differential relations - TAM 210/211 Engineering Mechanics:...

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1 Lecture 21 Differential Relations Between q(x), V(x), M(x) Stephen D. Downing Mechanical Science and Engineering © 2001 - 2008 University of Illinois Board of Trustees, All Rights Reserved TAM 210/211 Engineering Mechanics: Statics TAM 210/211 - Lecture 21 © 2007 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 14 Exam #2 ± Wednesday Mar12 th ± 50 minutes
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2 TAM 210/211 - Lecture 21 © 2007 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 2 of 14 Exam 2 Dates ± Review Session #1 ± Wed 3/5/2008 7-8 PM 1320DCL ± Review Session #2 ± Thu 3/6/2008 7-8 PM 1320DCL ± Exam #1 ± Wed 3/12/2008 8-9 AM 1320DCL TAM 210/211 - Lecture 21 © 2007 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 3 of 14 Relations Between q(x), V(x), M(x) q(x) = 120 lb/ft 15’ A B R A =900 lb R B =900 lb q(x) = 120 lb/ft x A 900 lb V(x) M(x) Suppose a beam is loaded uniformly by a load of 120 lb/ft over a length of 15 ft shown. Then R A = R B = 900 lb. To determine V(x) and M(x) at a general point x 0 x 120 ) x ( V 900 0 F Y = + = lbs 900 x 120 ) x ( V = 0 ) x ( M ) x ( xV 2 x ) x 120 ( 0 M A = + + = lbsft x 900 x 60 ) x ( M 2 + = lbs ft x 900 x 60 ) x ( M lbs 900 x 120 ) x ( V ft / lb 120 ) x ( q 2 + = = = ) x ( V dx dM ) x ( q dx dV = =
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This note was uploaded on 04/08/2008 for the course TAM 210/211 taught by Professor Downing during the Spring '08 term at University of Illinois at Urbana–Champaign.

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differential relations - TAM 210/211 Engineering Mechanics:...

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