Bending Moment of a Simply Supported Beam with Point Load Calculator

Bending Moment of Simply Supported Beam with Point Load Calculator

Load (P):

Distance of applied load from the left support (a):

Distance between the two supports (L):

Distance from left support (x):

How This Is Calculated

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

M = Bending Moment (Nm)

P = Load (N)

L = Distance between the two supports (m)

x = Some distance from the left support (m)

a = Distance of applied load 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 at Center of Simply Supported Beam

UDL Over Entire Span of Simply Supported Beam