# Useful Formulae

36 STRESS, STRAINANDHEAT expansion, contraction, tension and compression E When a material is stretched or squashed it changes shape.The stress, ,in the material is defined as the force Fper unit area A the strain, , is defined as the change in length,l, relative to the original length,l0. Youngs ModulusEfor the material is then Substances also possess a Bulk Modulus K,relating inversely to its volumetric compressibility,and a Shear Modulus G,the ratio of shear stress and strain shown opposite. Heating and cooling cause expansion and contraction of materials in a linear relation to the temperature increase or decrease.The linear expansivity,, of a substance relates its change in length l to its change in temperature T, so that l l0T , wherel0 is its starting length. Hookes Lawstates that a spring or equivalently elastic object stretched xunits of distance beyond its equilibrium position pulls back with a force F kx,where kis the spring constantof the spring in question. As a consequence, when a weight is attached to a vertical spring,the elongation is proportional to the weight. For any structure to be in equilibrium,the total forces at any point must be balanced as shown opposite. FA ll0 stress strain 37