How Do You Calculate the Moment to Relieve Load on Roller A in a Beam System?

[ur5pointos2sl]

The problem states: Construct a FBD of the system shown in 7.38(which i have attached). The beam is uniform and has a mass of 550 kg(I converted it to kN). Determine the moment M that will relieve roller A of any load. At this condition determine the resultant pin reaction at B.

This is not a mechanics class(so I have no background)but our instructor was just getting us started for next semester mechanics that he teaches. The book has few examples and not an example of this type. How would I determine the moment? Any help to get me started would be great. Thanks

 

[tiny-tim]

The problem states: Construct a FBD of the system shown in 7.38(which i have attached). The beam is uniform and has a mass of 550 kg(I converted it to kN). Determine the moment M that will relieve roller A of any load. At this condition determine the resultant pin reaction at B.

Hi ur5pointos2sl!

I can't see the picture yet,

but my guess is that you should find M by taking moments about B

(because then the reaction at B can be ignored )

 

[piercas]

I understand your confusion and hesitation in approaching this problem. However, it is important to remember that as scientists, we are trained to analyze and solve complex problems using logical and systematic methods. In this case, we can use the principles of mechanics and the concept of free body diagrams (FBDs) to solve this problem.

First, let's define the given system. The system consists of a uniform beam with a mass of 550 kg (or 5500 N) and two supports - roller A and pin B. The beam is in equilibrium, meaning that all forces acting on it are balanced. In order to determine the moment that will relieve roller A of any load, we need to create a FBD of the system.

A FBD is a simplified diagram that shows all the external forces acting on a body and their respective directions. In this case, the external forces acting on the beam are its weight (W) and the reaction forces at roller A (R_A) and pin B (R_B). The direction of the reaction forces can be determined by considering the constraints of the supports - roller A can only exert a vertical force while pin B can exert both a horizontal and vertical force.

Now, to determine the moment (M) that will relieve roller A of any load, we need to apply the principle of moments. This principle states that the sum of all moments acting on a body should be equal to zero for the body to be in equilibrium. In this case, the moment caused by the weight of the beam (W) should be counteracted by the moment caused by the reaction force at pin B (R_B). Therefore, we can set up the following equation:

M = R_B * x - W * (L/2)

Where x is the distance from the support pin B to the point where the weight of the beam is acting and L is the length of the beam. We can solve for M by plugging in the values of R_B, x and W.

Once we have determined the moment, we can use the principle of equilibrium to determine the resultant pin reaction at B. This principle states that the sum of all forces acting on a body in any direction should be equal to zero for the body to be in equilibrium. In this case, we can set up the following equations:

∑F_x = 0: R_B = 0
∑F_y = 0: R_A + R_B - W