Uniformly distributed load - Max bending moment help

[JohnP60]

Homework Statement

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 don't know how to work out the maximum bending moment.

Homework Equations

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 don't know how to work out the maximum bending moment would appreciate any help

 

[SteamKing]

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?

 

[JohnP60]

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?

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

 

[SteamKing]

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

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.