# Stresses in triangular plate with one edge under uniform loading

1. Nov 29, 2013

### roldy

1. The problem statement, all variables and given/known data
A 45° triangular plate ABC built in at BC and loaded by a uniform pressure p0 on the upper edge AB. The inclined edge AC is traction free. Find the stresses in the plate.

2. Relevant equations
Stress function:
$\phi = r^2\left[A_1\cos(2\theta)+A_2+A_3\sin(2\theta)+A_4\theta\right]$

3. The attempt at a solution
I know how to get the stresses in the plate. I'm just having trouble setting this problem up in terms of boundary conditions. I assumed that this is a punch on a rigid half-plane since one of the sides in fully built in. If my assumption is correct, then the boundary conditions below follow.

@ $\theta = 0;\ U_r = 0,\ U_\theta = 0$
@ $\theta = \pi/2;\ \sigma_{\theta r} = 0,\ \sigma_{\theta \theta} = -p_0$

Are these boundary conditions correct? Attached is an image of the plate.

#### Attached Files:

• ###### Triangular Plate.pdf
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