Equilibrium of a Rigid body
For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point 0 must be zero.
- Drawing an outlined shape: Isolate the body, cut free from constraining, draw the outline of the shape
- Show ALL forces and couple moments and label: Applied force, Support reactions, Weight
Support Reactions
Note, “If a support prevents translation of a body in a given direction, then a force is developed on the body in the opposite direction. Similarly, if rotation is prevented, a couple moment is exerted to the body.”
IN 2D:-
3 Degrees of Freedom (2 translation, 1 rotational)
IN 3D:-
6 Degrees of Freedom (3 translation, 3 Rotational)
Two force member
A two force member has forces applied at only two points on the member.
- The two Force must be equal in magnitude but opposite in direction. (sum of forces must be Zero)
- They both must be in the same line of action. ( the total moment must be Zero)
- Directed along the line joining.
Steps to solve 2D equilibrium problems
Note: we shall be using the equations of equilibrium, i.e sum of all forces about the x and y-axis are Zero, and the moment on the body is Zero.
- Establish x and y-axis
- draw FBD
- Apply the 3 equations of equilibriums
Pro tip: Solve the simpler axis first i.e with the least unknowns. If the final answer is negative then change the sense of the assumed force.
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