Cantilever Beam subjected to shear stress

[L.Richter]

Homework Statement

A cantilever beam (length, L, height, 2h, thickness 1). The top surface is subjected to shear stress tsubxy = s. Determine the stress function psi. The boundary conditions at the end of the free end (x=L) can be satisfied by integration (e.g., traction free can be expressed by integral from -h to h of sigma x dy = 0).

Homework Equations

Y runs vertical along the wall. X entends to the right. The shear stress runs along the +x direction.

The Attempt at a Solution

The only thing I need are the boundary conditions. I can solve for psi and the constants as long as I have the starting equations found from the boundary conditions. I am terrible at boundary conditions!

 

[L.Richter]

Got the boundary conditions! And now I'm working on solving the constants from these equations:

-B - 2Dx + 2Eh = 0
2A + 6Cx - 2Dh = 0
-B - 2Dx - 2Eh = -sx/I
2A + 6Cx + 2Dh = 0

Odd system of equations.