Mechanics of Materials Formulas

Thin-Walled Sections:
Angle Of Twist

Axial:

Strain

Axial:

Stress

Axial:

Stiffness

Axial:

Flexibility

Shear Modulus

Axial:

Shear Stress

Poisson's Ratio

Axial:

Temperature Strain

Axial:

Temperature Displacement

Load, Bending, & Shear
Relationships

Torque:
Angle of Twist

Torque:
Torsional Constant

Torque:
Angle of Twist (Integral)

Torque (Thin-Walled):
Shear Stress

Torque:
Stiffness

Torque:
Energy Density

Axial:
Temperature Strain

Torque (Thin-Walled):
Integral

Axial:
Temperature Deflection

Torque:
Maximum Shear Stress

Torque:
Shear Stress

Stress Concentration

Strain vs. Shear Strain

Axial:
Internal Energy

Section Modulus

Shape Factor

Torque (Thin-Walled):
Shear Flow

Shear Stiffness

Torque:
Shear Strain

Polar Moment of Inertia

Plastic Moment of Inertia

Power

Torque:
Rate of Twist

Axial:
Ramberg-Osgood Deflections

Mohr's Circle (Stress):
Stresses at Angles

Bending:
Moment-Stress Relationship

Bending:
Moment-Curvature Relationship

Moment of Inertia Relationships

Mohr's Circle (Stress):
Mean, Average, and Radius

Mohr's Circle (Strain):
Principal Strains

Mohr's Circle (Stress):
Principal Stresses

Mohr's Circle (Strain):
Strains at Angle

Mohr's Circle (Strain):
Mean, Average, and Radius

Torque:
Max Shear Stress

Torque:
Internal Energy

Axial:
Modulus of Resilience

Torque:
Max Shear Strain

Torque:
Internal Energy (Simplified)

Axial:
Internal Energy (Simplified)

Ramberg-Osgood Equation

Torque:
Internal Energy (Simplified)

Axial:
Internal Energy

Curvature, Load, Shear, & Moment Relationships

Bending:
Stress (Simplified)

Axial:
Deflection

Bending:
Strain (Simplified)

Centroid

Bending:
Shear Stress & Shear Flow

Bending:
Shear Stress

Bending:
Stiffness

Bending:
Moment-Stress-Curvature Relationships

Bending:
Radius of Curvature

Bending (Small Deflections):
Radius of Curvature

Bending:
Moment of Inertia

Bending:
Basic Moment-Stress Relationship

Bending:
Max Tensile Stress

Torque (Thin-Walled):
Angle of Twist

Bending:
Rate of Bending-Moment Relationship (Simplified)

Bending:
Max Compressive Stress (Simplified)

Bending:
Curvature vs. Radius of Curvature

Bending (Composites):
Moment-Curvature Relationship