Department of Power Engineering and Turbomachinery
Silesian University of Technology, Gliwice
INSTRUCTIONS FOR LABORATORY EXERCISES OF
STRENGTH OF MATERIALS
TORSION TEST
Dr inลผ. Katarzyna Stolecka
Gliwice, 2018
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Laboratory Exercise: Torsion Test for Determining Material Rigidity and Shear Stress, Lecture notes of Engineering
Instructions for a laboratory exercise on the torsion test to determine the modulus of elasticity in shear (rigidity modulus) and the characteristics of the torque-angle relationship for a material. The exercise involves measuring the angle of twist of a bar subjected to torsion and calculating the shear stress and polar moment of inertia.
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Department of Power Engineering and Turbomachinery
Silesian University of Technology, Gliwice
INSTRUCTIONS FOR LABORATORY EXERCISES OF
STRENGTH OF MATERIALS
TORSION TEST
Dr inลผ. Katarzyna Stolecka
Gliwice, 2018
1) The aim of the laboratory
The purpose of the exercise is to find the modulus of elasticity in shear G (rigidity modulus) of the material of which a bar with a cross-section is made, by measuring the angle of twist. The second purpose of the exercise is determination of the characteristics of Ms=f(ฯ) (dependence of the torque (twist moment) versus angle of twist).
2) Introduction
Torsion occurs when the twisting moments are applied to the bar.
Torsion is induced by two pairs of forces. These two forces act in two different planes perpendicular to the axis of the bar. Moments of these two forces are called twisting moments.
If the bar is loaded by two pairs of forces of equally magnitudes moments but opposite directions in two planes which are perpendicular to the axis then we obtained the state of strain and stress called pure torsion โ fig. 1.
Fig. 1. Models of pure torsion
Considering a simplified model of the bar. And then, assuming a three-dimensional grid and subjecting to a pure torsion, it can be seen that (Fig. 2):
๏ท the axis of the bar does not change its form and after deformation still remains straight line ๏ท the circles remain wheels, and the cross-sectional ends are flat ๏ท the horizontal lines of the grid will change its initial shape. This means that these lines are deflected from their initial position by an angle ฮณ ๏ท the surfaces of the front and end of the bar will rotate relative to each other by an angle of twist ฯ
Shear stress
Shear stresses are produced by the application the twisting moments to the end of the bar. Shear stress in sections orthogonal to the axis of the torsional bar can be expressed as:
๐
The highest shear stress occurs on the surface of the bar, where the radius is maximum.
๐๐๐๐ = ๐๐=๐ = ๐ด ๐ฑ๐ ๐
W 0 โ section modulus of torsion ๐พ๐ = ๐ ๐ ๐๐๐
ฯdop โ permissible stress
NOTE: Above formulas are valid for the bar of circular cross-section in the area of stress falling below the proportional limit (Fig. 3).
Fig. 3. The torque-twist plot of a torsion specimen
Mh โ torque corresponding to the proportional limit stress Msp โ torque corresponding to the elastic limit stress Mpl โ torque corresponding to the yield stress Mrs โ torque corresponding to the fracture (rupture strength)
In the torsion bar, a change of stress in the circular cross-section can be observed. Graph of shear stress to the proportional limit takes the form of a right triangle. After crossing the proportional limit, the triangular form of a graph passes in a rectangular form, where the shear stress corresponding to the yield stress already exists in the entire cross-section of the bar (see Fig. 4). The change of distribution of stresses (from triangular to rectangular) results from shifting the first layers of the external cross- section of the specimen beyond its yield stress. While the layers closer to the axis still remain in the elastic region.
Fig. 4. Shear stress in the twisted bar of circular cross-section: a) elastic region, b) elastic-plastic region, c) plastic region
4) Torsion test
Torsion test is usually carried out in the specimens of the circular cross-section for which determine the state of stress and strain is relatively simple. Specimens with different cross-sections are used for special tests. In this time, it is required to use different formulas than in the presented above. In the case of solid specimens of circular cross-section the gauge length of the bar is equal to (5โ20)d 0 , generally l=10d 0 where d 0 =(10-30)mm is a gauge diameter of specimen.
Fig 5. Specimens for torsion test
During the destructive torsion test, torsion fracture geometry may take the following forms:
a) When subjected to torsion a ductile specimen breaks along the plane perpendicular to the bar axis
Where:
๐
[ยฐ]
ฯ โ the angle of twist
x โ the displacement of the end of the spindle sensor caused by the angle of twist lp โ the distance between the spindle sensor and axis of the shafts
6) Torsion test
To perform the measurement do the following:
- Set the sensor to zero.
- Put the weight on the plate. The greater weights causes the increasing of the torque.
- Each time make a response of sensor reading and written in measurement card.
- After reaching the maximum load take off the weight and also write a response of the sensor.
7) Laboratory report
The laboratoryโs report should contain:
a) A short introduction to torsion test b) Brief description of the aim of the laboratory c) Calculations d) The formula for angle of twist e) Plot of function Ms = f(ฯ) f) Scheme of a test stand g) Complete measurement card h) Short conclusions.
Deadline for a laboratory report is 2 weeks.
Date of the laboratory:
Section:
Name Surname
Measurement data
lp = 90 mm (see fig. 6) lr = 700 mm (see fig. 6) length of specimen l = 500 mm diameter of specimen d = 20 mm
Lp. m [kg] x [mm] Ms = mฮlrฮg [N] ฯ [โ] Gi [MPa] (^) ๐ฎ๐๐ = ๐ ๐ โ ๐ฎ๐