# Stress and strain # Elasticity

Deformation of a solid When a force acts on a body it can change its shape - the amount of deformation will depend on a number of things: (a) the size of the specimen (b) the size of the force (c) the material of which the specimen is made Now there are many important cases where the deformation is important such as bridge design, buildings, flying buttresses in a cathedral, a belly flop on water and the use of oil in the hydraulics of a car brakes, even the tension in your belt to hold up your skirt or trousers! Many materials behave as you would expect - they stretch steadily as the force on them increases but some behave oddly - the silly putty - a small force - it creeps, a larger force and it bounces and a very large force and it shatters. How elastic do your socks and tights have to be and what about your skin itself! Rubber is elastic at room temperature but if it is cooled to the temperature of liquid nitrogen it shatters when hit with a hammer. Basic examples and uses of elasticity Rubber bands, Clothes, Balls, Aircraft wings flexing, Bridges, Skin, Steel girders, Bats such as cricket, Glass, Lift cables, Bouncy castle, Trainers, Fishing line.

Stress and strain

Every stress produces a strain!

Stress

Every elastic stress produces an elastic strain. A stress is a measure of the cause of the deformation produced by a force:

Stress = Force per unit area units are Nm -2 or Pa

.

Breaking stress

The maximum stress that a material can stand before it breaks is called the breaking stress. There are two types of breaking stress (a) compressive breaking stress - the maximum squashing stress before fracture (b) tensile breaking stress - the maximum stretching stress before fracture Some examples of both of these are given in the following table Material Steel Rubber Granite Compressive breaking stress/ MPa 552 145 Tensile breaking stress/MPa 400 - 800 2.1 4.8 Concrete Oak Porcelain Bone (compact) Nylon Glass Carbon fibre Cast iron 21 59 552 170 2.1 117 55 120 70 3.5 - 150 1000 30 - 140 1

Strain

Strain is a measure of the deformation produced by the stress.

## Strain = change in size/original size

Strain has no units as it is simply a ratio of two similar quantities

Linear stress and strain

When the stress is along the length of the specimen there are two ways in which it can be applied to give a strain. (a) compressive stress (b) tensile stress These two numbers are not necessarily the same for a given material.

The height of a granite column

The compressive breaking stress (F) of a material can be used to work out the maximum height of a rock column that is possible on the surface of the Earth. Maximum pressure at the base = F =  gh where  is the density of the rock. Therefore for granite F = 145x10 6 and  = 2500 kgm -3 so h = 145x10 6 /2500x9.81 = 5900 m h 8000 m Granite column This is smaller than the heig ht of many mountains but in a mountain the ‘column’ of rock would be supported from the sides by the rest of the mountain.

Example problems 1. Calculate the stress due to a force of 20 N acting on a steel wire of cross sectional area 0.2x10

-6 m 2 (about 0.5 mm diameter). Stress = 20/0.2x10

-6 = 10 8 Nm -2 2. What is the strain in a wire, initially 1 m long, that has stretched by 3 mm? Strain = 0.003/1 = 0.003 2