STRESS:

It is the force of resistance per unit area, offered by body undergoing deformation. —It is a tensor quantity.

TYPES OF STRESS:

1. Normal Stress: Stress that develops when an object is subjected to forces perpendicular to its cross-sectional area. Normal stress (σ) is calculated as the applied force (F) divided by the cross-sectional area (A) of the material:

   $$ σ = F/A. $$

   Further Division of Normal Stress:

   1. Tensile Stress: Tensile stress is a type of normal stress that occurs when forces act to stretch or elongate a material. It causes the material to become longer in the direction of the applied force.
   2. Compressive Stress: Compressive stress is another type of normal stress, but it acts to compress or shorten a material along the direction of the applied force.

   

2. Shear Stress: Shear stress is another form of mechanical stress that occurs when forces are applied parallel to the surface of an object or material. It results in a deformation of the material along the direction of the applied force. Shear stress is also calculated as the applied force (F) divided by the cross-sectional area (A) perpendicular to the applied force:

   $$  τ = F/A. $$

   

   Stress strain diagram of ductile material [Mild Steel, Aluminium]-

   

   Point A: The elastic limit is the limit beyond which the material will no longer go back to its original shape when the load is removed, or it is the maximum stress that may be developed such that there is no permanent or residual deformation when the load is entirely removed.

   Point B: It represents upper yield point of the material. After this point the curve is no longer a straight line. After this point, the material undergoes more rapid deformation. This point gives the yields strength of the material. Yield stress is defined as the stress after which material extension takes place more quickly with no or little increase in load.

   Point C: It represents the lower yield point of the material. It is point after which material try to regain its strength.

   Point D: It represents the ultimate strength of the material. It is the maximum stress value that material can withstand. It is the point of interest for design engineers. This ultimate strength is referred as the tensile strength of material.

   Point E: It represents breaking point. It is the point occurred after maximum deformation. The stress associates with this point known as breaking strength or rupture strength.

   Stress strain diagram of brittle material [Glass, Ceramic]-

Materials which show very small elongation before they fracture is called brittle material.

Stress on inclined plane:

Normal and Shear Stresses on an inclined plane

Stress in members with varying cross section area:

E : Common Young’s Modulus

Elastic Constants:

1. Young’s Modulus: Ratio of tensile stress (σ) to tensile strain (ε).

   $$ Y= \frac{σ}{ε} $$

   $$ \sigma=\frac{F}{A} $$

   $$ \epsilon=\frac{\Delta*l}{l} $$

2. Modulus of rigidity: Rratio of shear stress(τ) to the shear strain (θ).

   $$ G =\frac{\tau}{\theta} $$

   $$ τ = \frac{F}{A} $$

   

   $$ \theta =\frac{\Delta*x}{y} $$

<aside> 📌 There proofs have been asked in exam.

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Relation between Y, K and σ!Relation between Young's Modulus,Bulk Modulus,Poission's Ratio#bedkdian