The Design of Modern Steel Bridges - TEDI

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138 The Design of Modern Steel Bridges 5.5.2 The concept of optimum rigidity of stiffeners If the buckling stress s cr is plotted against the relative flexural rigidity g for a stiffened plate with ‘open’-type stiffeners, it can be found that initially s cr increases with g; but after g exceeds a certain value g*, there is no further increase in s cr. For g < g* the buckling of the stiffened plate involves bending of the stiffeners out of the plane of the plate as in mode (a) of Fig. 5.25, i.e. the overall buckling mode; but for g > g* the plate panels between the stiffeners and/or the boundaries buckle without any bending of the stiffeners, i.e. the stiffeners form the nodal lines of the buckling of the plate panels, as in mode (b) of Fig. 5.25, i.e. local buckling of plate panels. There is thus an optimum rigidity g* of the stiffeners for the maximum possible value of the buckling stress s cr of the whole stiffened panel (i.e. for overall buckling), which coincides with the elastic critical buckling stress of the individual plate panels of the stiffened plate (i.e. for local buckling). No further increase in the buckling load is possible by increasing g beyond this optimum value. The above concept of the optimum rigidity g* is thus based on the fundamental concept of the elastic critical buckling phenomenon of both the entire stiffened panel and the individual plate panels in it. As has been pointed out earlier, this concept is truly valid only for residual-stress-free perfectly flat plates with high yield stress; for a stiffened panel, in addition to this requirement the stiffeners must also be perfectly straight and residual-stressfree. In reality, just as plates have residual stresses and out-of-plane imperfections, so also the stiffeners have initial out-of-straightness and/or twist and residual stresses. As a result stiffeners tend to deflect even at low levels of applied loading. In the overall buckling mode, i.e. g < g*, there is thus often no critical value of loading at which sudden buckling of the stiffeners occurs. Instead, as the applied load is gradually increased, the deflection of the stiffeners continues to increase at a gradually faster rate until no further increase in load can be resisted. This maximum load is usually less than the theoretical elastic critical value, but there are cases where, due to post-buckling reserve, the maximum load is higher than the latter. In the local buckling mode, i.e. g > g*, because of their initial crookedness, the stiffeners start deflecting even at low levels of loading and thus do not form non-deflecting nodal lines for the local buckling of the individual plate panels; as a consequence the elastic critical buckling load of the individual plate panels is often not reached even when they have very low residual stress and out-ofplane imperfections. The rigidity of the stiffeners has thus got to be n-times the theoretical optimum value g* in order to ensure buckling in mode (b), i.e. local buckling, of Fig. 5.25. The value of n depends upon the geometry of the stiffened panel and the type of loading and is found to vary from 2.5 to 5. Thus, according to the linear buckling theory of stiffened plates, either (i) stiffeners are provided with n-times the optimum rigidity g* that will ensure that the overall critical buckling stress is equal to the local critical buckling stress, or
Rolled Beam and Plate Girder Design 139 Figure 5.25 Buckling modes of stiffened panel. (a) Overall buckling. (b) Local buckling. (c) Variation of critical buckling load with stiffener rigidity. (d) Variation of out-of-plane deflection with applied load. (ii) the value of the stiffener rigidity to be taken for calculating the overall critical buckling stress of the entire stiffened panel is obtained by dividing the actual rigidity value by n. The above method for designing stiffeners has the following two serious shortfalls: (1) the exact value of the multiplying factor n is uncertain (2) it does not represent the behaviour of the web panels, and, more particularly, the compressive force in the vertical stiffeners, when a tension field is set up in the web.
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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
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 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: 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
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
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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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The Design of Modern Steel Bridges - TEDI

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