ME 211 Homework 13 Solutions

ME 211 Homework 13 Solutions - ME 211 Homework Set#13...

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ME 211 Homework Set #13 Solutions 12-5-2008 Problem #1 16.35 The A-36 steel beam has a depth of 10in. and is subjected to a constant moment M o which causes the stress at the outer fibers to become σ y =36ksi. Determine the radius of curvature of the beam and the maximum slope and deflection. 1.) Moment – curvature relationship in Ec EI I c EI M y y o 78 . 4027 36 ) 5 )( 10 ( 0 . 29 1 1 1 3 = = = = = σ ρ 2.) Slope and elastic curve EI d 2 v dx 2 = M ( x ) EI d 2 v dx 2 =− M o EI dv dx =− M o x + C 1 EIv = M o x 2 2 + C 1 x + C 2 3.) Boundary Conditions
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dv dx ( L ) = 0 v ( L ) = 0 4.) Solve for the constants 0 =− M o ( L ) + C 1 C 1 = M o L 0 = M o L 2 2 + ( M o L ) L + C 2 C 2 = M o L 2 2 5.) Write the equations EI dv dx =− M o x + M o L EIv = M o x 2 2 + ( M o L ) x M o L 2 2 6.) Maximum slope happens at x=0 EI dv dx =− M o (0) + M o L dv dx = M o L EI 7.) Maximum displacement happens at x = 0 EIv = M o (0) 2 2 + ( M o L )(0) M o L 2 2 v =− M o L 2 2 EI
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Problem #2 – 16.38
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This note was uploaded on 05/12/2010 for the course MECHENG 211 taught by Professor ? during the Fall '07 term at University of Michigan.

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ME 211 Homework 13 Solutions - ME 211 Homework Set#13...

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