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Stress and strain

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Stress Types Normal / Shearing / Bearing Stress

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Stress Normal Stress

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Shearing Stress Shearing Stress through Shearing Force. Ex:Draw the Free body diagram of left and right sides of XX

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Stress Shearing Stress

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Shearing Stress Single Shear

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Shearing Stress Double Shear

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Bearing Stress

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Stress Application of loads Point/Distributed

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Saint-Venants Principle

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Saint-Venants Principle

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Stress Concentration

K Stresses Concentration Factor

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Stress Concentration Factor

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Stress Concentration Factor

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Photo-elasticity method Stress Distribution Many transparent non-crystalline materials that are optically isotropic when free of stress become optically anisotropic and display characteristics similar to crystals under stress. This behaviour is known as temporary double refraction.

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Photo-elasticity Experiment

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Photo-elasticity method

Stress Distribution in a Simply Supported beam with centre load

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Photo-elasticity method

Stress Distribution in a scaled down structure

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Photo-elasticity method Stress Raisers shown using photo-elasticity

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Stresses on an Oblique Plane under axial loading

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Stresses on an Oblique Plane under axial loading

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Max. Normal and Shearing Stresses under axial loading

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3D - Stresses State

Stresses under general loadingStresses under 2D case

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Stress at a point

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Why NOT Load Deflection Curve?

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Why NOT Load Deflection Curve?

* For same deflection, two different loads are applied* Stress and Strain are same in both cases whereas the load to make them are different

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Strain

Units for strain is micro strain or micro inch. Strain = deflection (micrometer/meter) = micro strain27

Tensile Test

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Stress Strain Diagram

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Stress Strain Diagram

No clear Yield Point for Aluminium Alloy

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Stress Strain Diagram : OFF SET Method Determination of Yield Strength by Offset method

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Stress Strain Diagram

For Brittle material s, Breaking strength and Ultimate strength are same

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Fracture due to Tensile Load

Ductile Material

Brittle Material

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Deflection

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Problem

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Problem

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Problem

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Problem

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Generalized Hookes Law

- Poissons ratio

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Generalized Hookes Law

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Generalized Hookes Law

Unit Volume cube before loading

Parallelepiped Volume after loadingVolume

Change in the Volume:

Remember the initial sides of the cube is one. So, change in length is equal to strain since initial length is one.41

Generalized Hookes Law

Substituting strain values

when the body is subjected to uniform hydrostatic pressure (compressive load, hence ve )

Remember the initial sides of the cube is one. So, change in length is equal to strain since initial length is one.42

Generalized Hookes Law

Introducing a constant, k

then where e is the Dilatation (or) Change in the vol. per unit volume where k is the Bulk Modulus (or) Modulus of Compression

For all engineering materials

Remember the initial sides of the cube is one. So, change in length is equal to strain since initial length is one.43

Generalized Hookes Law when shear stresses are also acting

Let us take one set of shear stresses

OR

Remember the initial sides of the cube is one. So, change in length is equal to strain since initial length is one.44

Generalized Hookes Law With Shear Modulus (or) Modulus of Rigidity

Remember the initial sides of the cube is one. So, change in length is equal to strain since initial length is one.45

Stress Transformations

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Stress Transformations 2D

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Stress Transformations 2D

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Stress Transformations 2D

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Stress Transformations 2D

In the firs equation, if we substitute theta + 90, then we can get the second equation. There is no need to remember the sigma y equation separately 50

Principal Stress

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Principal Stress

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Stress Transformations

Max. shearing stress occurs on a plane that makes 45 angle with principal stress planes

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Problem

S. Prob: 7.1

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Problem

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Problem

Principal Stress

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Problem

Cross Check

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Problem

Maximum Shearing Stress

Maximum Shearing Stress Plane

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Stress States are Similar to para. Eq. of a Circle

Above stress transformation equations can be converted into a parametric eqn. of a circle

Using

In the Sigma x equation, if we substitute theta + 90, then we can get the Sigma y equation. There is no need to remember the sigma y equation separately.

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Stress Space and Stress States

All stress states will fall on the circumference of the circle.60

Construction of Mohrs Circle 2D

Conventions used to denote the stresses in Mohrs circle

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Stress Transformations Mohrs Circle 2D

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Stress Transformations Mohrs Circle 2D

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Stress Transformations - Mohrs Circle 2D

Stress state on given planeStress state on a 45 plane

Mohrs Circle

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Stress Transformations - Mohrs Circle 2DStress state on given planeStress state on a 45 planeMohrs Circle

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Problem using Mohrs Circle

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Problem using Mohrs Circle

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Problem using Mohrs Circle

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Problem using Mohrs Circle

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Problem using Mohrs Circle

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Problem using Mohrs Circle

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Problem using Mohrs Circle

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Problem using Mohrs Circle

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