【正文】 adily decrease as the applied moment increases. Because of this, the inelastic buckling moment decreases in an approximately linear fashion as the slenderness increases, as shown in 39。The inelastic buckling moment of a beam with residual stresses can be obtained in a similar manner, except that the pattern of yielding is not symmetrical about the section major axis, so that a modified form of equation for a monosymmetric Ibeam must be used instead of equation . The jnelastic buckling moment varies markedly with both the magnitude and the 。屈曲系數(shù)隨著應(yīng)力消除后的鋼截面比率的變化而變化。E和G在彈性階段中應(yīng)用，而應(yīng)變硬化模量和在屈服階段和應(yīng)變硬化階段應(yīng)用（）。For beams with equal and opposite end moments（）, the distribution of yield across the section does not vary along the beam, and when there are no residual stresses, the inelastic buckling moment can be calculated from a modified form of equation as對(duì)于承受等大異號(hào)彎矩的梁來(lái)說(shuō)（），截面的屈服部分并不沿梁而變化，：in which the subscripted quantities ( )e are the reduced inelastic rigidities which are effective at buckling. Estimates of these rigidities can be obtained by using the tangent moduli of elasticity (see section ) which are appropriate to the varying stress levels throughout the section. Thus the values of E and G are used in the elastic areas, while the strainhardening moduli and are used in the yielded and strainhardened areas (see section ). When the effective rigidities calculated in this way are used in equation , a lower bound estimate of the buckling moment is determined (section ,3). The variation of the dimensionless buckling moment with the ratio of a typical stressrelieved rolled steel section is shown in Fig. . In the inelastic range, the buckling moment increases almost linearly with decreasing slenderness from the first yield moment to the full plastic moment，which is reached after the flanges are fully yielded, and buckling is controlled by the strainhardening moduli，.其中下標(biāo)表示非彈性剛度的減少，是屈曲時(shí)的有效值。對(duì)于短跨梁，屈服在達(dá)到極限彎矩前達(dá)到，當(dāng)梁開(kāi)始屈曲時(shí)，梁的截面一部分處于塑性狀態(tài)。短梁的限制彎矩接近屈服彎矩My，而長(zhǎng)梁的限制彎矩接近彈性屈曲彎矩。As the deformations increase with the applied moments M, so do the stresses. It is shown in section that the limiting moment at which a beam without residual stresses first yields is given byin which is the nominal first yield moment, when the central lack of straightness is given by變形隨著施加彎矩的增加而增加，壓力也是。The simple loaddeformation relationships of equations and are of the same forms as those of equations and for pression members with sinusoidal initial curvature. It follows that the Southwell plot technique for extrapolating the elastic buckling loads of pression members from experimental measurements (see section ) may also be used for beams.，曲率為正弦曲線形式。 BENDING AND TWISTING OF CROOKED BEAMSReal beams are not perfectly straight, but have small initial curvatures and twists which cause them to bend and twist at the beginning of loading. If a simply supported beam with equal and opposite end moments M has an initial curvature and twist which are given byin which the central initial lack of straightness and twist rotation are related bythen the deformations of the beam are given byin whichas shown in section . The variations of the dimensionless central deflection and twist are shown in Fig. , and it can be seen that deformation begins at the mencement of loading, and increases rapidly as the elastic buckling moment M^ is approached. 曲梁的彎曲與扭轉(zhuǎn)曲梁并不是理想直線，而是存在初始彎曲和初始扭曲，導(dǎo)致荷載剛作用便會(huì)發(fā)生彎曲和扭轉(zhuǎn)。【16，1921】是幾種使用的數(shù)學(xué)方法。關(guān)于存在梁端彎矩引起的均勻彎曲的懸臂梁的彈性屈曲問(wèn)題的解決，只要把長(zhǎng)度L換為懸臂梁的長(zhǎng)度的兩倍，此處：這種處理方法跟應(yīng)用于獲得懸臂柱屈曲荷載的有效長(zhǎng)度法原理相同。For other beam loadings than those shown in Fig. , the moment modification factor may be approximated by usingin which Mm is the maximum moment,，the moments at the quarter points, and the moment at the midpoint of the beam.，彎矩修正系數(shù)適用于公式:為最大彎矩，是1/4位置的彎矩，為梁跨中彎矩。許多特殊情況適用于【1316】，【2，3，5，13，15，17】適用于彈性屈曲荷載，【18】是一個(gè)可以分析彎扭屈曲的比較好的電腦程序?；蛘?，梁的最大屈曲彎矩近似適用于公式：當(dāng)時(shí)， Other loading conditionsThe effect of the distribution of the applied load along the length of a simply supported beam on its elastic buckling strength has been investigated numerically by many methods, including those discussed in [35]. A particularly powerful puter method is the finite element method [610], while the finite integral method [11, 12], which allows accurate numerical solutions of the coupled minor axis bending and torsion equations to be obtained, has been used extensively. Many particular cases have been studied [13 16], and tabulations of elastic buckling loads are available [2, 3, 5, 13, 15, 17], as is a userfriendly puter program [18] for analysing elastic flexuraltorsional buckling. 其他荷載情況承受沿直線分布荷載的簡(jiǎn)支梁的荷載分配情況對(duì)彈性屈曲長(zhǎng)度的影響有很多種方法考慮，包括【35】中討論的。比起長(zhǎng)跨短柱型截面來(lái)，這種影響在短跨深梁型截面中更加重要。當(dāng)梁的上下翼緣相等時(shí)，適用于公式：where is the distance between flange centroids. The variation of the buckling load with lyt^jds is shown by the solid lines in Fig. 6,6, and it can be seen that the differences between top and bottom flange loading increase with the beam parameter K. This effect is therefore more