Shaft Sizing & Stress Analysis (DIN 743 / ASME)
Calculate shaft bearing reaction forces, shear-moment diagrams, combined torsion-bending equivalent stresses, and safety factors per DIN 743 and ASME B106.1M.
Simply supported shaft, single point load. Ra = F(L−a)/L, Rb = Fa/L, M = Fa(L−a)/L. σb = 32M/(πd³), τ = 16T/(πd³), σvm = √(σb² + 3τ²). Diameter from distortion-energy: d = [32n/(π Sy) · √(M² + 0.75 T²)]⅓. Steady torsion + static bending; not a fatigue (DE-Goodman) check.
▸Formula · assumptions · worked example(DIN 743-1/2:2012 · ASME B106.1M · Euler-Bernoulli Statics)
Formula
M_{\max} = \frac{F \cdot a \cdot (L - a)}{L}, \quad \sigma_{vm} = \sqrt{\sigma_b^2 + 3\tau^2}, \quad \text{FoS} = \frac{S_y}{\sigma_{vm}}
Simply supported transmission shaft under point load F and driving torque T. Calculates bearing reactions RA/RB, max bending moment, von Mises equivalent stress, and safety factor.
Assumptions
- · Simply supported boundary condition with ideal rigid knife-edge or self-aligning bearing supports
- · Uniform circular shaft cross-section with elastic stress distribution below yield limit Sy
- · Minimum required design factor of safety nreq ≥ 2.00 under nominal operating conditions
Stepped Drive Shaft Bearing Reactions & Combined Stress Analysis
Simply supported transmission shaft under transverse point load and steady torque with bearing reactions, maximum bending moment, von Mises stress, and diameter verification.
RA = F · (L - a) / L, RB = F · a / LMmax = (F · a · (L - a)) / Lσb = (32 · Mmax) / (π · d³), τ = (16 · T) / (π · d³)σvm = √(σb² + 3 · τ²)dreq = [ (32 · nreq / (π · Sy)) · √(Mmax² + 0.75 · T²) ]^(1/3)