Simplified Design to BS 5400
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
Version Date of Issue
Purpose
1
Distribution to universities DCI
27/6/01
Author
Technical Approved Reviewer CWB
GWO
2 3 SCI reference: RT877 The Steel Construction Institute Silwood Park Ascot Berkshire, SL5 7QN. Telephone: +44 (0) 1344 623345 Fax: +44 (0) 1344 622944 Email:
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
FOREWORD BS 5400 is a document combining codes of practice to cover the design and construction of steel, concrete and composite bridges and specifications for loads, materials and workmanship. It consists of 10 ‘Parts’. Part 3 (BS 5400-3:2000) is the Code of Practice for Design of Steel Bridges; Part 2 (BS 5400-2:1978) is the loading specification; and Part 5 (BS 5400-5:1982) relates to composite design. This document contains ‘simplified versions’ of Parts 2, 3 and 5 for the use of undergraduate students. It is written to explain both the Code provisions and background concepts at easily understood levels. It is emphasised that a bridge designed to this simplified version will not necessarily meet all the requirements of BS 5400; some clauses that are important are not covered because of their complexity and the scope of loading and constructional details has been limited. BS 5400 should be consulted if further information is required.
Note to Lecturers This document is intended as the first introduction to the use of BS 5400 for the design of a composite bridge, in particular the structural steel elements of the bridge. It is assumed that sufficient background of stability of steel structures has already been covered in the regular lectures. For the design of composite beams, the treatment of the effects of staged construction is mentioned but it is suggested that, for greater simplicity, all the dead load, superimposed dead load and live load may be applied to a single model of the composite structure. Even when the effects of staged construction are ignored, it might nevertheless be appropriate in some cases to check the adequacy of the steel beams acting alone during construction, when they are carrying the weight of the wet concrete, because that is frequently a prime consideration for the bridge constructors. In order to make the best use of this document it is suggested that the any design exercise defines the details of the deck slab and its reinforcement, rather than seeking the detailed design of that element. More comprehensive advice on the design of composite bridges is available in the following Steel Construction Institute publications:•
Design guide for composite highway bridges (P289)
•
Design guide for composite highway bridges: Worked Examples (P290)
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
© The Steel Construction Institute
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RT877 Version 01 (June 2001)
Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
PART A - Simplified version of the steel bridge code, BS 5400-3:2000, covering the design of rolled sections and plate girders (For the use of Undergraduate Students) CONTENTS Page No. FOREWORD
3
1
SCOPE
7
2
DEFINITIONS AND SYMBOLS
7
3
DESIGN OBJECTIVES
9
4
PROPERTIES OF MATERIALS
10
5
GLOBAL ANALYSIS FOR LOAD EFFECTS
10
6
STRESS ANALYSIS
11
7
DESIGN OF BEAMS
11
8
SHAPE LIMITATIONS
12
9
EFFECTIVE SECTION
16
10
EVALUATION OF STRESSES
17
11
EFFECTIVE LENGTH FOR LATERAL TORSIONAL BUCKLING
17
12
SLENDERNESS OF BEAMS
19
13
LIMITING MOMENT OF RESISTANCE
21
14
STRENGTH OF BEAMS
22
15
RESTRAINTS TO COMPRESSION FLANGES
29
16
RESTRAINTS AT SUPPORTS
30
17
TRANSVERSE WEB STIFFENERS OTHER THAN AT SUPPORTS
30
18
LOAD BEARING SUPPORT STIFFENERS
33
19
WELDED CONNECTIONS
34
20
BOLTED CONNECTIONS
36
© The Steel Construction Institute RT877 Version 01 (June 2001)
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
© The Steel Construction Institute
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RT877 Version 01 (June 2001)
Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
1
SCOPE This simplified version of the Steel Bridge Code gives recommendations for the design of structural steelwork in bridges. It covers the design of simple bridges using: •
Rolled sections, (Universal beams).
•
Plate girders – unstiffened or with transverse web stiffeners only.
Simple bridges considered here consist of a reinforced concrete slab supported on beams. The detailed design of deck slabs is outside the scope of this document. Trusses, box Girders and plate girders with longitudinal stiffeners are also outside the scope of this document. Simplified procedures are given for the design of steelwork components, assemblies and connections. It is assumed that structural steels comply with the requirements of BS EN 10025 (the specification for ordinary structural steels).
2
DEFINITIONS AND SYMBOLS
2.1
Definitions Highway loading is generally modelled by an equivalent uniformly distributed load plus a knife edge load, to represent normal loading ((HA loading); in addition, consideration has to be given to a single abnormal vehicle (HB loading). Design loads. Design loads are the loads obtained by multiplying the nominal loads by γFL, the partial safety factor for loads. The relevant values of nominal load and γFL are given in Part 2 of BS 5400. [In practice, highway authorities refer to document BD 37/88, part of the Design Manual for Roads and Bridges, which implements and amends BS 5400-2 for use in UK.] For loading to be used in conjunction with this simplified version of BS 5400-3, refer to the ‘simplified’ BS 5400-2 (Part B of this document). Load Effects. “Load effects” is the term used to describe a variety of effects such as bending moments, shear forces and deflections.
2.2
Symbols Main symbols A Cross-sectional area a Length of panel; longitudinal spacing of transverse stiffeners B Overall width; spacing of beams b Width of panel; width of element D Overall depth; d Depth of element E Modulus of elasticity F Internal Force
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
G Shear modulus of elasticity g Throat thickness of weld; gauge of holes h Height of element I second moment of area i Factor, as defined in text k Factor, as defined in text L Span; overall length l Length of element M Moment m Ratio, as defined in text P Applied force Qk Nominal load r Radius of gyration t Thickness of plate or section V Shear force in webs v Factor, as defined in text y Distance from neutral axis or centroid Z Section modulus γfL,γf3 Partial load factors γm Partial material factor η Factor, as defined in text λ Slenderness parameter λLT Slenderness parameter for lateral torsional buckling ν Poisson’s ratio Σ Sum σ Direct stress σy Nominal yield stress (N/mm2) τ Shear stress τo Shear stress at onset of tension field action τy Shear yield stress Subscripts A axial b bending, bearing B beam c compressive D design resistance e Effective, equivalent E Euler buckling f flange g throat of weld h horizontal, hole i buckling; instability; l limiting n integer value to be taken, 1 to n o stiffener outstand p plastic q shear R reference value s stiffener t tensile v vertical w web; weld © The Steel Construction Institute
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x y z 1 2
about X-X axis about Y-Y axis centroid of plate normal; longitudinal; primary transverse; horizontal; secondary
Common Abbreviations SLS Serviceability Limit State ULS Ultimate Limit State
3
DESIGN OBJECTIVES
3.1
General The purpose of a bridge is to carry a service over an ‘obstacle’ (which may be another road or railway, a river, a valley etc). The designer has to ensure that bridges are both safe and economic. BS 5400 is based on safety factor/limit state philosophy. The loads to be considered in determining the load effects are described throughout as nominal loads. For various combinations of load, statistical distributions are available as a result of previous studies, using a return period of 120 years. Each type of load is multiplied by various partial load factors which represent the likelihood of that type of load being exceeded in the life of the bridge. The “design loads” comprising “factored” loads in different combinations are applied to the structure and the load effects determined. The load effects are then compared to the design strength of elements based on yield strength divided by partial strength factors to take account of the variability of the material and of inaccuracies in fabrication and design. There are two limit states adopted in BS 5400: the ultimate limit state and the serviceability limit state. Collapse, failure, overturning, buckling or rupture of the whole or part of the structure are ‘disasters’ and are classed as the ultimate limit state (ULS). A high load factor is used. Permanent deformation due to yielding of steel, cracking of concrete etc are ‘nuisances’ in that they require repair or may limit the usefulness of the structure. There are classed as the serviceability limit state (SLS). A lower load factor is adequate. In some situations, both limit states will need to be checked; in others, due to the choice of load factors, one state will obviously govern and therefore it is only required to carry out a check for that state.
