Bending Moment Calculator

Bending Moment (M):

Moment of Inertia (I):

Modulus of Elasticity (E):

Radius of Curvature (R):

Bending Stress (σ):

Distance from Neutral Axis (y):

How This Is Calculated

$$ \frac{M}{I} = \frac{E}{R} = \frac{\sigma}{y} $$ where:

M = Bending Moment (Nm)

I = Moment of Inertia (m⁴)

E = Youngs Modulus (N/m² or Pa)

R = Radius of Curvature (m)

σ = Bending Stress (N/m² or Pa)

y = Distance from neutral axis (m)

Assumptions

The material is homogeneous and isotropic.
The material behaves according to Hooke's Law, i.e. it is linearly elastic.
The deflections of the beam are small compared to its overall dimensions.
The beam is sufficiently slender that shear deformations are negligible.
The cross sections of the beam remain perpendicular to the neutral axis after bending (i.e. the beam does not undergo warping or twisting).

Related Calculators

Euler's Buckling Load

Bending Stress

Uniformly Distributed Load