# Lecture 15 - ENGR-1100 Introduction to Engineering Analysis...

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Lecture 15 Notes courtesy of: Prof. Yoav Peles ENGR-1100 Introduction to Engineering Analysis

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Homework Assignment (due in class on Tuesday) Problem 6-76 Problem 6-80 Problem 6-86
Today Lecture outline (Truly end of “tools” before we start engineering applications) Equilibrium of a rigid body in 3D. F ree B ody D iagrams in 3D Equilibrium equations (6 independent equations in 3D)

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Resultant of a general 3D system of nonparallel noncoplanar forces 2 F 1 F 3 F 1 x y z y 1 x y z x R y R C R 1) Choose a point O (arbitrary). 2) Replace each force by a force at O and a couple perpendicular to it. 3) Combine the forces at O (vectorially) to obtain the resultant force. 4) Combine the couples at O (vectorially) to obtain the resultant couple The procedure
Necessary and sufficient conditions of equilibrium of a rigid body The necessary AND sufficient condition for a rigid body to be in equilibrium is that the resultant force and couple acting on the rigid body must be zero . 0 F R 1 i = = = n i 0 M M 1 i = = = n i Particle equilibrium Rigid body equilibrium Generally a system of forces in 3D can be reduced to a force-couple system .

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0 F R xi x = = = n i 1 0 F R yi y = = = n i 1 0 F R zi z = = = n i 1 0 M M
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## This note was uploaded on 04/04/2011 for the course ENGR 1100 taught by Professor Anderson during the Fall '06 term at Rensselaer Polytechnic Institute.

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Lecture 15 - ENGR-1100 Introduction to Engineering Analysis...

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