Problem shown as image
Also shown in image
The Attempt at a Solution
Made a cut between A and the z-line, so ∑M = 0 = M - wx(x/2) = M - (wx2)/2 ⇒ M = (wx2)/2
and d2y/dx2 = -M/EI
∴ d2y/dx2 = - (wx2)/2EI
So dy/dx = ∫ d2y/dx2 dx = -w/2EI ∫ x2 dx = -wx3/6EI + c1
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 ∫ x3 dx + ∫ c1 dx = -wx4/24EI + c1x + c2
Letting x = L
dy/dx = -wL3/6EI + c1 (as in the question)
y = -wL4/24EI + c1L + c2 (which is different to the answer given in the question)
How/why is the answer to equation 5.2 wL4/8EI ??
I probably made a silly mistake somewhere or I'm just too tired :P
Thanks for any help.