The Design of Modern Steel Bridges - TEDI

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122 The Design of Modern Steel Bridges steel. The cross-sectional area of the strip adjacent to the weld will then be given by (CA w/sy). The compressive stress s R in the remaining area will have to balance the tensile force in the yielded area and thus will be given by sR ¼ CAw Ag ðCAw=syÞ where A g is the total cross-sectional area of the welded assembly. In Fig. 5.16, A g is equal to (A S þ bt) per panel. Taking an example of a 15 mm plate of yield stress 355 N/mm 2 stiffened by stiffeners of size 200 20 at 300 mm centres, each of which is welded to the plate by two 6 mm size fillet welds deposited simultaneously by a submerged arc-welding machine Figure 5.16 Residual strains and stresses due to welding.
Aw ¼ 40 mm 2 , allowing for a small concavity of the weld surface CAw ¼ 12:5 40 ¼ 500 kN Ag ¼ 300 15 þ 200 20 ¼ 8500 mm 2 sR ¼ 500 000 ¼ 70:5N=mm2 8500 ð500 000=355Þ As compressive and tensile residual stresses in the cross-section balance, residual stresses do not cause any resultant axial force or bending moment on any cross-section. If it is possible for the whole of the cross-section to squash, i.e. yield in compression, then the axial load or bending moment capacity of the cross-section will be unaffected by residual stresses. However, those parts of the cross-section where the residual stress is of the same nature as the applied stress will reach yield stress earlier. For example, a welded box column that can resist 300 N/mm 2 applied compressive stress in a residual-stress-free condition may have some parts of its walls yielding at an applied stress level of 260 N/mm 2 if the welding compressive residual stress in the zone is 40 N/mm 2 . For further applied loading these initially yielded parts of the cross-section will not contribute any resistance and thus the effective stiffness of the crosssection will fall. In the case of slender struts, the flexural rigidity of the crosssection is the most important parameter for their strength, and this is the reason why residual stresses cause a reduction in their strength. The same applies to that type of welded stiffened plate assembly where the buckling of the stiffener out of the plane of the plate is more critical than the buckling of the plate between the stiffeners. For the strength of plate panels in compression the important question is whether the plate panel, in a residual-stress-free condition, behaves in a stable or unstable manner when the axial straining is continued after it reached its maximum capacity. This is illustrated in Fig. 5.17. In the case of plate (a), in the residual-stress-free condition the plate continues to sustain the peak load su when further strained; the same plate cross-section with welding residual compressive stress sR departs from its initial primarily linear behaviour at an applied stress (su sR), but with further applied strains reaches an ultimate load s 0 u Rolled Beam and Plate Girder Design 123 which is almost the same as or just below su. In the case of plate (b), in the residual-stress-free condition the plate sheds off its axial load when the straining is continued beyond the peak strength su; with residual stress the plate reaches a peak strength s 0 u which is substantially below s u. Stocky plates, i.e. with b/t ratios such that the critical buckling stress s cr is more than twice the yield stress s y, behave like Fig. 5.17(a); so do very slender plates, i.e. those with critical buckling stress less than half the yield stress. But plates with intermediate slenderness, i.e. with critical buckling stress between half and twice the yield stress, tend to behave as in Fig. 5.17(b), and their strength is thus affected by the level of welding compressive residual stress.
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The Design of Modern Steel Bridges
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The Design of Modern Steel Bridges
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Contents Preface vii Acknowledgemen
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Preface Bridges are great symbols o
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Acknowledgements The figures in Cha
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2 The Design of Modern Steel Bridge
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10 The Design of Modern Steel Bridg
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Table 2.1 Properties of some commer
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Chapter 3 Loads on Bridges 3.1 Dead
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3.3 Design live loads in different
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interstate highways are designed fo
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a coefficient that depends on the n
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Loads on Bridges 59 In Germany, a n
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Table 3.6 Typical values of U and P
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3.5 Longitudinal forces on bridges
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wind loading on the traffic. An upl
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where r is the air density ¼ 1.226
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Loads on Bridges 69 minimum and max
Page 83 and 84: 3.8 Other loads on bridges There ar
Page 85 and 86: References Loads on Bridges 73 wher
Page 87 and 88: Chapter 4 Aims of Design 4.1 Limit
Page 89 and 90: critical components of the structur
Page 91 and 92: But this is an attempt to achieve u
Page 93 and 94: If the basic variables R and S are
Page 95 and 96: educed variables defined by oi ¼ x
Page 97 and 98: will have a probability of failure
Page 99 and 100: Aims of Design 87 g m ¼ g m1 g m2
Page 101 and 102: Table 4.2 Failure probabilities of
Page 103 and 104: Chapter 5 Rolled Beam and Plate Gir
Page 105 and 106: as possible. But deep and thin webs
Page 107 and 108: eam, with an effective area equal t
Page 109 and 110: and stresses caused by lateral defl
Page 111 and 112: Figure 5.3 Beam cross-section. In t
Page 113 and 114: Rolled Beam and Plate Girder Design
Page 115 and 116: Table 5.2 Effective length factors
Page 117 and 118: stress is equal to p 2 E/(Le/r) 2 )
Page 119 and 120: equation (5.16) has been adopted fo
Page 121 and 122: The strain energy of the elastic re
Page 123 and 124: Figure 5.6 Buckling of plates in co
Page 125 and 126: Figure 5.8 Buckling of plate under
Page 127 and 128: techniques. It may be noted that th
Page 133: 5.4.3 Effect of residual stresses R
Page 141 and 142: Basler and Thurlimann were the firs
Page 143 and 144: Ostapenko/Chern gave the following
Page 145 and 146: where m ¼ Mp b 2 twsyw ty ¼ syw p
Page 147 and 148: the case of equal flanges, the tota
Page 149 and 150: emains flat until an elastic critic
Page 153 and 154: longitudinal compression is given b
Page 155 and 156: where Peq ¼ s1tB PE Ps Pcro Peq1
Page 157 and 158: Figure 5.27 Tension-field forces in
Page 159 and 160: 5.5.6 Design of longitudinal web st
Page 161 and 162: when Le is the effective length for
Page 163 and 164: pffiffiffiffiffiffiffiffiffiffiffif
Page 165 and 166: een derived as a condition for trea
Page 167 and 168: For interaction of various stress c
Page 169 and 170: must be at least i.e. 1 IsxbB 4 2 a
Page 171 and 172: Chapter 6 Stiffened Compression Fla
Page 173 and 174: Stiffened Compression Flanges of Bo
Page 175 and 176: cross-section in which the secant s
Page 177 and 178: longitudinal compression of the lon
Page 179 and 180: webs of main girders is denoted by
Page 181 and 182: Stiffened Compression Flanges of Bo
Page 183 and 184: wherefrom Ms ¼ 2 3 PE P The net be
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Stiffened Compression Flanges of Bo
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Chapter 7 Cable-stayed Bridges 7.1
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Cable-stayed Bridges 185 cables con
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The following is a list of cable-st
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(a) Fan system (b) Harp system (c)
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7.3.2 Ropes causing lateral compres
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The spiral winding of wires around
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polyethylene or even steel tube. Or
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See Fig. 7.7. Imagine a cable-stay
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It may be noted that: Et is higher
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Reference Cable-stayed Bridges 201
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204 The Design of Modern Steel Brid
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206 The Design of Modern Steel Brid
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The Design of Modern Steel Bridges - TEDI

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