1. When a plate with a hole is under uniaxial loading in x-direction, the stresses at a point at
(r,) (polar coordinates) is given by:
.
(you may understand the angle between the radial line and loading direction.)
Using linear superposition technique to get the stress field for the following two cases.
T2
T
T1
T
b) pure shear
2.Determine the maximum pressure at the contact point between the outer race and a ball in the
single row ball bearing assembly shown below. The ball diameter is 50mm; the radius of the
grooves, 30mm, the diameter of the outer race, 250mm; and the highest compressive force on the
ball, F=1.8KN. Take E=200GPa, and =0.3.
3. For the figure shown above (b), a wheel of radius r1=480mm and a rail of crown radius of the
head r2=340mm. Calculate the maximum contact pressure between the members. Given:
contact force F=4KN. Assumption: both roller and ring are made of steel having E=200GPa and
and =0.3.
4. a) Determine the size of the contact area and the maximum contact pressure when two
cylinders of radii 𝑟1 and 𝑟2 are in contact and the total contact force is F. Assume the two
cylinders are made of same material of stiffness E and Poisson ratio  and the angle between
the two axes of the cylinders is θ.
b) calculate the size of the contact rea and the maximum contact pressure when
E=200GPa, =0.3, 𝑟1=0.1m, 𝑟2 = 0.2𝑚 , 𝜃 = 45° , F=1000N.
5.
6.