The Design of Modern Steel Bridges - TEDI

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160 The Design of Modern Steel Bridges Figure 6.1 Typical construction details of stiffened compression flange. buckling of longitudinal stiffeners between transverse stiffeners, and overall buckling of the orthotropically stiffened panel between girder webs. (4) Geometric imperfections and residual stresses in the flange plate and the stiffeners. Any interaction between local buckling of a stiffener outstand and either local plate buckling or overall strut buckling would lead to sudden and substantial drop of load resistance. Hence design rules for stiffened plate structures specify such geometrical limitations on stiffener outstands that they are neither prone to premature buckling nor sensitive to any initial imperfections in them. 6.2 Buckling of flange plate It will generally be uneconomical to limit the plate slenderness to such a value that it will not deform out-of-plane before the whole strut buckles. Therefore the flange plate may have a non-linear load-deformation response; and the flange plate being one component of the strut cross-section, this will affect the behaviour of the strut. The stress in the flange plate due to axial force P and bending moment M on the strut is given by s ¼ ks P Ae þ My Ie ð6:1Þ when ks is the secant stiffness factor of the flange plate, appropriate to the value of stress s in it, as shown in Fig. 6.2. A e and I e are the area and the second moment of the area of the strut cross-section in which k s times the flange plate area is taken as effective, and y is the distance of the mid-plane of the flange plate from the centroidal axis of the effective strut section. k s is given by
Stiffened Compression Flanges of Box and Plate Girders 161 Figure 6.2 Load-shortening behaviour of flange plates. (a) Residual stress free plates. (b) Plates with welding residual stress. s/(eE), where e is the longitudinal shortening per unit length of the flange plate corresponding to s. For very stocky plates not liable to deform out-of-plane, eE equals s and ks equals unity. For slender plates, s and ks are interrelated and hence a method of successive approximation or trial-and-error is necessary for obtaining the stress s in the flange plate due to any given applied loads and moments P and M on the strut. Obviously the stress s must not exceed the ultimate strength s u of the plate shown in Fig. 6.2. A rational design method for the flange stiffeners is thus: (1) To use a stiffness factor corresponding to s u, i.e. k s ¼ s u/(e uE ), where e u is the longitudinal strain at s u, for calculating the effective plate area, and (2) To limit the stress in the plate, calculated for the effective stiffener section by equation (6.1), to su, i.e. sy times a strength factor su/sy. There are thus two necessary plate factors.
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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
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Table 4.2 Failure probabilities of
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Chapter 5 Rolled Beam and Plate Gir
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as possible. But deep and thin webs
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eam, with an effective area equal t
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and stresses caused by lateral defl
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Figure 5.3 Beam cross-section. In t
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Rolled Beam and Plate Girder Design
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Table 5.2 Effective length factors
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stress is equal to p 2 E/(Le/r) 2 )
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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 and 130: 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: Chapter 6 Stiffened Compression Fla
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 181 and 182: Stiffened Compression Flanges of Bo
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)
Page 203 and 204: 7.3.2 Ropes causing lateral compres
Page 205 and 206: The spiral winding of wires around
Page 207 and 208: polyethylene or even steel tube. Or
Page 209 and 210: See Fig. 7.7. Imagine a cable-stay
Page 211 and 212: It may be noted that: Et is higher
Page 213: Reference Cable-stayed Bridges 201
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