3.2
Partial safety factors to be used For a satisfactory design, the criterion to be met can be summarised as follows: Load effect due to factored loads ≤ Resistance of the structural element; or (The effects of γFLQk) ≤
© The Steel Construction Institute RT877 Version 01 (June 2001)
1 (function of σy and geometric variables) γ f3γ m
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
where γfL
is a partial factor for load.
γf3
is a factor that takes account of inaccuracies in load assessment, stress distribution and construction.
γm
is a single factor which takes account of material strength.
Qk
is the specific nominal load.
The loads to be used in simplified design, and the partial factors to be used with the loads, are given in Part B of this document The values of γm and γf3 to be used are given in Table 3.1 Table 3.1
3.3
Partial factors γm and γf3 ULS
SLS
γm
1.05
1.0
γf3
1.1
1.0
Structural Support Provisions should be made in the design for the transmission of vertical, longitudinal and lateral forces to the bearing and supporting structures.
4
PROPERTIES OF MATERIALS
4.1
Nominal yield stress σy for steel to BS EN 10025 Grade S275 Grade S355
4.2
σy = 275 N/mm2 σy = 355 N/mm2
Properties of steel Modulus of elasticity, Shear Modulus Poisson’s ratio Coefficient of thermal expansion
4.3
E = 205000 N/mm2 G = 80000 N/mm2 ν = 0.3 = 12 × 10-6/oC
Properties of reinforced concrete For the purposes of simplified design, it may be assumed that concrete is ‘grade 40’ to BS 5400-4. See Part C of this document.
5
GLOBAL ANALYSIS FOR LOAD EFFECTS
5.1
General Global analysis of a structure should be carried out elastically to determine the load effects (i.e. bending moments, shears, etc). Plastic analysis of the structure (i.e. redistribution of moments due to plastic hinge formation) is not allowed.
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5.2
Section properties The section properties to be used in global analysis should be calculated for the gross section.
5.3
Composite beams constructed in stages It is usual for composite bridges to be constructed in stages, such that the steel beams initially carry the weight of wet concrete and the composite beams subsequently carry superimposed dead loads and live loads. See Part C of this document for further advice on global analysis of composite beams.
6
STRESS ANALYSIS
6.1
Longitudinal stress in beams Longitudinal stresses will be developed due to bending and due to axial force. The distribution of longitudinal stress between the flange and web of a beam may be calculated on the assumption that plane sections remain plane, but using the effective section in accordance with Section 9.2.
6.2
Shear stresses Shear force due to vertical loads will induce a shear stress in webs. The design values of the shear stress in webs of rolled or fabricated I or channel section may be calculated in accordance with Section 10.2.
6.3
Shear lag For certain types or proportions of bridges, the effect of shear lag at the SLS can increase locally the elastic stresses near supports of concentrated loads. However, consideration of this effect is beyond the scope of this document, and shear lag should be ignored.
7
DESIGN OF BEAMS
7.1
General Beams are defined as members with solid webs, subject primarily to bending; these include members of rolled section, plate girders, and composite members. Only beams without longitudinal stiffeners are considered in this document.
7.2
Ultimate limit state (ULS) All beams should be designed to provide adequate strength to resist the design loads, using the partial factors that are appropriate to the ULS. The following need to be considered. •
Material strength.
•
Limitations on shape on account of local buckling of individual elements (i.e. webs and flanges).
•
Plastic moment capacity of compact sections.
•
Effective sections (reductions for compression buckling and holes).
•
Lateral torsional buckling.
•
Web buckling (governed by depth to thickness ratio of web and panel size).
•
Combined effects of bending and shear.
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7.3
Serviceability limit state (SLS) Beams should also be designed to ensure that no yielding or permanent deformation takes place under the (lower) design loads that are appropriate to SLS. When the beam has been designed at the ULS as a non-compact section, (see Section 8.2) and the strength is based on an essentially elastic basis, the requirements at the SLS are automatically satisfied and no further checks need to be made. When the beam has been designed at the ULS as a compact section, (see Section 8.3) utilising the plastic moment capacity, it is quite possible that yielding could occur in extreme fibres under the SLS design loads. Beams of compact section must therefore be checked at the SLS, but in that case a linear elastic stress distributions must be used, i.e. the beams must be treated in the same manner as non-compact beams. The considerations are generally similar to those listed under 7.2. However, different values of γf, γm and γf3 must be used.
7.4
Fatigue If a stress or range of stress is applied repetitively to an element of a structure, it may fail prematurely by fatigue at a stress below (and sometimes well below) its static strength. The methods used for calculating fatigue endurance are contained in BS 5400-10 and are beyond the scope of this document.
7.5
Brittle fracture To avoid brittle fracture at low temperature, steel material needs to have sufficient ‘notch toughness’. This is achieved by specifying a suitable grade of steel; suitable grades for most steel bridges are available in BS EN 10025. The selection of the appropriate grade is outside the scope of this document
8
SHAPE LIMITATIONS
8.1
General The capacity of a section can be limited by local buckling of the flange or web in compression or shear, or by local shear lag across the width of a tension flange. Local buckling is mainly of concern in thin-walled sections and occurs when the elements of the member are sufficiently slender for short wavelength compression buckles to develop before yield stress is reached in the element; the buckles may form at right angles to an applied direct compression, or across the diagonal of an element subjected to shear. Such effects are guarded against by limiting the proportions of the elements (plates and stiffeners) of the cross section. Two classes of section are distinguished: (a) non-compact sections, where the stress distribution is assumed linear and proportional to strain and the idealised moment capacity is reached on the first attainment of yield stress on the cross section. © The Steel Construction Institute
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(b) compact sections, where the stress distribution is given by the rectangular block shown in Figure 8.1. Since considerable plastic yielding is necessary to develop this distribution, the shape limitations are more stringent than those for non-compact sections.
