Engineering reference for Indian students

Mechanics & design

Machine Design

5 self-contained study topics — notes, diagrams, formulas, and worked examples for exams and GATE.

Topics

Design for Static Load
$n = \frac{Strength}{Working} stress$
Design of Shafts
A shaft is sized so the combined torsional shear from τ = 16T/(πd³) and bending stress σ_b = 32M/(πd³) stay within the allowable value fixed by the ASME code. Diameter follows from d = (16/π · √(M² + T²)/τ_allow)^(1/3), the equivalent-torque route in VB Bhandari.
$ASME: \tau_{allow} = 0.3 S_{ut} or 0.18 S_{yp} for ductile shafts$
Keys and Couplings
A sunk key is checked for both shear (τ = 2T/(d·l·b)) and crushing (σ_c = 4T/(d·l·h)); the weaker mode fixes the key length. Couplings then transmit that same torque between shafts, with friction couplings using T = μ·F·r·n, following VB Bhandari.
Bearings and Lubrication
Rolling bearings are selected from rated life L₁₀ = (C/P)^a × 10⁶ revolutions (a = 3 for ball, 10/3 for roller) with equivalent load P = X·V·F_r + Y·V·F_a. Journal bearings are analysed through the Sommerfeld number S = (μN/P)(R/C)², as in VB Bhandari.
$Hydrodynamic bearing: eccentricity ratio \varepsilon = \frac{e}{C}$
Springs and Fasteners
A helical compression spring deflects by δ = 8FD³n/(Gd⁴) giving stiffness k = Gd⁴/(8D³n); its shear stress τ = 8FD/(πd³)·K_w must include the Wahl curvature factor. Bolted joints are preloaded to F ≈ 0.7·σ_yp·A_t, per VB Bhandari.
$Bolt tightening: torque T = K\cdot F\cdot d$