points the combination of maximum moment and co-existent shear and the combination of maximum shear and co-existent moment.
4.2.1.3
W
Deflection limits given in Clause 2.5.1.
d
The resistance of a member to lateral torsional buckling unless the compression flange has full lateral restraint,
4
Local buckling (of slender elements).
e)
Web buckling and web bearing.
3.3.2 Shear Shear force F, should not exceed the shear capacity P, which is given by: P, = 0.6 pyA,.
4.2.3
For rectangular hollow sections with the applied load parallel to the web the shear area A, is: A, = (D/D+B)) x A For circular hollow sections, A, = 0.6 A A further check is given in the Code for shear buckling of thin webs (where d/t ratio exceeds 63&), but since the sizes in the current BS 4848: Part 2 range do not exceed this limit the check is not applicable.
3.3.3 Lateral torsional buckling Where a flexural member is not provided with sufficient lateral restraint to the compression flange, then lateral torsional buckling will occur before the member can develop its maximum bending capacity.
4.3 4.2.2
Hollow sections possess a high degree of torsional stiffness and do not generally suffer from lateral torsional buckling. It can be seen from Appendix B that for square and circular hollow sections (where I, = IY) the factory’ will always be equal to zero. It follows that the buckling index @t., and the equivalent slenderness h LT will also be equal to zero, indicating that lateral torsional buckling does not occur with square or circular hollow sections.
B.2.5
14
BS 5950 Part 1 The Code (Appendix B.2.6.1. Table 38) gives a limiting slenderness ratio below which box sections of uniform wall thickness (including RHS) need not be checked for lateral torsional buckling effects. In practice, where normal deflection limits apply, this limit of slenderness is unlikely to be exceeded, and consequently hollow sections in bending may generally be considered as beams with full lateral restraint.
B.2.6.1
By applying the limits as given in Table 38 to the current range of Rectangular Hollow Sections sizes in Design grades 43 and 50 the following limiting values of h are obtained:
Table 38
-_ D/B
h for design grade 43
h for design grade 50 D
1 2
infinity 350
infinity 271
-_ 01 B ! i - i
D and B are overall depth and breadth of RHS respectively. It follows that based upon these values of h (which is equal to L&y) for each RHS size there is a corresponding limiting length L,, beyond which a check should be made for lateral torsional buckling. For example, consider a simply supported laterally unrestrained rectangular hollow section beam 200 x 100 x 5 design grade 43 with D/B = 2.
200 x 100 x 5 (Design grade 43)
----------m-------B-------~~~~~~--_------I
AL
AL
I
LC = 14.7m
sl
I
The limiting value of h is 350
L
= 350 x 4.2 x 1Omm = 14.7m
This length (14.7m) is termed the limiting length L, and is tabulated on pages 147, 148, 321 and 322 of the Steelwork Design Guide Volume 1 (Reference 9). Square and circular hollow sections have a limiting length of infinity and, as indicated previously need not be checked for Lateral Torsional Buckling.
15
BS 5950 Part 1 3.3.4 Moment capacity M, The Code gives two sets of expressions for determining M, moment capacity in the absence of axial load, the first for members with low shear load (where F, 5 = 0.6 Pv) and the second, giving reduced moment capacity, for members with high shear load (where Fv > 0.6 P,).
4.2.5 4.2.6
Since RHS beam members have two vertical webs it is unlikely that the shear load will exceed 0.6 of the shear capacity and therefore the moment capacity can usually be taken as follows: Class 1 + 2 Class 3 Class 4
Plastic or Compact sections M, = pYS 5 = 1.2 pYZ * Semi-compact sections M, = pYZ. Slender sections M, = PyrZ where pyr < pY (Clause 3.6)
4.2.5
* This restriction is to ensure that plasticity does not occur at working load. For most I-sections the shape factor S/Z is less than 1.2. Only for hollow sections is S/Z greater than 1.2 and in such cases the constant 1.2 may be replaced by the average load factor (i.e. the ratio of the factored load to the un-factored load). Note that in the Steelwork Design Guide - Volume 1 (Reference 9) most of the tabulated values of M, for hollow sections are governed by M, 5 = 1.2 pYZ. Since in most design cases the average load factor is greater than 1.2 it generally follows that M, can be taken as the higher value derived from M, = pYS.
