Shear stress strain curve & modulus of rigidity (10.01.03.039)

A Presentation on shear stress strain curve & modulus of rigidity

1. Welcome To My Presentation Presented by- Afsana Ishrat Khan Dept. of Civil Engineering 4 th Year 2 nd Semester ID: 10.01.03.039

2. Course No. : CE 416 Course Title : Pre-stressed Concrete Lab. Course Teacher : Sabreena Nasrin Madam & Munshi Galib Muktadir Sir Topic Of Presentation “Shear Stress-Strain Curve & Modulus Of Rigidity”

3. Shear Stress Shear stress that acts parallel to a surface. It can cause one object to slide over another. It also tends to deform originally rectangular objects into parallelograms. The most general definition is that shear acts to change the angles in an object. Shear stress = τ = Force(F)/Area(A)

4. Shear Strain It is the amount of deformation  perpendicular  to a given line rather than  parallel  to it. The ratio turns out to be tan A, where A is the angle the sheared line makes with its original orientation.. Generally, shear strain = γ = Δ x / l

5. Shear Stress-Strain Curve The relationship between the shear stress and shear strain for a particular material is known as that particular material's Shear Stress-Strain curve. Shear stress-strain curves are an extremely important graphical measure of a material's mechanical properties

6. Cont'd

7. Various Stress-Strain Curves For Different Materials Linear elastic material:   A linear elastic material is one in which the strain is proportional to stress as shown below:

8. Cont'd Rigid Materials: It is the one which do not experience any strain regardless of the applied stress.

9. Cont'd Perfectly plastic: A perfectly plastic i.e. non-strain hardening material is shown below:

10. Cont'd Rigid Plastic material(strain hardening): A rigid plastic material i.e. strain hardening is depicted in the figure below:

11. Cont'd Elastic Perfectly Plastic material: The elastic perfectly plastic material is having the characteristics as shown below:

12. Cont'd Elastic – Plastic material: The elastic plastic material exhibits a stress Vs strain diagram as depicted in the figure below:

13. Typical Stress-Strain Curve For Ductile Material

14. Modulus of Rigidity (Definition) Modulus of rigidity is the ratio of shear stress to the displacement per unit sample length (shear strain). More specifically modulus of rigidity (or Shear Modulus) is the coefficient of elasticity for a shearing force. In materials science, shear modulus or modulus of rigidity, denoted by  G defined as the ratio of shear stress to the shear strain, i.e. G =  τ / γ

15. where, τ =F/A= shear stress, F=force, A=area on which the force acts,   γ = Δ x / l = shear strain, Δ x= transverse displacement, l=  initial length. Shear modulus' derived SI unit is the  pascal  (Pa)

16. Modulus of Rigidity (PURPOSE) Modulus of rigidity, or the shearing modulus, is used to determine how  elastic or bendable materials will be if they are sheared, which is being pushed parallel from opposite sides. This property becomes the useful part of many calculations, and it is called the coefficient of elasticity during shearing .

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