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Rifath Ara Rimi 10.01.03.145

Section: C

Presentation TopicShear Strain (Due to Shear

& Torsional Stress)

Definition of Strain

Strain:The ratio of change in a dimension that takes place with a material under stress. Strain is a measurement of stress.

O The Cauchy strain or engineering strain is expressed as the ratio of total deformation to the initial dimension of the material body in which the forces are being applied. The engineering normal strain or engineering extensional strain or nominal strain e of a material line element or fiber axially loaded is expressed as the change in length ΔL per unit of the original length L of the line element or fibers. The normal strain is positive if the material fibers are stretched and negative if they are compressed. Thus, we have

O where  is the engineering normal strain,  is the original length of the fiber and  is the final length of the fiber.

Definition of Shear Strain

Shear StrainO Shear strain is defined as the strain

accompanying a shearing action. It is the angle in radian measure through which the body gets distorted when subjected to an external shearing action.

We can define shear strain exactly the way we do longitudinal strain: the ratio of deformation to original dimensions. In the case of shear strain, though, it's 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. Note that if A equals 90 degrees, the shear strain is infinte.

Pure shear

Pure Shear: Any time an object is deformed, shear occurs.

For example, in the top row a block is deformed without changing area. It looks like the only deformation involved is compression and extension.

Directions of greatest compression and extension are constant. The major and minor axes of the deforming ellipse remain constant. All other lines rotate.

Torsional Stress

Shear stress developed in a material subjected to a specified torque in torsion test. It is calculated by the equation:

where T is torque, r is the distance from the axis of twist to the outermost fiber of the specimen, and J is the polar moment of inertia.

Formulas

Formulas for bars of circular section

Formulas for bars of non - circular section. Bars of non -circular section tend to behave non-symmetrically when under torque and plane sections to not remain plane. Also the distribution of stress in a section is not necessarily linear. The general formula of torsional stiffness of bars of non-circular section are as shown below the factor J' is dependent of the dimensions of the section and some typical values are shown below. For the circular section J' = J.

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