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TR-06_ENGR111A_2011C (3)

TR-06_ENGR111A_2011C (3) - Review Calculating Reaction...

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ENGR 111 - Track A - Fall 2011 1 Review: Calculating Reaction Forces in a Truss. Two Force Members. TR-6
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ENGR 111 - Track A - Fall 2011 2 Learning Objectives Review: Calculating force components and moments; equilibrium of rigid bodies. Find unknown external forces by using the equations of force equilibrium. When you complete this module you will be able to Identify two force members Calculate forces in two force members This information will be useful in future courses: ENGR 221, CVEN 305, etc.
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ENGR 111 - Track A - Fall 2011 3 Standard Protocol for Finding Force Components 1. Mark all angles CCW from the positive x-axis (angle in standard position). 2. Then the force components are ALWAYS given by θ θ sin cos F F F F y x = = F θ F θ F θ θ F R E V I E W
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ENGR 111 - Track A - Fall 2011 4 x y F x > 0 F y > 0 F x > 0 F y < 0 F x < 0 F y > 0 F x < 0 F y < 0 F F F F II I III IV If you don’t use Standard Protocol for Finding Force Components then keep in mind: R E V I E W
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ENGR 111 - Track A - Fall 2011 5 Moment (or Torque) due to a Force How do you calculate the turning action of a force? Consider the wrench with a force on it. We want to calculate the turning action of the force F around the center of the bolt. The magnitude of the turning action about a point = distance from turning point (pivot) to the line of action of the force times the force . The sign convention: if the tendency to rotate is CCW about the pivot then positive , if CW then negative . Units: N·m or ft·lb. M = F·d d F pivot R E V I E W
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ENGR 111 - Track A - Fall 2011 6 STANDARD PROTOCOL for MOMENTS There is a standard way to calculate moments using vector components. To calculate the moment produced by force F about point O we need to: Step 1. Find horizontal and vertical components F x , F y of the force. Step 2. Sketch the coordinate system with origin in point O. Find the coordinates (x,y) of the point of application of the force (blue dot). Step 3. Then the moment is given by M = x · F y - y · F x (CCW) . x (x,y) F x F y F O y Positive values of M mean that the turning action is counter clockwise (CCW) whereas negative values mean that the turning action is clockwise (CW). R E V I E W
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ENGR 111 - Track A - Fall 2011 7 Equilibrium of a Rigid Body Two conditions must be met for equilibrium (immobility): FORCE EQUILIBRIUM: The vector sum of all external forces acting of the body must be zero (same as the requirement that the Force polygon must be closed).
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