Question

A closed-end cylinder of 2 m diameter is subjected to an internal pressure of 1 MPa. Using a safety factor 2 and a yield stress 500 MPa, calculate the required thickness on the basis of Tresca criterion.

A 5.4 mm
B 2 mm
C 4 mm
D 6.1 mm
E 3 mm
F 1.2 mm

Answer 1

The minimum required thickness of the cylinder, calculated using the Tresca criterion and given specifications, is 4 mm to ensure safety.

Step-by-step explanation:

To calculate the required thickness of a closed-end cylinder using the Tresca criterion, we need to apply the formula for hoop (circumferential) stress which for a thin-walled cylinder can be expressed as σ = Pd / (2t), where σ is the hoop stress, P is the internal pressure, d is the diameter, and t is the wall thickness. Given that the internal pressure (P) is 1 MPa (which is 1x10¶ N/m²), the diameter (d) is 2 m, and the yield stress (σ_yield) is 500 MPa, we can set up the inequality σ = Pd / (2t) ≤ σ_yield / safety factor. Substituting the given values and rearranging to solve for t gives us t ≥ Pd / (2 σ_yield / safety factor). Using the safety factor of 2, t ≥ (1 MPa × 2 m) / (2 × 500 MPa / 2) = 0.004 m or 4 mm. So, the minimum required thickness is 4 mm to ensure the cylinder is within the safe limits prescribed by the Tresca criterion for yielding.