翻译
6 Lateral buckling of beams
6.1 Introduction
In 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 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 beam's 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 two 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 and 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 induced 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- elastically, 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 behaviour 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 beams
6.2.1 BUCKLING OF STRAIGHT BEAMS
6.2.1.1 Simply supported beams with equal end moments
A perfectly straight 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 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 buckling moment is given by
(6.2)
Where
展开阅读全文