Theory & Equations
Torsion tests involve applying a twisting moment (torque) to a specimen to measure shear stress and strain. The main property derived is the Modulus of Rigidity (G).
When a specimen is subjected to Torque (T), it twists by an angle (θ). This creates maximum shear stress at the outer surface.
Torsion Testing Setup Schematic
CELL
Mechanics Solver (Interactive)
1. Shear Stress (Elastic)
2. Shear Strain
3. Modulus of Rigidity
Torsion Protocol
Measure the diameter and the length of the test specimen. Draw a line on the specimen to observe twisting.
Fix both ends of the specimen into the holders. Ensure the shifting holder is in the mid position.
Zero the measurement amplifier. Turn the hand wheel to apply torque.
Testing Sequence:
- 1st Rotation: 90° increments
- 2nd-3rd Rotation: 180° increments
- 4th-8th Rotation: 360° increments
- Then every 5-10 rotations until fracture.
Note: Record the final torque reading at failure and measure the fracture diameter. Count rotations and convert to degrees later.
Safety Measures
1. Eye Protection
Mandatory safety glasses. Brittle materials (Cast Iron) can shatter explosively upon failure.
2. Machine Guards
Ensure all polycarbonate safety guards are securely in place before engaging the motor.
6.0 Result
1. The experimental data should be filled in the table as provided in the worksheet and complete the tables by using the appropriate equations (i.e. calculate the shear strain from experimental angle of twist and shear stress from applied torque).
2. Plot the graph:
- Torque (y-axis) vs angle of twist (x-axis)
- Shear stress (y axis) vs shear strain (x-axis)
3. Determine the experimental modulus of rigidity from the graph (i) (i.e. the slope of the line). Then, in conjunction with the modulus of elasticity from a reference value, calculate the Poisson`s ratio. Also, determine the yield shear stress, ultimate shear stress and fracture shear stress.
4. Sketch the fracture surface of the tested specimen.
Table 1: Specimen Dimensions
| Material | Overall Length L (mm) | Gauge Length Lg (mm) | Diameter d (mm) | Polar Moment J (mm⁴) |
|---|---|---|---|---|
| Mild Steel | ||||
| Cast Iron |
Table 2: Observation Data (Mild Steel)
| No | Torque (Nm) | Angle of Twist (°) | Angle (rad) | Shear Stress (MPa) | Shear Strain (x10⁻³) |
|---|
Table 3: Observation Data (Cast Iron)
| No | Torque (Nm) | Angle of Twist (°) | Angle (rad) | Shear Stress (MPa) | Shear Strain (x10⁻³) |
|---|
📷 Specimen Photo Documentation
Capture photos of your specimen before and after the torsion test.
1 Before Test
2 After Test (Fractured)
Table 6.0: Calculated Results
| Property | Material | Value | Unit |
|---|---|---|---|
| Modulus of Rigidity (G) | Mild Steel | GPa | |
| Cast Iron | |||
| Max Shear Stress (τ_max) | Mild Steel | MPa | |
| Cast Iron |
7.0 Discussion
Virtual Torsion Lab
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Test Your Knowledge
1. What is the unit of Shear Stress?
2. Brittle materials in torsion typically fail at:
3. What is the recommended increment for the first rotation?
4. What must be measured at the fracture point after failure?
5. Why is a straight line drawn on the specimen?
8.0 Conclusion
9.0 References
Lab Assessment Rubric
MEQ 491: Laboratory Report Rubric (March 2025)
| Item / Criteria | Excellent (9-10) | Good (7-8) | Satisfactory (5-6) | Poor (3-4) | Very Poor (0-2) |
|---|---|---|---|---|---|
| 1. Appearance, Organization, Front Page | All lab sections in correct order, well formatted, very readable, neat. Few spelling/grammar errors. Complete front-page info (title, names, date, signature). Tape/ring binding. Own self cover report with computer typing. Submit in single PDF format. | Sections in correct order, good formatting. Some spelling/grammar errors. Missing one piece of information except title and name. Tape/ring binding. Few improper format issues. | Sections in order, rough but readable formatting. Multiple spelling/grammar errors. Missing two pieces of information. Stapled without binding. Improper own self cover (no logo, no title, etc). | Sections out of order, sloppy formatting. Too many spelling/grammar errors. Missing more than two pieces of information. Stapled at the end. | Most of the 'poor' conditions are not met. (Score 0) |
| 2. Objective and Theory Information | All objectives clearly identified and stated in new sentences. Detailed paragraph of prior knowledge. Includes outside research. | All objectives identified but somewhat unclear. Some copied directly with some attempt at new sentences. Detailed prior knowledge paragraph. | Objectives partially identified and unclear. Mostly copied from lab manual. Theory mostly copied with some new sentences. | Objectives may not be identified and not clear. Some objectives missing. Very little prior knowledge described. | Most of the 'poor' conditions are not met. (Score 0) |
| 3. Apparatus and Procedures | All equipment and materials listed. Detailed, labeled diagrams. Clear step-by-step numbered procedures. Includes safety tips/guidelines. Safety report with pictures attached. | Vital items listed with maybe one omission. Includes diagram. Clear step-by-step procedures. Procedure mostly copied with some new sentences. Safety report attached but lacks picture. | Some items listed with many omissions. Necessary diagram missing. Procedures not clear, not enough, confusing. Procedure mostly copied from lab manual. | Most items not listed. Diagram missing. Procedure very incomplete and confusing. | Most of the 'poor' conditions are not met. (Score 0) |
| 4. Results — data, graphs, calculations (×2 weight) | Results correct, clearly recorded and organized with visible trends. All figures/graphs/tables correctly drawn, numbered with titles/captions and units/labels. All calculations shown. Example calculation with MS Word equation formula. | Results correct, clearly recorded but trends not obvious. Minor problems in figures/graphs/tables. Units/labels included. A few calculations missing. A few equations use formula. | Some results missing, unorganized and incorrect. Some figures/graphs/tables incomplete or sloppy. Some units/labels missing. Some calculations missing and wrong. | Most results missing, very unorganized and incorrect. Most figures/graphs/tables contain errors. Most units/labels missing. Most calculations missing and wrong. | Most of the 'poor' conditions are not met. (Score 0) |
| 5. Discussion (×2 weight) | Answer all questions correctly and clearly. All important trends and data comparisons interpreted correctly. Explains how results support/don't support theory. Errors, effects, and ways to reduce errors discussed. | Missing one question, others correct and clear. Almost all results interpreted correctly with minor improvements needed. Errors and possible effects discussed. | Missing two questions. Some results correctly interpreted with partial understanding. Experimental errors mentioned. | Missing more than two questions with incorrect answers. Incomplete/incorrect interpretation. Discussion of theory and objectives missing. No discussion of errors. | Most of the 'poor' conditions are not met. (Score 0) |
| 6. Conclusions | Summarizes essential data and results. States whether findings achieved all objectives. States validity including experimental error. Includes suggestion for improvement and what was learned. | One of the 'excellent' conditions is not met. | Two of the 'excellent' conditions are not met. | More than three of the 'excellent' conditions are not met. | No conclusion. (Score 0) |
| 7. References | Multiple sources (journal, book, magazine, internet etc.) — more than 9 references. Standard format as mentioned in lab manual. 30% references from previous 5 years. | Multiple sources (6–8 references). Written in standard format. | Only two sources (3–5 references). Not written in standard format. | Only one source (1–2 references). Not written in standard format. | No references listed. (Score 0) |
Attendance Note:
i. Absent: Score = 0%
ii. Doing an experiment but lab report is not submitted: Maximum score = 10%
📚 Resource Center
📋 Standards
- • ASTM E143 (Shear Modulus)
- • ISO 7800 (Wire Torsion)
- • BS 18 (Torsion Testing)
🔢 Key Formulas
- • τ = Tr/J (Shear Stress)
- • γ = rθ/L (Shear Strain)
- • G = τ/γ (Modulus of Rigidity)
- • J = πd⁴/32 (Polar Moment)
🎯 Key Concepts
- • Ductile: Fails on flat plane (shear, 90° to axis)
- • Brittle: Fails at 45° helix (max tensile stress)
- • Max stress at outer surface
- • Linear stress distribution
⚠️ Safety & Tips
- • Use safety shield always
- • Measure diameter accurately
- • Apply torque gradually
- • Record angle at each step
💡 Common Material Properties (Typical Values)
Mild Steel
G ≈ 80 GPa
E ≈ 200 GPa
Poisson's ratio ν ≈ 0.30
Ductile — flat fracture
Cast Iron (Grey)
G ≈ 41 GPa
E ≈ 100–120 GPa
Poisson's ratio ν ≈ 0.26
Brittle — 45° helical fracture
Aluminum
G ≈ 26 GPa
E ≈ 70 GPa
Poisson's ratio ν ≈ 0.33
Brass
G ≈ 40 GPa
E ≈ 100 GPa
Poisson's ratio ν ≈ 0.34
🔗 Relationship: E, G, and ν
G = E / 2(1 + ν)
Where: G = Modulus of Rigidity (Shear Modulus), E = Young's Modulus, ν = Poisson's Ratio.
Once G is experimentally determined from the torsion test slope (τ vs γ), Poisson's ratio can be calculated as: ν = (E / 2G) − 1