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CV2101 Chapt 4 - Equilibrium of a Rigid Body

# CV2101 Chapt 4 - Equilibrium of a Rigid Body - Equilibrium...

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Chapter 4 Equilibrium of a Rigid Body

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4 1 Conditions for equilibrium R ll th t 4.1 Conditions for equilibrium Recall that Any system of external forces acting on a rigid body can be reduced to an equivalent force-couple system at an arbitrary point O. For equilibrium the net force as well as the net moment at that For equilibrium, the net force as well as the net moment at that point must be equal to zero. Σ F = 0 and Σ M O = 0 External forces include applied loads, support reactions, and the weight of the body A b d i id d i id h d f ti b t it t A body is considered rigid when deformations between its parts are negligible before and after applying a load. 4-2
4 2 Free-Body Diagram T l h i l t fi t t id li d d l 4.2 Free Body Diagram To analyze a physical system, first create an idealized model. 1. Isolate the body. 2. Draw an outline shape. 3. Show all the external forces (known & unknown) exert on the body. 4. Apply the equations of equilibrium to solve for any unknowns. Pin support prevents translation 4-3

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Example 4 1 Example 4.1 Draw the FBD of the uniform beam. The beam has a mass of 100 kg. Fixed support prevents translation & rotation Free-body diagram The reactions at the wall are shown as A x , A y and the couple M A . Their sense h b d has been assumed. The weight of the beam W = 100× 9.81 = 981 N acts through the center of it G hi h i 3 f A 4-4 gravity G, which is 3 m from A.
Example 4 3 Example 4.3 Two smooth pipes, each having a mass of 300 kg, are supported by the forks of the tractor. Draw a FBD for both pipes together , assuming no friction at all contact surfaces. F b d di The weight of the pipe =300×9.81= 2943N passes through the centroid of the body. Th ti T F P l t th Free-body diagram The reactions T, F, P are normal to the supporting surface. Internal forces between the pipes are not shown as they are a pair of equal but opposite 4-5 collinear forces which cancel each other

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Reactions at support in 2-D problems Reactions at support in 2 D problems Types of No. of unknowns Types of connection Reaction 4-6
Reactions at support in 2-D problems Gene al les Reactions at support in 2 D problems cont . General rules 1. If a support prevents translation of a body in a given direction, then a force is developed on the body in the opposite direction.

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