Problem 2.7-8The statically indeterminate structure shown in thefigure consists of a horizontal rigid bar ABsupported by five equallyspaced springs. Springs 1, 2, and 3 have stiffnesses 3k, 1.5k, and k,respectively. When unstressed, the lower ends of all five springs liealong a horizontal line. Bar AB, which has weight W, causes thesprings to elongate by an amount d.(a) Obtain a formula for the total strain energy Uof the springs in terms of the downward displacement dof the bar. (b) Obtain a formula for the displacement dby equating the strainenergy of the springs to the work done by the weight W. (c) Determine the forces F1, F2, and F3in the springs. (d) Evaluate the strain energy U, the displacement d, and the forces in the springs if W 5 600 N and k 5 7.5 N/mm.Solution 2.7-8Rigid bar supported by springsSECTION 2.7Strain Energy1431.5
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