Mecanica de Materiales

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.