Fundamental mechanical equations across 9 categories derived from Shigley, Machinery's Handbook, Roark's Formulas, and ISO/ASME standards. Every equation includes derivation steps, symbols, and unit conventions.
Fundamental stress, strain, and deflection equations for beams, shafts, and structural elements.
Calculate maximum beam bending stress (σ = My/I = M/S) and flexural stress distribution per Euler-Bernoulli beam theory with step-by-step derivation.
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Calculate maximum torsional shear stress (τ = Tr/J = 16T/πd³) and polar moment of inertia for solid and hollow circular shafts under applied torque.
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Combined loading criteria, fatigue analysis, and sizing equations per ASME and Shigley methods.
Standard ASME B106.1M transmission shaft diameter equation under combined steady torque and cyclic bending fatigue using the ASME DE-Goodman criterion.
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Kinematics, dynamics, power transmission, and rotational motion relationships.
Calculate rotational power, motor torque, and shaft speed (RPM) across SI (kW, N·m) and Imperial (HP, lbf·ft) engineering units.
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Pipe flow, head loss, friction factors, and fluid power equations.
Calculate friction head loss and pressure drop in fluid flow through circular pipes using the Darcy-Weisbach equation and Moody friction factors.
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State equations, gas laws, and thermodynamic property relationships.
Calculate pressure, volume, temperature, and molar amount for ideal gas systems across SI and US customary units.
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Forming, machining, and fabrication calculation formulas.
Calculate bend allowance (BA), setback, and flat blank length for sheet metal fabrication using neutral axis K-factor geometry.
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Calculate precision CNC spindle speeds (RPM), linear table feed rates (mm/min or ipm), and volumetric material removal rates (MRR) for milling, turning, and drilling.
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Determine cutting tool lifespan, Taylor speed constants (C, n), and Gilbert economic optimal cutting speed balancing tooling cost with machine shop overhead.
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Elasticity, plasticity, and material property relationships.
Calculate normal stress, linear elastic strain, and Young's modulus (σ = E·ε) for materials within proportional elastic limits.
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Bolt preload, torque, joint analysis, and thread engagement formulas.
Calculate fastener assembly tightening torque, axial clamp preload, and nut factor (K) per VDI 2230 and ISO 898-1 standards.
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Fatigue life, load ratings, and selection criteria per ISO 281.
Calculate ISO 281 basic rating fatigue life (L10) in millions of revolutions and operating hours for ball and roller bearings under dynamic loads.
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TRANSPARENT EQUATIONS, ASSUMPTIONS, AND REFERENCES
Every formula cites Shigley, Machinery's Handbook, Roark's, or ISO/ASME standards.
All variables include symbol, unit conventions, and applicability limits.
Step-by-step derivation paths connect to textbook chapter references.
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