This document contains three engineering problems involving stresses in structural elements: 1) A propeller shaft subjected to torsion and axial thrust with given shear and compressive stresses. Determine principal stresses and maximum shear stresses. 2) A simple beam carrying a uniform load, find principal and maximum shear stresses at the neutral axis and 2" above it. 3) An arm made of two welded steel bars, given the maximum tensile stress at the top, determine the bar diameter.

1. A propeller shaft subjected to combined torsion and axial thrust
is designed to resist a shear stress of 56 MPa and a compressive stress of 85 MPa
(see figure).
(a) Determine the principal stresses and show them on a sketch of a properly
oriented element.
(b) Determine the maximum shear stresses and associated normal stresses
and show them on a sketch of a properly oriented element.

2. A simple beam of rectangular cross section
(width 4 in., height 10 in.) carries a uniform load of 1200 lb/ft
on a span of 12 ft (see figure).
Find the principal stresses s1 and s2 and the maximum shear
stress tmax at a cross section 2 ft from the left-hand support at
each of the following locations: (a) the neutral axis, (b) 2 in. above
the neutral axis.

3. An arm ABC lying in a horizontal plane and
supported at A (see figure) is made of two identical solid steel
bars AB and BC welded together at a right angle. Each bar is
20 in. long.
Knowing that the maximum tensile stress (principal stress)
at the top of the bar at support A due solely to the weights of the
bars is 932 psi, determine the diameter d of the bars.