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Formula Library
Reference equations and calculators
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Reference equations and calculators
Normal Stress
Stress is force per unit area acting on a material
Normal Strain
Strain is the ratio of deformation to original length
Hooke's Law
Linear relationship between stress and strain in elastic region
Shear Stress
Average shear stress from transverse force
Torque
Torque (moment) from a perpendicular force
Moment of Inertia (Rectangle)
Second moment of area for a rectangular cross-section about centroidal axis
Moment of Inertia (Circle)
Second moment of area for a circular cross-section
Newton's Second Law
Force equals mass times acceleration
Kinetic Energy
Energy of motion
Gravitational Potential Energy
Energy due to height in a uniform gravitational field
Power (Work/Time)
Average power over a time interval
Power (Rotational)
Mechanical power from torque and angular velocity
Linear Momentum
Product of mass and velocity
Impulse
Change in momentum from force over time
Gear Ratio
Ratio of gear teeth or angular velocities
Spring Force (Hooke's Law)
Force exerted by a spring
Helical Spring Rate
Spring constant for helical compression spring
Factor of Safety
Ratio of yield strength to working stress
V-Belt Length
Length of V-belt for two pulleys
Ohm's Law
Voltage equals current times resistance
Electrical Power (V×I)
Power equals voltage times current
Electrical Power (I²R)
Power dissipated in a resistance
Resistors in Series
Total resistance of two resistors in series
Resistors in Parallel
Total resistance of two resistors in parallel
Capacitance
Capacitance is charge stored per unit voltage
Capacitor Energy
Energy stored in a capacitor
RC Time Constant
Time constant of RC circuit
Impedance Magnitude
Impedance magnitude of a series RLC circuit
Inductive Reactance
Opposition to current by inductor
Capacitive Reactance
Opposition to current by capacitor
Resonant Frequency
Frequency at which XL equals XC
Power Factor
Cosine of the phase angle between voltage and current
Real Power (AC)
Actual power consumed in AC circuit
Cantilever Beam Deflection (Point Load)
Maximum deflection at free end of cantilever with point load
Simply Supported Beam Deflection
Maximum deflection at center of simply supported beam
Bending Stress
Stress due to bending moment
Section Modulus
Geometric property for bending strength
Shear Stress in Beams
Shear stress distribution in beams
Euler Buckling Load
Critical buckling load for slender columns
Slenderness Ratio
Ratio determining column buckling behavior
Radius of Gyration
Geometric property for column stability
Manning's Equation
Velocity in open channel flow
Hydraulic Radius
Ratio of flow area to wetted perimeter
First Law of Thermodynamics
Energy balance: change in internal energy equals heat added minus work done
Ideal Gas Law
Equation of state for ideal gases
Heat Transfer (Sensible)
Heat required to change temperature
Carnot Efficiency
Maximum possible efficiency of heat engine
Fourier Heat Conduction (1D)
Heat transfer through a solid by conduction
Newton's Law of Cooling
Heat transfer by convection
Stefan-Boltzmann Radiation
Emitted radiative power from a diffuse gray surface
Reynolds Number
Dimensionless number indicating laminar or turbulent flow
Continuity Equation
Conservation of mass in fluid flow
Darcy-Weisbach Equation
Head loss due to friction in pipe flow
Pump Power
Power required by pump
Hydrostatic Pressure
Pressure due to fluid column
Buoyancy Force
Upward force on submerged object
Poisson's Ratio
Ratio of lateral to axial strain
Shear Modulus
Relationship between elastic modulus and shear modulus
Bulk Modulus
Resistance to uniform compression
True Stress
Stress based on instantaneous area
Von Mises Stress
Equivalent stress for 2D plane stress
Basquin Equation (Fatigue)
High-cycle fatigue life prediction
Torsional Shear Stress
Shear stress in a shaft due to torsion
Angle of Twist
Angular deflection of shaft under torsion
Polar Moment of Inertia (Solid Circle)
Polar moment of inertia for solid circular shaft
Polar Moment of Inertia (Hollow Circle)
Polar moment of inertia for hollow circular shaft
Hoop Stress (Thin-Wall Cylinder)
Circumferential stress in thin-walled pressure vessel
Longitudinal Stress (Thin-Wall Cylinder)
Axial stress in thin-walled pressure vessel
Stress in Thin-Wall Sphere
Stress in thin-walled spherical pressure vessel
Work (Constant Force)
Work done by a constant force
Centripetal Force
Force required for circular motion
Angular Momentum
Rotational momentum of a body
Rotational Kinetic Energy
Kinetic energy of rotating body
Simple Pendulum Period
Period of small oscillations
Spring-Mass Period
Period of spring-mass oscillation
Friction Force
Friction force between surfaces
Parallel Axis Theorem
Moment of inertia about parallel axis
Inductor Energy
Energy stored in an inductor
RL Time Constant
Time constant of RL circuit
Capacitors in Series
Total capacitance of capacitors in series
Capacitors in Parallel
Total capacitance of capacitors in parallel
Transformer Voltage Ratio
Voltage ratio equals turns ratio
Three-Phase Power
Total power in three-phase system
Apparent Power
Product of RMS voltage and current
Reactive Power
Power stored and returned by reactive elements
Voltage Divider
Output voltage of resistive voltage divider
Current Divider
Current through one branch of parallel resistors
Coulomb's Law
Force between two point charges
RMS to Peak Voltage
Relationship between peak and RMS for sinusoids
Simply Supported Beam (Uniform Load)
Maximum deflection under uniform distributed load
Cantilever Beam (Uniform Load)
Maximum deflection of cantilever under uniform load
Maximum Moment (Simply Supported, Uniform)
Maximum bending moment at center
Maximum Moment (Simply Supported, Point Load)
Maximum bending moment at center
Euler Critical Stress
Critical buckling stress for slender columns
Chezy Equation
Velocity in open channel flow
Combined Gas Law
Relates pressure, volume, and temperature changes