【文章內(nèi)容簡(jiǎn)介】 equation （），彎矩修正系數(shù)公式為： （）It can be seen that the more dangerous loadings are those which produce more nearly constant distributions of major axis bending moment, and that the worst case is that of equal and opposite end moments for which .可見危險(xiǎn)荷載布置是那些產(chǎn)生恒定的強(qiáng)軸彎曲彎矩的情況，承受等大異號(hào)彎矩，的情況為最不利情況。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。 CantileversThe support conditions of cantilevers differ from those of simply supported beams in that a cantilever is usually pletely fixed at one end and pletely free at the other. The elastic buckling solution for a cantilever in uniform bending caused by an end moment M which rotates with the end of the cantilever [16] can be obtained from the solution given by equations and for simply supported beams by replacing the beam length L by twice the cantilever length 2L, whenceThis procedure is similar to the effective length method used to obtain the buckling load of a cantilever column (see Fig. ).懸臂梁的支撐情況與簡(jiǎn)支梁不同，一端自由，一端固結(jié)。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。（）Cantilevers with other loading conditions are not so easily analysed, but numerical solutions are available [16, 1921]. The particular case of a cantilever with an end concentrated load Q is discussed in section , and plots of the dimensionless elastic buckling moments for bottom flange, centroidal, and top flange loading are given in Fig. , together with plots of the dimensionless elastic buckling moments of cantilevers with uniformly distributed loads q.受其它形式荷載的懸臂梁就不這么容易求解了?！?6，1921】是幾種使用的數(shù)學(xué)方法。，下翼緣要乘以無量綱屈曲彎矩系數(shù)，受均布荷載q的懸臂梁無量綱屈曲彎矩系數(shù)為。 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)。，如果作用有等大異號(hào)端彎矩M的簡(jiǎn)支梁存在初彎曲和初扭轉(zhuǎn)，便有公式：初始彎曲缺陷和扭轉(zhuǎn)角之間滿足關(guān)系式：梁的變形符合公式：其中：，可以看出變形始于荷載剛剛作用，隨著彎矩接近屈曲彎矩變形迅速增加。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。通過針對(duì)受壓構(gòu)件的實(shí)驗(yàn)得出結(jié)論它服從索斯維爾繪圖法，這同樣適用與梁。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。，一個(gè)沒有初次屈服產(chǎn)生殘余應(yīng)力的梁的限制彎矩服從公式：其中是名義初始屈曲彎矩，中心曲率給出公式：in which Noy is given by equation . Equation is similar to equations and for the limiting axial force in an elastic pression member. The variation of the dimensionless limiting moment is shown in Fig. , in which the ratio plotted along the horizontal axis is equivalent to the modified slenderness ratio used in Fig. for an elastic pression member. Figure shows that the limiting moments of short beams approach the yield moment My, while for long beams the limiting moments approach the elastic buckling moment .，是為了限制彈性壓縮構(gòu)件的軸力。，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。 Inelastic beamsThe solution for the buckling moment of a perfectly straight simply supported Ibeam with equal end moments given by equations and is only valid while the beam remains elastic. In a short span beam, yielding occurs before the ultimate moment is reached, and significant portions of the beams are inelastic when buckling mences. The effective rigidities of these inelastic portions are reduced by yielding, and consequently, the buckling moment is also reduced.。對(duì)于短跨梁，屈服在達(dá)到極限彎矩前達(dá)到，當(dāng)梁開始屈曲時(shí)，梁的截面一部分處于塑性狀態(tài)。隨著屈服的進(jìn)行，塑性部分的有效剛度逐漸減少，相應(yīng)的，屈曲彎矩也逐漸減少。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)彎矩的梁來說（），截面的屈服部分并不沿梁而變化，：in which the subscripted quantiti