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 0.75in, and an inner diameter of 0.68in, whereas the larger pipe has an outer diameter of 1in and an inner diameter of 0.8in. 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.

Answer 1

Concepts and reason

Torque: It is the tendency of force which causes rotational motion in a body. It is a vector quantity.

Shear stress: It is caused when the forces acting on the parallel surface cause the body to shear.

Fundamentals

Shear stress:

Shear stress due to the twisting couple is given by,

Here, is the torque or twisting couple, is the radius of the shaft, and is the polar moment of inertia.

Polar Moment of inertia is given by,

Here, is the diameter of the shaft.

Calculate the torque acting on the body as follows:

Here, is the force acting, and are the perpendicular distance.

Substitute for , for , and for .

Calculate the shear stress in section AB as follows:

Here, is the shear stress in section AB, is the torque acting, is the radius of the shaft, and is the polar moment of inertia.

Substitute for , for , and for .

Calculate the shear stress in section BC as follows:

Here, is the shear stress in section BC, is the torque acting, is the radius of the shaft, and is the polar moment of inertia.

Substitute for , for , and for .

Ans:

The torque acting is .

The shear stress in section AB is .

The shear stress in section BC is .