Problem 1. Consider the simply supported beam below, loaded with a uniform distributed vertical load po. L/3 X ро E, I 2

[answerhappygod]

1 (96.88 KiB) Viewed 11 times

Problem 1. Consider the simply supported beam below, loaded with a uniform distributed vertical load po. L/3 X ро E, I 2L/3 The beam material stiffness is E, moment of inertia I, total length L, and cross-sectional area A. The deflection of the beam is v. (a) Write down the expression of the total potential energy for this structural system. Suppose we are interested in using the Rayleigh Ritz Method to solve the problem, with the basis functions sin(kx/L), cos(kx/L) based on the Fourier Series, where k = 1, 2, 3, (b) State the essential/natural boundary conditions for this problem, and comment on the suitability of using sin(kx/L) or cos(kx/L) as basis functions for the problem above. (c) Using the Rayleigh Ritz Method with a single-term expansion using either sin(kx/L) or cos(kx/L) with the smallest possible k, obtain the deflection of the beam v(x).