Analysis of stress and strain;
What is stress and strain?
Stress is the intensity of a force per unit area; so the unit is N/m2
. Stress is indicated with the character σ (sigma).
Strain describes the deformation of a material, it is the change in length divided by the original length;
Stress and strain relationship
Most materials have a linear relationship between stress and strain. This is known as Hooke's law:
E is the modulus of elasticity, also known as the Young's modulus.
Suppose a steel 5x5 cm beam with length of 2 meters and a mass of 400 kg on it. The force of gravity is 400*9,81 = 3924 N. The cross section equals 0,05 * 0,05 = 0,0025 m2
. When these values are entered in the stress formula, you will find a pressure of 3924/0,0025 = 1,57 MPa
The modulus of elasticity of steel is 210 GPa, which can be found in tables. With the pressure and modulus of elasticity known, it is possible to calculate the strain and the decrease in length;