The Design of Modern Steel Bridges - TEDI

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130 The Design of Modern Steel Bridges Many tension-field mechanisms have been postulated on the assumption that the ultimate shear capacity is the sum of the resistance of the following three separate and successively occurring mechanisms, as shown schematically in Fig. 5.20: (a) a pure shear field, (b) a diagonal tension field, and (c) a frame mechanism, involving the flanges. Mention may be made of the mechanisms proposed by Fujii and also by Ostapenko and Chern, in which there is an off-diagonal central band of yielding where the magnitude of the membrane tension takes account of the stress that existed at the onset of buckling, and smaller tension in the two triangular areas that can be resisted by the flanges – see Fig. 5.21. Figure 5.20 Three stages of tension-field mechanism. (a) Stage 1, pure shear; (b) Stage 2, diagonal tension; (c) Stage 3, frame mechanism. Figure 5.21 Tension-field mechanisms of Fujii and Ostapenko/Chern.
Ostapenko/Chern gave the following expression for the ultimate shear strength Vu ¼ tcrbt þ 1 2 stbt sin 2yt ð1 pÞ a h a i þð1 pÞ cos 2yt b b þ 2 a mpb þ mpt ð5:31Þ where p is the ratio of tensions in the outer and inner bands, mpb and mpt are the plastic moments of resistance of the bottom and top flanges, respectively, st is the tension in the central band, given by equation (5.27). Vu is differentiated with respect to yt to find the maximum Vu (to avoid this the authors gave some formulae for the shear strength). tcr is modified to take account of three levels of buckling, namely (i) the unmodified elastic critical buckling value, with the web panel edges rotationally fully restrained by the flanges but simply supported by the transverse stiffeners, (ii) modified for inelastic buckling if the elastic critical buckling stress exceeds half the shear yield stress, (iii) modified for strain hardening if it exceeds the shear yield stress. A versatile model that has been used in Reference [2] is due to Porter, Rockey and Evans[8], with some minor modifications. The limit of the first stage of pure shear stress is assumed to occur when the elastic critical value tcr is reached. However, to allow for initial imperfections and residual stresses, a limiting value tl is taken less than tcr when tcr is greater than 0.8 times the shear yield stress ty, and equal to ty when tcr is greater than 1.5 ty. The exact values of tl are given by where t1 ty ¼ 904 , 2 b when b533:62 ¼ 1:0, when b524:55 ¼ð1:54 0:22bÞ, when 24:55 Design 131 k ¼ 5:34 þ 4 , 2 f when f51 ¼ 5:34 þ 4, 2 f f ¼ aspect ratio when f < 1 a b In the second stage, tensile membrane stresses s t develop in the web panel in a direction which does not necessarily coincide with the diagonal. The maximum shear capacity is reached in stage three when (i) the pure shear stress t l of the first stage and the membrane tensile stress s t of the second stage cause yielding
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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
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3.8 Other loads on bridges There ar
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References Loads on Bridges 73 wher
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Chapter 4 Aims of Design 4.1 Limit
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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 and 134: 5.4.3 Effect of residual stresses R
Page 135 and 136: Aw ¼ 40 mm 2 , allowing for a smal
Page 141: Basler and Thurlimann were the firs
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 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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