The Design of Modern Steel Bridges - TEDI

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148 The Design of Modern Steel Bridges where s 1 ¼ applied longitudinal stress on the stiffener t ¼ shear stress in the web s 2 ¼ transverse stress in the web ks ¼ defined in Section 5.5.4. 5.6 Restraint at supports The lateral buckling strength of beams has been derived in Section 5.3 on the assumption that its cross-section at the supports is restrained fully against any lateral deflection of its flanges. In reality the stiffeners at the support restraint to prevent twisting of the beam section is likely to be finite. Flint[12] has derived a reduction in the elastic critical bending strength scr of a perfect simply supported beam as scr ¼ scr 4 GJ for a central concentrated load 3 LeS ¼ 2GJ for constant bending moment on the LeS whole length of the beam: where GJ ¼ torsional rigidity of the beam L e ¼ effective length of the beam S ¼ stiffness of the support against twisting of the beam section. The reduction s b in the limiting bending stress s b of the imperfect simply supported beam is, taking the worse of the above two cases sb sb ¼ scr scr sb scr scr sb ¼ 2GJ LeS sb scr scr sb If we decide to limit sb to n% ofsb, then 2GJ LeS sb scr 4 0:01 n scr sb or S 5 200 GJ n Le sb scr scr sb ð5:45Þ From equations (5.7) and (5.8) in Section 5.3.1, assuming k, and the shape factor (i.e. the ratio of the plastic to elastic modulus) to be each approximately equal to unity, scr can be expressed as scr sy 2 Le ¼ p ry rffiffiffiffiffi 2 sy E ¼ 5700 b 2
when Le is the effective length for lateral torisional buckling of the beam ry is the radius of gyration of the beam cross-section about the y–y axis b ¼ Le rffiffiffiffiffiffiffi sy ry 355 The ratio sb=sy is equal to the ratio MR=MU for which an expression was derived in equation (5.13) of Section 5.3.2; thus sb ¼ sy MR ¼ MU 1 5700 1 þð1þ ZÞ 2 b 2 1 1 þð1þ ZÞ 2 5700 b 2 2 22 800 b 2 " # 1=2 where Z ¼ 0:008ðb 30Þ for beams fabricated by longitudinal welding ¼ 0:0035ðb 30Þ for other beams. From the above two expressions for scr/sy and sb/sy, the product of ( sb / scr)(scr / sb) has been found conservatively given by 0.0075b. Hence S 5 200 GJ ð0:0075Þ n Le rffiffiffiffiffiffiffi sy 355 i.e. ry Le 5 1:5 rffiffiffiffiffiffiffi GJ sy n 355 If 1% fall in the allowable bending stress sb is acceptable, then the stiffness of the torsional restraint at support should not be less than rffiffiffiffiffiffiffi 1:5 GJ sy 355 ry When the torsional restraint at the support section of a simply supported I-beam consists only of a load-bearing stiffener anchored to the pier or the abutment, the actual stiffness of the restraint is equal to 3EIs D where Is is the second moment of area of the cross-section of the load-bearing stiffener about a horizontal axis along the web of the beam. 5.7 In-plane restraint at flanges Rolled Beam and Plate Girder Design 149 In Section 5.4.4 it was stated that the behaviour and strength of an initially imperfect plate subject to in-plane loading depended upon the degree of inplane restraint on the edges. In British Standard BS 5400: Part 3[2] separate ry
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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
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 and 158: Figure 5.27 Tension-field forces in
Page 159: 5.5.6 Design of longitudinal web st
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
Page 209 and 210: 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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The Design of Modern Steel Bridges - TEDI

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