## Bending Stress Calculator

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 beamwith a length of2 metersand arectangular cross-sectionof0.1 m widthand0.05 m height. If aforceof1000 Nis applied at the center of the beam, the bending stress calculator would determine themaximum bending stressexperienced by the beam.

## Bending Stress Examples Chart

Beam Type | Length (m) | Width (m) | Height (m) | Applied Force (N) | Max Bending Stress (MPa) |
---|---|---|---|---|---|

Rectangle | 2 | 0.1 | 0.05 | 1000 | 12 |

I-Beam | 3 | 0.15 | 0.2 | 2000 | 15.6 |

Circular | 1.5 | 0.08 (diameter) | – | 500 | 9.95 |

Hollow Tube | 2.5 | 0.1 (outer) | 0.08 (inner) | 1500 | 23.7 |

## Bending Stress Formula

The general formula for calculating **bending stress** is:

**σ = (M * y) / I**

Where:

σ (sigma)is the bending stressMis thebending momentyis thedistancefrom theneutral axisto the point of interestIis themoment of inertiaof 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:

Fis the applied forceLis the length of the beamZis thesection 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 = (bh^2) / 6 = (0.10.05^2) / 6 = 4.17 × 10⁻⁵ m³

Then, apply the formula:

σmax = (10002) / (44.17 × 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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