Beam deflection by superposition

[Jim Newt]

Homework Statement

In this problem, I'm trying to solve for the Reaction, Rb

Homework Equations

I believe for the distributed load, the deflection equation would be:

v = (-qx/24EI) * (L^3 - 6Lx^2 + x^3)

For the support, Rb, the deflection equation could be:

v = (-Pbx/6LEI) * (L^2 - b^2 - x^2)

where L = 3L

total deflection at Rb = db1 - db2 = 0

I could solve for Rb with the proper equations.

The Attempt at a Solution

For db1:

When I plug in x=L and L=3L, I end up with db1 = (11qL^4) / 12EI.
This answer matches the solution manual.

I can't figure out db2...I think I might be using the wrong deflection equation, but I'm not sure. The correct answer for db2 is db2 = (4RbL^3) / 9EI

How do I go about solving for db2?

 

[Jim Newt]

Ok, maybe my whole method is bunk. Given the standard beam deflection equations, how would you solve for Rb?

 

[PhanthomJay]

Ok, maybe my whole method is bunk. Given the standard beam deflection equations, how would you solve for Rb?

You set up the equations perfectly! You may have made a math error in your db2 equation, perhaps forgetting to convert l to 3L. Note that in using the beam tables, you could have used db2 = (R_ba²b²)/3EIl, the deflection at the point of the applied reaction load. The result is the same.

 

[Jim Newt]

Hey thanks buddy! I went through it again and ended up with the correct answer. Its always the tidbit math that gets me...