173_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

173_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.5.qxd 9/25/08 3:00 PM Page 167 SECTION 2.5 Thermal Effects 167 Solution 2.5-18 Plate supported by three posts EQUILIBRIUM EQUATION 2P1 P2 P (Eq. 1) COMPATIBILITY EQUATION 1 shortening of outer posts 2 shortening of inner post 1 2 s (Eq. 2) FORCE-DISPLACEMENT RELATIONS d1 s size of gap 1.0 mm L length of posts A 40,000 mm2 2.0 m 20 MPa E 30 GPa C concrete post s Ea b L Substitute (3) and (4) into Eq. (2): P Stress in the two outer posts when the gap is just closed: E (30 GPa) a (Eqs. 3, 4) P2L + s or P1 EA P2 EAs (Eq. 5) L Solve simultaneously Eqs. (1) and (5): DOES THE GAP CLOSE? s P2 L EA d2 SOLUTION OF EQUATIONS P1L EA allow P1 L EA 1.0 mm b 2.0 m 3P1 EAs L By inspection, we know that P1 is larger than P2. Therefore, P1 will control and will be equal to allow A. Pallow 3sallow A EAs L 2400 kN 600 kN 1.8 MN ; 15 MPa Since this stress is less than the allowable stress, the allowable force P will close the gap. 1800 kN ...
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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.

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