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