# Lecture 13 - ENGR-1100 Introduction to Engineering Analysis...

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Lecture 13 Notes courtesy of: Prof. Yoav Peles ENGR-1100 Introduction to Engineering Analysis

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Homework Assignment (due in class next class ) Problem 6-41 Problem 6-42 Problem 6-58
Last Lecture outline Rigid body equilibrium. FBD- Free Body Diagram.

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Rigid bodies -A rigid body is an ideal object that has dimensions and mass but does not deform under loading. - The size and shape do significantly affect the response (reaction at supports) to applied force/s -A force applied to a rigid body may be translated along its line of action without altering its effects ( principle of transmissibility )
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 Those are vector equations 0 M M 1 i = = = n i How many scalar equations in the 2D? In the 3D? Particle equilibrium Rigid body equilibrium

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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 xi x = = = n i 1 0 M M yi y = = = n i 1 0 M M z = = = n i 1 0 F R xi x = = = n i 1 0 F R y = = = n i 1 0 M M z = = = n i 1 3 independent equations in 2 D 6 independent equations in 3D
- Equilibrium equations in 2D - Solving problems of equilibrium of a rigid body in 2D Free body diagram Application of physical laws - Statically indeterminate reaction and partial constraints Today lecture outline

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Equilibrium equations in 2D The necessary and sufficient conditions for a body to
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Lecture 13 - ENGR-1100 Introduction to Engineering Analysis...

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