3.3.5 Design procedure for hollow sections The design procedure will normally be similar to that for a beam with full lateral restraint.
1)
Select section and check that L&y < Limiting h Or check that span < L,
B.2.6.1
2)
Determine the value of the design strength pY
Table 6
3)
Determine the section classification
Table 7
4)
For slender sections reduce the value of design strength using the same procedure given section 3.2.2 page 10 for members in compression.
3.6.4
5)
Check the shear capacity
4.2.3
6)
Check the moment capacity With low shear load With high shear load
4.2.5 4.2.6
7)
Check the buckling resistance of the webs
4.5.2.1
8)
Check the bearing resistance of the webs
4.5.3
16
BS 5950 Part 1 4.0
AXIALLY LOADED MEMBERS WITH MOMENTS
4.1
TENSION MEMBERS Tension members with moments should be checked for the following two effects:
4.8.2
1) Lateral torsional buckling under the action of moment alone
4.3
and 2) check for capacity under the combined effects of axial load and moment at the points of greatest bending moments and axial loads, usually at the ends. The following relationship should be satisfied: F
Mx
+
-
Ae Py
+
MC,
MY -
Il.0
MC,
where F
is the applied axial load in member; is the effective area;
PY
is the design strength;
WC
is the applied moment about the major axis at critical region;
MC,
is the moment capacity about the major axis in the absence of axial load;
MY
is the applied moment about the minor axis at critical region;
MC,
is the moment capacity about the minor axis in the absence of axial load
(3.3.3)
(4.2.5 and 4.2.6) (4.2.5 and 4.2.6)
Alternatively for greater economy in plastic or compact cross sections only the following relationship should be satisfied.
where Mr x* and Mr y * are the reduced moment capacities about the major and minor
axis respectively in the presence of axial load obtained from the published tables (see Ref 10). andzl = Z2
are
constants taken as:
2.0
for hollow circular sections;
513
for hollow rectangular sections;
)ie”rx and Mr Y are the reduced moment capacities which are calculated by using a
reduced plastic modulus. The published tables (ref. 9) are for the case where the plastic neutral axis lies within the area bounded by the walls of a rectangular section or the internal radius of a circular section. When the plastic neutral axis lies within the wall thickness of rectangular sections the modified reduced plastic modulus is given in Appendix B of this publication.
17
BS 5950 Part 1
4.2 COMPRESSION MEMBERS Check for
1)
4.8.3.2 4.8.3.3
1) local capacity 2) overall buckling
4.8.3.2
Local capacity a)
F
Mx -
+
MC,
Ai? PY or
b)
+
MY
Il.0
MC,
for plastic or compact sections only (M,) Z 1
Il.0
(My) Z2 +
-
0% YJ
(Mr y>
4.8.3.3
Note: for further reference to M rx and M ry see Page 17 of this publication.
2)
Overall buckling
a>
4.8.3.3.1
Simplified approach F +
mMx -
+
Mb*
A, PC
&Y
Il.0
PY ZY
* Note: Mt., must not be taken as greater than M,,
b)
+
Max Where Max
-
May
is the maximum buckling moment about the major axis in the presence of axial load, taken to be the lesser of:
MC,
Ma,
4.8.3.3.2
Alternatively, more exact approach
(I- $3 (1+&q
is the maximum buckling moment about the minor axis in the presence of axial load taken as:
M
CY
(l-e) (1+y)
where M,x MC,
P cx P CY
is the moment capacity about the major axis is the moment capacity about the minor axis but not subject to the restriction M, I 1.2~~ Z; is the compression resistance about the major axis; is the compression resistance about the minor axis.
