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What Is Modulus of Rigidity?

By Richard Nelson
Updated May 21, 2024
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Modulus of rigidity, or the shearing modulus, is used to determine how elastic or bendable materials will be if they are sheared, which is being pushed parallel from opposite sides. This property becomes the useful part of many calculations, and it is called the coefficient of elasticity during shearing. It can be measured by a shear strain test, which is conducted by placing a rod of a given material into a clamp and applying force at a measured distance away from the clamp to only one side of the rod.

There are three popular applications for the shearing modulus formula. Young’s modulus for strings and Bulk’s modulus for gases both need the shearing modulus to predict how waves form in gases. The shear strain test is also used if it is already known to predict the amount of force needed to bend a material.

Material scientists and applied physicists use the this concept in special ways. Understanding the modulus of rigidity will help select the correct material to use for construction under many circumstances. The smaller the force is, the easier the material will bend. It is calculated and publicly recorded for most materials. A rod made of gold will bend more easily than one of the same thickness made of steel, for example, and the shearing modulus displays this clearly for most comparisons.

At tiny levels, the modulus of rigidity relates to atoms sliding over one another. This helps explain why temperature and pressure also affect it. The colder an object and the more pressure it is under, the more rigid or stiff it becomes. At high temperatures and low pressures, most materials start to melt and become easier to bend.

Predicting this property can be very difficult. Doing a shear strain test can give a measure for available materials. It becomes difficult to discover new materials that show better performance under certain conditions, such as at the bottom of the ocean. In some cases, the materials have never been created and scientists use math to predict the shearing modulus.

Common experience with materials can be explained by this property. Most people understand that diamonds are very hard — they have a modulus of rigidity that is 10 times higher than that of steel. Rubber bands wrap and twist without effort, and their measurement is very small. Thin metal cans are easy to bend, but thick plastics are not because even though metals are more rigid, the thicknesses are not the same.

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Discussion Comments

By anon333937 — On May 08, 2013

What is furnished rigidity? I do not understand from this article.

By irontoenail — On Jan 08, 2013

@umbra21 - Even today I think we find it difficult to take all of that kind of thing into account. That's why everyone holds their breath when, for example, a lander is flying down to Mars.

There are so many things to factor in and the modulus of rigidity of every material involved is only one of them (and it has to be recalculated again and again for potential different environments).

If we didn't have computers to help us out with these kinds of things we couldn't do nearly the amount we end up achieving.

By umbra21 — On Jan 07, 2013

I think I read somewhere that it was a miscalculation of this formula that helped lead to the Titanic disaster.

They had tried using the most advanced materials to make the ship, some of which hadn't been used in the same way before. And they didn't factor in the fact that the ocean was going to be so cold. So, they had miscalculated the strain that the materials were able to take without shearing off.

I don't know if that was just a contributing factor, or how important it was in the long run, but I believe the investigation did lead to them using better materials in the next ship.

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