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214_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

214_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 2.7-11 A block B is pushed against three springs by a force P (see figure). The middle spring has stiffness k 1 and the outer springs each have stiffness k 2 . Initially, the springs are unstressed and the middle spring is longer than the outer springs (the difference in length is denoted s ). (a) Draw a force-displacement diagram with the force P as ordinate and the displacement x of the block as abscissa. (b) From the diagram, determine the strain energy U 1 of the springs when x 2 s . (c) Explain why the strain energy U 1 is not equal to P /2, where 2 s . 208 CHAPTER 2 Axially Loaded Members Solution 2.7-11 Block pushed against three springs Force P 0 required to close the gap: P 0 k 1 s (1) F ORCE - DISPLACEMENT RELATION BEFORE GAP IS CLOSED P k 1 x (0 x s )(0 P P 0 ) (2) F ORCE - DISPLACEMENT RELATION AFTER GAP IS CLOSED
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