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### Solid Thin Uniform Disk Rotating External Pressure Stress

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

The stresses are

The radial stress at any radius r Forumula
Eq. 1
σr = -po + ρ ω2 ( ( 3 + v ) / 8 ) ( ro2 - ri2 )

The tangential stress at any radius r
Eq. 2
σθ = -po + ρ ω2 ( ( 3 + v ) / 8 ) ( ro2 - ( 1 + 3 v ) / ( ( 3 + v ) )

The maximum radial stress at r = 0
Eq. 3
σr(max) = - ρ + ρ ω2 ( 3 + v ) / 8 ro2

The maximum radial stress at r = ro
Eq. 4
σr = -po

The maximum tangential stress at r = 0
Eq. 5
σθ(max) = σr(max)

The displacement u at any radius r
Eq. 6
u = ( r / E ) ( 1 - v ) { -po + ρ ω2 / 8 [ ( 3 + v ) ro - ( 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)
ro = outside radius, m (in)
ρ = mass density, kg/m3 (lbm/in3)
po = pressure, Pa [psi (lb/in2)]
ω = angular velocity of the ring, rad/s
v = Poisson's ratio
u = displacement, m (in)

Related:

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