Rotating Rings Bodies Stress Equations and Calculator

Related Resources: calculators

Rotating Rings Bodies Stress Equations and Calculator

Engineering Analysis
Strength and Mechanics of Materials Menu

Hollow Disk Ring Rotating at ω rad/s

Preview: Rotating Ring Bodies Stress Calculator

The outside radius of the ring, or disk, is large compared with the thickness: r_o ≥ 10t.
The thickness of the ring or disk is constant.
The stresses are constant over the thickness.

The stresses are

The general expression for the tangential stress of a rotating disk of uniform thickness
Eq. 1
σ_t = ρ ω² [ ( 3 + v ) / 8 ] [ r_i² + r_o² + r_i² r_o² / r² - ( 1 + 3 v ) / ( 3 + v ) r² ]

The general expression for the radial stress of a rotating disk of uniform thickness
Eq. 2
σ_r = ρ ω² [ ( 3 + v ) / 8 ] [ r_i² + r_o² - r_i² r_o² / r² - r² ]

The maximum radial stress occurs at r² = r_i r_o
Eq. 3
σ_r = ρ ω² ( r_o - r_i )² ( 3 + v ) / 8

The maximum tangential stress occurs at inner boundary where r = r_i

σ_θ(max) = [ ( 3 + v ) / 4 ] ρ ω² ( r_o² + ( 1 - v ) / ( 3 + v ) ) r_i²

For a rotating disk, use r_i = 0 in these equations.

where

r = radius to the stress element under consideration, m (in)
ρ = mass density, kg/m³ (lbm/in³)
ω = angular velocity of the ring, rad/s
v = Poisson's ratio
r_i = inside radius, m (in)
r_o = outside radius, m (in)

For a rotating disk, use r_i = 0 in these equations.

Figure 1 Rotating disk of uniform thickness.

Figure 2 Simplified Rotating Ring Stress

Source: Shigley, Joseph E., and Charles R. Mischke, Mechanical Engineering Design, 5th ed., New York: McGraw-Hill, 1989.