Deflection simply supported beam

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    Beam Deflection
AI Thread Summary
To find the deflection at midspan of a simply supported beam with two triangular loads, the relevant equation is δ = \frac{Qx}{960LEI}(5L^2-4x^2)^2. The integration for the moment and shear must be consistent over the correct domains, which are critical for accurate calculations. One participant initially did not multiply by 2 but still arrived at the correct answer, prompting discussion about potential errors in their approach. Clarifications were made regarding the expressions for qx and the integration limits for Mx and mx. Ultimately, the correct deflection expression was confirmed through collaborative corrections and validation.
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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

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

Attempt at solution: http://goo.gl/qFYMoG
 
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Excellent work, raymanmusic. Your answer is correct.
 
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