定跨度变截面梁的弯曲问题

一.引言 在处理梁的弯曲问题时,人们经常利用函数级数来表示有关的各量,并后而得到各该量的近似值。胡海昌曾经指出:在横向载荷和轴向力同时作用下,适宜于用梁的屈曲的本徵函数展开式来表示梁的挠度;其中φ_n是满足所给的梁的支座情况的屈曲本徵函数,a_n是常数系数。他求得一个相当简单的公式以已知的本徵函数和本徵值表示诸系数

ON THE DEFLECTION OF A BEAM OF VARIABLE CROSS SECTION WITH FIXED SPAN

The buckling problem of various beams of variable cross sections has been fully considered by many authors, and the eigenfunctions and eigenvalues of the buckling problem of those beams are available in books and papers on this subject. Firstly, this paper shows that the deflection of these beams under the combined action of lateral load and axial tensile force can be expanded in a series of buckling eigenfunctions and that the coefficients in such an expansion can be simply expressed in terms of the known eigenfunctions, eigenvalues, the axial tensile force and the lateral load. Furthermore making use of the eigenfunction expansion, an approximation method is given to determine the axial tensile force acted on the supports of a beam of fixed span.