THEORYLike bending, torsion is an important type of loading that can produce critical stresses in engineering applications. Under torsion, shear stresses are produced. The stiffness under shear stress is called the modulus of rigidity, G (MPa). It is also called the shear modulus. The modulus of rigidity of mild steel was determined by performing this test. The theory that were applied in this laboratory are;1. Torque: Twisting effect of couple or force is called as torque. It is denoted by double head arrow.2. Torsion: Torque applied in a plane perpendicular to the longitudinal axis of a member is called as torsion.3. Difference between Torque and Moment:

4. Twisting Moment: It is the summation of torque either left or right section.

5. Bending Theory:

6. Torsion Theory: Assumptions:a. Material is homogenousb. Circular section remains circular and do not wrapc. A plane section of a material is perpendicular to its longitudinal axis remain plane and do not warp after the torque is applied.d. Shaft is loaded by a couple or torque in a plane perpendicular to the longitudinal axis of the plane.e. Shear stress is proportional to shear strain, it means that Hooks Law is applicable.f. In circular shafts subjected to torque shearing strain varies linearly.

Where,t, shearing stressr, radius of shaftT, twisting momentJ, polar moment of inertiaG, modulus of rigidity,, angle of twistL, length of specimen

7. Polar moment of inertia: The geometric rigidity of the X-sec is termed as polar moment of inertia. It is the resistance against twisting, summation of 2 moment of area about x-axis.Circular section:

Hollow Shaft:

Torsional Rigidity/ Modulus of Rigidity/ Modulus of Elasticity in Shear:

When material is subjected to pure twist loading, the slope of shear stress verses shear strain curve is termed as modulus of rigidity (modulus of elasticity in shear, torsional rigidity)

8. Poisons Ratio: The ratio of lateral strain to longitudinal strain when material is subjected to axial loading and always less than 1

9. Relation between yield strength in tension to torsion for mild steel: The relationship between yield stress in simple tension and that in pure shear can be found from VON MISES for a yield criteria

10. Torsional Strength: It is the ultimate strength of a material subjected to a torsional loading It is maximum torsional stress that a material sustains before rupture It is similar to the tensile strength11. Torsional Deformation: Angular displacement of specimen caused by specified torque in torsion test. It is equal to angle of twist in radians divided by gauge length or effective length.12. Torsional strain, y: Strain corresponding to specified torque in torsion test. It is equal to torsional deformation multiplied by the radius of the shaft. Its units are radians.

13. Torsional Stress, T: Shear stress developed in a material subjected to a specified torque in torsion test for a circular shaft. It can be calculated using the expression

14. Expected failure for mild steel and cast iron specimens and reasoning: Fracture in torsion for ductile materials generally occur in the plane of maximum shear stress perpendicular to the axis of bar where as for the brittle material failure occurs along 45 to the axis of bar due to tensile stress across that plane.