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BRANCH:- MECHANICAL ENGINEERING

SEMESTER:-3RD SEMESTER

SUBJECT:- STRENGTH OF MATERIALS (SOM)

CHAPTER:-1 ( SIMPLE STRESS AND STRAIN)

PREPARED BY:-ER.B.N.MOHANTA

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STRENGTH OF MATERIALS

SIMPLE STRESS

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STRAIN

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INTRODUCTION�

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�Strength of materials is a subject which deals with the detailed study about the effect of external forces act on materials and ability of material to resist deformation.

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TYPES OF LOAD��

  • STATIC LOAD
  • DYNAMIC LOAD
  • IMPACT LOAD
  • FATIGUE

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STRESS

When an external force acts on a body , an internal resisting force is developed , this internal resisting force per unit cross-sectional area is known as stress.

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Mathematically:- Stress = Force / Area

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Units :- N /mm2 ,Mpa, Gpa,Kpa etc.

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TYPES OF STRESS�

  • TENSILE STRESS ( DIRECT STRESS)
  • COMPRESSIVE STRESS (DIRECT STRESS )
  • SHEAR STRESS

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STRAIN

When an external force is applied on a body, there is some change occur in the dimension of the body. The ratio of this change of dimension in the body to its actual dimension is called strain.

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TYPES OF STRAIN

  • TENSILE STRAIN ( LINEAR AND LATERAL)
  • COMPRESSIVE STRAIN
  • VOLUMETRIC STRAIN
  • SHEAR STRAIN

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Tensile strain:

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The strain produced in a body due to tensile force is called the tensile strain. The tensile force always results in the increment of the length and decrease in the cross-section area of the body. In this case, the ratio of the increase in length to the original length is called tensile strain.

Compressive strain:

The strain appears due to the compressive force is called compressive strain. In compressive force there is a decrease in the dimension of the body. So the ratio of the decrease in the length of the body to the original length is called compressive strain.

Volumetric strain:

The ratio of the change in the volume of a body to the original volume is called the volumetric strain. In volumetric strain there is a change in the volume of the body due to application of the external forces.

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Shear strain:

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The strain which is produced in a body due to shear force is called shear strain.

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HOOKE’S LAW

  • when a material is loaded within elastic limit, the stress induced in the material is directly proportional to the strain .
  • It means that the ratio of stress with the corresponding strain gives us a constant within elastic limit. The constant is known as Modulus of Elasticity.

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Young’s Modulus�

  • It is defined as the ratio of stress to the strain within elastic limit. It is denoted by the letter ‘E’
  • It represents the elastic property of a material.
  • The unit of Young’s modulus is N/m2.�or N/mm2 etc .
  • The unit of young’s modulus is same as that of units of stress.

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Modulus of Rigidity�

  • It is defined as the ratio of shear stress to the shear strain within elastic limit. It is denoted by G or C or N.
  • The unit of Modulus of Rigidity is N/m2.�or N/mm2 etc .
  • The unit of Modulus of Rigidity is same as that of units of stress.

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BULK MODULUS

  • It is defined as the direct stress to the volumetric strain.
  • It is denoted by K.
  • The unit of Bulk Modulus is N/m2.�or N/mm2 etc .
  • The unit of Bulk Modulus is same as that of units of stress.

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PRINCIPLE OF SUPERPOSITION

  • The principle of superposition says that when a number of loads are acting on a body, the resulting strain, according to the principle of superposition, will be the algebraic sum of strains caused by individual loads.

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COMPOSITE SECTION

  • Composite sections may form by combination of two or more bars of equal lengths but of different material rigidity and fixity so as to act as one unit .

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  • In composite bars, the following factors are considered:

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1.The change in length in each bar and the corresponding strain is equal.

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2. Total load on composite section=load on bar(1)+ Load on bar(2)+……

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TEMPERATURE STRESS

1. Increase or decrease of temperature of a free body causes the body to expand or contract and no stresses are induced. However, if the deformation of the body is constrained, some stresses are induced in the body, and such developed stresses are called temperature stresses which may be tensile or compressive based on either the contraction is prevented or extension is prevented.

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  1. A bar whose ends are fixed to rigid supports, so that the expansion is prevented, is considered.
  2. Let the length of the bar be l subjected to an increase in temperature T°. The expansion of the bar will be

δl = lαT

where α is the coefficient of thermal expansion of the material of the bar.

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STRAIN ENERGY

  • Strain energy is defined as the energy stored in a body due to deformation.
  • Resilience:- It is a common term used for the total strain energy stored in a body. Sometimes the resilience is also defined as the capacity of a strained body for doing work (when it springs back) on the removal of the straining force.

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Proof Resilience :-

It is also a common term, used for the maximum strain energy, which can be stored in a body. (This happens when the body is stressed up to the elastic limit). The corresponding stress is known as proof stress

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Let P = Load gradually applied,

A = Cross-sectional area of the bar,

l = Length of the bar,

E = Modulus of elasticity of the bar material

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δ = Deformation of the bar due to load.

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