Bending Moment of a Cantilever Beam with a Center Point Load Calculator

Load (P):

Distance between the two supports (L):

Distance from left support (x):

How This Is Calculated

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

M = Bending Moment (Nm)

P = Load (N)

L = Distance between the two supports (m)

x = Some distance from the left support (m)

Assumptions

The beam behaves according to Hook's Law.
The load is concentrated at a single point.
Deflections of the beam are assumed to be small relative to its length.
The cross-section is uniform.
The weight of the beam is negligible.

Related Calculators

Point Load on a Cantilever Beam

UDL Over Entire Span of Cantilever Beam