How to Determine the Modulus of Rupture

If you need to figure out how strong a material is, one way is to test how easy it is to break. The modulus of rupture, also known as the flexural strength or transverse ruptural strength, gives you the maximum load capacity right before a material breaks. For a material like wood, the modulus of rupture has applications in engineering and construction.

The modulus of rupture is a measurement of pressure, or force per unit area. Scientists and engineers use an array of magnitudes for pressure in determining the modulus of rupture. You can find it expressed in units of pascals or megapascals as well as pounds per square inch, or psi.

As materials bend in response to stress, they compress along one side and stretch along the other. As you push downward on a piece of wood, for example, the stretched side will expand in leftward, downward and rightward directions. Researchers often use Young's modulus, a measure of stiffness, to describe this effect.

Calculate Modulus of Rupture

You can calculate the modulus of rupture, "sigma," using the equation σr = 3Fx/yz2 for the load force F and size dimensions in three directions, x, y and z, of the material. In this case, the load is the external force put on the material of interest. The load force is applied to the center of a beam of the material elevated slightly above ground. From this experimental setup, known as the center point loading test, you can observe the deformation of the material in response to stress applied to it.

Keep your units consistent when performing this calculation. If you use inches for the dimensions and pounds for the load force, the modulus of rupture would have units of pounds per square inch.

Make sure not to confuse the modulus of rupture with tensile strength, σTS, a material's ability to resist breaking when under tension. While modulus of rupture measures the specific pressure at which a material is about to break, the tensile strength represents the material's capacity to bend and deform before breaking.

Three-Point Bend Test

Engineers use a three-point bend test in determining the bond strength, or modulus of rupture, of a material. In contrast to the center point loading test, this method uses two different forces along the material of the beam that divide it into three equal parts.

As the applied forces bend the material, be it wood, cement or any other substance, they keep track of temperature and how particles in the material distribute themselves in response to the stress. They do this to make sure the material can withstand the pressures in applications such as foundations for buildings or other projects.

As engineers create graphs of how the material displaces itself in response to different amounts of force, they study how materials undergo deformation. They can then calculate Young's modulus and modulus of rupture.

Components of Strength

For a cement matrix, a type of material used in civil infrastructure, the carbon fibers, nanofibers or nanotubes that make the material provide the structural strength. You can use these components of the cement matrix in sensing, electromagnetic shielding of harmful radiation and preventing substances from corroding.

Depending on the type of components that make these cement matrices, you can study them for physical and chemical properties such as susceptibilty to heat and electricity, ability to conduct current and capacity to store or transfer heat.

Some materials use grain-sized composites on a nanometer scale. These nanocomposite-based substances tend to have higher values for modulus of elasticity, how quickly the stress on the material changes when under pressure. The chemical arrangements of molecules on the nanoscale mean these materials have greater tensile strengths, hardness, toughness and resistance to being worn down.

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About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.