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# shear strain(due to shear stress&torsional stress)

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• if a bar is subjected to a direct load, and hence a stress the bar will change in length. If the bar has an original length L and changes by an amount dL, the strain produce is defined as follows:Strain is thus, a measure of the deformation of the material and is a nondimensional Quantity i.e. it has no units. It is simply a ratio of two quantities with the same unit.
• ### shear strain(due to shear stress&torsional stress)

1. 1. 11/24/2013 1
2. 2. 11/24/2013 2
3. 3. Stress This is a measure of the internal resistance in a material to an externally applied load. Stress is designated and is defined as: stress 11/24/2013 load W = area A 3
4. 4. STRAIN When a body is subjected to some external force, there is some change of dimension of the body. The ratio of change of dimension of the body to its original dimension is known as strain. Strain may be:- a) Tensile strain b) Compressive strain c) Volumetric strain d) Shear strain Tensile strain- Ratio of increase in length to original length of the body when it is subjected to a pull force Compressive strain- Ratio of decrease in length to original length of the body when it is subjected to a push force Volumetric strain- Ratio of change of volume of the body to the original volume Shear strain-Strain due to shear stress` 11/24/2013 4
5. 5. Concept of strain 11/24/2013 5
6. 6. Sign convention for strain: • Tensile strains are positive whereas compressive strains are negative. • The strain defined earlier was known as linear strain or normal strain or the longitudinal strain. 11/24/2013 6
7. 7. Shear Stress Similarly in shear the shear stress is a measure of the internal resistance of a material to an externally applied shear load. shear stress 11/24/2013 load W = area resisting shear A 7
8. 8. Concept of Shear Stress • Shear stress is defined a the component of force that acts parallel to a surface area. • Shear stress is a stress state where the shape of a material tends to change (usually by "sliding" forces – torque by transversely-acting forces) without particular volume change. 11/24/2013 8
9. 9. Shear stress and strain Area resisting shear Shear displacement (x) Shear Force Shear force 11/24/2013 L Shear strain is angle 9
10. 10. Shear Stress Shear stress tends to change the shape of a body without changing its volume Note: we apply shear force and shear stresses develop in the interior of the material 11/24/2013 10
11. 11. Sign convention of shear stress The sign convention for shear force and stress is based on how it shears the materials as shown below. 11/24/2013 11
12. 12. Hooke’s Law for Shear By conducting a similar material testing to normal stress (Section 2.4), there is a linear relationship (for most engineering materials) between the shear stress and shear strain Fig : Relationship of shear stress τ – shear strain γ for linear elastic material 11/24/2013 12
13. 13. 11/24/2013 13
14. 14. Torsion Torsion occurs when an external torque is applied and an internal torque, shear stress, and deformation . 11/24/2013 14
15. 15. Torsion and Shearing Stress • There is also an internal shear stress which develops inside the shaft. • This shearing stress on the cross sectional area varies from zero at the center of the shaft linearly to a maximum at the outer edge. • This may be thought of as being due to the adjacent cross sectional areas of the shaft trying to twist passed each other. 11/24/2013 15
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