Calculating Maximum Bending Moment?

[RStars]

Homework Statement

A Beam ABCDE is 10m long and supported at its left hand end A and at a point D which is 9m to the right of A. The beam carries concentrated loads of 5kN at B, which is 2m to the right of A, 10kN at C, which is 6m to the right of A, and 3kN at E. It also carries a distributed load of 4kN/m between points A and D Determine i) the reactions at A and D; ii) the position and magnitude of the maximum bending moment and the position of any point of contra flexure; iii) draw the Shearing Force and Bending Moment diagrams for the beam indicating principal values.

Homework Equations

The Attempt at a Solution

I have already solved part i) the reactions, I have already figured out all the bending moments at each points and the shearing forces. I have already drawn the shearing force diagram. However I am having an issue trying to figure out how to calculate the magnitude and position of the maximum bending moment along with the position of the point of contra flexure. I think I missed the lecture when this was covered. So far I know that:

When shearing force = 0 the bending moment is at a maximum or minimum.

Therefore when I drew the shearing force diagram I could see that the maximum point falls between point B and C. However how do I calculate the magnitude and find the exact position of the max bending moment and the contraflexure point? Is there some kind of formulae?

Many thanks.

Homework Statement

Homework Equations

The Attempt at a Solution

Note I also tried to balance the shear force to zero, solving for x by:

adding the reactions:

RA + RB = 3+10+5+4x
where 4 x is the UDL*x

ended up with x = 9 which I know for sure isn't the position of the max bending moment because it does not coincide with my values of the bending moments for each point.

 

[pongo38]

It's very easy to make mistakes, and your work should be self-checking. You should submit your detailed calcs and sketches so that we can see where you have either a computational error or a misconception of the principles of equilibrium.