A weight of 50lb is hung from the end of a pressurized pipe. The weight is applied at the centroid, so there is no torque pointing to the right. There is a weak spot in the material 3in from the end of the nozzle. The weak spot is in the same horizontal plane as the centroid. The pressure in the line is 50psi, the outer diameter is 2:25in, the inner diameter is 2in. The elastic modulus is E = 30; 000ksi and Poisson's ratio is  = 0:3.

(a) Draw the normal and shear stresses for the element shown in the gure.

(b) Find the maximum in-plane shear stress at the location of the element.

(c) Find the maximum out-of-plane shear stress at the location of the element, (the element is on the outside of the pipe, so 3 = 0.)

(d) Use the principle stresses to nd the maximum strain at the location of the element.