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Torsion

Fenner and other (1984) indicated that the modulus of rigidity is given by the ratio of stress to shear strain often represented mathematically as ?/?. As widely cited, modulus of rigidity is essential in measuring the material’s shear stiffness and it is known to be analogous to Young’s modulus for any elastic behaviour in compression or tension (Benham, Crawford & Armstrong, 1996). Given that a ductile material component useful in providing shear, an individual need to note that the maximum shear stress is safety, which is less than the materials yield shear stress (?y). However, a brittle material the criterion of failure is based upon its tensile stress (Gere &Timoshenko, 1984). Research indicate that the theory of torsion often give the torque in form of rotation as (1) The equation 1 above is often derived from Hooke’s law and it is also valid for the shear stresses though somewhat lower than shearing proportional limit (Case, Chilver & Ross, 1993). In a solid circular section, it has been outlined mathematically that the polar second moment of the area of cross section is given by equation (2) (Ryder, 1969) (2) This implies that from (1), it can be shown that the maximum shear stress, that occurs at r = d/2, is provided by equation (3) (3) This experiment deals with determining yield shear stress along with the modulus of rigidity for the specimen of brass and mild steel of a circular cross section. Apparatus In this experimental set up, there were various sets of apparatus used. Among them were the torsion machine, a torsion bar, a gearbox, a torque meter, two protractors, a counter, and a hand-wheel. This way, a torsion machine was used for carrying out a test involving a specimen that was accommodated within the socket at each end. The 60:1 reduction gearbox served the purpose of manually applying the angular displacement at the left- hand side. The torsion bar was essential in this experiment given that it was used for measuring the torque when at right-side with a torque meter being used for reading digital data. The two protractors listed above were vital in this experiment since they were used for purposes of measuring the rotation of the specimen. They were placed at the gearbox, in which case, one was placed at the input hand wheel along side a 6 degrees scale, while the second gearbox was placed at the specimen shaft at 360 degrees scale. The counter, on the other hand, was used in providing the number of revolutions each of which might be zeroed. Last but not least, the hand-wheel placed at the torque meter assembly was used in returning the right-hand of the given specimen back to the original position. Procedure It is worth enlisting that this lab exercise involved 2 experiments: experiment 1 and experiment 2. This implies that there were specific procedures for specific experimental set up. In experiment 1, which involved determining the modulus of rigidity G for brass and mild steel, the procedure for the experiment involved the following steps. 1. The diameter of the each of the cylindrical portion of the specimen was measured. 2. Using the level, the torque meter hand-wheel was adjusted in ensuring that the torsion bar, as well as the deflection bar is maintained close to and as parallel as possible. 3. The dial gauge was then set to zero through rotating the outer bezel. 4. The specimen was then accommodated in the right hand hexagonal
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