Elasticity | General Awareness for SSC CGL PDF Download

Introduction

Elasticity is a fundamental property of materials that describes their ability to return to their original shape and size after undergoing deformation due to applied forces. Understanding elasticity is crucial in material science and engineering because it helps us predict how materials behave under various loads and stresses. Here’s a detailed overview of the key concepts related to elasticity:

What is Elasticity?

Elasticity is the capacity of a material to undergo deformation when subjected to external forces and then return to its original shape and size once these forces are removed. This property is essential for analyzing how materials respond to different stresses and loads.

SI Unit of Elasticity

• The SI unit of elasticity is the pascal (Pa). Elasticity measures how materials deform under tension and recover their shape once the force is removed.
• One pascal is equal to one newton per square meter (N/m²), and it is used to quantify pressure and stress in the SI system.

What is Elastic Stress?

Elastic stress refers to the internal resistance a material develops when subjected to an external force. This stress causes temporary deformation, but the material returns to its original shape when the force is removed.

Types of Elastic Stress

• Longitudinal Stress: Longitudinal stress occurs when a material is subjected to an axial force along its length. It is also known as axial or tensile stress when the material is being stretched.
  Formula: σ = F/A
  Where σ is the stress, F is the axial force, and A is the cross-sectional area.
• Volume Stress (Bulk Stress): Volume stress, or bulk stress, arises from changes in the volume of a material due to pressure changes. This stress affects the material uniformly in all directions.
  Formula for Fluids: σ_bulk  =−P
  Where P is the pressure exerted on the fluid.
• Tangential Stress (Shear Stress): Tangential stress, or shear stress, occurs when forces act parallel to a material’s surface, causing adjacent layers to slide relative to each other.
  Formula: τ = F/A
  Where τ is the shear stress, F is the applied force, and A is the area over which the force acts.

What is Strain?

Strain measures the deformation of a material in response to an applied force. It represents the relative change in shape or size of the material compared to its original dimensions and is dimensionless.

Types of Strain

• Longitudinal Strain: Longitudinal strain, also called axial or linear strain, measures the change in length of a material in the direction of the applied force.
  Formula: ∈ ΔL/L₀
  Where ϵ is the strain, ΔL is the change in length, and L₀ is the original length.
• Volume Strain: Volume strain, or bulk strain, measures the change in volume of a material when subjected to external pressures or forces.
  Formula: ∈_V =Δ𝑉/𝑉₀ 
  Where ϵ_v  is the volume strain, ΔV is the change in volume, and V₀  is the original volume.
• Tangential Strain: Tangential strain, or shear strain, measures the distortion of a material’s cross-sectional elements due to shear stress.
  Formula: γ= Δθ/θ₀ 
  Where γ is the shear strain, Δθ is the change in angle, and θ₀ is the original angle.

Elastic Hysteresis 

Elastic hysteresis refers to the energy loss observed in materials during cyclic loading and unloading, even when the material remains within its elastic deformation range. This phenomenon can be seen in materials like rubber and certain metals, where the loading and unloading paths differ, leading to energy dissipation.

Hooke’s Law

Hooke’s Law describes the linear relationship between the stress applied to a material and the resulting strain, as long as the material remains in its elastic range.
Formula: σ = E⋅∈
Where σ is the stress, E is Young’s modulus, and ∈ is the strain.

Modulus of Elasticity

The modulus of elasticity, or Young’s modulus (E), measures a material’s stiffness by quantifying how much it deforms in response to applied stress.
Formula: E = ∈/σ
Where E is Young’s modulus, σ is the stress, and ∈ is the strain.

Types of Elasticity Modulus

• Young’s Modulus (E): Measures a material’s stiffness or resistance to elastic deformation under axial loading. It is a ratio of stress to strain within the elastic range.
• Shear Modulus (G): Also known as the modulus of rigidity, it quantifies a material’s resistance to shear deformation. It describes how much a material deforms under shear stress.
• Bulk Modulus (K): Measures how a material responds to changes in volume under uniform pressure. It indicates how much a material compresses or expands under pressure.
• Poisson’s Ratio (ν): Describes the ratio of lateral strain to axial strain when a material is subjected to axial stress. It indicates how a material’s shape changes in response to stretching.
• Stress Concentration Factor (Kt): Describes the impact of geometric discontinuities (like notches or holes) on stress distribution. Although not a modulus, it is related to how stress is distributed in materials with irregular shapes.