Simplified rectangular stress block Strain
Stress
Bending stresses and strains in a compact section
Figure 8.1
It is emphasised that the use of the plastic modulus for compact sections does not imply that the plastic global analysis can be employed. In fact, it is specifically excluded by BS 5400-3. The use of a rectangular stress block does not imply redistribution of moment along the member. The classification of a section depends on the width to thickness ratio of elements of the cross-section; hence the ratios presented in the following sections are used to determine whether or not a section is compact. bfo tfo yc
tfo
dw
Figure 8.2
Parameters relevant to classification of cross section
Note: Strictly, the overall depth of the web should be measured in its plane and taken clear of root fillets for rolled sections and welds or flange angles for fabricated sections, but for simplicity it may be taken as the distance between the flanges. The notation generally used for evaluating shape parameters is given in Figure 8.3 and Figure 8.4. 8.2
Shape limitation for non-compact sections The following criteria need to be satisfied: Outstand in compression For any section: bfo/tfo should not exceed 12
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355 σ yf
(8.1)
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
where bfo
is the width of the outstand measured from the edge to the toe of a root fillet of a rolled section or in the case of welded construction, to the surface of the supporting part of the member.
tfo
is the mean thickness of the outstand
σyf
is the nominal yield stress of the flange material
Outstand in tension For robustness, all flange outstands should be such that: bfo/tfo is not greater than 20
(8.2)
Webs There are no restrictions on web proportions in non-compact sections, but there are penalties in the strength of the webs if they are very slender (see Section 14.2) 8.3
Shape limitations for compact sections Webs The depth of the web should not exceed: 34 t w m
355 when m does not exceed 0.5 σ yw
(8.3)
374t w 355 when m does exceed 0.5 (13m − 1) σ yw
(8.4)
where m
is the ratio of the depth of web on the compressive side of the web plate (i.e. m = yc/dw)
σyw
is the nominal yield stress of web material.
tw
is thickness of the web plate
Compression flange outstands The projection of the compressive flange outstand in a compact section should be such that: bfo does not exceed 7tfo 8.4
355 σ yf
(8.5)
Openings Openings in webs or compression flanges should not be made in a section that is designed as compact. Any opening in webs or compression flanges should be framed and the stiffened sections designed for local load effects.
8.5
Stiffeners to webs Stiffeners to webs should be in accordance with the following: © The Steel Construction Institute
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Flat stiffeners The proportions should be such that: hs ts
σy
does not exceed 10
355
(8.6)
Angle stiffeners Angle stiffeners should be proportioned such that (a) bs does not exceed hs bs ts
(b)
σ ys
does not exceed 11
355
(8.7) (8.8)
Tee stiffeners Tee stiffeners should be proportioned such that (a)
bso tso
(b)
ds ts
σ ys 355
does not exceed 10
σ ys + σ a 355
does not exceed 41
(8.9)
(8.10)
where σys
is the nominal yield stress of stiffener
σa
is the longitudinal stress (positive when compressive) for the ultimate limit state at the centroid of the effective section of stiffener.
Figure 8.3
Geometric notations for beams
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
Figure 8.4
Geometric notations for beams (continued)
9
EFFECTIVE SECTION
9.1
Effective section for global analysis Gross section properties may be used for global analysis.
9.2
Effective section for bending stress analysis The elastic or plastic modulus of a section should be determined taking the account of the following: (a) deduction for holes. (b) effective web thickness. No allowance should be made for shear lag, as noted in 6.3. © The Steel Construction Institute
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9.3
Deduction for holes Holes should be deducted whether the longitudinal stress is tensile or compressive.
9.4
Effective web thickness The effective web thickness, twe, to be used in determination of longitudinal stresses is as follows: Table 9.1
Effective web thickness
Limits σ yw
yc tw
yc tw
≤ 68
355
y 68 < c tw
σ yw 355 σ yw 355
Effective web thickness, twe
< 228
tw 1.425 − 0.00625 y c tw
≥ 228
σ yw tw 355
(9.1)
0
where yc
is the depth of web measured in its plane from the elastic neutral axis of the gross section of the beam to the compressive edge of the web
σyw
is the nominal yield stress of web material.
10
EVALUATION OF STRESSES
10.1
Longitudinal stresses Longitudinal stresses due to bending, and to axial force if any, should be calculated on the basis of an effective section in accordance with Section 8.
10.2
Shear stresses The shear flow in a web due to applied shear force may be taken as the average value throughout the net depth of the web, equal to (dw - hh). where: dw
is the full depth of a rolled section or a depth of a web plate between flanges in a fabricated section both as shown in Figure 3.
hh
is the height of any hole in the section.
11
EFFECTIVE LENGTH FOR LATERAL TORSIONAL BUCKLING
11.1
General Lateral-torsional buckling is a phenomenon that can occur in a beam that is unrestrained transversely and can occur with the beam subjected to bending moments below the idealised capacity of the cross section. Figure 11.1 shows a simply supported beam having a deep I section and loaded vertically, thus
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
producing bending about its major axis. It may also move laterally and twist, as shown. The condition for buckling is generally expressed in terms of a critical value of either the maximum bending moment or the compressive bending stress. The buckling resistance depends on several geometric parameters – the beam length, support conditions and pattern of loading, the lateral stiffness and the torsional properties and warping resistance of the section.
Figure 11.1 Lateral torsional buckling of a simply supported beam The effects of lateral-torsional buckling are allowed for by determining the effective length of the beam (11.2 to 11.4), hence its slenderness (12) and from this the limiting moment of resistance (13) to be used in the expressions for the bending resistance (14.1). 11.2
Beams with intermediate lateral restraints When a compression flange of a beam is provided with effective discrete lateral restraints in accordance with Section 15.1, the effective length of beam for lateral buckling should be taken as the greatest distance between such points of lateral restraint or between a restraint and a support.
11.3
Beams (other than cantilevers) without intermediate lateral restraints When there is no intermediate lateral restraint to a compression flange, le should be taken as: le = k1k2keL
(11.1)
where: le
is the effective length of the beam
L
is the span of the beam (i.e. between lateral restraints at supports)
k1
=1.0 if the compression flange is free to rotate in plan at the points of support; or = 0.85 if the compression flange is partially restrained against rotation in plan at the points of support; or = 0.7 if the compression flange is fully restrained against rotation in plan at the points of support.
k2
= 1.0 or = 1.2 if the load is applied to the top flange and both the flange and the load are free to move laterally.
ke
may be taken as 1.0, provided that the stiffness of the restraint to the beam at each support is in accordance with Section 16.3
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Ic 11.4
is the second moment of area of the compression flange about its centroidal axis parallel to the web of the beam
Beams continuously restrained by deck When restraint to the compression flange is provided by a deck connected to the flange over the length of the beam, in accordance with Section 15.2, le may be taken as zero.
12
SLENDERNESS OF BEAMS
12.1
General The slenderness parameter λLT required for the calculation of the limiting moment of resistance (see Section 13) should be determined for all beams in accordance with Section 12.2 or section 12.3 using the effective length for lateral torsional buckling obtained from Section 11.
12.2
Uniform I, Channel, Tee or angle sections The value of λLT for a beam of I, channel, tee or angle section, uniform between points of effective lateral restraint to the compression flange and bending about its x-x axis (see Figure 8.3 and Figure 8.4 for definition of axes) should be taken as: λLT =
le ηv ry
(12.1)
where le
is the effective length determined in accordance with Section 11
ry
is the radius of gyration of the whole beam section about its y-y axis
η
is a factor which depends on the distribution of bending moment along the beam which may be conservatively taken as 1.0
ν
is dependent upon the shape of the beam, and may be conservatively taken as 1.0 for symmetric I and channel sections. Accurate values may be obtained from Table 12.1 using the parameters: λF
=
l e tf ry D
and
i
=
I Ic + It
tf
is the mean thickness of the two flanges of an I or channel section, or the mean thickness of the table of tee or leg of an angle section.
