SUMMARY
The tensile stress on a spinning ring can be calculated using specific formulas derived from Roark's Formulas for Stress and Strain. The equations for radial and tangential stresses are given by: \sigma_r = \frac{3+\nu}{8} \rho \omega^2 \left(a^2+b^2-\frac{a^2b^2}{r^2}-r^2\right) and \sigma_{\theta} = \frac{3+\nu}{8} \rho \omega^2 \left(a^2+b^2+\frac{a^2b^2}{r^2}-\frac{1+3\nu}{3+\nu}r^2\right). Key variables include the outer radius (a), inner radius (b), mass density (ρ), Poisson's ratio (ν), and angular velocity (ω). The maximum radial stress occurs at r=\sqrt{ab}.
PREREQUISITES
- Understanding of tensile stress and strain concepts
- Familiarity with Roark's Formulas for Stress and Strain
- Knowledge of material properties including Poisson's ratio
- Basic principles of rotational dynamics
NEXT STEPS
- Study the derivation of stress formulas in Roark's Formulas for Stress and Strain
- Learn about the implications of Poisson's ratio on material behavior
- Explore the effects of angular velocity on tensile stress in rotating bodies
- Investigate material selection for high-speed rotating rings
USEFUL FOR
Mechanical engineers, materials scientists, and anyone involved in the design and analysis of rotating machinery, particularly those focusing on flywheel applications.