y نیستی Р ▬▬▬▬▬▬▬▬▬▬ L The deformation of a simply supported beam under a distributed load p, shown in the figure above, is governed by the equation d²y__M(x) EI dx² where M(x) is the internal bending moment and is given by M(x) = px(L-x) 2 X Other relevant data are E=29×10° lb/in², I = 3100 in¹, L=20 ft = 240 in, p=5000 lb/ft=5000 lb/(12 in). 1) Obtain the exact solution by integration, and find the maximum deflection y max. 2) Assume an approximate deflection solution of the form X y(x) = c [(i)* - ( Note that the proposed form satisfies the boundary conditions. Use the following methods to evaluate C₁ and calculate the maximum deflection ymax: (a) the collocation method (using the midpoint of the beam for collocation); (b) the subdomain method; (c) Galerkin's method. Compare the approximate results with exact solution. 3) Draw the exact solution and approximate solutions obtained from 2) on one figure (as Figure 2-4 in lecture 2 shows) to show how exaction and approximate solutions look like and are different from one another. Comment on the solutions ontained using different methods.

y نیستی Р ▬▬▬▬▬▬▬▬▬▬ L The deformation of a simply supported beam under a distributed load p, shown in the figure above, is governed by the equation d²y__M(x) EI dx² where M(x) is the internal bending moment and is given by M(x) = px(L-x) 2 X Other relevant data are E=29×10° lb/in², I = 3100 in¹, L=20 ft = 240 in, p=5000 lb/ft=5000 lb/(12 in). 1) Obtain the exact solution by integration, and find the maximum deflection y max. 2) Assume an approximate deflection solution of the form X y(x) = c [(i)* - ( Note that the proposed form satisfies the boundary conditions. Use the following methods to evaluate C₁ and calculate the maximum deflection ymax: (a) the collocation method (using the midpoint of the beam for collocation); (b) the subdomain method; (c) Galerkin's method. Compare the approximate results with exact solution. 3) Draw the exact solution and approximate solutions obtained from 2) on one figure (as Figure 2-4 in lecture 2 shows) to show how exaction and approximate solutions look like and are different from one another. Comment on the solutions ontained using different methods.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.5.12P: A C 200 x 17.1 channel section has an angle with equal legs attached as shown; the angle serves as a...

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