beam_bending_tutorial

beam_bending_tutorial -...

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Unformatted text preview: __________________________________________________________________________ Copyright 2008 D. G. Taggart, University of Rhode Island. All rights reserved. Disclaimer . 1 ABAQUS Tutorial - Beam Bending Consider the beam bending problem: Assume that the beam is made of steel (E=30x10 6 psi, G=11.5x10 6 psi) and has a 2" deep x 5" high rectangular cross section (I z =(2)(5 3 )/12=20.83 in 4 , I y =(5)(2 3 )/12=3.333 in 4 ). Determine the maximum deflection and stress in the bar and the using 8 beam elements. Compare the solution to the beam theory solution. Beam theory solution Beam theory gives the following displacement solution: ( ) ( ) ( ) ( ) 2 2 2 2 3 3 2 2 2 3 3 ( ) 2 , 6 24 ( ) ( ) 2 2 , 6 24 Pbx wx v x x b L Lx x L x a EIL EI Pa L x wx v x x a L x Lx x L a x L EIL EI = + + = + + where v(x) is the displacement, P is the concentrated force (-5000 lb), x is the distance from the left end of the beam, EI is the flexural stiffness of the beam, w o is the uniform distributed load (- 50 lb/ft = -4.167 lb/in), a =15 ft and b =5 ft. The displacement field and bending stress distribution predicted by beam theory are shown below. Note that the maximum deflection, approximately -1.89 in, occurs between x=11 ft and x=12 ft and the maximum bending stress is approximately 29,700 psi at x=15 ft. __________________________________________________________________________...
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This note was uploaded on 10/03/2011 for the course MCE 561 taught by Professor Sadd during the Spring '11 term at Rhode Island.

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