(torsion)(10.01.03.092) (1)
DESCRIPTION
presentation on torsionTRANSCRIPT
AHSANULLAH UNIVERSITY OF SCIENCE & TECHNOLOGY
Name: Mehedi hossain
Student I.D. : 10.01.03.092
Section: B
TORSIONAL STRESS
TORSION Torsion is a twisting moment that is applied on an object by twisting one end when the other is held in position or twisted in the opposite direction.
TorsionFor the purpose of deriving a simple theory to describe the
behavior of shafts subjected to torque it is necessary make the following base assumptions.
Assumption: (i) The materiel is homogenous i.e. of uniform elastic
properties exists throughout the material. (ii) The material is elastic, follows Hook's law, with shear
stress proportional to shear strain. (iii) The stress does not exceed the elastic limit. (iv) The circular section remains circular (v) Cross section remain plane. (vi) Cross section rotate as if rigid i.e. every diameter
rotates through the same angle.
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.
Fig: The shear stress distribution about neutral axis.
Torsional stresshighest tortional shear stress will be at farthest away from
center. At the center point, there will be no angular strain and therefore no tortional shear stress is developed.
This states that the shearing stress varies directly as the distance ‘r' from the axis of the shaft and the following is the stress distribution in the plane of cross section and also the complementary shearing stresses in an axial plane.
Distribution of shear stresses in circular Shafts subjected to torsion :
Torsional stress acting in Uncracked Beam The variations of the torsional shear stress (τ)
along radial lines in the cross-section are shown. It can be observed that the maximum shear stress (τ max) occurs at the middle of the longer side.
Fig: Beam subjected to pure torsion
Crack Pattern under torsional stress
The cracks generated due to pure torsion follow the path of principal
stress. The first cracks are observed at the middle of the longer side.
Next, cracks are observed at the middle of the shorter side . After the
cracks connect, they circulate along the periphery of the beam.
Fig: Formation of cracks in a beam subjected to pure torsion
Mode of failure due to torsional stressFor a homogenous beam made of brittle material,
subjected to pure torsion, the observed plane of failure is not perpendicular to the beam axis, but inclined at an angle. This can be explained by theory of elasticity. A simple example is illustrated by applying torque to a piece of chalk
Fig: Failure of a piece of chalk under torque
Effect of Prestressing Force
In presence of prestressing force, the cracking occurs at higher load. This is evident from the typical torque versus twist curves for sections under pure torsion. With further increase in load, the crack pattern remains similar but the inclinations of the cracks change with the amount of prestressing. The following figure shows the difference in the torque versus twist curves for a non-prestressed beam and a prestressed beam.
Fig: Torque versus Twist curves
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