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 normal flexural and maximum beam bending stress (σ = My/I = M/S) in beams, shafts, and structural shapes per Euler-Bernoulli beam theory.
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Calculates the maximum and radial torsional shear stress (τ = T·r/J) in solid and hollow circular shafts under torsional moments.
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Combined loading criteria, fatigue analysis, and sizing equations per ASME and Shigley methods.
Standard ASME B106.1M governing equation for transmission shaft diameter sizing under combined steady torque and reversed bending fatigue loads.
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Kinematics, dynamics, power transmission, and rotational motion relationships.
Calculate mechanical power, motor torque, and rotational 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.
Evaluates the energy head loss due to friction in fluid flow through a circular pipe of constant diameter.
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State equations, gas laws, and thermodynamic property relationships.
Relates pressure, volume, temperature, and substance amount for ideal gas systems.
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Forming, machining, and fabrication calculation formulas.
Determines the flat sheet length required to form a bend with a specific inside radius, thickness, and K-factor.
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Elasticity, plasticity, and material property relationships.
Defines the linear elastic proportional relationship between normal stress and resulting strain in materials.
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Bolt preload, torque, joint analysis, and thread engagement formulas.
Estimates the required installation assembly torque to generate target thread preload tension.
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Fatigue life, load ratings, and selection criteria per ISO 281.
Calculates the statistical fatigue rating life of ball or roller bearings in millions of revolutions.
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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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