Deflection by integration of load equation

[Freyster98]

Homework Statement

Determine the equation for the deflection curve for the cantilever supported at A with a load given by: q=q₀*sin($$\pi$$x/L).

Homework Equations

The Attempt at a Solution

I think this is pretty straightforward, but want to be sure. I did a similar problem with a simply supported beam with the same load equation, shown in the attached diagram. Am I safe to assume that the ONLY difference in this problem with a cantilever is the boundary conditions used to solve for C₁, C₂, etc?

The boundary conditions would be:
at x=0,y=0...and at x=0,moment=0.
right?

 

[minger]

Right, typically you say to yourself what is zero at the boundaries. For a simply supported beam, the deflections are zero; for a fixed-fixed beam, both deflections and angles are zero. In the case of a cantilevered beam, on the fixed end you have zero angle and zero deflection, but the million dollar question is what is zero at the free end?

 

[Freyster98]

Right, typically you say to yourself what is zero at the boundaries. For a simply supported beam, the deflections are zero; for a fixed-fixed beam, both deflections and angles are zero. In the case of a cantilevered beam, on the fixed end you have zero angle and zero deflection, but the million dollar question is what is zero at the free end?

The moment, right?

Going back to my "attempt at a solution", I believe I screwed up. For the cantilever, at x=0, y=0...and at x=0, dy/dx=0. I had put that at x=0,moment=0, which is wrong. Also, I'm going to need to use: @x=L,shear force=0...and @x=L,moment=0.

 

[minger]

Yup, you're right on track now. Good luck