845_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

845_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 10.5 Temperature Effects 839 Temperature Effects The beams described in the problems for Section 10.5 have constant flexural rigidity EI. Problem 10.5-1 A cable CD of length H is attached to the third point of a simple beam AB of length L (see figure). The moment of inertia of the beam is I , and the effective cross-sectional area of the cable is A . The cable is initially taut but without any initial tension. (a) Obtain a formula for the tensile force S in the cable when the temperature drops uniformly by degrees, assuming that the beam and cable are made of the same material (modulus of elasticity E and coefficient of thermal expansion ). Use the method of superposition in the solution. (b) Repeat part (a) assuming a wood beam and steel cable. a ¢ T A C B D Cable ± T H 2 L —— 3 L 3 Solution 10.5-1 = Decrease in temperature. Use method of superposi-
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Unformatted text preview: tion. Select tensile force S in the cable as redundant. I ² Moment of inertia of beam A ² Cross-sectional area of cable R ELEASED STRUCTURE ¢ T C OMPATIBILITY S OLVE FOR S: (b) W OOD BEAM , STEEL CABLE (downward) C ABLE (downward) C OMPATIBILITY S OLVE FOR S : S ² 243 E S E W IAH a s ( ¢ T ) 4 AL 3 E S + 243 IHE W ; ( d c ) 1 ² ( d c ) 2 4 SL 3 243 E W I ² a s H ( ¢ T ) ³ SH E S A ( d c ) 2 ² a s H ( ¢ T ) ³ SH E s A ( d c ) 1 ² 4 SL 3 243 E W I S ² 243 EIAH a ( ¢ T ) 4 AL 3 + 243 IH ; ( d c ) 1 ² ( d c ) 2 4 SL 3 243 EI ² a H ( ¢ T ) ³ SH EA ( δ C ) 1 ( δ C ) 2 S S S (a) B EAM & CABLE ARE SAME MATERIAL (downward) C ABLE (downward) ( d c ) 2 ² a H ( ¢ T ) ³ SH EA 1 d c 2 1 ² 4 SL 3 243 EI 10Ch10.qxd 9/27/08 7:37 AM Page 839...
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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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