The Design of Modern Steel Bridges - TEDI

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40 The Design of Modern Steel Bridges parameters; for example, for the determination of yield stress British Standard BS 18[1] limits the rate of straining at the time of yielding to 0.0025 per second; when this cannot be achieved by direct control, the initial elastic stressing rate has to be controlled within the values stipulated for different testing machine stiffnesses. Within a zone of, say, 50 mm from a rolled edge, yield stress may be up to 15% higher than in the remainder of a plate. Yield stress in the transverse direction may be approximately 21 2 % less than in the longitudinal direction of rolling. The yield stress (and also the tensile strength) varies with the chemical composition of the steel, the amount of mechanical working that the steel undergoes during the rolling process and the heat treatment and/or cold working applied after rolling. Thinner sections produced by an increased amount of rolling have higher yield stresses; even in one cross-section of a rolled section the thinner parts have higher yield stresses than the thicker parts. Heat treatment or cold working may remove the yield phenomenon. The stress–strain behaviour under compression is normally not determined by tests and is assumed to be identical to the tensile behaviour. In reality the compressive yield stress may be approximately 5% higher than the tensile yield stress. The state of stress at any point in a structural member may be a combination of normal stresses in orthogonal directions plus shear stresses in these planes. Several classical theories for yielding in three-dimensional stress states have been postulated; the theory that has been found most suitable for ductile material with similar strength in compression and tension is based on the maximum distortion energy and attributed variously to Huber, von Mises and Hencky. According to this theory, in a two-dimensional stress state yielding takes place when normal stresses s1 and s2 on the two orthogonal planes and shear stress t on these planes satisfy the following condition: s 2 1 þ s2 2 s1s2 þ 3t 2 ¼ s 2 y where sy is the measured yield stress of the material. It may be noted that, according to this theory: (i) the pffiffiffi yield stress ty in pure shear, i.e. without any normal stresses, is equal to sy/ 3 and (ii) in the biaxial stress state, the normal stress in one direction may reach values higher than the measured uniaxial yield stress sy before yielding takes place; e.g. if s1 ¼ 2s2, yielding will not take place until s 1 reaches approximately 15% higher than the uniaxial yield stress of the material. The other elastic properties that influence the state of stress at any point are: (1) Young’s modulus E, which is in the range 200 to 210 kN/mm 2 . (2) The shear modulus or modulus of rigidity G, which is the ratio between shearing stress and shear strain and is in the range 77 to 80 kN/mm 2 . (3) Poisson’s ratio m, which is the ratio between lateral strain and longitudinal strain caused by a longitudinally applied stress and is usually taken as 0.3 for structural steel.
2.4 Ductility (4) The coefficient of thermal expansion which is the expansion/contraction per unit length caused by one degree change in the temperature and is normally taken as 12 10 6 / C. There is a theoretical relationship between E, G, and m, given by G ¼ E/{2(1 þ m)}. Ductility of a material is measured by its capacity to undergo large strains after the onset of yielding and before fracture. This property enables a structure to exhibit large deformation when the load it carries exceeds the value corresponding to its yield stress, thus providing an advance warning of possible failure. In a structure with redundancy, i.e. alternative load paths, when yield strain is exceeded in a critical component, this property enables it to redistribute the excess load to other components while the critical component retains its yield load. In a tensile test, after the maximum load, i.e. tensile strength Rm (see Fig. 2.1(a)), is reached, necking occurs in one cross-section, accompanied by large local elongation. After fracture, the two pieces are held together to measure the total permanent elongation of the original gauge length. This elongation represents the ductility of the material. However, it is affected by the geometrical parameters of a test piece, e.g. cross-sectional shape and gauge length. By international agreement, the relationship between gauge length Lo and crosssectional area So in the gauge length of tensile test pieces has been established as Lo ¼ 5.65 ffiffiffiffi p So. However, other gauge lengths are often used, e.g. 200 mm or 8 inches are quite common in the UK and USA, respectively. Structural steel specifications prescribe a minimum value of this percentage elongation, in the range of 17 to 26%. Good ductility through the thickness of thick rolled products is necessary to prevent lamellar tearing when high stresses occur in the direction of the thickness. 2.5 Notch ductility Types and Properties of Steel 41 Notch ductility is a property of metals indicating their resistance to brittle fracture. Brittle fracture is a form of failure that occurs suddenly under a load well below the level to cause yielding. It is initiated by the existence of a small crack or other form of notch. Very high concentration of stress occurs at the root of a natural crack. Any sudden change in the cross-section of a loaded member has a notch-like effect, namely it disturbs the stress pattern and causes
Page 1: The Design of Modern Steel Bridges
Page 5 and 6: The Design of Modern Steel Bridges
Page 7 and 8: Contents Preface vii Acknowledgemen
Page 9 and 10: Preface Bridges are great symbols o
Page 11: Acknowledgements The figures in Cha
Page 14 and 15: 2 The Design of Modern Steel Bridge
Page 22 and 23: 10 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 and 92: But this is an attempt to achieve u
Page 93 and 94: If the basic variables R and S are
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
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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
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The strain energy of the elastic re
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Figure 5.6 Buckling of plates in co
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Figure 5.8 Buckling of plate under
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techniques. It may be noted that th
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5.4.3 Effect of residual stresses R
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Aw ¼ 40 mm 2 , allowing for a smal
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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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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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