D
is the overall depth of the cross section.
Ic, It are the second moments of area of the compression and tension flange, respectively about their y-y axes. For beams with Ic = It or with λF ≥ 8, λLT may be conservatively taken as
© The Steel Construction Institute RT877 Version 01 (June 2001)
le ry
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Table 12.1 Slenderness Factor v for Beams Of Uniform Section i λf
1.0
0.8
t 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0
0.6 c
c
0.791 0.784 0.764 0.737 0.708 0.679 0.651 0.626 0.602 0.581 0.562 0.544 0.528 0.512 0.499 0.486 0.474 0.463 0.452 0.442 0.433
0.5 c
0.932 0.922 0.895 0.859 0.818 0.778 0.740 0.705 0.674 0.645 0.620 0.597 0.576 0.557 0.539 0.523 0.509 0.495 0.482 0.471 0.460
0.3
1.000 0.988 0.956 0.912 0.864 0.817 0.774 0.734 0.699 0.668 0.639 0.614 0.591 0.571 0.552 0.535 0.519 0.505 0.492 0.479 0.468
0.2
0.1
c
0 c
t
t
t 0.842 0.834 0.813 0.784 0.752 0.719 0.688 0.660 0.633 0.609 0.587 0.567 0.549 0.533 0.517 0.503 0.490 0.478 0.466 0.456 0.446
0.4
1.119 1.102 1.057 0.998 0.936 0.878 0.824 0.777 0.736 0.699 0.667 0.639 0.613 0.590 0.570 0.551 0.534 0.518 0.504 0.491 0.478
1.291 1.266 1.200 1.116 1.031 0.954 0.887 0.829 0.779 0.736 0.699 0.666 0.638 0.612 0.589 0.568 0.550 0.533 0.517 0.503 0.489
1.582 1.535 1.421 1.287 1.162 1.055 0.966 0.892 0.831 0.780 0.736 0.698 0.665 0.636 0.611 0.588 0.567 0.548 0.531 0.516 0.502
t 2.237 2.110 1.840 1.573 1.359 1.196 1.071 0.973 0.895 0.832 0.779 0.735 0.697 0.664 0.635 0.609 0.586 0.566 0.547 0.530 0.515
∞ 6.364 3.237 2.214 1.711 1.415 1.219 1.080 0.977 0.896 0.831 0.778 0.733 0.695 0.662 0.633 0.607 0.585 0.564 0.546 0.529
NOTE 1 Configurations that give values of v greater than 2.0 should not be used in simplified design
NOTATION for clause 13 The moduli of the cross-section are required in the application of various clauses which follow. The derivation of these should be based on the following: Zpe
is the plastic modulus of the effective section derived in accordance with Section 9.2, and is defined as Mpe/σyc
Mpe
is the plastic moment of resistance of the effective cross-section (derived in accordance with Section 9.2) and based on rectangular stress blocks (see Figure 8.1) of intensity equal to the strength of the elements. In the case of elements in structural steel, the strength should be taken as the nominal yield stress of the elements. In the case of concrete flanges in compression, the area of reinforcement should be ignored and the strength should be taken as 0.4fcuγm . In the case of concrete flanges in tension, the area of concrete should be ignored and the strength of the reinforcement taken as 0.87fyγm NOTE In the above, γm is the value for structural steel (see Section 3.2) and is applied to the concrete or reinforcement strengths to achieve a value of Mpe that is unfactored.
fcu
is the concrete cube strength (see simplified BS 5400-5)
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fy
is the characteristic strength of the reinforcement (see simplified BS 5400-5)
σyc
is the nominal yield stress for the compression flange of the steel section
Zxc, Zxt are the elastic moduli of the section with respect to the extreme compression and tension fibres respectively, based on the effective section Zxw
is the minimum elastic modulus of the section with respect to the web, based on the effective section.
NOTE: For composite sections, Zxc, Zxt and Zxw should be based on the transformed section. See simplified BS 5400-5.
13
LIMITING MOMENT OF RESISTANCE The limiting moment of resistance is the maximum bending moment that can be developed in the beam. It is limited either by the strength of the steel material (in compression and in tension) or by lateral torsional buckling of the beam (which in turn depends partly on the yield strength of the material).
13.1
General The limiting moment of resistance MR should be determined from the basic bending strength of the cross section, Mult according to the value of the modified slenderness: σ yc M ult ëLT M 355 pe
(13.1)
where λLT
is the slenderness parameter derived in accordance with Section 12
σyc
is the nominal yield stress of the compression flange
Mult
is the moment of resistance of the cross section if lateral torsional buckling is prevented, that is: Mult = Mpe for compact sections Mult = the least of Zxcσyc, Zxtσyt or Zxwσyw for non-compact sections
The inclusion of the multiplier Mult/Mpe in the modified slenderness allows the same relationship to be used for both compact and non-compact sections. Essentially, it allows a smaller value of slenderness to be used as ‘input’ to the buckling curve when the section is non-compact than when it is compact. The result is (for non-compact sections) a slightly higher value of the ratio of limiting moment of resistance to cross section bending resistance, although that cross section resistance is of course less for a section that is non-compact than it would be if it were deemed to be compact. The limiting moment of resistance should be determined from Figure 13.1
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1.10 1.00 0.90 0.80
M R/M ult
0.70 0.60 0.50 Other sections
0.40 0.30
Fabricated by welding
0.20 0.10 0.00 0
50
100 λ
150
200
250
300
350
0.5 LT [(σ y/355)(M ult/M pe)]
Figure 13.1 Limiting moment of resistance MR
14
STRENGTH OF BEAMS
14.1
Bending resistance As stated previously, all sections should be designed for the ULS. The smaller flange of unsymmetric beams designed as compact should additionally be checked for the SLS, treating the beams as non-compact. Compact and non-compact sections The bending resistance MD of a beam should be taken as: MD =
MR γ m γ f3
(14.1)
where MR is the limiting moment of resistance given by Section 13. The total design bending moment (the effects due to factored loads) at a particular section should not exceed the bending resistance MD. 14.2
Resistance of beams built in stages Where a composite beam is built in stages (see Part C of this document), the total stresses at extreme fibres of a cross section should also be checked. © The Steel Construction Institute
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For a non-compact beam, the total stresses at ULS (due to factored loads) should not exceed: σy
in the structural steel. See Part C for the corresponding limiting γ m γ f3 stresses in reinforcement and concrete. For a compact beam, the total stresses at SLS (due to factored loads) should not exceed σyf. See Part C for the corresponding limiting stresses in reinforcement and concrete. Note: Compact beams need to be checked at SLS because redistribution of stresses is allowed at ULS but not at SLS. There is no need to check noncompact beams at SLS because the ULS requirements are more onerous. If stage construction is not considered in simplified design, there is no need to check the stresses at extreme fibres. 14.3
Shear resistance under pure shear The shear resistance of a web of a beam with transverse stiffeners at supports and with or without intermediate transverse stiffeners is given by: t (d − hh ) τl VD = w w γ m γ f3
(14.2)
where: tw
is the thickness of web
dw
= D, the overall depth of a rolled section or is the depth of the web measured clear between flanges of a fabricated section.
hh
is the height of the largest hole or cut-out if any, within the panel being considered, but in the case of beams without intermediate transverse stiffeners, the hole or cut-out may be ignored at sections further than 1.5hh longitudinally from the edge of the hole. (Note hh = 0 when there is no opening in the web).
