Additional Problem $1$:

A metal pipe that has a wall thickness of $12$ mm and an outer diameter of $420$ mm is made by

welding sections together along an inclined joint at an angle of $22$ degrees from the axis

perpendicular to the pipe length, as shown in the sketch below. If the maximum allowable

normal stress for the weld is $58$ MPa and the maximum allowable shear stress for the weld is $42$

MPa $,$ determine the largest axial force, P $,$ that can be applied to the pipe. Note: Assume the

formula for stresses on an inclined plane given in class can be applied directly to the cross$-$

sectional area of the hollow circular pipe $($do not try to refine the correction for the oval shape of

the cross$-$section at the welded joint$).$ Anwser is $1038$ KN$.$