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Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.3.6P: A cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A...

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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

Problem 1: (Please solve parts A and B of problem)

A) A uniformly distributed load is subjected on the clamped-clamped beam and it is supported by a spring in the middle of the beam. Using Castigliano’s theorem, find the deflection in the spring. (Please use only Castigliano’s theorem to solve this part)

B) Remove the spring in part A and use the Rayleigh-Ritz method to solve for the deflection at the middle of the beam.

Assume that v(x) = C (1- Cos((2Pi*x)/L)) (Please use only Rayleigh-Ritz method for this part)

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Part A is already answered and correct please solve part B
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