# Help with a BMD and deflection of beam problem

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1. Oct 19, 2016

### kostoglotov

1. The problem statement, all variables and given/known data

I am given this beam:

and asked to express the slope at A and the max deflection in terms of a, E, I, and Mo.

I am being told that my answer has the wrong multiplier...so I assume that my overall approach is ok (??) but I've missed dividing something by 2 somewhere or something like that.

I transform that above diagram into an equivalent:

(I whited out the bending moments, pretend they aren't there anymore)

I figure those same bending moments could be produced by a load P like the one I've drawn.

Doing that leads to the shear force and bending moment diagrams that look something like this:

The lines on the BMD are $y = \frac{P}{2}x$ and $]y = \frac{-P}{2}x+\frac{3Pa}{2}$

Thus I get $P = \frac{2Mo}{a}$

and I have the equations $v_{max}=\frac{-PL^3}{48EI}$ and $\theta_{max}=\frac{-PL^2}{16EI}$

Now that I have P in terms of Mo and a, and L = 3a, through basic substitution I get $v_{max}=\frac{-9M_0a^2}{8EI}$ and $\theta_{max}=\frac{-9M_0a}{8EI}$

It does seem strange to me that the constant is the same out the front of both, and I am being told that my multiplier out the front is wrong. What have I missed?

2. Relevant equations

3. The attempt at a solution

2. Oct 24, 2016