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P L The deformation of a simply supported beam under a distributed load p, shown in the figure above, is governed by the equation d'y M(x) dx² EI where M(x) is the internal bending moment and is given by px(L-x) M(x)= 2 y(x) = C, X Other relevant data are E=29×10° lb/in², I = 3100 in, 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 (주)-( 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.

P L The deformation of a simply supported beam under a distributed load p, shown in the figure above, is governed by the equation d'y M(x) dx² EI where M(x) is the internal bending moment and is given by px(L-x) M(x)= 2 y(x) = C, X Other relevant data are E=29×10° lb/in², I = 3100 in, 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 (주)-( 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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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.
Transcribed Image Text: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.
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