【摘要】 <正> 均等连续樑的差分方程解法已为人们所习用。本文利用连分数法求得了任意不均等连续樑的解法。 今设有一连续樑共有n+1个支点,这些支点不一定距离相等,它们把樑分成n段,我们给每一个支点以一个数字来代表,自左至右共有0,1,2,…n等支点。每一段樑的长度自左至右也用l₁,l₂,l₃…l_n等来表示。这些段樑的材料和截面的惯性矩也不一定是相等的,它们将用E₁,E₂,…En和I₁,I₂…I_n来表示。（图1）更多还原

【Abstract】 In this paper, the method of continued fraction is used for the determination of the bending moments of a continuous beam with non-uniform stiffness.In the problem of continuous beam, it is required to find the solution of the following set of three-moment equations togather with a set of ends conditions:Here M_x is the moment at the support no. x, p_x and q_x are quantities denoting the relative stiffness, and F_x is the loading factor.Let a_x and β_x be the two independent solutions of the homogenuous equation It can be proved that β_x/a_x is the x-th convergent of the continued fractionThat is, if we denotethen we have the reourrence formulaeFurthermore, by using the definition of β₂ and a₂ we obtain from the recurrence formulae Hence the general solution of the homogenuous equation iswhere P and Q are the two integration constants.For the solution of the inhomogenuous equations of three moments （A）, it can be easily proved that the following is a particular solution:Hence the general solution of equation （A） is given bywhere P and Q are constants to be determined by ends conditions.A straight forward numerical method of solution based upon this method is given at the end of this paper.更多还原