# Deflection simply supported beam

raymanmusic

## Homework Statement

How do I find an expression for the deflection at midspan of this beam? The beam is simply supported and there is two triangular loads on each side of the beam.

Illustration of problem: http://goo.gl/gk68Fl [Broken]

## Homework Equations

$Deflection = \Delta = \int \frac{Mx*mx}{EI}$
Elastic curve equation of the simply supported beam for this case:
$\delta = \frac{Qx}{960LEI}(5L^2-4x^2)^2$

## The Attempt at a Solution

I found Mx and mx, and I integrate from $\frac{L}{2}$ to $L$. My answer is: $\frac{QL^4}{120EI}$.

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Homework Helper
raymanmusic: After you integrated from 0.5*L to L, did you multiply by 2? You must multiply by 2, which I think you did, because your current answer in post 1 is correct.

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raymanmusic
Actually I did not multiply by 2, but I still got the correct answer. What did I do wrong?

Attempt at a solution: http://goo.gl/qFYMoG [Broken]

Last edited by a moderator:
Homework Helper
raymanmusic: First, your expression for qx currently looks wrong.

Secondly, your domain (0.5*L, L) for mx looks different from your domain for Mx. But then you combine these two incompatible domains in your integral. Or are you seeing a novel approach I did not envision yet?

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raymanmusic
Thanks! I've made some corrections to my calculations. I think it's easier to understand now.

Attempt at solution: http://goo.gl/qFYMoG [Broken]

Last edited by a moderator: