# 20.9 Stiffness and strength

Concrete is stiff – you can’t see it change dimensions or shape (it doesn’t deform very much) when subjected to a force. Steel is stiff too – you don’t usually see appreciable deformations in most of its applications.

We think that concrete and steel are strong – they don’t easily break in their normal applications. We call the process when something breaks fracture. Be careful – in engineering and physics “fracture” applies to anything breaking; in orthopaedics bones “fracture” but ligaments “rupture” (see post 17.14). It is because concrete and steel are reasonably stiff and strong that they are so widely used in construction of buildings; they neither deform appreciably nor fracture under the forces to which they are subjected.

As a result, people sometimes think that a stiff material is strong and that a strong material is stiff. They may even sometimes confuse “stiffness” and “strength”. The two examples below show that stiffness and strength are completely different.

If we stretch a rubber band (see picture above), it doesn’t feel stiff – it deforms easily. But it feels strong – it is difficult to pull it until it breaks. So, in tension (post 20.2), rubber feels strong but not stiff.

To find an everyday example of a material that feels stiff, but not strong, we need to think about bending an object. In the picture above, a slab of material is being bent. The top half becomes longer – it is in tension (post 20.2). The top surface has the highest tensile strain (post 20.2) because it gets longer than any other layer in the slab. The bottom half of the slab becomes shorter – it is in compression. So bending involves simultaneous tension and compression.

Now let’s think about bending a potato chip (if you’re British you’ll call it a potato crisp). You don’t see it deform. But, suddenly, it breaks – before there is any appreciable deformation. A potato chip seems stiff but not strong.

The table below lists a range of materials in order of tensile stiffness (Young’s modulus – post 20.2) and tensile strength. Ultimate tensile stress is used as a measure of strength; it is the highest stress (post 20.2) that a material can withstand before it fractures. Numbers are precise to only one significant figure (post 16.7); prefices G and M in the units are defined in post 16.12.

Let’s look at the numbers. Of the materials I have chosen, steel and silk are equally strong. But steel is the stiffest material and silk is the least stiff. Glass is the second stiffest material but next to last in strength.

You can see that there is no relationship between stiffness and strength.

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