MAE_101-Quiz_2-solution - Quiz 2 Solution 1 MAE 101 Statics...

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MAE 101. Statics and Strength of Materials © G. E. Orient 2006 1 Quiz 2 - Solution
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MAE 101. Statics and Strength of Materials © G. E. Orient 2006 2 From x = 0 to x = l 1 , the cross sectional area of the bar is A 1 = 1 in 2 . From x = l 1 to x = l 2 , A=A 2 x, A 2 =0.1 in . The modulus of elasticity of the material is E = 12 × 10 6 psi . There is a gap d = 0.02 in between the right end of the bar and the rigid wall. If an F=40 kip axial force toward the right is applied to the bar at x = l 1 , what is the resulting normal stress in the left half of the bar? l 1 =10 in l 2 =10 in Is the load sufficient to close the gap? Analysis of the two parts Free body diagrams, equilibrium (including the reaction force on the right end) Force-deflection Displacement compatibility Problem 1 in in E A Fl 02 . 0 033 . 0 1 1 = = δ F l 1 l 2 d F B A C R R R R R R R L E A l l R dx x E A R dx E x A R R l l l R l l l R R 2 1 2 2 2 ) / 1 ln( 1 2 1 1 2 1 1 + - = - = - = + + δ E A l R F R L 1 1 ) ( - = δ R L R L x R F R R F R F - = = - + - = 0 d E A l l R E A l R F d R R R L = + - - = + 2 1 2 1 1 ) /
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