Question

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?

          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?

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) = c1xy + c2x^2 + c3y^2 + c4x^2y + c5xy^2 + c6x^3 + c7y^3, Determine the expression of the stress tensor, as a function of x, y, c1, c2, c3, c4, c5, c6 and c7; assuming the problem is in plane-stress, if the gravitational forces are not neglected and that the density of the beam is ρ=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 τ that can be applied to the structure?

Added by Michelle P.

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