How Do You Plot a Bending Moment Diagram for a Propped Cantilever Beam?

[db330]

Homework Statement

A steel (Young's modulus = 210x109N/mm2) propped cantilever beam (Figure 1) supports a uniformly
distributed load (UDL) of 20kN/m. The beam cross section is a 150mm x 75mm x 8mm rectangular
hollow section (RHS), i.e. 150mm deep, 75mm wide and has an 8mm wall thickness. The cross
section is oriented so that bending occurs about its major axis of bending.
Figure 1
a) Calculate the support reactions at A and B,
b) Plot the shear force diagram,
c) Plot the bending moment diagram (on the tension side) and indicate maximum bending moment
value,
d) Calculate the maximum bending stress and state where it occurs,
e) Calculate the deflection at the mid-point between A and B.

i'm working on part c and am a bit confused as to how the bending moment diagram works.

Homework Equations

just moment equations

The Attempt at a Solution

I have the shear stress diagram and part of the bending moment.

the reaction forces at A and B are 26 2/3 and 53 1/3.

the equations
for Vx and Mx are as follows

0<=x<=3
Vx = 26 2/3 -20x
mx = 26 2/3 x - 10x²

3<=x<=4
Vx = 53 1/3 - 20x
Mx - 53 1/3 - 10x²

but the peace i struggle with I'm getting the end peace of the beam to deflect by a lot more then the middle part, so if you have any input it would be very much appreciated.

 

[PhanthomJay]

You are incorrectly treating this beam as one on pinned supports at x=0 and x=3, , but it is given that the end at x=0 is a fixed end, which is capable of providing both force and moment. The problem is staticallly indeterminate to the first degree, so you have to use another equation besides the static equilibrium equations in order to solve for the reaction forces and moments. Then once you get them, I'm not sure of your graph in the middle, it seems to be an attempt at a deflection curve and not a bending moment diagram.