Lecture 15a

# Lecture 15a - Method ME221 Lecture 15 5 V M V M Sign...

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ME221 Lecture 15 1 ME 221 Statics Lecture #15a Sections 7.3 - 7.4

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ME221 Lecture 15 2 Homework #6 Chapter 7 problems: Chapter 6 problems Due Monday, June 28 MatLab Group Problems 7.19, 7.26 & 6.15 Due Monday, June 28
ME221 Lecture 15 3 Last Lecture: Internal Forces in Structures Reviewed internal/external forces Found internal forces Started shear & moment diagrams

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ME221 Lecture 15 4 Generate a shear / bending diagram as follows: 2. Take a section on each side of an applied force or moment and inside a distributed load (take a new section whenever there is a change in the load or shape of the beam) - draw a FBD and sum forces / moments 3. Repeat 2 along the length of the beam 1. Find reaction forces w(x ) distributed load V(x ) shear force M(x ) moment Shear and Moment Diagrams using Sectioning

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Unformatted text preview: Method ME221 Lecture 15 5 V M V M Sign Convention Positive Shear and Positive Moment ME221 Lecture 15 6 Positive Shear M M Positive Moment Effect of External Forces ME221 Lecture 15 7 Relations Between w , V , and M In balancing forces, we can come up with differential equations relating w , V , and M . These are as follows: ( 29 ( 29 ( 29 ( 29 , dM x dV x V x w x dx dx = = This means you can integrate the shear diagram to obtain the moment diagram. dx M+dM M V V+dV w ( x ) ∑ = + +-⇒ = ) ( ) ( dx x w dV V V F ) ( = +-+ ⇒ = ∑ dM M Vdx M M Thus, ME221 Lecture 15 8 Shear Forces • Area under load curve ∫ = x du u w x V ) ( ) ( ME221 Lecture 15 9 Bending Moments • Area under shear force curve ∫-= x du u w u x x M ) ( ) ( ) (...
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## This note was uploaded on 07/25/2008 for the course ME 221 taught by Professor Buch during the Summer '08 term at Michigan State University.

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Lecture 15a - Method ME221 Lecture 15 5 V M V M Sign...

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