# #9. 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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