A weight on a beam held up by two columns - force problem

In summary, Peter is attempting to calculate the forces on a beam with a weight and two supports. He has found that the forces are RL and RR (or R1 and R2), and that the origin for the statics equations is at the top of one of the columns.
  • #1
bpollard
10
0

Homework Statement


A weight (mass given) is sitting on a beam that is supported by two columns. Given the location of the weight on the beam, calculate the force on each column.


Homework Equations


not sure


The Attempt at a Solution


not sure
 
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  • #2
You haven't given nearly enough detail !
 
  • #3
Start by drawing a diagram and labelling what you know. There is a beam with length L, let's say, and there is a weight W sitting somewhere on the beam. The beam is held up by two supports, one at each end. Assume for the time being that the reaction forces are RL and RR (or R1 and R2). If the weight W is located a distance a from the left support, use the equations of statics to determine what RL and RR are in terms of W, L, and a.

After all, this is how beam tables are developed.
 
  • #4
Thank you Steam King. This is the type of information I'm looking for. One hint I was given is to use a coordinate system that makes the problem easier to attack. I'm not sure what to do with that. Also, can you point me in the right direction with the basic statics equations?
 
  • #5
You could also attack this from a static equilibrium point of view, realizing that both net force and net torque must be zero for the thing to stay still.

Your first step is to find the center of mass of the weight and horizontal beam as a distance from a column.

Once you've done that, set the net torque and net force equal to zero and solve.

Also, choosing the left pillar as the origin would be easiest in my opinion.
 
  • #6
oh, this is it Firestorm! can you help me out with some equations? I just need to be pointed in the right directions with some equations. any help you can provide would be great.
thanks!
 
  • #7
Sure; first, realize that FL + FR = m * g
and that torque is [itex]\tau[/itex]= r x f

That should get you going.
 
  • #8
I tried this problem again, and am still stuck. Please see the attachment for my work thus far.
I know that I need to be able to pick an origin that will make the problem easier and cancel some stuff out, but I don't know what this is.
any other help/ideas/hints?
very much appreciated.
 

Attachments

  • center of mass problem.jpg
    center of mass problem.jpg
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  • #9
bpollard said:
I tried this problem again, and am still stuck. Please see the attachment for my work thus far.
I know that I need to be able to pick an origin that will make the problem easier and cancel some stuff out, but I don't know what this is.
any other help/ideas/hints?
very much appreciated.

I don't think the centre of mass is necessary to calculate.

For an overlaying coordinate system, have the origin at the top of one of the columns - eg the left one.
The mas is then at (4,0) and the top of the other column is at (5,0)

Does the beam have a mass??

Peter
 
  • #10
the beam does not have a mass...
 
  • #11
bpollard said:
the beam does not have a mass...

Well that makes calculating the torques more simple.

Peter
 

FAQ: A weight on a beam held up by two columns - force problem

What is the formula for calculating the force on a beam held up by two columns?

The formula for calculating the force on a beam held up by two columns is F = (W1 + W2) * L / d, where F is the force, W1 and W2 are the weights on each column, L is the length of the beam, and d is the distance between the columns.

Do the weights on each column have to be equal for the beam to be in equilibrium?

No, the weights on each column do not have to be equal for the beam to be in equilibrium. As long as the total weight on one side of the beam is equal to the total weight on the other side, the beam will be in equilibrium.

What factors can affect the force on the beam?

The force on the beam can be affected by the weights on each column, the length of the beam, and the distance between the columns. Other factors that can affect the force include the material and strength of the beam, the stability of the columns, and external forces such as wind or vibrations.

How can I determine the stability of the columns?

The stability of the columns can be determined by calculating the moment of the force on each column. This can be done by multiplying the weight on the column by its distance from the center of the beam. If the moments on each column are equal, then the columns are stable.

What is the significance of solving a "weight on a beam held up by two columns" problem?

Solving a "weight on a beam held up by two columns" problem is important in engineering and construction. It allows us to determine the necessary dimensions and materials needed to support a certain weight and ensure the stability of a structure. It also helps us understand the forces acting on the structure, which is crucial for safety and structural integrity.

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