Beam resting on wide supports with a distributed load

[jet1985]

Homework Statement

A beams is 3.0m long, it rests on two wide supports. The support A is 0.5m wide. Support B is unknown. Point A is taken to be the end of the beam on your left.

Support A has a loading intensity of 75 N/m.

The load on the beam acts with a force of 300N, 2.0m from point A.

The question requires working out the width AND loading intensity of support B, such that the "resultant force and couple moment" about point A is Zero.

Homework Equations

Unsure!

The Attempt at a Solution

I cannot find any examples that use wide supports on beams, or involve loading intensities on those supports. All examples I have found use pivot points! How do I account for the fact that the beam is resting on wide supports, not pivot points, and how would I go about working out the dimensions for Support B and it's loading intensity?

Can someone please point me in the right path?

 

[hotvette]

Think of the supports as uniformly distributed loads in the opposite direction of the 300N load. The 2 unknowns are the width of the load and intensity at B (the problem doesn't state but you can assume point B is the end of the beam). You are asked to find the width and intensity of the support load at B such that the resultant force is zero and moment about point A is zero. Two equations and two unknowns.

 

[tomcue]

I would approach this problem by first understanding the concept of equilibrium. In order for the resultant force and couple moment about point A to be zero, the beam needs to be in a state of equilibrium, meaning that all forces acting on it must balance out.

To begin, we can start by drawing a free body diagram of the beam, with all the forces acting on it. From the given information, we know that there is a distributed load of 75 N/m on support A, and a point load of 300N acting 2.0m from point A.

Next, we can apply the equations of static equilibrium, which state that the sum of all forces in the x direction and the sum of all forces in the y direction must equal zero, as well as the sum of all moments about any point must also equal zero.

In this case, we can choose point A as our reference point and set up the following equations:

ΣFx = 0
ΣFy = 0
ΣM = 0

Using these equations, we can solve for the unknowns, which are the width and loading intensity of support B. Since the beam is in equilibrium, we can assume that the forces acting on it are balanced, and therefore the width and loading intensity of support B must be such that the resultant force and couple moment about point A is zero.

By solving these equations, we can determine the values for support B and its loading intensity. If you are still having trouble, I suggest consulting with a physics or engineering tutor for further guidance.