 #1
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Homework Statement
Problem shown as image
jan2010 Q5.jpg
Q5. a)
Homework Equations
Also shown in image
The Attempt at a Solution
Made a cut between A and the zline, so ∑M = 0 = M  wx(x/2) = M  (wx^{2})/2 ⇒ M = (wx^{2})/2
and d^{2}y/dx^{2} = M/EI
∴ d^{2}y/dx^{2} =  (wx^{2})/2EI
So dy/dx = ∫ d^{2}y/dx^{2} dx = w/2EI ∫ x^{2} dx = wx^{3}/6EI + c_{1}
I was fine up to this point. My answer here agrees with the answer in the question ( equation 5.2) as x = L.
So what I got next:
y = ∫ dy/dx dx = w/6EI ∫ x^{3} dx + ∫ c_{1} dx = wx^{4}/24EI + c_{1}x + c_{2}
Letting x = L
dy/dx = wL^{3}/6EI + c_{1} (as in the question)
and
y = wL^{4}/24EI + c_{1}L + c_{2} (which is different to the answer given in the question)
How/why is the answer to equation 5.2 wL^{4}/8EI ??
I probably made a silly mistake somewhere or I'm just too tired :P
Thanks for any help.
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