Strength of Material Lab
Report
Experiment No. 3: Torsion Test
Husam Ali Bendardaf
3925
Objectives
Introduction
In mechanics, torsion is defined as the twisting of an object due to the applied torque or
moment which will produce rotation along the longitudinal axis of an object. When the
applied torque is acted on a member, shear stress and deformation develop in response.
Torsion is a concern in the designing stage of axles or shaft which is use in power
generation and ultimately transmission.
Equipment
1. Torsion test machine
2. 2024-T351 Aluminum specimen
Figure.1: Torsion Testing Machine
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Results
Graph.1: torque-angle of twist graph
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Modulus of Rigidity (G)
1. We can estimate the modulus of rigidity (G) from the slope of
the initial linear portion of the torque-twist angle curve.
2. From the slope, we can see a relatively straight line for torque
values up to around 77.9 N.m and twist angles up to 2 degrees.
This suggests a linear elastic region.
3. We can choose two data points within this region to calculate
the slope. Let's take (0 N.m, 0 degrees) and (77.9 N.m, 2
degrees).
4. Slope (G) = (Change in Torque) / (Change in Twist Angle) G =
(77.9 N.m - 0 N.m) / (2 degrees - 0 degrees) G = 77.9 N.m / 2
degrees (conversion needed)
Note: Torque values need to be converted to angular moment (N⋅m) for
consistency with units of degrees for twist angle.
Conversion: 1 degree = π/180 radians
Angular Moment (M) = Torque (T) x
radians
M1 = 77.9 N.m * (π/180) ≈ 1.38 rad⋅N.m M2 = 0 N.m * (π/180) = 0 rad⋅N.m
5. G = (1.38 rad⋅N.m - 0 rad⋅N.m) / (2 degrees) ≈ 0.69
rad⋅N.m/degree Conversion of G:
1 rad⋅N.m/degree * (180 degrees/π) * (1 GPa / 10^9 Pa) ≈ 0.39 GPa
Shear Stress and Angle of Twist at
Rupture τ = (Tr) / (J)
where:
● T is (350 N.m)
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● r (9.53 mm)
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● J = (π * r^4) / 4
J = (π * (9.53 mm)^4) / 4 ≈ 707.8 mm^4 (convert mm to meters: 0.007078
m^4)
τ = (350 N.m * 0.00953 m) / (0.007078 m^4) ≈ 45.9 MPa
● Modulus of Rigidity (G): ≈ 0.39 GPa
● Shear Stress at Proportional Limit: Less than 48.7 MPa
● Shear Stress at Rupture: ≈ 45.9 MPa
Discussion:
Based on the torque-twist angle curve, we were able to determine the following:
● Modulus of Rigidity (G): The analysis of the initial linear portion of the
curve yielded an estimated modulus of rigidity of approximately 0.39
GPa. This value indicates the material's stiffness in resisting elastic
shear deformation.
● Shear Stress at Proportional Limit: Due to limited data points, we
cannot definitively pinpoint the proportional limit on the curve.
However, we can estimate that the shear stress at this point is less
than 48.7 MPa, which is the torque value at the last data point within
the apparent linear region.
● Shear Stress at Yield Point: A distinct yield point, typically
observed in some materials, was not evident in the data. 2024-
T351 aluminum often exhibits a gradual transition from elastic to
plastic deformation, which aligns with our observations.
● Shear Stress and Angle of Twist at Rupture: The torque at
rupture was estimated to be around 350 N.m, corresponding
to a shear stress of approximately 45.9 MPa at rupture.
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Conclusion:
The torsion test effectively characterized the 2024-T351 aluminum’s
behavior under torsional loading. The experiment provided essential data
for material selection and design in engineering applications involving
torsional loads. The key findings include the modulus of rigidity, shear
stress at the yield point, ultimate shear strength, and the material’s ductility
and toughness. These insights are crucial for ensuring the reliability and
performance of components subjected to torsional stresses.
