Question

The assembly consists of two sections of galvanized steel pipe connected together using a reducing coupling at B. The smaller pipe has an outer diameter of 0.75 (in.) and an inner diameter of 0.68 (in.), whereas the larger pipe has an outer diameter of 1 (in.) and an inner diameter of 0.86 (in.). If the pipe is tightly secured to the wall at C, determine the maximum shear stress developed in each section of the pipe when the couple shown is applied to the handles of the wrench. Also, draw stress distribution at 12 O'clock and 3 O'clock on any section cut between A and B so that it would be visible to the person tightening the pipe.

Answer 1

Concepts and reason

Shear stress is the component of stress coplanar with cross section.

Shear stress is perpendicular to the axis of the member.

Shear stress is varying from zero to maximum value.

Polar moment of inertia is the moment of inertia of the cross-section with respect to the pole of intersection and plane.

Torque is the twist moment of a member about its longitudinal axis.

Internal torques are formed due to external torque is applied to the pipe.

When forces are applied on a body at a distance between them they constitute a couple. The couple produced is the product of the force and the perpendicular distance.

In this problem, the torsion (or torque) formula is used to calculate the shear stresses in pipes AB and BC.

Fundamentals

Write the polar moment of inertia relation for pipe.

Here, the outer diameter is and the inner diameter is .

Write the shear stress relation for pipe.

Here, the outer diameter is .

Calculate the couple created due to force.

Here, the force applied is and the perpendicular distance is .

Calculate the maximum internal torque by using the couple moment.

Calculate the polar moment of inertia of the smaller pipe.

Substitute for and for.

Calculate the polar moment of inertia of the larger pipe.

Substitute for and for.

Calculate the maximum shear stress in small pipe.

Substitute for , for J_AB and 0.75 in. for D_AB.

Calculate the maximum shear stress in small pipe.

Substitute for , for J_BC and 1 in. for D_BC.

Draw the stress distribution at section between AB.

Ans:

Therefore, the maximum shear stress in section AB is.

Therefore, the maximum shear stress in section BC is.

The stress distribution at section between AB is