τl
is the limiting shear strength of the web panel determined from Figure 14.1 to Figure 14.5 as appropriate (see note below).
τ
=
φ
=
a
is the clear length of panel between transverse stiffeners
mfw
=
σ yw 3
a , the aspect ratio of the panel dw σ yf bfe t f 2 2σ yw d we 2 t w
taking the smaller value at the top or bottom flange
and ignoring any concrete (mfw may be conservatively taken as zero) bfe
is the smaller of:
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(a) 10tf
355 σ yf
or
(14.5)
(b) the distance from the mid plane of the web to the nearer edge of the flange where tf
is the flange plate thickness
σyf
is the nominal yield stress of flange.
Note: For shallow webs,
d we tw
σ yw 355
will not be greater than 54 and then
τl = τy. For deeper webs, the shear strength is limited by buckling of the web, though it is also enhanced by tension field action. The contribution from tension field action depends on the aspect ratio of the web panel and the stiffening effect of the flanges (expressed by the parameter mfw). See further discussion in Section 14.5.
Figure 14.1 Limiting shear strength τl for mfw = 0
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Figure 14.2 Limiting shear strength τl for mfw = 0.010
Figure 14.3 Limiting shear strength τl for mfw =0.020
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Figure 14.4 Limiting shear strength τl for mfw =0.060
Figure 14.5 Limiting shear strength τl for mfw =0.120
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14.4
Combined bending and shear
Shear force
The values of the maximum moment within the panel, M, and the maximum shear force in the panel, V, should lie within the boundary shown on Figure 14.6. [NB these values are not necessarily at the same cross section, they are just the maximum values within the panel length.]
VD VR
VR 2
Mf 2
Mf MD Bending moment
Figure 14.6 Limiting interaction between moment and shear resistances In the diagram: VD
is the shear resistance of the panel from 14.2.
VR
is the value of VD obtained by taking mfw = 0 when applying 14.2.
MD
is the bending resistance of the cross section from 14.1.
Mf
is the bending resistance of the cross section ignoring the contribution from the web, and is calculated as: Mf
=
Ff d f but not greater than MD γ m γ f3
df
is the distance between the centroids of the flanges.
Ff
= σf Afe, the limiting force in the flange, to be taken as the lower value for the two flanges.
σf
= (for the tension flange) σyt, the nominal yield stress, or = (for the compression flange) the lesser of σyc the nominal yield stress and MR/Zxc
MR
is as defined in Section 13
Afe
is the area of the appropriate tension or compression flange section.
For webs with transverse stiffeners at the supports only, the above provisions should be applied at all sections, with V and M defined as follows: V
is the shear force at any section of the beam
M
is the coexistent bending moment at the same section of the beam.
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It can be seen that following simplifications may be used:
Shear force
(a) If VD = VR (which is true, amongst other sections, to all rolled I and channel sections of grade S275 and S355) then the interaction diagram above is simplified to that shown in Figure 14.7. VD= VR
VD/2= VR/2
Mf
MD
Bending moment
Figure 14.7 Interaction diagram when mfw = 0 (b) Bending moments up to a value MD can be resisted by any beam if the shear force V is less than 0.5VR. (c) Shear forces up to a value VD can be resisted by any beam if the bending moment M is less than Mf. 14.5 14.6
Discussion of tension field action Figure 14.8 shows the effects of shear in a rectangular plate whose edges are subjected to a shear stress. A square element whose edges are orientated at 45o to the plate edge experiences tensile stresses on two opposing edges and compressive stresses on the other two, as shown. On a thin web these compressive stresses would induce local buckling resulting in elongated waves orientated diagonally as indicated in the second part of the Figure. As the applied shear stress is increased beyond the critical shear stress (τcr) the plate buckles elastically and retains little stiffness in the direction in which the compressive component acts. However, the inclined tensile stress is still resisted fully by the plate. The inclined buckles would become progressively narrower and the plate acts like a series of bars in the tension direction, developing a so called “tension field”. Further increase of applied stress causes plastic deformation in a part of the tension field, which lines up more closely with the plate diagonal as shown in the third element of the Figure.
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Stresses on square element
Elastic buckling of web panel
Development of tension field
Figure 14.8 Web Panels in shear : buckling and tension field action The introduction of transverse web stiffeners increases the shear-carrying capacity in two ways. First, the shear buckling resistance of the web is increased, and second the stiffeners participate in a truss-like action (see Figure 14.9) that is able to carry loads considerably in excess of the load at which web buckling occurs. Tension field action is enhanced by the local bending resistance of the flanges, which provide boundary restrain at the ‘anchorage’ of the tension band (this contribution is recognised by the use of the mfw parameter).
Figure 14.9 Tension field action in a beam with transverse stiffeners
15
RESTRAINTS TO COMPRESSION FLANGES
15.1
Elements Providing Effective Intermediate Discrete Lateral Restraints One means to improve the resistance to lateral torsional buckling is to provide intermediate restraints to the compression flange. The effective length is then determined in accordance with Section 11.2. Such restraints need to be sufficiently stiff and strong that they act as effective restraints. A typical restraint system used during construction is triangulated plan bracing to the top flange; this stabilises the compression flange when the beam is carrying the weight of the wet concrete. In simplified design, this design case will probably not be checked. Another use of intermediate restraints is triangulated cross bracing between beams a little way into the span from an intermediate support of a continuous bridge. The plan stiffness of the deck slab plus the triangulated cross bracing restrains the bottom (compression) flange in these regions. Where intermediate restraint is provided by bracing, the bracing members should be so arranged and proportioned that a restraining lateral shear force F plus the effects of any wind or other lateral forces can be resisted. The force F is given by: F=
ΣPf 80
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(15.1)
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where: ΣPf
is the sum of the greatest forces in two of the compression flanges of the beams connected by the bracing at the section under consideration.
Triangulated bracing is sufficiently stiff to provide the restraint and its stiffness need not be checked in simplified design 15.2
Continuous restraint provided by deck When a deck is continuously connected to the main beams at the level of the compression flange, the deck and its connections should be capable of withstanding a lateral restraining force equal to 2½% of the force in the flange at the point of maximum bending moment. This lateral restraining force should be uniformly distributed along the span of the main beams.
16
RESTRAINTS AT SUPPORTS
16.1
General All beams should be restrained against rotation about their longitudinal axes at each support. The restraint should be able to resist the force given by 16.2 and the stiffness of the restraint should be in accordance with 16.3.
