The Design of Modern Steel Bridges - TEDI

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150 The Design of Modern Steel Bridges graphs are given for the strength of: (1) plates without any in-plane restraint on the longitudinal edges, i.e. free to pull in (2) plates with longitudinal edges constrained to remain straight but allowed to move inwards in the plane. Any in-plane restraint on the horizontal edges of an external web panel will apply a distributed load on the flange of a beam in the plane of the web; similarly, vertical edges at the ends of a beam will be subjected to in-plane pulling-in forces for which a vertical stiffener over an external support needs to be designed. Along the internal edges of web plate panels the pulling-in forces in adjacent panels will tend to balance, and hence such edges may be deemed to remain virtually straight. For plates subjected to shear, its strength in the tension field mechanism depends upon the bending capacity of the flange (see Section 5.4.5). For plates subject to any pattern of in-plane loading, it is necessary to establish some criteria as to when the edges adjacent to a flange may be assumed to remain straight. 5.7.1 Plates under compression For a plate panel under longitudinal compression s1, with initial imperfections in the critical buckling mode and with longitudinal edges held straight but free to pull in, the author has derived[14] the following expression for the transverse in-plane stresses at the longitudinal edges where s2 ¼ p2 8 ðm2 1Þ d2E 2pNx cos b2 L L ¼ length of the plate in the longitudinal direction x x ¼ longitudinal distance from the transverse centre line N ¼ number of half-waves in direction x ( L/b) b ¼ width of the plate d ¼ amplitude of the initial imperfection m ¼ factor of magnification of initial imperfections under the loading s l E ¼ Young’s modulus. ð5:46Þ From the above expression, the maximum amplitude of s2 can be expressed as where s2 sy ¼ p3 8 ðm2 1Þ d0 S d 0 ¼ a non-dimensional imperfection parameter d/t t ¼ plate thickness 2 ð5:47Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi S ¼ a non-dimensional slenderness parameter (b/t) ðsy=EÞ sy ¼ yield stress of the plate. The author has also shown[14] that the value of m that is reached when the applied stress s1 reaches the ultimate strength of the panel is given by 0:7d 2 0m2 1 m ¼ 0:2766S2 þ 0:7d 2 0 1 ð5:48Þ In Section 5.4.4 it was stated that, on the basis of the specified tolerances on workmanship, d0 can be assumed as 0.145S. For any particular value of S, d0 can thus be quantified, and then from equation (5.48) the value of m may be obtained by successive approximation. The amplitude of the cosine distribution for s2/sy can then be obtained from equation (5.47). By this procedure a graph for s2/sy against slenderness parameter S was drawn. It was found that s2/sy could be taken as: (1) zero, up to S ¼ 1.0 (2) 0.5, for S > 3.6 (3) 0.192 (S 1), for 1.0 < S < 3.6. The cosine distribution of s 2 on the edge, given by equation (5.46), causes a bending moment distribution on the girder flange on the edge, given by M ¼ b2 s2t 4p2 The moment of resistance of the flange section MR has to be at least a safety factor times the maximum value of the above bending moment. Taking account of the longitudinal stress already present in the flange due to the bending moment on the girder, the plastic moment of resistance MR can be taken as where MR ¼ 1 4 syfBT 2 f 1 B ¼ width of the flange T f ¼ thickness of the flange s f ¼ longitudinal stress in the flange s yf ¼ yield stress of the flange. Rolled Beam and Plate Girder Design 151 " # sf syf Assuming a safety factor of 1.25 MR51:25M or 1 4 syfBT 2 f 1 " # 2 sf 5 1:25b2 s2t 4p2 syf 2
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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
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eam, with an effective area equal t
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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 and 158: Figure 5.27 Tension-field forces in
Page 159 and 160: 5.5.6 Design of longitudinal web st
Page 161: when Le is the effective length for
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
Page 209 and 210: See Fig. 7.7. Imagine a cable-stay
Page 211 and 212: 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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