How do you calculte bebding moment for simply supported beam?

Answer 1

First, pick the point along the beam at which you need the bending moment. Then make sure that all the forces on the beam to the right of the chosen point are correctly known. Then calculate the moment about the chosen point each of those forces contributes . Add these up and that is the answer.

For example, consider a 12 metre beam supported at the 4 metre point and the 12 metre point. There is a 10 Kg load at the 0 metre end and a 40 Kg load at the 10 metre point.

Find the bending moment at the 8 metre point.

First we need the loads at the two supports, L1 and L2.

L1 + L2 = 10 + 40 = 50 Kg Total forces up equals total forces down.

And we shall work out all clockwise and anticlockwise moments about the support at the 4 metre point. (The total moments about any point is zero.)

Clockwise: 40x6

Anticlockwise: 10x4 + L2x8

Putting clockwise = anticlockwise we get 240 = 40 + 8xL2 hence L2 = 200/8

And from L1 + L2 = 50 we now get L1 + 25 = 50 hence L1 = 25

So to answer the question - Find the bending moment at the 8 metre point -

we just sit at the 8 metre point and look right. We see the 40 Kg load 2 meters away pushing down and the 25 Kg up-force at the end, 4 meters away.

That makes a moment of 40x2 mKg clockwise and 25x4 anticlockwise. That results in a total of 25x4 - 40x2 anticlockwise. The answer is 20 mKg anticlockwise ( upward) about the 8 meter point.