Bending Moment Problem: Finding the Moment & Shear Force

[stephen765uk]

The question.

A beam with a solid square cross section of 200mm x 200mm with a length of 30m is simply supported at both ends. Weight of beam = 10kn/m. The beam has a UDL of 120KN which lies between 8m and 20m from the left hand side.

I am fairly new to this so please bear with me. I have found moments for r1 and r2 as follows.

r1=214kn r2=206kn

I need to find the bending moment and shear force however can't remember the method for this. Could anyone just run me through the rough calculations without giving me the answer. Many Thanks.

 

[mathmate]

If the beam is simply supported at each end, and has a uniform section and weight, and the load is uniform, I would expect the reactions to be equal at each end.
The total of the reactions should add up to the total load, includeing weight.
Your attempt at the solution does not seem to satisfy the above criteria.

To calculate the reactions, you take moments about points 1 and 2 in turn, which leaves you with an equation with one unknown at a time (r2 and r1). If they come out not equal for a symmetrical beam with symmetrical load, you understand that there is a little problem. Another check is to add up r1 and r2, the sum of which should equal the total loads including self-weight.

The shear force at a particular section is relatively easy to calculate, namely it is the sum of all external forces on the left (or on the right, since they should be equal but opposite in direction) of the section. The beam's cross section is resisting this difference in forces.

If you have a chance to rework on your calculations and post the details of the calculations, I would be more than glad to help you check your calculations.

If you have a chance to go to the university library, look up some books on Strength of Materials. They should all explain the subject in much more details than we can do at a forum.
Some classic titles are :

Strength of materials by Stephen Timoshenko
https://www.amazon.com/dp/0898746213/?tag=pfamazon01-20
Strength of materials by Den Hartog
https://www.amazon.com/dp/0486607550/?tag=pfamazon01-20

 

[Mene]

I would suggest using the equations for bending moment and shear force to solve this problem. The bending moment at any point along the beam can be calculated by taking the sum of all the forces acting on one side of the point and multiplying it by the distance from that point to the support. The shear force at any point can be found by taking the sum of all the forces acting on one side of the point.

In this specific case, the beam is simply supported at both ends, so the bending moment and shear force will be highest at the supports and decrease towards the center of the beam. To find the bending moment and shear force at a specific point, you will need to consider the forces acting on either side of that point, including the weight of the beam and the UDL.

It may also be helpful to draw a free body diagram to visualize the forces acting on the beam. Remember to use the units of kilonewtons (kn) for force and meters (m) for distance in your calculations. I hope this helps guide you in solving the problem. Good luck!