PROBLEMS 1.1-1.5 Obtain an approximate displacement equation for the simply supported beam of length H and section prope
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- Problems 1 1 1 5 Obtain An Approximate Displacement Equation For The Simply Supported Beam Of Length H And Section Prope 1 (54.25 KiB) Viewed 79 times
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PROBLEMS 1.1-1.5 Obtain an approximate displacement equation for the simply supported beam of length H and section property El shown in Figure P1.1. Assume that the trial displacement equation is y(x)= A sin ax/H. Compare the deflec- tion at the center with the theoretical value y=-5WH/384E1. The govern- ing differential equation is EI d²y Wx(H-x) 2 -=0 dx² 14 BASIC CONCEPTS W M(x) Figure P1.1 1.1 Evaluate A by minimizing the integral EI II ¹- [[ ²² (1)² + ( Wx(H-x) 2 dx 2 dx 1.2 Evaluate A by requiring that the residual vanish at (a) x=H/3, and (b)x=H/2. 1.3 Evaluate A using the subdomain method. Evaluate A using Galerkin's method. 1.4 1.5 Evaluate A using the least squares method. · ΕΙ -H Wx(H-x) M(x)=