Abu Dhabi University
College of Engineering
Department of Mechanical
Engineering
MEC‐430 Machine Design II
Assignment‐1
Stress Analysis and static
failure theories.
1. Draw the shear and moment diagrams for the shown shaft. The bearings at A and D exert only vertical
(radial) reactions. If the shaft has a uniform diameter of 1.5 inch, determine the maximum stress due to
bending moment in the shaft.
2. Determine the normal force, shear force and bending moment at point C for an applied load of P=8 kN.
If the cross section at C is circular with a diameter equal to 20 mm, plot the stress distribution at the
section and find the principal stresses at critical point.
3. For the plane stress state listed below, draw a Mohr’s circle diagram properly labeled, find the principal
normal and shear stresses, and determine the angle from the x axis to σ1.
σx = 16 kpsi, σy = 9 kpsi, τxy = 5 kpsi ccw
4. A countershaft carrying two V-belt pulleys is shown in the figure. Pulley A receives power from a motor
through a belt with the belt tensions shown. The power is transmitted through the shaft and delivered to
the belt on pulley B. Assume the belt tension on the loose side at B is 15 percent of the tension on the
tight side.
a. Determine the tensions in the belt on pulley B, assuming the shaft is running at a
constant speed.
b. Find the magnitudes of the bearing reaction forces, assuming the bearings act as
simple supports.
c. Draw shear-force and bending-moment diagrams for the shaft. If needed, make
one set for the horizontal plane and another set for the vertical plane.
d. At the point of maximum bending moment, determine the bending stress and the
torsional shear stress.
e. At the point of maximum bending moment, determine the principal stresses and
the maximum shear stress.
5. A 30-mm-diameter shaft, made of AISI 1018 HR steel, transmits 10 kW of power while rotating at 200
rev/min. Assume any bending moments present in the shaft to be negligibly small compared to the
torque. Determine the static factor of safety based on
(a) the maximum-shear-stress failure theory.
(b) the distortion-energy failure theory.
6. Cantilevered rod OA is 0.5 m long, and made from AISI 1010 hot-rolled steel. A constant force and
torque are applied as shown. Determine the minimum diameter, d, for the rod that will achieve a
minimum static factor of safety of 2 (a) using the maximum-shear-stress failure theory. (b) using the
distortion-energy failure theory.
7. A cast aluminum 195-T6 exhibits Sut = 36 kpsi, Suc = 35 kpsi, and εf = 0.045. The given stress state is
σx = 15 kpsi, σy = 8 kpsi, τxy = -8 kpsi. For the given state of plane stress, determine factor of safety
using:
(a) using the Coulomb-Mohr theory
(b) using the modified-Mohr Coulomb theory