CE 526 Homework 05 Due Date: 21/04/2015 The beam is linearly elastic and experiencing small deformations due to its self-weight. It is supported by an elastic foundation. Left half of the beam can be modeled as a beam on an elastic foundation (the basic formulation is provided in the following pages). • • • • • Obtain the finite element formulation of the problem. Implement the formulation. Verify your code. Assume the gap is zero and the beam is very rigid (use very high values of EI so that the beam doesn’t bend). This problem can be solved analytically by equating the moment due to the self-weight of the beam to the resisting moment due to the distributed force applied by the elastic foundation on the beam. Compare the numerical solutions obtained with 2, 4, 8, and 16 elements to the analytical solution graphically. Remove the rigid boundary on the right (gap is too big, the beam can’t touch the rigid surface) and solve for the overhanging beam deflection using 2, 4, 8, and 16 elements. Compare your results. Take gap = 0.1 m, solve for the beam deflection using 2, 4, 8, and 16 elements. Compare your results graphically. Plot the shear force and bending moment diagrams (use the solution obtained with 4 elements). Advanced Mechanics of Materials and Applied Elasticity by A. C. Ugural and S. K. Fenster.

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