Question

A hollow steel cylinder with an outside diameter of 100 mm is required to carry a tensile load of 500 kN. Given that the allowable stress is limited to 120 MPa, determine the maximum inside diameter of the tube.

Answer 1

Answer:

Maximum inside diameter is 68.52 mm.

Explanation:

Apply stress formula to calculate inside diameter of the tube. Take the allowable stress for safe design and maximum inside diameter of the steel tube.

Step1

Given:

Outside diameter is 100 mm.

Tensile load is 500 kN.

Allowable stress is 120 Mpa.

Calculation:

Step2

Inside diameter is calculated by the stress formula as follows:

$\sigma_{a}=\frac{F}{A}$

$\sigma_{a}=\frac{F}{\frac{\pi}{4}(d_{o}^{2}-d_{i}^{2})}$

$120=\frac{500\times1000}{\frac{\pi}{4}(100^{2}-d_{i}^{2})}$

$(100^{2}-d_{i}^{2})=5305.164$

$d_{i}=68.52$mm

Thus, the inner diameter is 68.52 mm.