Deflection simply supported beam

  • #1
raymanmusic
31
1

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


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

The Attempt at a Solution


I found Mx and mx, and I integrate from [itex]\frac{L}{2}[/itex] to [itex]L[/itex]. My answer is: [itex]\frac{QL^4}{120EI}[/itex].
 
Last edited by a moderator:

Answers and Replies

  • #2
nvn
Science Advisor
Homework Helper
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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.
 
Last edited:
  • #3
raymanmusic
31
1
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:
  • #4
nvn
Science Advisor
Homework Helper
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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?
 
Last edited:
  • #5
raymanmusic
31
1
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:
  • #6
nvn
Science Advisor
Homework Helper
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Excellent work, raymanmusic. Your answer is correct.
 

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