A cylindrical air drum is 2·25 m in diameter with plates 1·2 cm thick. The efficiencies of the longitudinal and circumferential joints are 75% and 40% respectively. If the tensile stress in the plate is limited to 120 MN/m², the safe maximum air pressure will be
- A0·84 MN/m²
- B0·96 MN/m²Correct
- C1·02 MN/m²
- D1·56 MN/m²
Solution
Concept
Thin cylinder with joint efficiencies
Formula
p = 2σ t ηl / D (hoop); p = 4σ t ηc / D (longitudinal)
Step-by-step solution
1. Hoop (circumferential) stress is resisted by the longitudinal joint: p = 2 × 120 × 12 × 0.75 / 2250 = 0.96 MN/m². 2. Longitudinal stress is resisted by the circumferential joint: p = 4 × 120 × 12 × 0.40 / 2250 = 1.02 MN/m². 3. Safe pressure = smaller = 0.96 MN/m².
Explanation
Both joints must be checked, and the lower pressure governs. The hoop stress is twice the longitudinal stress, so the longitudinal joint governs here.
Why the other options are wrong
1.02 MN/m² is the limit for the circumferential joint only, and it would overstress the longitudinal joint. 0.84 and 1.56 do not follow from either joint.
Shortcut
Check both joints; take the smaller pressure.
Common mistake
Choosing the larger pressure.
Correct answer: B) 0·96 MN/m²