- #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 z-line, 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.