Strength Of Materials -I

According to RTU Syllabus

UNIT-I

PART-2

UNIT-I

SIMPLE STRESSES AND STRAINS:

  • Concept of stress and strain in three dimension and generalized hooke's law
  • Direct stress and strain
  • Free body diagram
  • Hooke's law
  • Young's Modulus
  • Tension test of mild steel and other Materials
  • True and apparent stress
  • Ultimate Strength
  • Yield stress and permissible stress
  • Stresses in prismatic and non prismatic members and in composite members
  • Thermal stresses
  • Shear stress
  • Shear strain
  • Modulus of Rigidity
  • Complementary Shear Stress
  • Poisson's Ratio
  • Volumetric strain
  • Bulk modulus
  • Relation between Elastic Constants
  • Strain Energy for gradually applied,Suddenly applied and Impact loads

 Stress

Stress = Resisting force per unit area

As there is no resistance against F force,there will be no stress in the body.

Stress develops in body.

Stress develops in body

  • Stress are generated as a resistance to the applied external forces or as a result of restrained deformations.

Stresses are broadly classified as-

 

1. Normal stress  -   acts perpendicular to surface.

 

 2.Shear stress -  acts along the surface

 

 

 

Concept of stress

STRAIN

  • Strain is defined as deformation per unit length.

Strain is classified as-

 

  • Normal strain
  • Shear strain

Normal Strain

Shear strain

ADITI SHARMA

STRENGTH OF MATERIALS - I

UNIT-I

PART-2

According to RTU Syllabus

Tension Test of Mild Steel

  • Normally Gauge length = 5.65 √A    for both rectangular and circular section.
  • Test is done on U.T.M i.e. Universal Testing Machine.

Text

Stress Strain curve for Mild Steel

O

A

B

C

D

E

F

G

  • OA = Linear Curve
  • A = Proportional Limit
  • B = Elastic Limit
  • C = Upper Yield Point
  • D = Lower Yield Point
  • DE = Plastic region
  • EF = Strain hardening region
  • FG = Necking region
  •  F = Ultimate Stress Point
  • G = Fracture point

 

Region OA

 

  • From O to A stress is proportional to strain.
  • Stress strain curve is linear
  • Strains are small
  • Normal stress is responsible for Elongation
  • Volume of specimen increases

Region AD

  • Strain increases more rapidly as compared to stress.
  • If specimen is unloaded at point B i.e.Elastic limit,the material will regain its original shape.
  • volume of specimen increases
  • Point C i.e lower yield point is the load required to maintain yield.
  • Point C' i.e. upper yield point is the load reached just before yielding starts.

Region DE

  • After reaching Yielding stress,the specimen undergoes large deformation with a small increase in load.
  • This is caused due to slippage of materials along oblique surfaces.

 

 

 

 

  • It is caused due to shearing stresses.
  • These deformation are called plastic deformations and are permanent.
  • Volume of specimen does not change.

Region EF

  • After undergoing large strains due to yielding,the steel begins to strain harden.
  • It is due to change in material crystalline structure.

Region FG

  • After point F,the diameter of a portion of the specimen begins to decrease.This is called Necking.

 

 

 

 

  • After Necking ,lower loads are sufficient to keep the specimen elongating until it finally ruptures.
  • Rupture occurs along a cone shaped surface at an angle of 45 degree with the original surface.

 

 

 

 

 

 

 

 

 

 

 

 

  • It indicates that shear is primarily responsible for failure of ductile materials.
  • This failure is called Cup cone failure.

ADITI SHARMA

STRENGTH OF MATERIALS - I

UNIT-I

PART-3

According to RTU Syllabus

True and Apparent Stress

  • As Elongation takes place,cross-sectional area  and length of the specimen also changes.
  • If stress and strain are plotted corresponding to actual area of cross section and actual length at any time,we get true stress strain curve.

 

Hooke's law

  • Stress is proportional to strain within proportional limit.

 

 

 

 

 

 

 

 

 

  • It is valid for isotropic,homogeneous and linearly elastic material.

Young's Modulus / Modulus of Elasticity

Yield stress and Permissible stress

ADITI SHARMA

STRENGTH OF MATERIALS - I

UNIT - I

PART - 4

According to RTU Syllabus

Stress strain curve for other Materials

Brittle Material (Cast Iron)

Aluminium and Copper

Stress strain curve for Brittle Material (Cast Iron)

Stress strain curve for Aluminium and Copper

ADITI SHARMA

STRENGTH OF MATERIALS - I

UNIT-I

PART-5

According to RTU Syllabus

Stresses in Prismatic Members

Stresses in Non-Prismatic Members

ADITI SHARMA

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