The Design of Modern Steel Bridges - TEDI

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118 The Design of Modern Steel Bridges Figure 5.12(a) Transverse stresses in buckled plates, with different longitudinal edge conditions. (i) Restrained against pulling in. (ii) Straight but free to pull in. (iii) Completely free to pull in. post-buckling stage, the axial stiffness of the plate, i.e. the longitudinal compressive force per unit area of cross-section divided by the longitudinal shortening per unit length, is given by: (1) 0.75E, when the longitudinal edges are restrained against any pulling in (2) 0.5E, when the longitudinal edges are constrained to remain straight but free to pull in (3) 0.41E, when the longitudinal edges are completely free to pull in. These post-buckling stiffnesses are shown in Fig. 5.12(b). As the buckling of the plate continues with increase in applied loading, the maximum longitudinal stress along the longitudinal edges reaches yield stress, or alternatively the longitudinal stress along an interior longitudinal strip combined with flexural stresses in the plate due to the buckles reaches the yield stress locally on the
Rolled Beam and Plate Girder Design 119 Figure 5.12(b) Post-buckling stiffness of plates, with different longitudinal edge conditions. surface. In the former case that stage signifies the ultimate state of the plate; in the latter case, further increase in applied loading spreads the yielding gradually over a wider surface area and through the thickness of the plate, though with a gradually falling plate stiffness and until no increase in load can be resisted. In a plate subjected to shear stresses there is often a substantial reserve of strength after the elastic critical buckling value of the shear stress is reached. In a state of pure shear stress there are principal tensile and compressive stresses in directions at 45 to the direction of the shear stress, as shown in Fig. 5.13. Buckling of the plate is caused by the principal compressive stress in direction 2–2, resulting in ripples forming with their crests stretched in the direction of principal tension, i.e. 1–1. Because of the ripples, the compressive stress cannot increase beyond the value at the critical buckling stage, but the diagonal tension continues to increase with applied shear. The increased diagonal tensile stresses form what is known as a tension field. These tensile stresses have to be resisted on the horizontal and vertical boundaries. The flexural rigidity of the flanges resists the pulling-in effect of the tension field, while the transverse web stiffeners act as struts to provide support to the flanges, thus forming a truss-type system of forces. The ultimate shear capacity is reached when the plate in the diagonal tensile band yields and also plastic hinges are formed
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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
Page 79 and 80: where r is the air density ¼ 1.226
Page 81 and 82: 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 129: Rolled Beam and Plate Girder Design
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 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
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Stiffened Compression Flanges of Bo
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wherefrom Ms ¼ 2 3 PE P The net be
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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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