The Design of Modern Steel Bridges - TEDI

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136 The Design of Modern Steel Bridges Figure 5.24 Interaction between bending moment and shear. by the flexural rigidity of the stiffener. Buckling of stiffened plates occurs in two different modes, namely (i) the overall buckling in which the stiffeners buckle, and (ii) the local buckling in which the stiffeners remain stable forming nodal lines but the plate panels between the stiffeners buckle. As in the case of plate buckling, an ideally flat residual-stress-free stiffened panel initially
emains flat until an elastic critical value of the loading is reached. Also, as in the case of plates, stiffened plates may often have substantial post-buckling strengths. 5.5.1 Elastic critical buckling of stiffened panels Two basic methods are available for the analysis of elastic critical buckling of ideally flat residual-stress-free stiffened plates. In the classical method, either (i) a differential equation of equilibrium is solved in general terms by assuming a deflected shape and then the boundary conditions are used to obtain a characteristic equation for the elastic critical buckling load, or (ii) a Fouriertype series representation is set up for the possible deformation mode consistent with the boundary conditions and then an energy or work approach is applied. The second method, i.e. the numerical or computer-based method, can tackle the complex problems; in this method a solution is formed in terms of a discrete number of unknowns located at many points in the stiffened plate. Thus a large-order matrix equation is formed, whose coefficients are given by the geometry of the stiffened plate and its loading conditions; the elastic critical buckling load is the value of the load at which the determinant of the coefficients is zero. The critical buckling load of a stiffened panel is generally expressed as scr ¼ k p2 D b 2 t where k is a buckling coefficient that depends on the geometry of the stiffened plate, the loading pattern and the boundary conditions, plus three relative rigidities of the stiffener, given by flexural: g ¼ EIs=bd torsional: y ¼ GJs =bd extensional: d ¼ As=bt Rolled Beam and Plate Girder Design 137 and D is the flexural rigidity of the plate, equal to Et 3 =12ð1 m 2 Þ b ¼ spacing of the stiffeners t ¼ thickness of the plate I s ¼ is the second moment of area of the stiffener cross-section, with the width of the plate acting with it, about its centroidal plane parallel to the plate Js ¼ torsional constant of the stiffener cross-section A s ¼ area of the cross-section. Many solutions are available for a large range of stiffened panel geometries and loading types in References [10] and [11] for ‘open’-type stiffener crosssections (i.e. not ‘closed’- or box-type cross-sections) with negligible torsional rigidity.
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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
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 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: the case of equal flanges, the tota
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
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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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