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SECTION 2.5 Misfits and Prestrains 115 Solution 2.5-13 Bar with a gap L 5 25 in. S 5 0.008 in. D T 5 50 8 F (increase) a 5 9.6 3 10 2 6 / 8 F E 5 16 3 10 6 psi d 5 elongation of the bar if it is free to expand 5 a ( D T ) L d C 5 elongation that is prevented by the support 5 a ( D T ) L 2 S e C 5 strain in the bar due to the restraint 5 d C / L s c 5 stress in the bar Note: This result is valid only if a ( D T ) L $ S . (Otherwise, the gap is not closed). Substitute numerical values: 2 0.008 in.] 5 2,560 psi [(9.6 3 10 2 6 / 8 F)(50 8 F)(25 in.) s c 5 16 3 10 6 psi 25 in. 5 E e C 5 E d C L 5 E L [ a ( ¢ T ) L 2 S ] L A B S Problem 2.5-14 A bar AB having length L and axial rigidity EA is fixed at end A (see figure). At the other end a small gap of dimension s exists between the end of the bar and a rigid surface. A load P acts on the bar at point C , which is two-thirds of the length from the fixed end. If the support reactions produced by the load P are to be equal in magnitude, what should be the size s of the gap? Solution 2.5-14 Bar with a gap (load P ) B AC P 2 L 3 L 3 s L 5 length of bar S 5 size of gap EA 5 axial rigidity Reactions must be equal; find
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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