Core relationships

σ = My/I = M/Z

κ = M/(EI)

EI = flexural rigidity

Z = I/c

Common deflections

Simply supported, center P: PL³/(48EI)

Cantilever, end P: PL³/(3EI)

Simply supported UDL: 5wL⁴/(384EI)

Cantilever UDL: wL⁴/(8EI)

Before calculating

• Draw the free-body diagram.
• Confirm support idealization.
• Confirm load position/distribution.
• Use the correct bending axis and I.
• Use consistent units.

After calculating

• Check stress and deflection criteria.
• Check buckling/stability where relevant.
• Review local stress concentrations.
• Consider shear deformation for short/deep beams.
• Consider fatigue and dynamic loads.