The flexural modulus of a material is a critically important calculation because it helps engineers quantify the load an item can bear in bending to design safe components and structures. An error in the calculation of the flexural modulus of a material can have dire consequences. Therefore, it’s important for engineers and builders to understand what flexural modulus is, in order to avoid potentially catastrophic situations. This article will define the flexural modulus, show how it is calculated, and describe its importance in engineering design.

## What Is Flexural Modulus?

The flexural modulus (sometimes referred to as the *bending modulus* or *tangent modulus*) of a material is a mechanical property. It describes its stiffness or resistance to a bending action or its ability to deform in bending. Specifically, the flexural modulus is the ratio of stress (the force applied over a certain area) to strain (the change in length over the original length) experienced by a material during bending where tension and compression occur on opposite sides of the material. The flexural modulus of a material is dependent on its chemical composition and the arrangement of atoms throughout its structure. A higher flexural modulus indicates a material is more resistant to bending, while a lower flexural modulus indicates a material has a higher tendency to bend when a given amount of bending stress is applied.

## How To Determine the Flexural Modulus of a Material

The flexural modulus of a material can be determined using the standard ASTM (American Society for Testing and Materials) procedure D790. This standard describes the testing method for determining the flexural properties of reinforced and unreinforced plastics (including thermoplastics and thermosets), composites, and electrical insulation materials.

ASTM D790 details the method for a 3-point bending test used to determine the flexural modulus of a material. A bar of the test material is supported at each end, and a force is applied to it at a point halfway along its length. The stress (y-axis) is graphed against the strain (x-axis) as increasing force is applied. The relationship between stress and strain is linear until the yield stress (the highest stress that can be experienced by a material before deformations become permanent) is exceeded. This linear portion of the graph is used to calculate the flexural modulus of the material. By dividing the value of the stress at the end of the linear portion by the value of the strain at that point, the flexural modulus can be determined.

### What Is the Formula for Flexural Modulus?

The formula for flexural modulus is given below: