Springiness of Solids or The History of Elasticity

Disclaimer: This article is written keeping general readers in view and hence the usage of mathematical equations was strictly avoided. However, hyperlinks are provided for further reading.

Let us twitch with an interrogation

“Why any inanimate solid, for that occasion any material is capable of carrying load?”

            The answer lies at the root of the whole study of structures and the intelligentsia behind this is quite complex. If there is anyone whom the credit shall be due is Sir Robert Hooke.

Sir Robert Hooke
Courtesy: Wikipedia

            Hooke realized that materials can carry load by only pushing back at it with an equal and opposite force. This is an implicit equivalence of Newton’s Third Law.

            To put this up rhetorically, a force just cannot get away. In any circumstance force must be balanced and fought back by another equal and opposite force at every point in the structure.

“Thou shalt not go unreacted or unbalanced”

            

         This statement holds firm for however small and simple or however large and complex the structures may be. It is true not only for cathedrals and floor but also for airplanes, balloons, furniture, lions, tigers, cabbages and even earthworms.

            As a consequence of Hooke’s pushing theory, He suggested a law which we commonly recognize as Hooke’s Law or as I call it as Springiness of Solids.

          

           “The power of any spring is in the same proportion with the tension (Hooke’s Time tension meant what we should call an Extension) thereof: i.e. if one power stretch or bend it in one space, two will bend it two, three will bend it three if there and so forth and forward and this is rule of nature, upon which all manners of restitute or springing 
   -          Sir Robert Hooke

By 1676, Hooke concluded that not only most solids resist weights or mechanical loads by pushing back at them but also that:

•  Every Solid changes its mechanical shape under the action of force.
• It is this change in shape which enables the solid to do the pushing back.

Thus when we suspend a weight with a string, the string gets longer and just this extension enables the string to pull upwards and carry the weight and prevent it from falling. It is of great importance that it is perfectly normal for any and every structure to change its physical dimensions in response to load. Unless otherwise the deflection is too large for the purpose of the structure, it is no way a fault but an vital characteristic for a structure to work.

Deformation of String under weight
Courtesy: Lumen Learning

Hooke even postulated as a reasoning to his analogies of which most people often find it difficult to follow is that when a structure deflects under load as we were talking about earlier, the material with which it is made also gets stretched to a very fine scale upto atomic bonds and molecules in perfectly uniform proportions. As a matter of fact, masonry is more flexible than you think. If you observe closely, almost all the old structures and buildings are bent noticeably.

Defomed Stones of Khafrey Valley Temple
Courtesy: Heidi Kontakanen, Flickr

It should also be kept in thought that Hooke knew nothing about chemical bonds, and not very much about atoms or molecules either at his time. Yet, his intuition and hypothesis that something of this sort was happening inside the perfectly fine structure of material. He set out to determine, what might be the macroscopic relation relationship between forces and deflection of solids.

His intuitions towards the behavior of materials under the action of load encouraged him to perform successive experiments on a variety of materials and various geometric forms. He hung weights with these materials and found that the load and deflection are directly proportionate.

Furthermore, within the accuracy of Hooke’s experiments which was not so good in any means, he found that most of the materials tested regained their original form after the load was removed. As a matter of fact he could repeat these tests indefinitely on and off without causing any permanent deformation. This phenomena is termed as elastic. The term elastic might be used with rubber band or undergarments usually but it is just as applicable to steel, stone, brick and biological substances like wood, bone and tendon.

However, some solids do not recover as mentioned and such solids are called plastics. In fact, many materials which Hooke thought to be plastic in reality, when tested with sufficiently accurate methods were plastic.

After a series of private confrontations with the then researchers, Hooke published his paper with famous statement “Ut tension sic vis” (As the extension, so the force) which was widely known for 300 years as Hooke’s Law.

Although Hooke’s contributions had been helpful for engineers but their practical form applicability was rather limited. To be clear Hooke was the only person then actually talking about deflections in structure as a whole under the action of loads.

If we pause and introspect for a moment, the deflection of a structure is based on its geometric shape and material with which it is made. For instance a spring made from steel is much easier to deflect under the action of force. But, a girder made of steel is perfectly an opposite case. These examples can go on and on. However, the important phenomena here to remember is that the stiffness of a material varies greatly with form.  Although no material is truly rigid, materials like sapphire and diamond are very stiff indeed. We need to sort this whole thing out and quantify the aforementioned effects.

All of this was a promising start for the structural science. However, it came to a dead stop after Hooke’s death and was rather left out until reemerging after 120 years. The rivalry of Newton and Hooke could be kept in reference here. Although, their rivalry is beyond the scope of this article, Newton was a better constituted person to detest Hooke and loathe everything he stood for including elasticity. It was a good fortune for newton to have lived for 25 years after Hooke died, he spent significant amount of time trying to denigrate Hooke’s memory and importance of applied science. But, both Hooke’s and Newton’s theories were proved correct later.

Although Newton was a great mind, his enmity with practical approach of science and inability to take criticism was a deterrent factor for his intellect. Thus the situation throughout the 18^th Century was that, while the manner the in which the structures was broadly explained by Hooke, his work was not much followed or exploited by researchers for a very longtime.

So long as this, the practical and theoretical applicability of Theory of Elasticity was limited. French Engineers despite knowing this, built structures basing on this theory which quite often fell down. The English Engineers however, were indifferent to use so called theories and built structures based on what may be called rule of thumb practical methods. Those structures fell but not as quite as often.
                                                                                Inspired by JE Gordon's Structures