Basics of Strength of materials- (with PDF and PPT)

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First, let’s start with the basics and further we will drill down the various concepts of strength of materials, later on down the road.

Classification of Engineering mechanics-

Engineering mechanics is classified into three categories-

  • Static
  • Dynamic
  • Mechanics of materials or strength of materials

Static and Dynamic mechanics-

Static and dynamic mechanics deals with the external effect on the rigid body with applied load. It can not tell about the internal effect that happens inside the body with applied load. The study of the non-deformative body comes under these mechanics, In general.

Mechanics of Materials-

Mechanics of materials deals with the Internal effect and deformations that are caused by the applied load. Mechanics of materials are also known as Strength of materials (SOM).

The study of deformative body or change in shape with applied load, known as strength of materials and it deals with the behaviour of stresses and strains on the solid body with an applied load such as beams, columns and shaft.

Why we study strength of materials-

As the name suggests, The study of materials strength deals with the strength of materials. It plays a very crucial role in designing the body or component such as engines, machines, bridges, flyovers, cranes, lifts etc.

This can be used to-

  • To evaluate the load applied on the body
  • To select the material which can sustain the load

SOM is used to select the material and evaluate the strength of the materials as per load about to be put on, to prevent the failure of the component with applied over time. As you know, when induced stress is gone beyond the material strength, the failure of material occurs.

In general, the ability to withstand an applied load without failure or plastic deformation, known as the strength of material.

Now, Let’s discuss the basics of SOM with its equations.

Strength of materials basics with equations used-

Here are some basic definitions of SOM along with its equations-

Stress-

Stress is the internal resisting force developed in the body due to externally applied load. It is further denoted by σ.

Stress formula is given by-

stress formula

Where P= Force.  A= Area and the unit is- N/mm2

Strain-

When an applied load causes deformation in the body, the deformation per unit length is called strain. It is denoted by ∈.

Strain formula is given by-

strain formula

Where, δl= change in length, l= original length and there is no unit of the strain.

Stress-strain curve diagram-

stress-strain curve

When the steel specimen is subjected to tensile load, the stress is directly proportional to the strain till the elastic limit, This is also known as Hook’s law.

The constant proportionally, known as young’s modulus law. It presents the slow of this curve before the elastic limit. Upon loading it further, the permanent deformation produces and this behaviour is known as strain hardening.

After further loading, the cross-sectional area of the specimen rapidly decreases and this phenomenon is known as necking.

And finally, the specimen reaches its point and get fractured in cup and cone shape.

Modulus of elasticity-

It is the ratio of stress in the body to the strain applied to the body. The unit of modulus of elasticity is – N/mm2

The formula of Modulus of elasticity given by-

Modulus of elasticity

Poisson Ratio-

Poisson’s ratio is the ratio between lateral strain to the linear strain within elastic limit under direct loading. It is denoted by µ or 1/m.

The famous French mathematician Simeon Denis Poisson is the founder of the Poisson’s ratio in 1827.

The formula of poison’s ration is given by-

Poisson's Ratio

The volumetric strain of a rectangular body subjected to an axial load-

volumetric strain of a rectangular body subjected to an axial load formula

Where, b= width, t=thickness, E=modulus of elasticity, 1/m= Poisson’s ratio

The volumetric strain of a rectangular body subjected to three mutually perpendicular forces-

volumetric strain of a rectangular body subjected to three mutually perpendicular forces formula

Where, ∈= Strain in x-direction, ∈y= Strain in y-direction, ∈z= strain in z-direction

Bending Equation-

Destruction in component due to applied load in any of the longitudinal planes, known as bending.

The bending equation is given by-

Bending Equation

Where, M= bending moment, I= moment of inertia, σ= Bending stress, y= (D/2) distance from the neutral axis, E= modulus of elasticity, R= radius of curvature

Torsional Equation-

torsional equation

θτ

Where, T= torque, J= Polar moment of inertia, C= Torsional Rigidity, θ= Angle of twist, τ= shear stress, R= Radius of the circular shaft.

Here is the video guide to help you more go deep into Introduction to the strength of materials

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