CE Statics Chapter 6 – Lecture 22

FRAMES AND MACHINES Frames And machines are structures composed of pin-connected members. Those members are subjected to more than two forces. The forces acting at the joints and supports can be determined by applying the three equilibrium equations (  Fx=0;  Fy=0;  Mo=0) to each member. This is done by disasembling the structure and drawing the free-body diagram of each member.

Free-Body Diagram 1. Isolate each part 2. Include all forces and couple moments acting on each part 3. Identify knowns and unknowns 4. Keep the dimensions of of the original structure 5. Find rectangular components of forces with respect to x and y coordinates 6. Assume the direction of unknowns or find it by inspection 7. Identify all two-force members in the structure 8. Forces common to two members act with equal magnitude but opposite direction.

Equations of Equilibrium By applying equilibrium equations, the unknown forces at the supports and connections can be determined. As long as the structure lies in the x-y plane, then  Fx=0;  Fy=0; and  Mo=0.

 Fx=0  Fy=0  Mo=0

 Fx=0  Fy=0  Mo=0  Fx=0  Fy=0  Mo=0

 Fx=0  Fy=0  Mo=0  Fx=0  Fy=0  Mo=0  Fx=0  Fy=0  Mo=0