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363_Physics ProblemsTechnical Physics

363_Physics ProblemsTechnical Physics - 365 Chapter 12...

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Chapter 12 365 P12.40 When the concrete has cured and the pre-stressing tension has been released, the rod presses in on the concrete and with equal force, T 2 , the concrete produces tension in the rod. (a) In the concrete: stress = × = = F H G I K J 8 00 10 6 . N m strain 2 Y Y L L i a f Thus, L L Y i = = × × stress N m m N m 2 2 a f e j a f 8 00 10 1 50 30 0 10 6 9 . . . or L = × = 4 00 10 0 400 4 . . m mm . (b) In the concrete: stress = = × T A c 2 6 8 00 10 . N m 2 , so T 2 6 4 8 00 10 50 0 10 40 0 = × × = . . . N m m kN 2 2 e je j (c) For the rod: T A L L Y R i 2 = F H G I K J steel so L T L A Y i R = 2 steel L = × × × = × = 4 00 10 1 50 1 50 10 20 0 10 2 00 10 2 00 4 4 10 3 . . . . . . N m m N m m mm 2 2 e j a f e je j (d) The rod in the finished concrete is 2.00 mm longer than its unstretched length. To remove stress from the concrete, one must stretch the rod 0.400 mm farther, by a total of 2 40 . mm . (e) For the stretched rod around which the concrete is poured: T A L L Y T L L A Y T R i i R 1 1 1 3 4 10 2 40 10 1 50 10 20 0 10 48 0 = F H G I K J = F H G I K J = × F H G I K J × × =
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