# 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.
Beer Johnston asked 12 months ago

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.

Mazurek Gravity answered 12 months ago

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 .

Mazurek Gravity answered 12 months ago