Question

A circular tube AB is fixed at one end and free at the other end. The tube is subjected to concentrated torques as shown in the figure. If the outer radius of the tube is 1.5in. and the thickness is 3/4in. , calculate the strain energy stored in the tube. Let G = 11800ksi.

Answer 1

To calculate the strain energy stored in the tube, we need to determine the total torsional deformation energy.

First, let's calculate the polar moment of inertia (J) of the tube. For a hollow circular tube, the polar moment of inertia is given by:

J = (π/2) * (outer_radius^4 - inner_radius^4)

Given that the outer radius is 1.5 inches and the thickness is 3/4 inches, we can calculate the inner radius as follows:

inner_radius = outer_radius - thickness
inner_radius = 1.5 - 0.75 = 0.75 inches

Now we can calculate the polar moment of inertia:

J = (π/2) * (1.5^4 - 0.75^4)

Next, we can calculate the torsional deformation energy using the formula:

U = (1/2) * (G * J * torsion_angle^2)

Given that G (shear modulus) is 11800 ksi (kips per square inch), and the torsion angle is not provided in the question, we'll assume a torsion angle of 1 radian for calculation purposes.

U = (1/2) * (11800 * J * 1^2)

Finally, substitute the calculated value of J into the equation and solve for the strain energy (U):

U = (1/2) * (11800 * ((π/2) * (1.5^4 - 0.75^4)) * 1^2)

Performing the calculations, the strain energy stored in the tube is the result of the above expression.