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Bending Moment of a Fixed Beam with a Uniformly Distributed Load (UDL)

Bending Moment Equations


Maximum Bending Moment (at the center): $$ M_{max} = \frac{P \cdot L^2}{12} $$ Bending moment for any distance x from the left support: $$ M_{x} = \frac{P \cdot L}{12} (6x - 4x^2) $$ where:

M   =   Bending Moment   (Nm)

P   =   Unifrom load per unit length   (N/m)

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 uniformly distributed.
  • The material of the beam behaves according to Hooke's Law.
  • The cross-section is uniform.
  • The weight of the beam is negligible.