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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