1. Department of Aerospace Engineering
AE 212 Mechanics of Solids
Tutorial 10 Topic covered: Transformation of Stresses
1. The state of stress at a point in a member is shown 3. The shaft has a diameter d and is subjected to the
on the element. Determine the stress components loadings shown. Determine the principal stresses
acting on the inclined plane AB and show the result and the maximum in plane shear stress that is
on a sketch. Verify using Mohr’s Circle method. developed at point A. The bearings only support
vertical reactions.
[Hint: Calculate the section properties, support
reactions, bending moments and find normal stress
( as ,then find the principal stresses
and maximum shear stress.
2. The state of stress at a pint is shown on the
element. Determine (a) the principal stresses and
(b) the maximum in plane shear stress and average 4. The solid propeller shaft on a ship extends
normal stress at the point. Specify the orientation outward from the hull. During operation it turns
of the element in each case. Solve using the at rad/s when the engine develops 900
equations derived and Mohr’s circle method. kW of power. This causes a thrust of F= 1.23 MN
on the shaft. If the shaft has a diameter of 250
mm, determine the maximum in plane shear
stress at any point located on the surface of the
shaft.
[Hint: Find the torque transmitted to
calculate and use the axial force to get
, then calculate maximum shear stress,
Ans: 23.2 MPa]

2. Department of Aerospace Engineering
AE 212 Mechanics of Solids
Tutorial 11 Topic covered: Transformation of Strains and Strain Rosette
1. The state of strain at the point on the gear 3. The 450 strain rosette is mounted on the surface
tooth has components of of the aluminum plate. The following readings
are obtained for each gauge:
.Use the strain transformation equations
to determine (a) the in plane principal strains .Determine the in plane principal strains.
and (b) the maximum in plane shear strain and
average normal strain. In each case specify the
orientation of the element and show how the
strains deform the element within the x-y plane.
Verify the solution using Mohr’s circle method.
4. The 600 strain rosette is mounted on the
surface of the bracket. The following readings
are obtained for each gauge:
2. A strain gauge is mounted on the 2.5 cm
diameter steel shaft in the manner as in figure .Determine (a) the principal strains and
below. When the shaft is rotating with an (b) the maximum in plane shear strain and
angular velocity of rev/min, using a associated average normal strain. In each case
slip ring the reading on the strain gauge is show the deformed element due to these
.Determine the power output strains.
of the motor. Assume the shaft is only subjected
to torque.