MATHEMATICAL MODELS · DERIVATION LIBRARY
Engineering Formula Library
Fundamental mechanical equations, symbols, unit conventions, and step-by-step derivations grounded in published standards.
EQU-001Strength of Materials
Beam Bending Stress Equation
\sigma = M * y / I
Calculates the normal bending stress in a straight beam subjected to transverse loading and bending moments.Inspect equation EQU-002Strength of MaterialsTorsional Shear Stress in Circular Shafts
\tau = T * r / J
Calculates the shear stress at any radial location in a circular solid or hollow shaft under torsional load.Inspect equation EQU-003Machine DesignASME Combined Shaft Sizing Equation
d = [ (32 * N_sf / (\pi * S_y)) * \sqrt{M^2 + T^2} ]^(1/3)
Sizing standard for transmission shafting under combined torsional shear and reversed fatigue bending loads.Inspect equation EQU-004MechanicsShaft Torque, Speed, and Power Relationship
P = T * n / 9550
Converts rotational velocity and torque load into equivalent mechanical power, and vice-versa, in standard units.Inspect equation EQU-005Fluid MechanicsDarcy-Weisbach Pipe Friction Head Loss
h_f = f * L * v² / (D * 2g)
Evaluates the energy head loss due to friction in fluid flow through a circular pipe of constant diameter.Inspect equation EQU-006ThermodynamicsIdeal Gas Equation of State
P * V = n * R * T
Relates pressure, volume, temperature, and substance amount for ideal gas systems.Inspect equation EQU-007ManufacturingSheet Metal Bend Allowance Equation
BA = \theta * \pi / 180 * (R + K * t)
Determines the flat sheet length required to form a bend with a specific inside radius, thickness, and K-factor.Inspect equation EQU-008MaterialsHooke's Law (1D Stress-Strain Relation)
\sigma = E * \epsilon
Defines the linear elastic proportional relationship between normal stress and resulting strain in materials.Inspect equation EQU-009FastenersBolt Tightening Torque & Preload (K-factor)
T = K * F_i * d
Estimates the required installation assembly torque to generate target thread preload tension.Inspect equation EQU-010BearingsRolling Element Bearing L10 Life Equation
L10 = (C / P)^p
Calculates the statistical fatigue rating life of ball or roller bearings in millions of revolutions.Inspect equation