### Stress and Strain

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So, Here were are going to see one of the Important concepts in civil engineering of engineering as a whole because all the discipline in engineering that deals with physical objects deal with this concept called Stress and Strain.

**About Stress**

** **Stress is nothing but the resisting force created within an object(Equal to the external force upto the elastic limit of an object) due to the applied external force that causes a change in the dimensions i,e deformation of an object either temporarily(within the elastic limit) or permanently(beyond the elastic limit). Mathematically Expressing,

**Stress = External Force or Load / Cross-sectional Area**

Hence the force applied per unit area is called the Stress. The Stress can be classified based on the direction or position to which the force is applied.

**Types of Stress**

**Direct Stress**

** **If the force applied to an object is perpendicular to the surface area of the object then the stress generated is known as Direct Stress.

**Shear Stress**

** **If the force applied to an object is parallel to the surface area of the object then the stress generated is known as Shear Stress.

**Unit of Stress**

** **In the S.I. system of units, the force is expressed in Newton(N) and the area in Metre Square(m^2). Hence the unit of Stress becomes

**Unit of Stress = N/ m^2**

Note : 1 N/m^2 = 1 Pascel.

**About Strain**

** **When a force is applied to an object due to the applied force there is a change in the dimension of the object either Temporarily or permanently, hence the ratio of change in the dimensions of the object to the original dimension is known as strain. Mathematically Expressing

**Strain = Change in Dimension/Original dimension **

**Types of Strain**

Based on the dimension change and the force that caused them the strains were classified as,

- Tensile Strain (Increase in Length)
- Compression Strain( Decrease in Length)
- Volumetric Strain (Change in Volume)
- Shear Strain( Caused due to Shear stress)

**Unit of Strain**

**Strain is Dimensionless.**

### Types of Stress and Strain

### 1. Normal Stress and Strain

### 1.1 Longitudinal Stress and Strain

**1.1.1 Tensile Stress & Tensile Strain**

In Tensile stress, the object is subject to pull on both sides so that a tensional force is created in the object making the molecules in the object move away from each other. Hence the length or the dimension of the object increases. So in tensile strain due to tensile stress, there is an increase in the dimension of the object.

Here Stress is expressed as Sigma(σ), Mathematically expressing,

**σ = Resisting force(R)/Cross-sectional Area = Tensile load(P)/A = P/A.**

Here Strain is expressed as epsilon(ε), Mathematically expressing,

**ε =Increase in Length/Orginal Length = dL/L**

**1.1.2 Compressive Stress & Compressive Strain**

When compression force is applied to an object, it creates Compressive stress in the object due to which a compressive strain is produced. The particles in the object end to move closer to each other hence the dimension of an object decreases which we call a Compressive Strain.

Here Stress is expressed as Sigma(σ), Mathematically expressing,

**σ = Resisting force(R)/Cross-sectional Area = Push(P)/A = P/A.**

Here Strain is expressed as epsilon(ε), Mathematically expressing,

**ε =Decrease in Length/Orginal Length = dL/L**

**1.2 Volumetric Stress & Volumetric Strain**

** **In Volumetric Stress, the force is applied on the object from all directions due to which there is a change in the volume or dimension of an object. Hence this kind of stress and strain are called Volumetric Stress or Bulk stress and Volumetric Strain respectively.

Mathematically Expressing,

**Volumetric stress = Load / Area = Pressure (dp)**

**Volumetric strain (Ev) = Change in Volume / Orginal Volume = dV/V**

**2. Shear Stress and Shear Strain**

** **Here, the two equal and opposite forces are applied or impact the object tangential or parallel to the surface area of the object hence the dimensional change or deformation in the object occurs in a tangential manner i.e the object shears off across the section. Such Stress and Strain are known as Shear Stress and Shear Strain.

Here Stress is expressed as Tau(τ), Mathematically expressing,

**τ = Shear Resistance/Shear Area = R/A**

Here Strain is expressed as Phi(φ), let's take two points in an object say A and D, A is fixed and D is subject to Shear Stress, due to the stress there is a transversal displacement of the point D to D1, Hence Mathematically expressing,

**φ = Transversal Displacement of D to D1 (dl) / Distance between points A and D(h) = dl/h**

**Next: **Elastic Constants

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