chap11 - PROBLEM 11.1 KNOWN A steel rod(circular...

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PROBLEM 11.1 KNOWN: A steel rod (circular cross-section) having: 6 2 m 10 in 0.25 in 30 10 lb/in 40 lb m L D E m = = = × = FIND: The change in length of the rod, L δ , ASSUMPTIONS: Rod is elastically deformed, such that m E σ ε = SOLUTION: The force resulting from 40 lb m in standard gravity is ( ) ( ) 2 m m 2 40 lb 32.174 ft/sec 40 lb ft lb 32.174 lb sec N c ma F g = = = The resulting uniaxial stress is N a c F A σ = where ( ) 2 2 2 2 0.25 0.049 in 4 40 lb 814.9 lb/in 0.049 in c a A π σ = = = = and 2 5 6 2 814.9 lb/in 2.716 10 30 10 lb/in a a m E σ ε = = = × × The change in length is then ( ) ( ) 5 2.716 10 10 in 0.00027 in a L L δ ε = = × = 10 in D=0.25 in F N Cross Section, A c
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PROBLEM 11.2 KNOWN: A steel rod (circular cross-section) having: 10 0.3 m 5 mm 20 10 Pa 50 kg m L D E m = = = × = FIND: The change in length of the rod, L δ . ASSUMPTIONS: Rod is elastically deformed, such that m E σ ε = SOLUTION: The force resulting from 50 kg in standard gravity is ( ) ( ) 2 2 50 kg 9.8 m/s kg m 1.0 s N N c ma F g = = 490 N N F = The resulting uniaxial stress is N a c F A σ = where ( ) 2 3 5 2 6 -5 2 5 10 1.96 10 m 4 490 N 25 10 Pa 1.96 10 m c a A π σ = × = × = = × × and 6 6 10 25 10 Pa 125 10 20 10 Pa a a m E σ ε × = = = × × The change in length is then ( ) ( ) 6 6 0.3 125 10 37.5 10 m a L L δ ε = = × = × 0.3 m D=5 mm F N Cross Section, A c
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