16.2
Restraining forces The restraint system at a support should be able to resist a force F, as given in 15.1, in conjunction with wind and any other lateral load, acting at the level of the top flange of the beam.
16.3
Stiffness A triangulated bracing system or a full-depth cross beam at a support provides a sufficiently stiff restraint to a beam. If any other form of restrain is provided (such as a simple crossbeam connected to bearing support stiffeners), it should be sufficiently stiff that the lateral deflection of the top flange relative to the bottom flange does not exceed le3/40EIc when unit forces act laterally in opposition directions at the level of the flanges. In determining this deflection, unit forces should be applied to both beams when they are joined by a common member.
17
TRANSVERSE WEB STIFFENERS OTHER THAN AT SUPPORTS
17.1
General Intermediate transverse web stiffeners are provided to enhance the shear capacity of webs. The usual form of stiffener is a simple flat (complying with the shape limitations of Section 8.5) welded to the face of the web. This effectively creates a T-shaped beam over the depth of the web. The neutral axis of this T-section is outside the web, so axial force from tension field action, which is in the plane of the web, causes both axial and bending stresses in the effective stiffener section. For simple design, only the vertical stress in the web part of the stiffener needs to checked. © The Steel Construction Institute
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17.2
Effective section of transverse web stiffener The effective stiffener section should comprise the stiffener, along with a portion of web plate of width bwe on each side of the stiffener connection centre line, taken as the lesser of: 16tw or
a 2
where:
17.3
tw
is the thickness of the web plate
a
is the spacing of transverse web stiffeners.
Loading on transverse web stiffeners Effects to be Considered A transverse stiffener should be designed to resist the following load effects, where these are present: (a) axial force and bending due to tension field action (acting in the plane of the web). (b) axial force representing the destabilising effect of the web Axial force Fts due to tension field action The axial force due to tension field action is given by: Ftw = (τ - τo) twdw (to be taken as zero if τ < τo) Where τ
(16.1)
is the average shear stress
d 2 t 2 σ d τo = 3.6E 1 + w w 1 − 1 w 2.9 E t w a d w t when σ1 < 2.9E w dw
2
2
t τo = 0 when σ1 ≥ 2.9E w dw
2
σ1
is the average longitudinal stress in the web panel, taken positive when compressive
a
is the panel length
dw
is the depth
tw
is the web thickness
The bending moment on the effective stiffener section is given by the value of the force Ftw multiplied by the distance of the neutral axis of the effective stiffener section from the mid-thickness of the web. Axial force representing the destabilising influence of the web In order to resist buckling of the web plate the effective stiffener section should be assumed to carry, along its centroidal axis, a compressive force Fwi given by: © The Steel Construction Institute RT877 Version 01 (June 2001)
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Fwi =
l 2s t w ksσ R a
where ls
= dw
a, tw are as defined above ks
is obtained from Figure 17.1 using the slenderness parameter l determined from: λ =
rse
17.4
ls rse
σ ys 355
is the radius of gyration of the effective stiffener section about the centroidal axis X-X (see Figure 8.4); σ τ R + σ1 + b 6
σR
=
τR
is equal to τ or τo whichever is less
σ1
is the average longitudinal stress in the web, taken as a positive when compressive, calculated without any redistribution to the flanges
σb
is the maximum value of the stress in the web due to bending
σys
is the nominal yield stress of the stiffener material
Strength of transverse web stiffeners Yielding of Stiffeners The maximum vertical stress in the web due to the relevant forces listed above should not exceed: σ ls γ m γ f3
σls
(16.3)
is determined from using the value of slenderness parameter λ determined from Figure 17.1.
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1.0 0.9 0.8 0.7 0.6
σls/σys
σ ys or ks σ l s/σ 0.5 0.4 0.3 0.2
ks
0.1 0.0 0
50
100
150
200
250
300
0.5 λ = l /rse(σ σ ys/355)
Figure 17.1 Parameters for the design of web stiffeners
18
LOAD BEARING SUPPORT STIFFENERS
18.1
General Webs of plate girders and rolled beams should be provided with a system of load bearing stiffeners at each support position. The stiffeners should be symmetrical about the web. The ends of the stiffener should be closely fitted or adequately connected to both flanges.
18.2
Effective section for bearing stiffeners Single leg stiffener The effective stiffener section should be taken to comprise the stiffener with a portion of web plate on each side having a width not exceeding the following: (a) half the spacing of transverse stiffeners. (b) the distance to the transverse edge of the web plate at the end of a beam. (c) 16tw, where tw is the thickness of the web plate. Multi-leg stiffeners The effective stiffener section should be taken to comprise the stiffeners, the web plate between the two outer legs and a portion of web plate not exceeding the widths given in Section 16.2 on the outer sides of the outer legs.
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If the spacing of the legs of adjacent stiffeners is greater than 25tw, the legs should be treated as independent stiffeners. 18.3
Load on bearing stiffeners A stiffener should be designed to resist the following load effects: (a) axial force due to the reaction from the bearing (b) bending arising from eccentricity of the bearing reaction. The bearing reaction should be taken to be eccentric from the centroid of the effective bearing stiffener by 10 mm transversely and longitudinally due to installation tolerances. Eccentricity due to thermal effects may be neglected in simplified design.
18.4
Strength of bearing stiffeners Yielding of stiffener The maximum stress in the stiffener itself, due to relevant load effects, calculated on the basis of the effective section, should not exceed: σys γ m γ f3 Buckling of effective stiffener section The effective stiffener section should be such that, under axial force P: P 1 ≤ Ase σ ls γ m γ f3
(17.1)
where Ase
is the area of the effective stiffener section
σls
is as defined for intermediate transverse stiffeners.
19
WELDED CONNECTIONS
19.1
General Welding offers a means of making continuous, load-bearing metallic joints between the components of a structure. All welded joints can be typified by or made up from four configurations. These are: 1.
In-line butt
2.
Tee
3.
Lap
4.
Corner
Fillet welds are generally used for configurations 2 and 3.
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19.2
Butt welds For simplified design, butt welds should be full strength butt welds. A full strength butt weld achieves full penetration through the thickness of the welded material.
19.3
Fillet welds A fillet weld is applied outside the surface profile of plates. Thus, the joint may be formed either by the overlapping of members of by the use of secondary joint material. End returns A fillet weld should be returned continuously around the corner of the end or the side of a part, for a length beyond the corner of not less than twice the leg length of the weld. End connections by side fillets If the end of a part is connected by side fillet welds only, both sides of the part should be welded and, where possible, the length of weld on each side should be not less than the distance between the welds ‘b’ on the two sides, nor less than four times the thickness of the thinnest part connected. Where the distance between the welds exceeds 16 times the thickness of the thinnest part connected, intermediate plug or slot welds should be provided to prevent separation. End connections by transverse welds The overlap between the connected parts should not be less than four times the thickness of the thinnest part and the parts should be connected by two transverse lines of welds. Where the distance between the welds exceeds 16 times the thinnest part connected, intermediate plug or slot welds should be provided to prevent separation.
Figure 19.1 End connections by fillet welds
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Effective throat of a fillet weld Effective throat of a fillet weld g is the height of a triangle that can be inscribed within the weld and measured perpendicular to its outer side (see Figure 18.2). For fillet welds between faces at right angles the effective throat g is equal to the leg length divided by 2 .
