# moment and force calculation for cantilever beam

1. The problem statement, all variables and given/known data A cantilever beam (prismatic, rectangular cross section) is loaded at the tip by a force
P and at half its length L by a moment M.

a. Calculate the reaction force and moment.
b. Draw the shear force and bending moment diagrams

2. Relevant equations
∑F=0; ∑M=0

3. The attempt at a solution
a) The reaction force should be -P, so that the total force is zero. But I am not sure if it works the same for the moment, because I think the moment should always be calculated around the same point? Or should the reaction moment just be -M?
b) The shear force I calculated by looking at just a part of the beam, from somewhere in the middle completely to the right. Since it’s total force should be zero, I think the shear force would be -P (positive shear is defined as if it would rotate the piece clockwise)
But for the bending moment diagram, I am at a complete loss. I know it should be zero at the right end, but I don’t know what I would get at the left and how the moment at the middle is reflected in the diagram.

I hope I made my thoughts clear, any help would be greatly appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Attached Images cantilever.jpg (5.7 KB)

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