Determination of Torsion in a Rod

Abstract:

The purpose of this experiment is determination of torsion in a rod fixed at one end while applying load on the other side of the rod attached with a gauge noting deflection in rod due to weight applied. The basic purpose of this experiment is to know methods of calculating and measuring torsion due to load.

Apparatus:

·         (1) Rod, 9.5 mm diameter and length 595 mm

·         (2) Column

·          (3) Load hanger

·         (4) Weights (up to 20 N)

·         (5) Dial gauge

Introduction:

The apparatus is used for investigation of torsion in rods. The apparatus consist of two columns attached with a base frame (ST 305 Universal base frame or ST 300 Universal Structural frame). One column clamp one end of the rod while other end of specimen i.e. rod is free to rotate thus producing torque.  A pulley for hanging loads is clamped to the free end of rod. Measurement of deflection is done by a dial gauge and torque is measured by load attached and diameter of pulley.

Procedure:

·        (1) Record the length L and pulley Diameter d.

·        (2) Place the dial gauge on the dial gauge base of frame.

·        (3) Set the needle of dial gauge on zero.

·        (4) Apply load on pulley with 2N increment. Starting value is 2.5N.

·        (5)  Go on reading dial gauge readings with increasing load.

Observations and Calculations:

Diameter = d = 9.5mm                              Length = l = 595mm

Polar moment of inertia = J =   πd ⁴/32 mm ⁴

Shear Modulus = 8 × 10⁴ N/mm²

Deflection _Calculated = φ _cal = TL/JG   radians = TL/JG  × ^180/π  degrees

Deflection _Experimental = φ _exp = tan^-1(y/100 )

Table 01:

No. of obs.	Weight (N)	Torque T = W × 100 (Nmm)	Gauge Reading (y)	Deflection (φ) Calculated	Deflection (φ) Experimental	Percentage Error (%)
01.	2.5	250	0.1	.133	.057	57.14
02.	4.5	450	0.26	.239	.148	38.07
03.	6.5	650	0.40	.346	.229	33.81
04.	8.5	850	0.51	.453	.292	31.54
05.	10.5	1050	0.72	.559	.412	26.29
06.	12.5	1250	0.87	.666	.498	25.22
07.	14.5	1450	1.01	.773	.578	25.22
08.	16.5	1650	1.16	.879	.664	24.46

Graph No. 1:

Discussion:


Our results show that experimental and theoretical values are within +15% of error. This small difference in error might be due to parallax errors when measuring deflections on the gauge. Furthermore, the gauge was a little faulty with the needle getting stuck sometimes and the needle not returning to its original position after a load was removed. Even the slightest of vibrations would cause the needle to change its position randomly. The least count of the gauge also contributes towards the errors shown by the results.