We consider a thin beam subjected to pure bending as illustrated above with h=2-cm, l=4-cm
1. Define the boundary conditions on the four edges of the beam
2. Considering the Airy function: $A(x, y) = c_1xy + c_2x^2 + c_3y^2 + c_4x^2y + c_5xy^2 + c_6x^3 + c_7y^3$, Determine the expression of the stress tensor, as a function of $x$, $y$, $c_1$, $c_2$, $c_3$, $c_4$, $c_5$, $c_6$ and $c_7$; assuming the problem is in plane-stress, if the gravitational forces are not neglected and that the density of the beam is $\rho$=4 kg.$m^{-2}$
3. Using the boundary condition, determine the expression of the stress tensor if the gravitational forces are neglected.
4. Since the Yield stress of the material is 2-MPa, what is the max of shear $\tau$ that can be applied to the structure?
