# Bending moment and stress of a washer shape

1. Feb 7, 2012

### ehilge

1. The problem statement, all variables and given/known data
I need to find the bending moment of a washer shape for a project I'm working on so I don't have an exact problem statement. Imagine that a washer was fixed (not pinned) around its inner radius and a force were applied evenly around the outer radius. How can I go about finding the max bending moment? After I find the max bending moment, what exactly do I take the moment of inertia of to find stress?

2. Relevant equations
stress = M*y/I

3. The attempt at a solution
I am familiar with how to find the stress in beams with moment diagrams and all that. My only thought on this would be to split the washer into small wedges and approximate the shape as a solid rectangular cantilever beam. I could then solve the problem normally. I realize that this won't give me an exact answer but will it even be close? Is anyone aware of an equation for the maximum stress in a washer shape?

2. Feb 9, 2012

### nvn

C8 = 0.5[1 + nu + (1 - nu)(r1/r2)^2],
C9 = (r1/r2){0.5(1 + nu)*ln(r2/r1) + 0.25(1 - nu)[1 - (r1/r2)^2]},
M = (C9/C8)*w*(r2^2)/r1,
sigma = 6*M/(t^2),

where nu = Poisson ratio, r1 = inside radius, r2 = outside radius, t = washer thickness, sigma = maximum bending stress, and w = transverse applied force per unit of circumferential length, applied all along outside perimeter.

Last edited: Feb 9, 2012
3. Feb 9, 2012

### ehilge

Thank you, that will be incredibly helpful