# Uniformly distributed load - Max bending moment help

1. Mar 20, 2015

### JohnP60

1. The problem statement, all variables and given/known data
I have to work out the reactions at A & D. Sketch the shear force diagram for the beam and sketch the bending moment diagram.

i have worked out the reactions at A=56kN and D=34kN. I have done the SFD. I am just struggling doing the bending moment diagram and dont know how to work out the maximum bending moment.

2. Relevant equations

3. The attempt at a solution
RA + RD = 90kN

5RD = (20X1) + (60X2) + (10X3)
5RD = 170kN
RD = 34kN

RA=56kN.

I have done the SFD.

Bending moment diagram i have to state the three significant values.

I have left side as (56x1) = 56kN M
right hand side is (34x2) = 68kN M
i just dont know how to work out the maximum bending moment would appreciate any help

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2. Mar 20, 2015

### SteamKing

Staff Emeritus
If you have the shear force diagram, this should tell you at which locations to look for the maximum bending moment.

After all, dM / dx = V, where V is the shear force and M is the bending moment.

What can you say about dM / dx where the bending moment is a maximum?

3. Mar 20, 2015

### JohnP60

How would i go about doing my bending moment diagram from this sfd. how do i put data into that equation. i worked out x as 1.2m

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4. Mar 20, 2015

### SteamKing

Staff Emeritus
The equation was not put there so that you could calculate M, but to illustrate how to use the shear force diagram to find the locations along the beam where M is a maximum.

If you want to find where a given function has a maximum, in this case the function is M(x), or bending moment as a function of position x along the beam, the point(s) at which the first derivative is zero coincide with the locations where the function has a maximum or minimum.

In other words, if you want to find x where M(x) has a max. or min. value, then dM(x) / dx = 0. Since also dM(x) / dx = V(x), then the points x1, x2, ..., at which the shear force V(x) = 0 are also the points at which the bending moment has a maximum or minimum value.

This is a basic application of the derivative and should have been covered in your calculus course.