The Design of Modern Steel Bridges - TEDI

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140 The Design of Modern Steel Bridges 5.5.3 Loading on a transverse web stiffener The design of a transverse web stiffener should take account of the following effects if they are present: (1) the destabilising effect of the in-plane longitudinal and shear stresses in the web plate (2) axial force due to tension field in the web (3) axial force due to a locally applied concentrated load on the flange (4) axial force due to curvature or change of slope in the flange (5) axial force or bending moment transferred from a connected crossbeam or crossframe or deck. In addition, a transverse stiffener at one end of a plate girder has also to resist the inward pull of the tension field in the plane of the web. 5.5.4 Destabilising effects of in-plane stresses in web Stiffeners are provided to prevent the web plate from buckling due to the inplane stresses in it. But when the loading is sufficiently increased the stiffeners themselves buckle. It may thus be assumed that the in-plane stresses in the web set up a bending tendency for the transverse stiffeners, which is resisted by their flexural stiffness. This tendency can be visualised more clearly for a web subjected to longitudinal compressive stresses, as shown in Fig. 5.26. The elastic critical buckling load of an orthogonally stiffened panel subjected to a y P B b x P L Half-wave-length of buckling Figure 5.26 Effect of longitudinal web stress on transverse stiffeners.
longitudinal compression is given by Pcro ¼ p2 B Dx f 2 þ Dyf 2 þ 2H where Dx and Dy are the flexural rigidities in the orthogonal directions, H is the torsional rigidity of the panel, and f is the aspect ratio L/B of the buckled panel, L being the buckling half-wave-length in the x-direction. For minimum value of Pcro, the half-wave-length L ¼ B (Dx/Dy) 1/4 and the minimum Pcro ¼ 2p 2 /B [Dx Dy) 1/2 þ H]. For orthogonally stiffened web Dx ¼ EIsx=b, and Dy ¼ EIsy=a when Isx and Isy are the moments of inertia of the longitudinal and transverse stiffeners, and b and a are their spacing respectively. For torsionally weak stiffeners, i.e. stiffeners of open cross-section like tees, angles or flats, it is convenient and conservative to ignore the torsional rigidity H. Hence Pcro ¼ 2p2 E B IsxIsy ab But if the critical half-wave-length L ¼ B ¼fðIsx=bÞða=IsyÞg 1=4 works out less than a, then some half-waves will not contain a transverse stiffener and hence the above solution will not be valid. In that situation we should evaluate Pcro by taking the lowest value for L that contain a transverse stiffener, i.e. L ¼ a. This leads to Pcro ¼ p2 E B 1=2 Isx B2 b a2 þ Isy a2 a B2 As transverse stiffeners will be at the crest of the half-waves, their strain energy will be double the strain energy of smeared stiffeners. Hence there is a good case for doubling the second term in the bracket above. Let us denote m ¼ Isx a b Isy Then and Rolled Beam and Plate Girder Design 141 n ¼ a=B if m 0:25 > n, Pcro ¼ p2 EIsy B 2 if m 0:25 < n, Pcro ¼ p2 EIsy B 2 2m 1=2 n m þ n 4 n 3
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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
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 and 150: emains flat until an elastic critic
Page 151: Rolled Beam and Plate Girder Design
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
Page 201 and 202: (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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The Design of Modern Steel Bridges - TEDI

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