A bronze bushing 60 mm in outer diameter and 40 mm in inner diameter is to be pressed into a hollow steel cylinder of 120-mm outer diameter. Calculate the tangential stresses for steel and bronze at the boundary between the two parts

The tangential stress for the steel at 30mm = 88.8MPa.

The tangential stress for the steel at 60mm = 35.5 MPa.

The tangential stress for the bronze at 20mm =  - 191.9 MPa.

The tangential stress for the bronze at 30mm =  - 138.6 MPa.

Explanation:

The outer radius bronze bushing = 60 mm/2 = 30 mm, the inner radius for bronze bushing = 40mm/2 = 20mm and the cylinder radius = 120mm/2 = 60mm.

Step one: The first step is to calculate or Determine the interface pressure.

The interface pressure = 0.05/ [ [ 30 × ( 1/210 ×10⁹) ] ×  [( 60² + 30²/ ( 60² - 30²) + 0.3 ] + [ 1/105 × 10⁹× [ ( 20² + 30²)/( 30² - 20²) - 0.3] ].

The interface pressure = 53.3 MPa

Step two: Determine the tangential stresses for steel and bronze as given below:

The tangential stress for the steel at 30mm = 10⁶ × 53.3 [ ( 0.06)² + (0.03)²/ ( 0.06)² - (0.03)² ] = 88.8 MPa.

The tangential stress for the steel at 60mm = 10⁶ × 53.3 × 2 × [0.03]²/  ( 0.06)² - (0.03)² ] = 35.5 MPa.

The tangential stresses for the bronze is calculated below;

=> The tangential stress for the bronze at 20mm = - [ 10⁶ × 53.3 × 2 × [0.03]² ] /  ( 0.03)² - (0.02)² ] = - 191.9 MPa.

The tangential stress for the bronze at 30mm = - [ 10⁶ × 53.3  × [ 0.03]² + (0.03)² ] /  ( 0.03)² - (0.02)² ] = - 138.6 MPa.