Bending Stress Calculator

Bending Stress Calculator

Enter the force applied in newtons (e.g., 500 N)
Enter the length of the beam in millimeters (e.g., 1000 mm)
Enter the moment of inertia in millimeters to the fourth power (e.g., 200000 mm⁴)
Enter the distance from the neutral axis in millimeters (e.g., 50 mm)
The bending stress will be calculated automatically based on the inputs.

A bending stress calculator is an essential to determining the stress experienced by a material when subjected to bending forces.

Bending stress occurs when an external force is applied perpendicular to the longitudinal axis of a structural element, causing it to bend.

Consider a simply supported beam with a length of 2 meters and a rectangular cross-section of 0.1 m width and 0.05 m height. If a force of 1000 N is applied at the center of the beam, the bending stress calculator would determine the maximum bending stress experienced by the beam.

Bending Stress Examples Chart

Beam TypeLength (m)Width (m)Height (m)Applied Force (N)Max Bending Stress (MPa)
Rectangle20.10.05100012
I-Beam30.150.2200015.6
Circular1.50.08 (diameter)5009.95
Hollow Tube2.50.1 (outer)0.08 (inner)150023.7

Bending Stress Formula

The general formula for calculating bending stress is:

σ = (M * y) / I

Where:

  • σ (sigma) is the bending stress
  • M is the bending moment
  • y is the distance from the neutral axis to the point of interest
  • I is the moment of inertia of the cross-section

For a simply supported beam with a point load at the center, the maximum bending stress formula is:

σmax = (F * L) / (4 * Z)

Where:

  • F is the applied force
  • L is the length of the beam
  • Z is the section modulus (Z = I / y)

Let’s calculate the maximum bending stress for a rectangular beam:

  • Force (F) = 1000 N
  • Length (L) = 2 m
  • Width (b) = 0.1 m
  • Height (h) = 0.05 m

First, calculate the section modulus: Z = (b h^2) / 6 = (0.1 0.05^2) / 6 = 4.17 × 10⁻⁵ m³

Then, apply the formula: σmax = (1000 2) / (4 4.17 × 10⁻⁵) = 12 MPa

What is Bending Stress?

Bending stress is the internal resistance offered by a material to an external force that attempts to bend it.

It occurs when a material is subjected to a load perpendicular to its longitudinal axis, causing the material to deform. Bending stress is a critical consideration in structural engineering and materials science.

For instance, consider a diving board at a swimming pool. When a diver stands on the end of the board, it bends downward.

The upper surface of the board experiences tensile stress (stretching), while the lower surface undergoes compressive stress (compression).

The bending stress varies through the thickness of the board, with maximum values at the surfaces and zero stress at the neutral axis (the center of the board’s thickness).

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