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Bending Moment of Simply Supported Beam with a Center Point Load

Bending Moment Equations


Maximum Bending Moment: $$ M_{max} = \frac{P \cdot L}{4} $$ Bending moment for 0 ≤ x ≤ L/2: $$ M_{x} = \frac{P \cdot x}{2} $$ Bending moment for L/2 < x ≤ L: $$ M_{x} = \frac{P \cdot (L-x)}{2} $$ where:

M   =   Bending Moment   (Nm)

P   =   Load   (N)

L   =   Distance between the two supports   (m)

x   =   Some distance from the left support   (m)


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Equation Assumptions


  • The beam is simply supported.
  • The load is concentrated at a single point at the center of the beam.
  • The material of the beam behaves according to Hooke's Law.
  • The cross-section is uniform.
  • The weight of the beam is negligible.