( 4.2.5 4.;: )
The simplified approach for overall buckling assumes that lateral / torsional buckling controls. This is not true for circular or square hollow sections and only true for rectangular hollow sections with long unrestrained lengths. It is therefore recommended that the more exact approach be generally used. 18
BS 5950 Part 1 4.3
WEB BEARING AND BUCKLING 4.5
The basic expression for web checks are given in Clause 4.5.2.1 (buckling) and Clause 4.5.3. (bearing) as follows: buckling resistance P, = (bl + nl) tpc
4.5.2.1
bearing resistance = (bl + n2) tP,,
4.53
In practice reference should be made to the Steelwork Design Guide - Volume 1 (Ref 9) which contains tables for the beam factor Cl, stiff bearing factor C2 and the flange plate factor C3. Details are shown in Figures 7 and 8.
I
D
Figure 7 Web bearing Where
Bearing web capacity = Cl + (bl.C2) +(tp.C3)
bl = length of stiff bearing t = thickness of web tp = thickness of flange plate Cl = beam factor c2 = stiff bearing factor c3 = welded flange plate factor Note Where the flange plate is non welded factor C3 should be divided by 2.5.
Figure 8 Web bearing Buckling web capacity P, = Cl + (b,.C2) + ($.C3)
19
The beam buckling factor Cl allows for dispersion of load in two directions and applies to a member which is continuous over bearing or an end bearing member with a continuously welded sealing plate (see Figure 9).
Figure 9
2)
There are two sets of values given for factor Cl, C2 and C3: the first (larger values) are for welded flange plates, and the second (smaller values) for non-welded flange plates. When loads or reactions are applied through non-welded flange plates the additional effects of moment in the web due to eccentric loading have to be taken into account, resulting in lower buckling values (see Figure 10).
t 07 iJ B
t-l
LT
D
e
MY
e
P
MY
P
Figure 10 Local moment in side walls of RHS
5.0 MEMBERS IN TORSION The total resistance of a member to torsional loading is composed of the sum of two components known as ‘uniform torsion’ and ‘warping torsion’. As the torsional rigidity of a Structural hollow section is very large compared with its warping rigidity, the section may be reasonably regarded as subject to pure torsion only. In this case the total angle of twist is given by:
Iz) = WhereTg z G J
TsZ GJ = = = =
the applied torque the length of member subject to T4 Shear modulus of elasticity (79000 N/mm*) Torsional constant for cross section
BS 5950 Part 1
BS 5950 Part 1 and the pure torsional shear stress is given by:
Tq
Tt
=-
C where C = Torsional Modulus Constant Torsional constants for circular, square and rectangular hollow sections plus basic theory and worked examples for members subject to torsion loading including combined bending and torsion, are given in the SC1 publication (Ref 11).
6.0
PURLINS AND SIDE RAILS
4.12
Purlins and side rails may be designed on the assumption that the cladding provides lateral restraint to the face against which it is connected. The type of cladding and its fixings should be such that it is capable of acting in this manner. Deflection should be limited to suit the characteristics of the particular cladding system. Wind loading, excluding local pressure effects, should be determined from CP3 Chapter V : part 2. 4.12.4
Alternatively, in the case of roof slopes not exceeding 30” from horizontal or wall cladding not exceeding 15” from vertical, purlins and side rails may be designed using empirical rules. For purlins a minimum substantially uniform loading of 0.75 N/mm2 should be used and the modulus (Z) and section depth (D) and width (B) for spans not exceeding 6.5m found by:
Purlins Section
Z (min)
D
CHS
WPL
L/65
B
Table 29
2000 RHS
L/70
WPL
L/150
1800 Where Wp is the total unfactored load on one span of the purlin (in kN), L is the l.ength centre to centre of the main supports (in mm). Side rails should generally be designed for wind loads and self weight of the cladding. The minimum values of the elastic modulus (Zl) about the axis parallel to the plane of cladding and the section depth (D) measured perpendicular to the cladding, and the corresponding elastic modulus (22) and section width (B) are found by:-
Side Rail
Zl (min)
22 (min)
D
B
CHS
WlL
W2L
L/65
-
2000
1350
WJ
W2L
1800
1200
RHS
Table 30 L/70
L/l00
Where W1 and W2 are total unfactored loads on one span of the side rail acting perpendicular to and parallel to the plane of the cladding respectively, (in kN), L is the span of the rail (in mm) for a) Zl andDandb)Z2andB. 21
BS 5950 Part 1
7.0 COLUMN BASES
4.13
BS5950 provides empirical rules for determining the thickness of concentrically loaded rectangular base plates but also allows other rational means to be used.
