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# lec2 - 2.001 MECHANICS AND MATERIALS I Lecture#2 Prof Carol...

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2.001 - MECHANICS AND MATERIALS I Lecture #2 9/11/2006 Prof. Carol Livermore TOPIC: LOADING AND SUPPORT CONDITIONS STRUCTURAL ANALYSIS Tools we need: 1. Recall loading conditions (last time) a. Forces - (”Point Loads ”) Point of Application Magnitude Direction b. Moments From forces applied at a distance from a point. 2. Recall equation of static equilibrium (last time) F = 0 F x = 0 , F y = 0 , F z = 0 M 0 = 0 M x = 0 , M y = 0 , M z = 0 3. Distributed Loads - Force per unit length 4. Concentrated Moment - Moment applied at a point (EX: Screwdriver) 1

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FREE BODY DIAGRAMS Draw like a mechanical engineer Fixed Support Cannot translate horizontally or vertically. Cannot rotate. Pinned Support - Cannot translate. - Free to rotate. Pinned on Rollers - Cannot translate in y. - Can translate in x. - Free to rotate. REACTIONS: (Forces applied by a support) 2
No can apply R x . ↑↓⇒ can apply R y . No rotate can apply M . So: Need R x , R y , M Need R x , R y 3

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Need R y OTHERS: CABLE: SMOOTH SUPPORT: EXAMPLE: DIVING BOARD Find reactions from the supports for this structure. 4
1. How to draw a Free Body Diagram (FBD) i. Remove all external supports. ii. Draw all relevant dimensions.

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