The Design of Modern Steel Bridges - TEDI

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80 The Design of Modern Steel Bridges Figure 4.1 Probability distribution of a two-variable limit state. Figure 4.2 Probability distribution of the safety margin Z. If R and S are normally distributed uncorrelated random variables, the probability of failure Pf is given by Pf ¼ mZ sZ ¼ mR mS ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 R þ s2 " # p S ¼ ½ bŠ where is the standardised normal distribution function of cumulative densities. A reliability index b is defined as the ratio (mZ/sZ), which is also the number of standard deviations by which mZ exceeds zero, as shown in Fig. 4.2.
If the basic variables R and S are replaced by a pair of reduced variables o R and o S given by oR ¼ oS ¼ R mR sR S mS then the failure condition gðoR, oSÞ¼0 is given by the equation of the straight line gðoR, oSÞ ¼oRsR þ mR This is shown in Fig. 4.3. oSsS mS ¼ 0 The frequency of occurrence of a particular value x of a normally distributed variable is given by the density function f ðxÞ ¼ 1 s ffiffiffiffiffi ð1=2Þðx p e 2p m=sÞ2 where m and s are the mean value and the standard deviation. Expressed in reduced coordinate o ¼ (x m)/s, the frequency of a particular value occurring is proportional to eð1=2Þo2. With two uncorrelated normally distributed variables, the frequency of occurrence of a particular set of values oR and oS Figure 4.3 Failure condition in the space of two reduced variables. sS Aims of Design 81
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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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Page 42 and 43: 30 The Design of Modern Steel Bridg
Page 58 and 59: Table 2.1 Properties of some commer
Page 63 and 64: Chapter 3 Loads on Bridges 3.1 Dead
Page 65 and 66: 3.3 Design live loads in different
Page 67 and 68: interstate highways are designed fo
Page 69 and 70: a coefficient that depends on the n
Page 71 and 72: Loads on Bridges 59 In Germany, a n
Page 73 and 74: Table 3.6 Typical values of U and P
Page 75 and 76: 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: But this is an attempt to achieve u
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 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
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Ostapenko/Chern gave the following
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where m ¼ Mp b 2 twsyw ty ¼ syw p
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the case of equal flanges, the tota
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emains flat until an elastic critic
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Rolled Beam and Plate Girder Design
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longitudinal compression is given b
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where Peq ¼ s1tB PE Ps Pcro Peq1
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Figure 5.27 Tension-field forces in
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5.5.6 Design of longitudinal web st
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when Le is the effective length for
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pffiffiffiffiffiffiffiffiffiffiffif
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een derived as a condition for trea
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For interaction of various stress c
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must be at least i.e. 1 IsxbB 4 2 a
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Chapter 6 Stiffened Compression Fla
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Stiffened Compression Flanges of Bo
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cross-section in which the secant s
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longitudinal compression of the lon
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webs of main girders is denoted by
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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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