# Torsion Testing

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Table of Contents Abstract 3 1.0 Introduction 3 2.0 Experiment Design 4 2.1 Apparatus 5 2.2 Methods 5 2.3 Procedure 6 3.0 Results and Discussion 7 4.0 Error Analysis 13 5.0 Conclusion and Recommendation 13 6.0 References 14 Abstract In this torsion testing experiment, the torsion test was evaluated as a system for calculating the torsional rigidity (GJ), modulus of rigidity (G) and the shear yield stress (τ) for aluminium, mild steel and brass. The both ends of the cylindrical specimen are tightened to hexagonal sockets, which one is fixed to a torque shaft and another is fixed to an input shaft. By turning the input handwheel, the twisting moment has applied to produce the torque until the specimen fails. In the end of the…show more content…
3.0 Results and Discussion T/J = τ/R = Gφ/L Torsion equation TJ= GφL G=TLJφ τ=πd^432 Where T = Torque applied, Nm G = shear modulus, N/mm2 J = Polar moment of inertia, mm2 φ = Angle of twist, radian L = Gauge Length, mm τ = shear stress, N/mm2 r = radius of the cylindrical bar, mm J=πd432=π(5)432=61.36mm2 1) For mild steel, for example using point (7.25, 17) G=TLJφ=7.25(115)61.36 0.2974=45.80N/mm2 τ=TRJ=7.25(2.5)61.36=0.295N/mm2 For brass, for example using point (5.85, 17) G=TLJφ=5.85(115)61.36(0.297)=36.95N/mm2 τ=TRJ=5.85(2.5)61.36=0.238N/mm2 2) Torsional rigidity is ratio of torque applied about the centroidal axis of a bar at one end of the bar to the resulting torsional angle, when other end is held fixed means torsional rigidity =torqueangle For mild steel, Torsional rigidity = 7.2517=0.426 For brass, Torsional rigidity = 5.8517=0.344 Therefore, torsional rigidity of mild steel is higher than brass. 3) Specimen: Mild Steel Scale Reading at Worm gear input in Revolution (degrees) | Angle of Twist of Specimen (col.1/62) | Torque (N.m) | 90 | 0 | 0.05 | 180 | 0 | 0.05 | 270 | 2 | 0.05 | 360 | 4 | 0.05 | 450 | 5 | 0.10 | 540 | 8 | 0.10 | 630 | 9 | 0.10 | 720 | 10 | 0.35 | 810 | 11 | 1.25 | 900 | 12 | 2.85 | 990 | 14 | 5.00 | 1080 | 17 | 7.25 | Until fracture | 4092 | 21.05 | Specimen: Brass Scale Reading at Worm gear input in Revolution (degrees) | Angle of Twist of Specimen (col.1/62) | Torque (N.m) | 90 | 1 |