# The steel pipe AB has a 102-mm outer diameter and a 6-mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and die maximum shearing stress at point K.

Question-AnswerCategory: Strength of MaterialsThe steel pipe AB has a 102-mm outer diameter and a 6-mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and die maximum shearing stress at point K.

The steel pipe AB has a 102-mm outer diameter and a 6-mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and die maximum shearing stress at point K. Step No: 1

Use the following relation to calculate the inner diameter of the Steel pipe: Here, the outer diameter is and thickness of the pipe is t.
Substitute 102 mm for and 6 mm for . Use the following relation to calculate the polar moment of inertia of the Steel pipe: Substitute 102 mm for and for . Step No: 2

Calculate the moment of inertia of the Steel pipe. Substitute for: Step No: 3 Here, is the force in the x-direction and is the perpendicular distance.
Substitute 10000 N for and 200 mm for .  Here, is the force in the x-direction and is the perpendicular distance.
Substitute 10000 N for and 150 mm for . Here, the negative sign in the moment about z-direction is due to the moment acts in the clockwise direction.
The force creates the moment about z axis and the force creates the torsion in y direction. Therefore, the moments and cause for the bending and twisting moments respectively and the respective stresses are bending stress and torsional shear stress.

Step No: 4

Calculate the bending stress at K as follows: Here, distance of the point K from the axis is c.
Substitute for  for and 0.051 m for y. Here, the negative sign indicates that the stress at the point K is compressive in nature.

Step No: 5

Calculate the shear stress at K as follows: Substitute for  for and 0.051 m for r. Step No: 6

Calculate the average stress as follows: Substitute for and 0 for  Calculate the maximum shear stress as follows. Substitute for  for and 0 for  Therefore, the maximum shear stress is .

Step No: 7

Calculate the maximum normal stress at K as follows. Substitute for and for . Therefore, the maximum normal stress at K is .

Step No: 8

Calculate the minimum normal stress at K as follows. Substitute for and for . Therefore, the minimum normal stress at K is .  