02-05ChapGere.0010

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Problem 2.7-8 The statically indeterminate structure shown in the figure consists of a horizontal rigid bar AB supported by five equally spaced springs. Springs 1, 2, and 3 have stiffnesses 3 k , 1.5 k , and k , respectively. When unstressed, the lower ends of all five springs lie along a horizontal line. Bar AB , which has weight W , causes the springs to elongate by an amount d . (a) Obtain a formula for the total strain energy U of the springs in terms of the downward displacement d of the bar. (b) Obtain a formula for the displacement d by equating the strain energy of the springs to the work done by the weight W . (c) Determine the forces F 1 , F 2 , and F 3 in 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 2.7-8 Rigid bar supported by springs SECTION 2.7 Strain Energy 143 1.5
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