Solid Thin Uniform Disk Rotating External Pressure Stress

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Solid Thin Uniform Disk Rotating External Pressure Stress

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Solid Thin Uniform Disk Rotating at ω rad/s Under External Pressure p_o Stress Equations and Calculator

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The stresses are

The radial stress at any radius r Forumula
Eq. 1
σ_r = -p_o + ρ ω² ( ( 3 + v ) / 8 ) ( r_o² - r_i² )

The tangential stress at any radius r
Eq. 2
σ_θ = -p_o + ρ ω² ( ( 3 + v ) / 8 ) ( r_o² - ( 1 + 3 v ) / ( ( 3 + v ) )

The maximum radial stress at r = 0
Eq. 3
σ_r(max) = - ρ + ρ ω² ( 3 + v ) / 8 r_o²

The maximum radial stress at r = r_o
Eq. 4
σ_r = -p_o

The maximum tangential stress at r = 0
Eq. 5
σ_θ(max) = σ_r(max)

The displacement u at any radius r
Eq. 6
u = ( r / E ) ( 1 - v ) { -p_o + ρ ω² / 8 [ ( 3 + v ) r_o - ( 1 - v )r² ] }

Figure 1 Rotating disk of uniform thickness under external pressure.

where

E = modulus of elasticity or Young’s modulus, Pa [psi (lb/in²)]
r = radius to the stress element under consideration, m (in)
r_o = outside radius, m (in)
ρ = mass density, kg/m³ (lbm/in³)
p_o = pressure, Pa [psi (lb/in²)]
ω = angular velocity of the ring, rad/s
v = Poisson's ratio
u = displacement, m (in)

Source:

Machine Design Handbook 2nd Edition, 2001
Prof. Dr. K. Lingaiah
Former Principal, Professor and Head, Department of Mechanical Engineering
University Visvesvaraya College of Engineering, Bangalore University, Bangalore