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). 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 du 2 dr² -w(x)udx where E is Young's modulus and I is second moment of area.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
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Author:Kreith, Frank; Manglik, Raj M.
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Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.40P
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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).
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 du
2 dr²
-w(x)udx
where E is Young's modulus and I is second moment of area.
Transcribed Image Text: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). 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 du 2 dr² -w(x)udx where E is Young's modulus and I is second moment of area.
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