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Problem 1 Consider two rigid bars, each of length L/2 and artic- ulated at their mid and end points. A linear spring of L2 L/2 stiffness constant k connects the mid-span joint located at point M to the ground; when the two bars are in the M horizontal position, the linear spring is un-stretched. The left joint is located at fixed point and the right joint at Figure 1: Articulated bars with tor- point P is constrained to move in the horizontal direction sional spring. only. A compressive load P is applied at the right joint. Let A be the lateral deflection of the mid-span joint. (1) Write the equilibrium equation of the linear spring. (2) Assume deflection A to be far smaller than L. Find the critical buckling load, Por, of the system. (3) Compute P/P& as a function of A = 2A/L for finite values of this trans- verse deflection. Plot P/Pc versus A. (4) Next, consider an imperfect system: the linear spring is un-stretched when the lateral deflection of the mid-span joint is Ac; deflection A, is a measure of the imperfection of the system. (5) Assuming deflection to be small, find P/P, as a function of A. Plot P/Pe versus À for Ao = 2A./L = 0.001, 0.005, 0.02, 0.05, and 0.1.