How to Calculate Midspan Deflection of a Cantilever Beam with Uniform Load?

AI Thread Summary
To calculate the midspan deflection of a cantilever beam under a uniformly distributed load, the relevant formula is δ = (Qx² / 24EI)(6L² - 4Lx + x²). The user initially calculated the deflection as (49QL⁴ / 1280EI) but later corrected it to (17QL⁴ / 384EI) after substituting x = L/2 into the elastic curve formula. Verification against beam tables is recommended to confirm the accuracy of the result. A clarification was made regarding the correct interpretation of the loading variable. The final correct expression for deflection is (17QL⁴ / 384EI).
raymanmusic
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Homework Statement


How do I find an expression for the deflection at midspan for a cantilever beam loaded with a uniformly distributed load?

Illustration of beam: http://goo.gl/3SxeVZ


Homework Equations


\delta = \frac{Qx^2}{24EI}(6L^2-4Lx+x^2)

The Attempt at a Solution


Attempt at solution: http://goo.gl/umUBkU

My current answer is: \frac{49QL^4}{1280EI}, I think this is wrong. Putting x = \frac{L}{2} in the elastic curve formula I get: \frac{17QL^4}{384EI}, I think this is the correct answer.
 
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You can always check your formula for the deflection by setting x = L and seeing if your result is the same as that from a beam table.
 
raymanmusic: qx = q, not qx = q*x/L. Try again.
 
Yes, that was the mistake. I got the correct answer now: \frac{17QL^4}{384EI}. Thank you nvn.
 
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