Draw shear force and bending moment diagrams

[bigu01]

Homework Statement

For the beam shown in the figure: a) Draw necessary free body diagrams

b) Calculate support reactions

c) Draw the shear force and bending moments

Homework Equations

∑Fy = 0; ∑M = 0; V(x) = ∫ L(x) ; M(x) = ∫ V(x)

The Attempt at a Solution

I reverted and flipped the figure in order to have it easier for me, as I am used to work in the most used system of coordinates. I have solved the problem, except when coming to the M(x)3, drawing the diagram of it, I should get -20 kN*m and not 0. If you can inspect the solution procedure and if you find the mistake , please give me some hints of what I have done wrong and how should I approach it

 

[SteamKing]

Your problems start with calculating the support reactions for the beam. In your equations for the moments, it appears you did not include the 20 kN-m couple in you moment summation. It's really hard to follow your calculations because: 1.) you have inverted the beam, and 2.) you don't indicate the origin of your moment arms.

It's not clear why you inverted the beam; it makes it very hard to check your calculations and you don't seem to have obtained any simplification to finding the solution to the problem.

 

[bigu01]

Oh, yes. So that means I am correct. But, looks like I have not solved the question I was asked, instead, I have solved another question without the moment given.

I inverted the beam in order to have the x-y system of coordinates with x positive - horizontal to the right , and y - positive vertical upwards. There is no simplification, it just fits me better solving like that. Apart for the initial silly mistake :(, there is not any other mistake is it?

 

[SteamKing]

Well, if the reactions aren't correct, then the shear force and bending moment diagrams aren't correct either.

 

[pongo38]

It might help to get the reactions to separate out the three contributions: (i) from the moment (ii) from the udl and (iii) from the triangularly distributed load. Then add the contributions together. Finally, check your reactions by taking moments about any point you haven't yet used. If it doesn't check, then there is an error somewhere, and, as steam king says, there is no point in continuing with m and v diagrams.