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# 10.01.03.096 -----2013

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### 10.01.03.096 -----2013

1. 1. Ahsanullah University Of Science & Technology Department of Civil Engineering
2. 2. Presented By: Arafat Hossain Roll No:10.01.03.096 th nd Yrear:4 Semester:2 Sestion:B
3. 3. Presentation On: Shear Stress Strain Curve & Modulus Of Rigidity
4. 4. Shear stress: Shear stress is the stress which is applied parallel or tangential to a face of a material; it differs from normal stress which is applied perpendicularly. Shear stress, tends to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress and may occur in both liquids and solids. Shear stress in most engineering texts is t (tau). t =F/A Shear strain : It is the components of a strain at a point that produce changes in shape of a body (distortion) without a volumetric change.That is, the tangent of the angular change in orientation of two initially perpendicular lines.
5. 5. Shear stress strain curve: . If the applied load consists of two equal and opposite parallel forces which do not share the same line of action, then there will be a tendency for one part of the body to slide over, or shear from the other part. In the figure , if the section LM is parallel to the forces and has an area A, then the average Shear Stress .t=F/A We can start by looking at an element of material undergoing a shear stress (the red arrows)
6. 6. shear stress The upper face has a force directed parallel,equal and opposite to the bottom face.These two forces equal in magnitude but opposite in direction generate a couple on the element.Since the element is in equilibrium.The two forces acting on the left and right faces produce a couple that is equal in magnitude to the couple produced by the forces acting on the top and bottom faces. This will always be the case when an element in under shear. The shear acting on the four faces of the element cause a deformation of the element. If the lower left corner is considered stationary, we can look at how much the upper left corner of the element moves. The upper left corner has moved a distance δ in the positive x direction. If we look at the angle made by the deformation and the positive y-axis. This is not the angle θ’.The sine of this angle is δ x/L. shear strain
7. 7. shear strain If δx is very small with respect to L, which is generally the case,then the value of the angle in radians is approximately equal to the sign of the angle δ x/L .γ(gamma) is the symbol for the shear strain, so we have γ y = δ x/L. It is labeled with an xy subscript because we are looking at the shear strain in the xy plane I have labeled it with a y subscript because it is the angle made with the y-axis.γ y = δ x/L. The shear is actually the difference between the original angle between the side along the y-axis and the side along the x-axis and the angle after loading θ’, γ y = δ x/L. The angle θ’ is determined by using θ '=π/2−γ y=π/2−δ x/L. If there is also a deformation above or below the x-axis, it must also be included to solve for θ’.θ ' = π/2−γ xy.
8. 8. Modulus of Rigidity: For Elastic materials it is found that within certain limits, Shear Strain is proportional to the Shear Stress producing it. The ratio of shear stress to shear strain is called modulus of rigidity. Modulus of Rigidity G = Shear stress/Shear strain= t/Y
9. 9. THE END