# Moment Equation

iviv
Hi again. First, I'd like to say thanks a ton to tiny-tim for helping me through with my last problem. He was a great help, though I didn't want to bump that thread to say thanks. Anyway, I've got a far simpler issue now, and I'm having a brain fart.

1. A simply supported beam of span, L, carries two equal point loads of magnitude, W, at the third points. The maximum MID-SPAN moment is given by:-

Now, I know that when its a single point load at the centre of a beam, the equation is WL/4
And I'm just having a little trouble getting my head around the doubling of the forces. We've been told its not WL/8 or WL/12.

WL/8 was my first guess, and I was pretty sure it was right, but I've been told its wrong, but I wasn't sure why. However, now I've actually written all this down, I think I've realised what I've been doing wrong. I was thinking 'double W so double the number'. But since we're dividing by the number, obviously it should be halved, not doubled >_>

Now, this is more simple maths than physics, but should it be WL/2? That was my current initial thought, but then the load isn't slap bang on the centre, its offset at third intervals, so now I'm leaning towards it being WL/3. However, this is just through logic and feel, rather than actual maths. And I'm sure there should be a mathmatical way to work it out, but I'm not seeing it at the moment.

Thanks!

Homework Helper
To get the moment at midspan, you need to start at the center and take moments as you go to one end of the beam.

iviv
Hmm. So, assume 10Kn loads, and a beam 3m long. Since its symmetrical, the moments would be 10Kn at each support.

The force is 10Kn at 1/3 of the beam, so at the centre it would be 15. Using the equation, 15=WL/x

15= 20*3/x

x=4

So the equation would be WL/4, which makes it the same as the equation if there were simply a point load at the mid-span of the beam?

Homework Helper
Hmm. So, assume 10Kn loads, and a beam 3m long. Since its symmetrical, the moments would be 10Kn at each support.

The force is 10Kn at 1/3 of the beam, so at the centre it would be 15. Using the equation, 15=WL/x

15= 20*3/x

x=4

So the equation would be WL/4, which makes it the same as the equation if there were simply a point load at the mid-span of the beam?

Your reactions at the supports would be 15kN.

The BM at mid-span would be the 10kN at a distance of 0.5 m (1.5-1) from the mid-point and the 15kN reaction at a distance of 1.5m from the mid-point.

One will produce a clockwise moment and the other an anti-clockwise moment.