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1、翻译6 Lateral buckling of beams6.1 IntroductionIn the discussion given in Chapter 5 of the in-plane behaviour of beams, it was assumed that when a beam is loaded in its stiffer principal plane, it deflects only in that plane. If the beam does not have sufficient lateral stiffness or lateral support to
2、 ensure that this is so, then it may buckle out of the plane of loading, as shown in Fig. 6.1. The load at which this buckling occurs may be substantially less than the beams in-plane load carrying capacity, as indicated in Fig. 6.2.6.梁的侧面翘曲6.1 说明在第五章关于梁的平面内性能的讨论中，假定梁按刚性主平面放置时，梁仅在该平面内倾斜。如果梁没有足够的侧向刚度
3、或侧面支撑，梁会发生平面外屈曲，如图6.1所示。如图6.2所示，当发生平面外屈曲时梁的承载能力会大大减小。For an idealized perfectly straight elastic beam, there are no out-of-plane deformations until the applied moment M reaches the elastic buckling moment M0b, when the beam buckles by deflecting laterally and twisting, as shown in Fig. 6.1. These tw
4、o deformations are interdependent: when the beam deflects laterally, the applied moment has a component which exerts a torque about the deflected longitudinal axis which causes the beam to twist. This behaviour, which is important for long unrestrained I-beams whose resistances to lateral bending an
5、d torsion are low, is called elastic flexural-torsional buckling.作为一个理想的弹性直梁，当施加弯矩达到弹性屈曲弯矩时，梁才会发生侧向弯曲和扭转变形，发生平面外屈曲，如图6.1所示。这两种变形是相互联系的：当梁侧向倾斜时，所承受的弯矩会对侧向梁轴产生扭矩并引起梁扭转。这种特性，对于抵抗侧向弯曲和扭转能力差的无限制I形梁来说很重要，被成为弯扭屈曲。The failure of a perfectly straight slender beam is initiated when the addi-tional stresses in
6、duced by elastic buckling cause first yield. However, a per-fectly straight beam of intermediate slenderness may yield before the elastic buckling moment is reached, because of the combined effects of the in-plane bending stresses and any residual stresses, and may subsequently buckle in- elasticall
7、y, as indicated in Fig. 6.2. For very stocky beams, the inelastic buckling moment may be higher than the in-plane plastic collapse moment in which case the moment capacity of the beam is not affected by lateral buckling.理想弹性直梁的屈服始于因为因为弹性屈曲产生的附加应力导致的屈服，然而，受平面内弯曲应力和残余应力的影响，理想弹性直梁的中间部位可能在到达屈服弯矩前先行屈服，并发
8、生塑形弯曲，如图6.2所示。对于短梁，其非弹性屈曲弯矩会大于平面内塑形破坏弯矩，受弯承载力不由侧向屈曲控制。In this chapter, the behaviour and design of beams which fail by lateral buckling and yielding are discussed. It is assumed that local buckling of the compression flange or of the web (which is dealt with in Chapter 4) does not occur. The behavio
9、ur and design of beams bent about both principal axes, and of beams with axial loads, are discussed in Chapter 7.在本章，将讲述由侧向屈曲和屈服引起破坏的梁的性能和设计方法。假设第四章中讨论的局部屈曲不会发生。第七章将讨论轴压及压弯构件的性能和设计方法。6.2 Elastic beams6.2.1 BUCKLING OF STRAIGHT BEAMS 6.2.1.1 Simply supported beams with equal end momentsA perfectly st
10、raight elastic beam which is loaded by equal and opposite end moments is shown in Fig. 6.3. The beam is simply supported at its ends so that lateral deflection and twist rotation are prevented, while the flange ends are free to rotate in horizontal planes so that the beam ends are free to warp (see
11、section 10.8.3). The beam will buckle at a moment A/0b when a deflected and twisted equilibrium position, such as that shown in Fig. 6.3, is possible. It is shown in section 6.10.1.1 that this position is given by where is the undetermined magnitude of the central deflection, and that the elastic bu
12、ckling moment is given by （6.2）Wherewhere EIy is the minor axis flexural rigidity, GJ the torsional rigidity, and E/w the warping rigidity of the beam. Equation 6.3 shows that the resistance to buckling depends on the geometric mean of the flexural resistance and the torsional resistance.6.2.弹性梁6.2.
13、1 直梁的屈曲6.2.1.1 端弯矩相等的简支梁如图6.3所示，一个承受相等梁端弯矩的理想弹性直梁。梁端简支侧向弯曲和扭转不会发生，因为端部可以在平面内自由转动从而不限制梁端转角。当侧移和扭转达到平衡时，在作用下梁会弯曲，如图6.3所示。这种情况在6.10.1.1中给出公式：为梁跨中挠度，大小未知，弹性屈曲弯矩计算公式为： （6.2）为侧向弯曲刚度，为扭转刚度，为翘曲刚度。公式6.3表示梁的抗屈曲能力取决于临界弯矩以及临界扭矩。Equation 6.3 ignores the effects of the major axis curvature and produces conservati
14、ve estimates of the elastic buckling moment equal to times the true value. This correction factor, which is just less than unity for most beam sections but may be significantly less than unity for column sections, is usually neglected in design. Nevertheless, its value approaches zero as Iy approach
15、es Ix so that the true elastic buckling moment approaches infinity. Thus an I-beam in uniform bending about its weak axis does not buckle, which is intuitively obvious. Research 1 has indicated that in some other cases the correction .factor may be close to unity, and that it is prudent to ignore th
16、e effect of major axis curvature.公式6.3忽略了强轴曲率，并且保守估计梁的屈曲弯矩等于真实弯矩乘以。这种修正，在大多数梁截面设计中是可以忽略的，柱的设计中则不然。它把梁的和当作零处理，使得梁的弹性屈曲弯矩接近无穷大。很明显，I型钢梁不会绕弱轴屈曲。研究【1】表明在其他情形下修正值接近真实值，忽略强轴曲率是可以的。6.2.1.2 Beams with unequal end momentsA simply supported beam with unequal major axis end moments M and as shown in Fig. 6.4a. It is shown in section 6.10.1.2 that the value of the end Jimoment Mab at