7.1 Empirical Rules. 4.13.2.2
The minimum thickness in mm for rectangular base plates carrying concentrically loaded RHS member is: 2.5 w (a* - 0.3b2)
t = PYP
1
t
> RHS wall thickness
and for circular or square base plates for solid rounds or CHS members the minimum thickness in mm is given by the following expression which was based on requirements for solid columns and may give unacceptably large thickness for CHS members. Reference to the effective area method is recommended for CHS baseplates. 3
W
t =
Dp (Dp - 0.9D) 2.4 Pyp
where
1
a is the greater projection of the plate beyond the column b is the lesser projection of the plate beyond the column w is the uniform pressure on the underside of the plate pYp is the design strength of the plate with a maximum of 270 N/mm* Dp is the length of side or diameter of base plate, not less than 1.5 (D + 75)nu-n D is the CHS diameter 4.13.2.3
If the bearing pressure beneath the base plate is not uniform, calculations should be made to determine the bending moments in the plate which should not exceed 1.2 pypZ where pyp I 270 N/mm* and Z is the elastic modulus of the base plate. Caution must be exercised in use of the above formulae as they assume uniform loading is present at the underside of the base plate and the maximum moment occurs at the external corner of the RHS. Resultant base sizes may not produce this condition particularly when dimension D is large in relation to dimension B. As an alternative the effective area method may be used.
7.2
Effective Area Method The basis and method are taken from the publication entitled ‘Joints in Simple Construction, Volume 1 Design Methods’ published by the BCSA and Steel Construction Institute. 1) Baseplates for RHS Columns The shaded area in figure 11 represents the area of base plate assumed to be effective in transmitting the factored column load onto the foundations by imposing a uniform pressure on the concrete not exceeding the limiting bearing strength. The bearing strength is taken as 0.6 fcU in accordance with BS 8110: Part 1: 1985. Required effective area Areq = =
( mean wall perimeter length ) x ( width of wall thickness plus two outstands ) (2D+2B-4t)(t+2K)
Note that when K is greater than ( B - 2t) /2 then the internal outstands overlap and the effective area becomes Areq = ( D + 2K ) ( B + 2K )
22
8.0
BS 5950 Part 1
DESIGN OF WELDED JOINTS Whilst the Code gives guidance for bolted connections no specific detail is included for overall design of welded joints. The following reference is therefore included to assist the designer. Lattice structures are usually designed on the basis of pin jointed frames with members in tension or compression and the forces noding at the joint. Bracing and chord members are determined in accordance with the normal laws of statics. Research work has shown that the strength of such joints is dependent on a number of factors: bracing width to chord width ratio chord width/thickness ratio chord compressive loading gap or overlap of bracings Work conducted with the International Institute of Welding and the CIDECT organisation has led to the publications (Ref 18) of design rules for welded joints for circular, square and rectangular chords, which will be included in Eurocode No. 3. This work has highlighted that the final joint strength is substantially influenced by the relative bracing-to-chord sizes and the general joint geometry which is the province of the design engineer as it involves his member selection for both analysis and design. Resulting from this, it becomes necessary for the designer to fully consider the joint design as part of his work. Final sizing of welds can be left to the fabricator provided one important point is specified. The weld at the toe of a bracing member (highest stressed point) should, if the bracing angle is less than 60” be bevelled and a butt weld used. Further information on welding can be found in BS 5 135 (Ref 5) and British Steel Welded Tubes publication SHS Welding (Ref 19).
