# Problem with values for a bending moment diagram

1. Sep 2, 2014

### PizzaWizza

1. The problem statement, all variables and given/known data

I have a 5m long simply supported beam, with supports at points 0m and 5m. There's a UDL of 10kNm^-1 from 0m to 4m. It has downward forces acting at 2m (10kN) & 4m (15kN). I need to sketch a bending moment diagram to determine the position & value of the max bending moment. I'm asked to show workings using 1m intervals for bend moment calcs.

2. Relevant equations

Taking moments from one end to determine upward supports.

3. The attempt at a solution

UDL = 4m x 10kN^-1 = 40kNm^-1 @ 2m (centre of)

Taking moments from Support 1 (R1) = 10x2 + 40x2 + 15x4 = R2 x5

R2 = 160/5 = 32kN. ∴ R1 - 33kN (As the sum of downward forces = 65kN)

I've sketch a shear force diagram that I'm happy with, now to where I'm becoming undone.

Calculating the bending moments for the beam @ 1m intervals

M0 = 0

M1 = 33x1 - (10x0.5x1(UDL)) = 33-5 = 28kN @ 1meter

M2 = 33x2 - (10x1x2(UDL)) - (10x1) = 66-30 = 36kN @ 2meters

M3 = 33x3 - (10x1.5x3(UDL)) - (10x2) = 99-65 = 34kN @ 3meters

M4 = 33x4 - (10x2x4(UDL)) - (10x3) - (15x1) = 132-125 = 7kN @ 4meters

I'm assuming M5 has to be zero. This just doesn't feel right to me. I've got 15kN acting @ 4m and it doesn't seem to be having an effect on the diagram if graphed. I have to be doing something wrong?

Thanks for any help.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 2, 2014

### SteamKing

Staff Emeritus
You should post you SF diagram.

The BM is the area under the SF curve starting at x = 0. I think you have incorrectly done your integrations of the SF curve for x = 1, 2, 3, and 4 m.

3. Sep 4, 2014

### PizzaWizza

Thanks for the feedback. Here's the Shear force diagram.

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4. Sep 4, 2014

### SteamKing

Staff Emeritus
So far, so good. And the bending moments?

5. Sep 6, 2014

### PizzaWizza

The bending moments I've highlighted in the original message. They're wrong, I know. I just don't know why?

M1 = 33x1 - (10x0.5x1(UDL)) = 33-5 = 28kN @ 1meter

M2 = 33x2 - (10x1x2(UDL)) - (10x1) = 66-30 = 36kN @ 2meters

M3 = 33x3 - (10x1.5x3(UDL)) - (10x2) = 99-65 = 34kN @ 3meters

M4 = 33x4 - (10x2x4(UDL)) - (10x3) - (15x1) = 132-125 = 7kN @ 4meters

6. Sep 6, 2014

### SteamKing

Staff Emeritus
Perhaps because you didn't use the shear force diagram correctly?

The shear force diagram is constructed, in part, to allow the ready creation of the bending moment diagram.

7. Sep 7, 2014

### PizzaWizza

Thanks. I appreciate it and I think it's sank in now :)

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