214_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

214_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Sec_2.7.qxd 9/25/08 208 11:42 AM Page 208 CHAPTER 2 Axially Loaded Members Problem 2.7-11 A block B is pushed against three springs by a force P (see figure). The middle spring has stiffness k1 and the outer springs each have stiffness k2. 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 U1 of the springs when x 2s. 2s. (c) Explain why the strain energy U1 is not equal to P /2, where Solution 2.7-11 Block pushed against three springs Force P0 required to close the gap: P0 (a) FORCE-DISPLACEMENT DIAGRAM k1s (1) FORCE-DISPLACEMENT RELATION BEFORE GAP IS CLOSED P k1x (0 x s)(0 P P0) (2) FORCE-DISPLACEMENT RELATION AFTER GAP IS CLOSED All three springs are compressed. Total stiffness equals k1 2k2. Additional displacement equals x s. Force P equals P0 plus the force required to compress all three springs by the amount x s. P P0 (k1 2k2)(x s) 2k2)x k1s k1s (k1 P (k1 2k2)x P1 force P when x Substitute x P1 2(k1 2k2s (x (b) STRAIN ENERGY U1 WHEN x 2k2s s); (P P0) (3) U1 Area below force - displacement curve 2s 2s into Eq. (3): k2)s 2s 1 1 P s + P0s + (P1 20 2 (4) P0)s P0s + 1 Ps 21 k1s2 + (k1 + k2)s2 U1 (2k1 k2)s2 ; (5) ...
View Full Document

This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

Ask a homework question - tutors are online