What is Hooke’s law?

We explain what Hooke’s law is, its formula and its applications in engineering and architecture. In addition, how elasticity is calculated.

  1. What is Hooke’s law?

Hooke’s Law of Elasticity, or simply Hooke’s Law, is the physical principle around the elastic behavior of solids . It was formulated in 1660 by British scientist Robert Hooke, contemporary of the famous Isaac Newton.

The theoretical precept of this law is that the displacement or deformation suffered by an object subjected to a force will be directly proportional to the deforming force or the load. That is to say, that with greater force, greater deformation or displacement , or as Hooke himself formulated in Latin: Ut tensio sic vis (“as the extension, thus the force”).

Hooke’s Law is extremely important in various fields, such as physics and the study of elastic springs (its most frequent demonstration). It is a fundamental precept for engineering and architecture , construction and design, as it allows us to anticipate the way in which a prolonged force or weight will alter the dimensions of objects over time.

It is said that this law was published by Hooke in the form of a mysterious anagram: ceiiinosssttuv , from which the Latin statement of his law can be reconstructed, because he was afraid that someone could take possession of his discovery illegally. A couple of years later, however, he made his findings public.

  1. Hooke’s Law Formula

The basic formula of Hooke’s law is as follows:

F = -kx


  • is the deforming force
  • is the length of the compression or elongation
  • is the constant of proportionality baptized as a spring constant , generally expressed in Newtons over meters (N / m).

For the calculation of x two measurements are necessary: ​​the initial length (L 0 ) and the final length (L f ), for the calculation of ΔL or the length variation, that is, the deformation. Hence the law can also be:

F = -k. ΔL

  1. Hooke’s Law Applications

hooke law physical elasticity bridge materialsHooke’s law allows us to predict the effect of weight on construction materials.

Hooke’s law is extremely useful in all those fields where full knowledge of the elastic capacity of materials is required. Engineering, architecture and construction are the disciplines in which it is most frequently used.

For example, this law allows to predict the effect that the weight of cars will have on a bridge and on the materials (such as metal) from which it is made. It also allows to calculate the behavior of a bellows or a set of springs, within a specific machine or industrial device.

The best known application of Hooke’s law is in the development of dynamometers : devices that allow scalar force measurement, composed of a spring and a scale.

  1. Hooke Law and Elasticity

The application of Hooke’s law for the calculation of elasticity varies whether it is springs, or elastic solids .

To calculate the spring elasticity, the “spring equation” is applied , which is the most general way of formulating the Hooke’s law formula (the same one we offered above: F = -k.ΔL). The difference is that k will be the spring’s elasticity constant, depending on the length of the spring and its constitution.

Among other things, this allows to calculate the angular frequency of oscillation of the spring (ω), using the mass of the load that causes it to stretch (m). For this we will apply the following formula:

ω = √ k / m

On the other hand, to calculate the elasticity of elastic solids, the law of springs should be generalized , since the distribution of tension in their bodies is much more complicated than a bellows.

To do this, Lamé-Hooke equations are used, which have specific formulas for each solid according to its specific form: one-dimensional, three-dimensional isotropic or three-dimensional orthotrope. But these are issues that require a much more complex and technical elaboration yet.

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