The Design of Modern Steel Bridges - TEDI

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146 The Design of Modern Steel Bridges ðstb cos yttwÞsin yt The shear force resisted by tension field action is ðt t1Þbtw Equating st ¼ ðt t1Þ sin yt cos yt Due to st, the pull on the flanges per unit length is and its vertical component is sttw sin yt sttw sin 2 yt ð5:43Þ The compressive force P tf on a vertical stiffener is equal to the vertical component of the total pull over length a on the flanges. Thus Ptf ¼ statw sin 2 yt t t1 ¼ sin yt cos yt ¼ðt t1Þatw tan yt atw sin 2 yt, using equation (5:43) ð5:44Þ The inclination of the membrane forces y t for the maximum shear resistance due to tension-field action has been found from parametric studies never to exceed p/4, nor does it exceed the angle of the diagonal of the web panel with the horizontal for aspect ratio a/b of the panel up to 3. Hence P tf can be taken as Ptf ¼ðt t1Þatw, or ðt t1Þbtw whichever is smaller. Due to st, the pull on an end vertical stiffener per unit height is and its horizontal component is sttw cos yt sttw cos 2 yt Assuming some end fixity, the bending moment on an end post is sttw cos 2 b yt 2 10 ¼ 1 10 ðt t1Þtwb 2 cot yt from equation (5.43). From parametric studies for the maximum shear resistance due to tensionfield action, an upper band for cot y t was found to be 80/y d, where y d is the inclination of the diagonal of the web panel with the horizontal in degrees. The design bending moment M y on an end stiffener can thus be expressed as My ¼ 8ðt t1Þtwb 2 =yd
5.5.6 Design of longitudinal web stiffeners The critical buckling load of a longitudinally loaded orthogonally stiffened web has been derived in Section 5.5.4 as Pcro ¼ 2p2 E B Isx Isy a b with the notations as in that section. For a particular ratio of the moments of inertia of the transverse and longitudinal stiffeners I sy and I sx, see Figure 5.26, P cro will be equal to the sum of the Euler buckling loads of the longitudinal stiffeners, i.e. when or 2p 2 E B Isx Isy a b Isy ¼ 1 IsxbB 4 2 a3 1=2 ¼ p 2 E Isx a 2 With this value of Isy, the half-wave-length L will be B Isx a 1=4 b Isy B b ¼ ffiffiffi p 2a 1 1=2 B b 2 B B b If I sy is greater than the above value, the sum of the Euler buckling loads will be less than Pcro; there is also the possibility that there may not be a transverse stiffener within the half-wave-length L, thus invalidating the evaluation of P cro as above. Hence in this situation the longitudinal stiffeners should be designed as struts with effective length equal to a. If I sy is less than the above value, the orthotropic critical buckling load P cro will be less than the sum of the Euler buckling loads of the longitudinal stiffeners. Hence the longitudinal stiffeners should be designed as struts with effective length leff greater than a and given by wherefrom p 2 EIsx l 2 eff B b leff ¼ B 2 Rolled Beam and Plate Girder Design 147 1 ¼ 2p2 E B B b 1 Isx Isy a b 1=2 abIsx The axial loading on a longitudinal stiffener should include not only the longitudinal stresses in the girder web, but should also allow for the destabilising effects of shear stresses and any transverse stresses in the web. Thus the applied longitudinal stress should be taken as s1 þ 2:5ksðt þ s2Þ Isy 1 1=2 1=2 1=4
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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
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But this is an attempt to achieve u
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If the basic variables R and S are
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educed variables defined by oi ¼ x
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will have a probability of failure
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Aims of Design 87 g m ¼ g m1 g m2
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Table 4.2 Failure probabilities of
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Chapter 5 Rolled Beam and Plate Gir
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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 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: Figure 5.27 Tension-field forces in
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
Page 195 and 196: Chapter 7 Cable-stayed Bridges 7.1
Page 197 and 198: Cable-stayed Bridges 185 cables con
Page 199 and 200: The following is a list of cable-st
Page 201 and 202: (a) Fan system (b) Harp system (c)
Page 203 and 204: 7.3.2 Ropes causing lateral compres
Page 205 and 206: The spiral winding of wires around
Page 207 and 208: 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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