The Design of Modern Steel Bridges - TEDI

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116 The Design of Modern Steel Bridges 5.4.2 Post-buckling behaviour of plates In the preceding section the magnitude of the applied in-plane stress at which an initially flat plate first buckles has been derived for various stress patterns. Depending on the in-plane restraints on its edges, a buckled plate can carry stresses higher than this elastic critical stress, with the buckles growing in size but still in a stable condition. If such stable buckles are acceptable, then considerable gain in the strength of such plates is thus possible. If the transverse edges of a rectangular initially flat plate approach each other by a uniform amount across the width of the plate, then longitudinal compressive stresses will also be uniform across the width, until the elastic critical stress is reached and the plate buckles. After buckling, however, the condition changes. Imagine the plate to be made up of a number of longitudinal strips; the total distance by which the extremities of each longitudinal strip will approach each other will be the sum of: (1) the axial shortening of the strip due to the longitudinal compressive stress carried by it, and (2) the reduction in the chord length due to the bowing out-of-plane, or buckling, of the strip. It has been shown in the preceding section that a rectangular plate under longitudinal compression buckles with only one half-wave across its width; hence the longitudinal strip along the longitudinal centre line of the plate will bow out-of-plane, or buckle, by a bigger amount than the strips nearer the longitudinal edges. If, after the onset of buckling, the transverse edges of the buckled plate continue to approach each other by a uniform amount across the width, it follows therefore that a central longitudinal strip will undergo less axial shortening and consequently carry lower longitudinal compressive stress, than the strips nearer the longitudinal edges; this redistribution of the longitudinal stress, i.e. a transfer of stress from the relatively flexible central region to the two regions near the longitudinal edges, is shown in Fig. 5.11. The conditions of in-plane restraint in the transverse direction along the two longitudinal edges of the plate influence its post-buckling behaviour and stress distribution. If these edges are free to move in-plane in the transverse direction, then stresses in the transverse direction are zero along these edges and are also small in the interior of the plate; the longitudinal edges will, however, not remain straight but will pull in more in the crest and trough regions of the buckles and less near the nodal lines. If the longitudinal edges are prevented against in-plane movement in the transverse direction, then significant transverse tensile stresses develop; these will be higher in the crest and trough regions of the buckles and less near the nodal lines. An intermediate state of transverse restraint along the longitudinal edges is when the edges are constrained to remain straight though allowed to pull in, the net of average transverse stress along the edge being zero; in this case the transverse tensile
Rolled Beam and Plate Girder Design 117 Figure 5.11 Distribution of longitudinal stress in a buckled plate. stresses in the crest/trough regions are balanced by transverse compressive stresses in the regions adjacent to the nodal lines. These transverse stress distributions are shown in Fig. 5.12. Transverse tensile stresses provide some stability against buckling and reduce the out-of-plane deflection. In the
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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
Page 77 and 78: 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: 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 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
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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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The Design of Modern Steel Bridges - TEDI

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