Proving Slope & Deflection of Cantilever Beam with Concentrated Load

[the white sou]

Homework Statement

"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"

Homework Equations

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

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 don't know what to do



thank you in advance

 

[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).