Bending Stress Calculator

Easily calculate the bending stress caused by bending moment in beams and similar members.

Calculate Bending Stress

Calculate Bending Stress (σb = My/I)

Bending stress is the stress that occurs in the cross-section of a beam at the point farthest from the neutral axis. When a bending moment is applied, tensile and compressive stresses occur in the fibers of the beam.

σb = (M ⋅ y) / I

**σb:** Bending stress (Pascal, MPa, psi etc.)
**M:** Applied bending moment
**y:** Distance of the fiber farthest from the neutral axis
**I:** Area moment of inertia with respect to the neutral axis of the section

The result will be given in **Pascals (Pa)** or **Megapascals (MPa)** for metric units and **psi (pound per square inch)** for imperial units.

What is Bending Stress?

**Bending stress (σb)** is the internal stress that occurs within the cross-section of a structural element (usually beams) when a bending moment is applied to that element. This stress, which causes the beam to bend, increases as it moves away from the neutral axis of the section and reaches its maximum value at the outermost fibers. Tensile stress occurs on one side of the beam and compressive stress occurs on the other side.

The formula is as follows:

σb = (M ⋅ y) / I

**M:** Applied bending moment (N·m, lbf·ft etc.)
**y:** The distance (m, mm, inch, etc.) from the neutral axis of the section to the (usually outermost) fiber for which the stress is calculated.
**I:** Area moment of inertia (m⁴, mm⁴, in⁴ etc.) with respect to the neutral axis of the section
**σb:** Bending stress (Pascal (Pa), Megapascal (MPa), psi (pound per square inch) etc.)

Unit and Conversions

Common units used for stress are the same as for normal and shear stress:

**Pascal (Pa):** 1 N/m²
**Kilopascal (kPa):** 10^3 Pa
**Megapascal (MPa):** 10^6 Pa or 1 N/mm²
**Gigapascal (GPa):** 10^9 Pa
**Pound per Square Inch (psi):** 1 lbf/in²
**Kilopound per Square Inch (ksi):** 1000 psi
**1 MPa ≈ 145.038 psi**

Consistent unit systems should also be used for moments, distances, and moments of inertia (e.g., N m, m, m⁴).

Situations Where Bending Stress Is Important:

**Civil Engineering:** Design of structural elements such as beams, slabs, columns.
**Machine Design:** In machine parts subjected to bending loads such as shafts, axles, gears.
**Aeronautical and Automotive Engineering:** Analysis of wings, chassis, and other structural components.
**Furniture Design:** Durability of elements such as table legs and chair arms.

This calculator performs simple bending stress calculations for homogeneous, linear elastic, and regular section members. In real engineering applications, factors such as stress concentrations, fatigue, buckling, dynamic loads, complex section geometries, and material nonlinear behavior can affect bending stress distribution and material behavior. More complex scenarios require advanced strength analysis, finite element methods, and engineering expertise.