Question

The double riveted joint with two cover plates for boiler shell is 1.5 m in diameter subjected to steam pressure of 1 MPa. If the joint efficiency is 75%, allowable tensile stress in the plate is 83 MN/m², compressive stress is 138 MN/m² and shear stress in the rivet is 55 MN/m², the diameter of rivet hole will be nearly
1. 8 mm
2. 22 mm
3. 36 mm
4. 52 mm

Answer 1

Correct Answer - Option 2 : 22 mm

Concept:

for a boiler shell, the thickness of the boiler shell is given by:

\(t = \frac{{PD}}{{2{σ _t}η }} + CA\)

where P is pressure, D is the diameter of the shell, σ_t = tensile stress in the plate, CA is corrosion allowance, η = joint efficiency

when t ≥ 8mm,

we use Unwin formula to find the diameter of the rivet (d) hole which is:

\(d = 6\sqrt t \)

Calculation:

Given:

P = 1 MPa, D = 1.5 m, η = 0.75

Allowable tensile stress in the plate σ_t = 83 MN/m­­²

Allowable compressive stress in the plate σ_c = 138 MN/m²

Allowable shear stress in the rivet τ = 55 MN/m²

thickness of the boiler shell is:

\(t = \frac{{PD}}{{2{σ _t}η }} + CA\)

t = \(\frac{{1 \times 1.5 \times 1000}}{{2 \times 83 \times 0.75}}\) + 2 mm

t = 14.04 mm ≥ 8 mm 

Since t > 8 mm, So using Unwin’s formula we get:

The diameter of the rivet (d) is

d= 6\(\sqrt {\rm{t}}\)

\(d = 6\sqrt {14.04} = 22.48\;mm\)