Mechanics of Materials

121/3337–11FE Reference Handbook 10.4 · Mechanics of Materials · Pressure vessels

Handbook formula

Thin-Wall Pressure Vessel

σ_{h} = \frac{p r}{t} σ_{ℓ} = \frac{p r}{2 t} (cylinder)

Thin wall means t << r. For a closed cylinder, hoop (circumferential) stress is twice the longitudinal. Sphere: σ = pr/(2t) in both directions. Use inside radius or mean as the Handbook specifies; gage pressure p.

$p$: Internal gage pressure
$r$: Radius
$t$: Wall thickness
$σ_{h}$: Hoop stress

Step-by-step solved example

p=2 MPa, r=250 mm, t=10 mm, closed cylinder. Hoop and long. stresses?

Thin cylinder: hoop stress pr/t, longitudinal pr/2t.

1. Hoop
σh= p r/t = 2×250/10=50 MPa.
2. Long
σℓ=25 MPa.
$σ_{h} = 50 MPa$

Answer: σh=50 MPa, σℓ=25 MPa

10 practice questions

0/10 correct

1.Hoop stress in a thin cylinder is

2.Longitudinal stress in a closed cylinder is

3.A sphere has σ=

4.Thin-wall assumption is typically

5.Open-ended cylinder (pipe as a tube with no cap) has

6.Doubling t halves

7.p is

8.Radial stress at the inside surface is

9.r=200 mm, t=5 mm, p=1 MPa. σh=

10.Yielding is often checked with