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### Stresses in Rotating Disks (Annular Rings) of Constant Thickness Equation and Calculator

**Manufacturing, Design and Engineering**

Stresses in Rotating Disks (Annular Rings) of Constant Thickness Equation and Calculator

A homogeneous annular disk of uniform thickness outer radius R, and weight per unit volume d, with a central hole of radius R_{o}, rotates about its own axis with a uniform angular velocity of ω rad/s. At any point a distance r from the center there is a radial tensile inertia stress.

Preview: Stresses in Rotating Disks (Annular Rings) of Constant Thickness Calculator

Radial Tensile Inertia Stress:

Tangential Tensile Inertia Stress:

Maximum Radial Stress occurs at r = ( R · R_{o} )^{0.5}

Maximum radial tangential stress occurs at the perimeter of the hole:

Change in outer radius:

Change in inner radius:

Where:

R = outer radius of disk,(in, m);

R_{o} = inner radius of disk or radius of bore (in, m);

r = tensile inertia stress at some radial distance (in, m);

δ = Mass per unit volume (lbs/in^{3}, (kg/m^{3});

g = G Force (386.4 in/s^{2}, 9.81456 m/s^{2})

ω = Angular rotation speed (rad/s);

r_{pm} = revolutions per minute

E = Elastic Modulus (psi, Pa);

v = Poisson's ratio.

Conversion:

1 rad/sec = 9.549296596425384 rpm

1 rpm = 0.104719755 rad/sec

Reference: Roark's Formulas for Stress and Strain, 7th Edition

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