Solve Friction Problem: Beam AB, P, BC (300N/m, .2, .5)

[Ne0]

Question:
Beam AB is subject to a uniform load of 300N/m and is supported at B by column BC. If the static coefficients of friction at B and C are (muB) = .2 and (muc) = .5, determine the force P needed to pull the column BC out from under the beam if P is .25m away from C and .75m away from B. Also the columb BC is 4 meters away from A. Neglect the weight of the members. I have a picture attached so you can get a better idea of the problem.

I started off by finding the Normal force pushing down on the beam which is (300N/m)x(4m) = 1200N. Form there I am stuck as I don't know how to set up the problem to solve for the force P. I tried to find the sums of the horizontal and vertical forces but that wasn't quite working out as I couldn't figure out how to incorporate the moment of the force P. If I could just get a hint towards the right direction I would appreciate that a lot. Thanks in advance.

 

[Astronuc]

One has to determine the load on the column BC - the distributed load is supported by column BC (right) and the pinned end on the left.

Then with that load, determine the static forces at B and C, which would oppose P.

Since P is assymetically located, one must determine the moment imposed by P at either B or C, and which is greater than the opposing force at B or C.

 

[piercas]

Based on the information provided, it seems like you are on the right track. Here are some steps you can follow to solve this friction problem:

1. Draw a free body diagram of the beam AB, including the forces acting on it (load, normal force, and friction forces at B and C).

2. Use the given information to calculate the normal force at B (1200N) and the friction forces at B and C (muB x normal force and muC x normal force).

3. Set up the equilibrium equations for the beam in the horizontal and vertical directions. Remember that in the horizontal direction, the sum of all forces must be equal to zero, while in the vertical direction, the sum of all forces must be equal to the normal force (1200N).

4. Since the beam is not moving, the sum of the moments of all forces acting on it must also be equal to zero. This includes the moment of the force P, which can be calculated using the distance from C and B and the magnitude of P.

5. Use the equations to solve for the unknown force P. You may need to use some algebra to manipulate the equations and isolate P.

6. Once you have solved for P, make sure to check your answer by plugging it back into the equations to see if the beam is still in equilibrium.

Remember to always label your forces and use the appropriate units in your calculations. I hope this helps guide you in the right direction, but if you are still stuck, don't hesitate to seek further assistance from your instructor or a classmate. Good luck!