Post on 14-Apr-2017
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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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