Figure 19.2 Effective throat of a fillet weld Effective area of a fillet weld The effective area of a fillet weld is its effective throat dimension multiplied by its length. Capacity of a fillet weld The stress in a weld, based on the resultant of all shear forces acting on any part of it, and the effective area of such part, should not exceed the capacity τD given by: τD =
(σ y + 455) 2 3 γ m γ f3
where: σy
is the nominal yield stress of the weaker part joined.
20
BOLTED CONNECTIONS
20.1
General Bolted connections in bridges are made using high strength friction grip bolts. These bolts are tightened in such a way that a reliable preload is is achieved in the bolt. This preload allows shear to be transferred between the interfaces (faying surfaces) by friction – i.e. the surfaces do not slip, one relative to another, until the frictional resistance has been overcome. Such bolts are used to ensure that there is no movement (slip) at a bolted joint under normal (i.e. serviceability limit state) conditions. It is acceptable to allow the bolts to slip at the higher ULS loads, at which time they act in bearing and shear (this is usually significantly greater than the ULS friction capacity).
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For simplified design in undergraduate projects, it is not expected that connections will need to be designed. However, for completeness and for the occasional situation where connection design may be appropriate, the following rules are given, together with typical design values. It should be noted that the requirement for no slip at SLS will normally be more onerous than for bearing/shear resistance at ULS. Girders are usually connected using ‘double cover plates’. See Figure 20.1. These are additional plates, one on each side of the element to be spliced. The bolts are then in ‘double shear’. Bracing is usually connected simply by lapping, in which case the bolts are in single shear.
Figure 20.1 Girder splice, showing cover plates and shear studs 20.2
Friction capacity The friction capacity of a HSFG bolt is given by: PD =
Fv µN γ m γ f3
where Fv
is the prestress load
µ
is the slip factor
N
is the number of friction interfaces
Typical friction values at SLS, for M24 and M27 bolts to BS 4395-1, and for shot blasted steel surfaces, are given in Table 20.1. Table 20.1 Friction values of HSFG bolted connections SLS capacity (KN) Double shear
Single shear
M24
173
86
M27
195
98
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20.3
Shear capacity of HSFG bolts The shear capacity of a HSFG bolt acting in bearing/shear is given by: PD =
Aeqτ n γ m γ f3
where Aeq
is the sectional area of the bolt
τ
is the shear strength ( shear yield stress) of the bolt
n
is the number of shear planes
Typical shear capacities, for M24 and M27 bolts, to BS 4395-1, in normal clearance holes, are given in Table 20.2. Table 20.2 Shear values of HSFG bolted connections ULS capacity (kN) Double shear
Single shear
M24
262
131
M27
340
170
The above values apply where the shear planes pass through the unthreaded portion of the bolt, which is the usual design condition.
It should be noted that, for the thicknesses of plates that are normally used in bridges, the shear capacity is less than the bearing capacity. Consequently, limitations for bearing capacity are not given in this simplified document. 20.4
Cover plates For simplified design, cover plates should be provided on both faces of the part being connected. The cover plates should be at least half as thick as the element joined and not less than 8 mm thick.
20.5
Spacing of bolts There are limitations on the maximum and minimum spacings of bolts. The maximum spacing depends on the thickness of the outer cover plates. The minimum spacing depends on the diameter of the bolt. For bolts arranged in an orthogonal pattern (lines of bolts parallel to the edges of the connected parts) a simplified table of maximum spacing is given in Table 20.3 Table 20.3 Maximum spacing of bolts Cover plate (mm)
Maximum spacing (mm)
8
96
10
120
12
144
15
160
20
180
The minimum spacing is 60 mm for M24 bolts and 68 mm for M27 bolts.
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PART B - Simplified version of the bridge loading specification, BS 5400-2:1978 (For the use of Undergraduate Students) CONTENTS Page No. 1
SCOPE
41
2
DEFINITIONS
41
3
LOADS
41
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1
SCOPE This simplified version of the bridge loading specification gives 1oadings to be applied to the design of highway bridges, using the design procedure recommended in the simplified version of the steel bridge code. It is based on Part 2 of BS 5400. Only vertical loadings are included in this version. Horizontal loads (wind, traction/braking etc.) and other loads such as temperature, which are given in the full specification, are excluded.
2
DEFINITIONS
2.1
Loads Dead Loads are the weights of the parts of the structure that are structural elements. Superimposed dead loads are the weights of all materials on the structure that are not structural elements - road surfacing, parapets etc. Live loads are the vertical loads due to the traffic.
2.2
Carriageway and lanes The carriageway is the running surface of the road, including all traffic lanes, hard shoulders, and white line markings. Where there are raised kerbs, it is the width between kerbs. In the absence of kerbs, it is the width between safety barriers less a clearance of 0.6 metres in front of each barrier. Traffic lanes are the lanes marked on the running surface. They have a maximum width of 3.65 metres.
3
LOADS
3.1
Design loads and load factors The load values given below are nominal loads. These are to be multiplied by appropriate 1oad factors γfL to derive the design loads. In general, a low factor is applied to loads which are known accurately, such as the weight of steel, and a higher factor to loads which are less certain, such as live loads. The highest load factor is applied to the weight of surfacing (superimposed dead load) to allow for the possible unintended overlay of additional material in the future. Factors to be applied at the two limit states are given in Tables 3.1 and 3.2. The code recognises that when loads are in combination, particularly combinations involving wind or HB loads, they are unlikely to exceed their specified values by large amounts simultaneously; hence, load factors for such combination are reduced.
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Table 3.1
Load factors at ultimate limit state Load
Dead load (steel) Dead load (concrete) Superimposed dead load (surfacing)
γfL at ultimate limit state Combination 1 2 1.05 1.05 1.15 1.15 1.75 1.75
Wind with Dead + superimposed dead with Dead + superimposed Dead + Live Vertical live load HA alone HA with HB or HB alone
Table 3.2
1.5 1.3
1.25 1.1
Load factors at serviceability limit state Load
Dead (steel) Dead load (structural concrete) Superimposed dead load (surfacing) Wind load with Dead + superimposed dead with Dead + superimposed Dead + Live Vertical live load HA alone HA with HB or HB alone
3.2
1.4 1.1
γfL at serviceability limit state Combination 1 2 1.0 1.0 1.0 1.0 1.2 1.2 1.0 1.0 1.2 1.1
1.0 1.0
Dead loads The weight of dead load materials may be based on the following specific weights: Steel 77 kN/m3 Concrete
3.3
24 kN/m3
Superimposed dead loads The weight of a 100 mm thick layer of surfacing may be taken as 2.2 kN/m2. The weight of a parapet may be taken as 0.5 kN/m.
