EQUILIBRIUM & REACTIONS

Question

Force “P” is pushing against a cantilever beam as shown. Draw a free body diagram indicating the three reactions at Point A: horizontal reaction (RX), vertical reaction (RY), and moment reaction (MA). The reactions will be equal and opposite to the forces produced by force “P”. To solve this problem, draw a “FREE-BODY DIAGRAM” (FBD) of the system that represents all the forces. (See textbook pages 74-81 for examples.) Draw the three reaction forces at Point A. Write the three equations of equilibrium and solve the system. Show your sketches & calculations for full credit. Remember to label units and round answers to the nearest one-thousandth.

Answer 1

This is a little murky without the diagram, but I can try to help, assuming that point A is the contact between the wall and the beam and that force P is acting somewhere on the beam, with both x and y components.

1. First, recall that the three equations of equilibrium are that the sum of the horizontal forces = 0, the sum of the vertical forces = 0, and the sum of the moments = 0. Therefore...
2. R_x will be equal and opposite to the x-component of force P
3. R_y will be equal and opposite to the x-component of force P
4. The moment reaction at A will be equal and opposite to the moment caused by the vertical component of force P only.
5. The horizontal component will not produce a moment, as it acts perpendicularly to the length of the cantilevered beam. This does not cause rotation.
6. The vertical component will produce a moment equal to the vertical force times the radial distance from the wall. This is also known as a Torque. Depending on your diagram, the moment will be either clockwise or counter-clockwise
7. M_A, the moment reaction, will be equal in magnitude and in the opposite rotational direction to that answer.