9.0
COMPOSITE CONSTRUCTION
4.14
BS 5950 : Part 1 gives guidance for the design of cased beam or column sections but no reference is made to hollow sections as this will be covered in Part 3, Code of practice for design in composite construction. A separate design manual for limit state design of concrete filled hollow sections based on BS 5400 : Part 5 (Ref 6), is available from British Steel Welded Tubes (Ref 20).
10.0 FIRE RESISTANCE The means to evaluate and define the fire resistance of Structural elements is given in BS 5950 : part 8 (Ref 7). The code recognises that Structural Steelwork can in certain conditions have the required fire resistance even when unprotected. Alternatively, adequate fire resistance can be achieved by use of either externally applied systems such as boards or spray materials or internal systems such as concrete or water filling. The thickness of externally applied systems is determined using the section factor Hp/A and fire protection manufacturers data (Ref 15). The evaluation of concrete filling is contained in the standard (Ref 7) and further information is contained in Welded Tubes publication for concrete filled columns (Ref 20) and, in the case of CHS columns, in ECCS Technical Note 55 *. The evaluation of water filling and the use of bare external structural steel is referenced by the standard to publications issued by the Steel Construction Institute (Ref 12 and 13) who also publish a handbook to BS 5950 part 8 (Ref 15). * ECCS publications are available through The British Constructional Steelwork Association Limited, 4 Whitehall Court, Westminster, London, SWlA 2ES.
24
Appendix A REFERENCES 1.
BS 4848 : Part 2 - Specification for hot-rolled Structural Steel Sections. Part 2 - Hollow Sections.
2.
EN 10210-l : Hot finished structural Hollow Sections in non alloy and fine grain Structural Steels - Part 1 : Technical delivery conditions.
3.
BS 5950 : Part 1 - Code of practice for design in simple and continuous construction. Hot rolled sections.
4.
BS 6363 - Specification for Welded Cold formed Steel Structural Hollow sections.
5.
BS 5 135 - Specification for Arc welding of carbon and carbon manganese steels.
6.
BS 5400 : Part 5 - Code of practice for design of composite bridges.
7.
BS 5950 : Part 8 - Code of practice for fire resistant design.
References 1 to 7 are available from the British Standards Institution, 2 Park Street, London, WlA 2BS
8.
Introduction to Steelwork design to BS 5950 : Part 1
9.
Steelwork Design Guide to BS 5950 : Part 1 : 1990, Vol 1. Section properties member capacities, 3rd Edition.
10.
Steelwork Design Guide to BS 5950 : Part 1, Vol 2. Worked Examples.
11.
Design of members subject to combined bending and torsion.
12.
Water cooled hollow columns.
13.
Fire Safety of bare external Structural Steel.
14.
Fire protection for Structural Steel in Buildings.
15.
Fire Resistant Design of Steel Structures - A Handbook to BS 5950 : Part 8
References 8 to 15 are available from The Steel Construction Institute, Silwood Park, Ascot, Berks SL5 7QN.
16.
TD 167
RI-IS & CHS Sizes, Properties
17.
TD 364
RHS & CHS Technical Data
18.
TD 338
Design of SHS Welded Joints, to BS 5950
19.
TD 328
SHS Welding
20.
TD 296
Design manual for SHS concrete filled columns
21.
TD 325
SHS Jointing
References 16 to 21 are available from British Steel Tubes & Pipes, SHS Technical Sales.
25
Appendix C C 1 Design Examples l
The publication of B.S. 5950 Part 1. Code of Practice for Design in Simple and Continuous Construction: Hot Rolled Sections, presents the engineer with a change in design philosophy with the use of limit state principles and, partly as a direct result of this, a change in the detail procedures of design. It is anticipated that the D.O.E. will withdraw approval for B.S. 449 by the end of 1987 and in this event, familiarisation of the new standard is important. To assist engineers a number of design examples have been prepared using Structural Hollow Sections. Whilst it has not been possible to cover every aspect of the code, it is hoped that the examples will be of practical use in the design of elements. In each case reference should be made to the appropriate clauses in B.S. 5950 which have been given in the margin throughout the examples. In addition reference is made to tables given in the “Steelwork Design Guide - Volume 1, Section Properties and Member Capacities” published by the Steel Construction Institute, and are shown in the margin thus 1x1. Appendix C2 contains relevant extracts from the ‘Steelwork Design Guide’.
