Background
The main objective of the torsion experiment carried out was to determine the relationship between the applied torque and angle of twist for a metal wire of various properties, and compare and contrast. Based on the measured torsional properties of the sample wires one can be able to determine the modulus of rigidity or shear stiffness and material. In turn this properties can be used to accurately identify the material. Below is a set up of the laboratory experiment carried out.
Figure 1: Torsion experiment set up
The formula for the applied torque is as shown below:
T=JrGα
Where,
T applied torque
G is the material’s shear modulus
α is the angle of twist
r is the cross section of the specimen
J is the moment of inertia
Chart 1: Chart showing the torque vs. angle of twist.
Torsion occurs mainly due to an applied torque on a material that leads to twisting. Torsion testing can be used to determine the rotational stiffness of a specimen. Rotational stiffness is defined as the ratio between the torque applied to a specimen and the displacement produced by the torque.
The formula for rotational stiffness is:
T = k * Ɵ
Where,
T is the rotational stiffness
k is a constant
Ɵ is the angle of twist
All the parts of the material that are perpendicular to the torque axis the resulting forces are directly proportional to the radius. This implies that for a shaft of uniform cross section the sections furthest from the center of the axis of torque experience the highest forces and vice versa. This is attributable to the fact that the applied torque is the product of the radial radius from the torque axis and vice versa. The SI units for torsion are Nm (Negi, 23).
Recommendation
During the experiment a number of errors may occur. This may affect the experimental calculation of Modulus of Rigidity for the specimen under test. These errors greatly contribute to the difference in the experimental values and the published values of the modulus derived from the experiment. They include:
- Precision errors
- Parallax errors when reading the equipment
- Calculation errors such as rounding off
These errors can be eliminated in the experiment by using equipment with higher precision in order to eliminate any parallax errors. Precision in the experiment can also be improved by improving the means through which the length and diameter of the wire are determined.
Conclusion
In conclusion, the torsion experiment conducted was successful since the main objective of the experiment was achieved. From the experiment, data, which included diameter, length, applied torque and angle of twist was determined for the three wires under test. From this information it, was possible to chart the relationship between torques and twist angle for the specimens. From the results obtained in the experiment, it is evident that the relationship between torque, T, and angle of twist, α is directly proportional. Furthermore, the modulus of rigidity was also measured from thus variables.
Work Cited
Megson, T. H. G. (2005). Structural and stress analysis. Amsterdam: Elsevier Butterworth Heineman.
Negi, L S. Strength of Materials. New Delhi: Tata McGraw-Hill, 2008. Print.
