STRESS, STRAIN, HOOKE’S LAW, AND MODULUS OF ELASTICITY

STRESS, STRAIN, HOOKE’S LAW, AND MODULUS OF ELASTICITY

INTRODUCTION

Structural materials used in Mechanical and Civil Engineering practice must generally have strength. What is strength ? Strength is due to the sum of forces of attraction between negatively charged electrons and positively charged protons within the material. When covalent bonds join large numbers of atoms to produce giant molecules as is the case of the carbon atoms in carbon fibre, the strength of the resultant material is great.

Constructional materials generally must be able to withstand the action of considerable forces without undergoing other than very small amounts of distortion. Materials must be capable of permanent deformation at the expense of as little energy as possible. That is, it must be malleable and ductile.

Malleability refers to the extent to which a material can undergo deformation in compression before failure occurs, whilst ductility refers to the degree of extension which takes place before failure of a material in tension. All ductile materials are malleable but malleable materials are not necessarily always ductile since a soft material may lack strength and those tear a part very easily in tension. Other mechanical properties include elasticity, hardness, toughness and also creep and fatigue properties. In each case, the property is associated with the behaviour of the material toward the application of force.

DEFINATION OF STRESS

When a force is transmitted through a solid body the body tends to undergo a change in shape. This tendency to deform is resisted by the internal resilience of the body and the body is said to be in a state of stress. Thus, a stress may be described as a mobilized internal force which resists any tendency towards
deformation. The definition to describe the force transmitted per unit area as the intensity of stress or unit stress.
Stress ‘a measurement of density of forces’ is defined as force per unit area of cross section. The Standard Imperial (SI) unit of stress is the Pascal (Pa) which is equivalent to a force of one Newton acting on an area of one square metre, i.e. N/m2 or Nm-2. Numerically it will be the same as that expressed in Mega Pascal (MPa).

All materials bodies will deform when placed in a state of stress, and as the stress is increased the deformation also increases. In such cases, when the loads causing the deformation are removed, the body returns to its original size and shape. A material or a body having this property is said to be elastic. It is also noticeable that if the stress is steadily increased, a point is sooner or later reached when, after the removal of the load, not all of the induced strain is recovered. This limiting value of stress is called the elastic limit.

STRAIN

When a force is transmitted through a solid body the body tends to be deformed. The measure of this change in shape is called strain. When a body is placed in a state of stress it undergoes strain according to the configuration of the stress applied. Thus, direct stresses cause changes in length or shearing stresses cause twisting and bearing stresses cause indentation in the bearing surface.

Strain refers to the proportional deformation produced in a material under the influence of stress. It is measured as the number of metres of deformation suffered per metres of original length and is a numerical ratio.
Strain may be either elastic or plastic. Elastic strain is reversible and disappears when the stress is removed. Strain is roughly proportional to the applied stress

HOOKE’S LAW

The relationship between the induced strain and stress causing it is found to be constant in elastic materials. Hooke’s Law defines that ‘strain is proportional to the stress causing it, providing that the limit of proportionality has not been exceeded’.



Modulus of Elasticity (Young’s Modulus),E

Young’s Modulus of Elasticity (E) is the ratio between the stress applied and the elastic strain it produces. That is, it is the stress required to produce a unit quantity of elastic

strain. It is related to the rigidity of the material. The modulus of elasticity is expressed in terms of either tensile or compressive stresses and its units are the same as those for stress.