3.4
HA live loads HA loading consists of a uniformly distributed load (UDL) and a knife edge load (KEL). The value of the UDL may be taken as 30 kN/m per metre of traffic lane spread uniformly over the lane. The UDL is to be applied to a loaded length corresponding to either the positive or the negative portion of an influence diagram relevant to the effects being considered. This means that, for example, in a two-span beam, only one span
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Structural steel design for undergraduates - Design to BS 5400 Part B - Simplified version of the loading specification
would be loaded for determination of worst moment in a span but two spans would be loaded to determine the worst reaction at the centre support. The value of the KEL may be taken as 120 kN, spread along a line across the width of the lane. It is to be applied where it will cause maximum moment or shear at the position in the bridge which is being checked. 3.5
HB live loads The HB vehicle represents an abnormal vehicle and consists of a group of sixteen identical wheel loads arranged as shown in Figure 1. A ‘unit’ of loading corresponds to load on four axles and should be taken as equal to 10 kN per axle; each axle has four equally loaded wheels. Either 30, 37.5 or 45 units of HB loading are normally specified, corresponding to total vehicle loads of 1200, 1500 or 1800 kN.
Figure 3.1
Dimensions of HB vehicle
The HB vehicle replaces one lane of HA loading and should be positioned for worst effect. For the purposes of a simple design, it is suggested that HB loading may be ignored. 3.6
Multiple lanes Full HA loading should be applied in up to two lanes on the bridge. When there are more than two lanes, the extra lanes should be loaded with 60% of HA loading. The choice of which lanes are loaded with full HA and which are loaded with 60% HA should be made such that the maximum bending moment or shear force is produced in the part of the structure which is being designed.
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Structural steel design for undergraduates - Design to BS 5400 Part A - Simplified version of the steel bridge code
© The Steel Construction Institute
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RT877 Version 01 (June 2001)
Structural steel design for undergraduates - Design to BS 5400 Part C - Simplified version of the composite bridge code
Simplified version of the composite bridge code, BS 5400-5:2000, covering the design of the connections between steel beams and concrete slab (For the use of undergraduate students) CONTENTS Page No. 1
SCOPE
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2
SYMBOLS
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3
MATERIAL PROPERTIES
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4
ANALYSIS
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5
DESIGN RESISTANCE
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© The Steel Construction Institute RT877 Version 01 (June 2001)
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Structural steel design for undergraduates - Design to BS 5400 Part C - Simplified version of the composite bridge code
© The Steel Construction Institute
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RT877 Version 01 (June 2001)
Structural steel design for undergraduates - Design to BS 5400 Part C - Simplified version of the composite bridge code
1
SCOPE This simplified version of the composite bridge code provides supplementary guidance to the simplified version of the steel bridge code for the treatment of the concrete elements of composite bridges and the interconnection of the steel and concrete elements. It is based on extracts from Part 5 of BS 5400, though it is considerably reduced in extent. Detailed design of the deck slab is excluded.
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SYMBOLS fcu
Characteristic concrete cube strength
fry
Characteristic strength of reinforcement
Pu
Nominal static strength of shear connector
γm
Partial safety factor for strength
σy
Nominal yield stress of the steel beam
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MATERIAL PROPERTIES
3.1
Material properties for concrete It is suggested that a characteristic (cube) strength of concrete of 40 N/mm2 is assumed. The elastic modulus should then be taken as 31 kN/mm2, giving a modular ratio of 6.6. (Long-term effects should be ignored for the purposes of this simplified approach).
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ANALYSIS
4.1
Global analysis In carrying out the global analysis for the composite structure, the cross sectional properties should be determined using the transformed slab area (i.e. divided by the modular ratio) or, for cracked slabs, using the area of tensile reinforcement. At the ULS, gross section properties should be determined. At SLS allowance should normally be made for shear lag using an effective breadth of slab, but for simplified design, this may be ignored. Uncracked concrete should be used, except for regions adjacent to an intermediate support. Cracked concrete should be assumed for a length of approximately 15% of the span either side of each intermediate support.
4.2
Sectional analysis Gross elastic sectional properties should be used to calculate stresses and shear flows (between steel beam and slab) except when the section is being checked as a compact beam. For compact beams, the calculation of the plastic modulus with an uncracked slab should assume a transformed slab area equal to: Gross area x
0.4 f cu σy γm
© The Steel Construction Institute RT877 Version 01 (June 2001)
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Structural steel design for undergraduates - Design to BS 5400 Part C - Simplified version of the composite bridge code
Where γm is the material factor for steel (= 1.05) Calculation of the plastic modulus with a cracked slab should ignore the concrete and use a transformed area of reinforcement equal to: gross reinforcement area x 4.3
0.87 f ry σy γm
Construction in stages It is usual for composite bridges to be constructed in stages, such that the steel beams initially carry the weight of wet concrete and the composite beams subsequently carry superimposed dead loads and live loads. This form of construction may be evaluated by analysing separately loads on a model with bare steel beams and loads on a model with composite beams. The total effects at any section are then the sum of the two separate results. For simplified design, no distinction is made between long-term and short-term loading on composite beams. For greater simplicity in the design of composite bridges, all the loads may be assumed to be applied to the composite beams.
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DESIGN RESISTANCE
5.1
Bending resistance Non-compact beams For a beam that is treated as non-compact, the stresses at any section are determined by summation of the stress distributions for the two stages. The stresses at any fibre are thus the sum of the values for each stage. At ULS, the total stresses in the steel beam should comply with 14.2 in Part A of this document and the total bending moment should not exceed MD, as given in 14.1 of Part A: Total stresses in the concrete due to longitudinal bending should not exceed 0.5fcu/γf3 at either ULS or SLS and total stresses in the reinforcement should not exceed 0.87fry/γf3 at ULS or 0.75fry/γf3 at SLS. Compact beams For a beam that is treated as compact at ULS, plastic redistribution within the cross section is allowed. For such beams the total bending moment should not exceed MD, as given in 14.1 of Part A:
5.2
Shear resistance Vertical shear should be assumed to be carried entirely on the steel section and should therefore be checked in accordance with Part A of this document. To ensure composite action between the steel beam and concrete, the interface must be able to resist the longitudinal shear flow (calculated on the elastic section using b theory). This is achieved by welding shear studs (see Figure 5.1) onto the top flange of the beam.
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RT877 Version 01 (June 2001)
Structural steel design for undergraduates - Design to BS 5400 Part C - Simplified version of the composite bridge code
Figure 5.1
Stud connector
Studs are provided two or three in a row across the flange at between 100 mm and 300 mm centres. The number and spacing should be sufficient to provide a resistance of at least the calculated shear flow. The design resistance of each shear stud should be taken as Pu/γm. Values of Pu for a 19 mm shear stud of minimum height 100 mm are 100 kN for grade 30 concrete and 109 kN for grade 40 concrete. Values of γm are 1.85 at SLS and 1.40 at UI.S. (The higher value at SLS is to ensure that there is no local crushing in service). 5.3
Slab design Design of the slab itself is considered outside the scope of the simplified bridge design covered by this and the related publications. For illustrative purposes, if needed, the slab reinforcement may be taken as shown in Figure 5.2. Extra longitudinal top reinforcement would be required over intermediate supports. Slab thickness should be taken between 230 mm and 250 mm.
Figure 5.2
Slab reinforcement
Note: In the Design Manual for Roads and Bridges, the covers shown above have been increased by 10 mm, for reasons of improved durability.
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