2.1 Ref.
EXAMPLE 2 CONTINUOUS MULTI-STOREY COLUMN (SIMPLE CONSTRUCTION)
Factored Loading 50 80 40 170 kN
40 3.0m
100
+I#140
f’
85
3.5m
I
Pinned Base
100 140 85 325 kN
5
Self Weight TOTAL FACTORED LOAD F,
500 kN
Generally, for axially loaded compression members with moments, cl. 4.8.3, separate checks are required for local capacity cl. 4.8.3.2., and overall buckling cl. 4.8.3.3. The requirements for overall buckling may be satisfied by either the ‘Simplified approach’ cl. 4.8.3.3.1, or the ‘More exact approach’ using cl. 4.8.3.3.2. However for columns of the type in this example a further option is available by reference to cl. 4.7.7, ‘Columns in simple multi-storey construction’ subject to compliance with the qualifying conditions. This clause dispenses with the need for a separate local capacity check, and it is only necessary to apply the rules defined in the ‘Simplified approach’.
4.7.7
Simplified Approach F A,p, Where
mM,
mM
+-+---ql.O Mb Pyz,
F = Applied axial load pc = Compressive strength A, = Gross cross - sectional area m = Equivalent uniform moment factor Mb= Buckling resistance moment Capacity (major axis) Z, = Elastic section modulus (minor axis) pY = Design strength
4.8.3.3.1
4.5 Ref. Using ‘STEELWORK DESIGN GUIDE to BS5950 Volume 1 (3rd Edition), Section properties, Member capacities’ RECTANGULAR HOLLOW SECTION 250 x 150 x 8 Design grade 50 Section is PLASTIC for bending about X-X
Web Shear Shear force F, (max) = 82.5 kN Shear capacity P, = 814 kN Check shear F, (at max. bending) = 60 kN < O-6 P, = 488 kN :. Shear force is ‘low’, and M, need not be reduced.
Moment Capacity Applied moment M, = 178 kNm Moment capacity M, = 176 kNm* *governedbyM,=1.2pYZ=176kNm Higher value may be used since S, = 1.22 Z, > 1.2 Z, and constant 1 - 2 may be replaced by 1 - 5 (average load factor). M,=p,S,<+5p,Z =355x505x10~3~1~5x355x413x10-3 = 179 kNm < 220 kNm O.K. :. M,= 179 kNm > M, = 178 kNm Limiting length L, = 16 - 7 m Since span 5.0 m < L, = 16.7 m LATERAL TORSIONAL BUCKLING need not be checked.
Web Bearing Bearing load = 82 - 5 kN Beam factor (end) Cl = 114 kN Stiff bearing factor (end) = 5 - 68 kN/mm = C2
322 El
I330 ]
4.2.5
I
322 Note 47 0
322 I
330 I
Bearing capacity = Cl + (b, x C2) + (tP x C3) =114+(75x5~68)+(Ox14~2) = 540 kN O.K.
Web Buckling Buckling load = 82.5 kN Beam factor (end) Cl = 798 kN Stiff bearing factor (end) C2 = 3 - 19 kN/mm Buckling resistance = Cl + (b, x C2) + (tP x C3) =798+(75x3*19)+(0x3.19) = 1037 kN O.K.
330 cl
APPENDIX C=2
Extracts reproduced from:STEELWORK DESIGN GUIDE TO BS5950 : PART 1 : 1990 Volume 1 - Section Properties and Member Capacities @THE STEEL CONSTRUCTION INSTITUTE
PO Box 101, Weldon Road, Corby, Northants. NN17 5UA Tel: 01536 404120/1 Fax: 01536 404005
TD 365/5E/94
