Confused on Calculating Deflection and Rotation for Non-Prismatic Beam?

[Fat Ryan]

Homework Statement

Homework Equations

[k]{delta}=F

The Attempt at a Solution

I found I(x) and confirmed it manually. Basically, I think my confusion comes when finding delta. Delta is a 2X1 array of -d and -theta, respectively. I used equations for deflection and rotation for a prismatic beam that's uniformly loaded...

dmax=-wL^4/(8EI)
thetamax=-wL^3/(6EI)

initially, i integrated the above equations WRT x, along the length 0-->L (with I=I(x) of course), but that gave me absurdly large answers. So then I used the above equations with I=integral(I(x)dx). This gave me reasonable deflections, but it left me with a resulting shear force of only 0.2kip on the right. equating vertical forces to 0 leaves me with a shear of 59.8kip on the left. This cannot be correct.

I can't seem to figure out what I am doing wrong, but once i get it, i shouldn't have a problem calculating the FEFs for w2. can someone please take a look, and let me know where I am going wrong? Thanks!

 

[Fat Ryan]

Ha, I meant E=5000ksi in the problem statement; my apologies.

 

[Fat Ryan]

Tried doing it a different way and got it to work