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Q3. Fig Q3 shows a uniform cantilever beam of length L which is loaded by a linearly varying load: w(x) = wo where w is the load per unit length at the fixed end (x =0). L w(x) Fig Q3: A uniform cantilever beam (a) Using Ritz method, derive a two-term polynomial function to approximate the transverse displacement (u) of the beam. Total potential energy (TPE) for a beam under bending load is: TPE= EI d'u Jo 2 dx² -w(x)u dx where E is Young's modulus and I is second moment of area. (b) Calculate the bending moment at x = L based on Ritz solution.

Q3. Fig Q3 shows a uniform cantilever beam of length L which is loaded by a linearly varying load: w(x) = wo where w is the load per unit length at the fixed end (x =0). L w(x) Fig Q3: A uniform cantilever beam (a) Using Ritz method, derive a two-term polynomial function to approximate the transverse displacement (u) of the beam. Total potential energy (TPE) for a beam under bending load is: TPE= EI d'u Jo 2 dx² -w(x)u dx where E is Young's modulus and I is second moment of area. (b) Calculate the bending moment at x = L based on Ritz solution.

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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Q3. Fig Q3 shows a uniform cantilever beam of length L which is loaded by a linearly varying load: w(x) = wo where w is the load per unit length at the fixed end (x =0). L w(x) Fig Q3: A uniform cantilever beam (a) Using Ritz method, derive a two-term polynomial function to approximate the transverse displacement (u) of the beam. Total potential energy (TPE) for a beam under bending load is: TPE= EI d'u Jo 2 dx² -w(x)u dx where E is Young's modulus and I is second moment of area. (b) Calculate the bending moment at x = L based on Ritz solution.
Transcribed Image Text:Q3. Fig Q3 shows a uniform cantilever beam of length L which is loaded by a linearly varying load: w(x) = wo where w is the load per unit length at the fixed end (x =0). L w(x) Fig Q3: A uniform cantilever beam (a) Using Ritz method, derive a two-term polynomial function to approximate the transverse displacement (u) of the beam. Total potential energy (TPE) for a beam under bending load is: TPE= EI d'u Jo 2 dx² -w(x)u dx where E is Young's modulus and I is second moment of area. (b) Calculate the bending moment at x = L based on Ritz solution.
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