Vb Bhandari Pdf 31 !!link!! - Machine Design Data Book By

Shaft torsion formula (polar): τ = T*r / J = 16T / (π d^3)
Bending stress: σ_b = M c / I = 32 M / (π d^3)
Combined bending and torsion (von Mises): σ_eq = sqrt(σ_b^2 + 3 τ^2)
Torque from power: T = (9550 × P_kW) / N_rpm (N in rpm)
L10 bearing life (revolutions): N = (C / P)^p × 10^6
Spring shear stress (Wahl): τ = (8 F D) / (π d^3) × K_w, where K_w ≈ (4C - 1)/(4C - 4) + 0.615/C, C = D/d
Lewis bending stress for spur gear tooth: σ = (W_t / (b m)) × Y, where W_t = transmitted tangential load, b = face width, m = module, Y = Lewis form factor.
Hertzian contact stress (approx): p_max = 0.418 × (E' × F / (a^2))^0.5 — use standard contact formulas with radii and material elastic moduli.

Create a printable one-page data-sheet styled exactly like a Bhandari machine design data-book entry for a specific element (shaft, key, gear, spring) tailored to a given loading and material.
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Formulas and relations:

Allowable stress approach: Use material yield or ultimate strengths with factor of safety (FS). For ductile metals often base design on yield strength; for brittle materials on ultimate strength.
Fatigue strength: Consider S-N curves, endurance limit (Se), modifying factors (surface, size, reliability, temperature, loading).
Combined loading: Use stress resultants (axial, bending, torsion) and failure theories—Distortion energy (von Mises) for ductile materials, Maximum normal stress for brittle.
Stress concentration: Apply concentration factors (Kt) and fatigue notch factors (Kf) where relevant.
Service factors: Account for actual operating conditions via service factor (Cs or Km).

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