# Proving slope

1. Apr 9, 2010

### the white sou

1. The problem statement, all variables and given/known data
"for a cantilever beam with a concentrated load in the middle of the span, prove that

the slope is WL2/8EI, and the deflection is 10WL3/96EI"

2. Relevant equations
the length of the span is L, the concentrated load is acting in the middle at L/2

3. The attempt at a solution

I used the double integration method

and I took M as Wl/2

EI y''= - Mx
so EI y''= - wl/2
EI y'= -wlx/2 +c1

EI y= -wlx2/4 +c1x+ c2

since y'=0, x=l

then c1= wx2/2

and since y''=0, x=l

then c2= -wx3/4 +wx2/2

then dunno what to do

thank you in advance

2. Apr 9, 2010

### PhanthomJay

It looks like the problem is asking for the slope and deflection at the free end of the cantilever. You need to calculate the defelection and slope at midpoint, then use geometry to find the deflection and slope at the free end (the 2nd half of the beam from midpoint to the free end goes along for the ride, with no loading, bending, shear, etc. in that section). Note also that you seem to have extra variables in your equation (EIy" = M, etc).

Last edited: Apr 9, 2010