Shear Modulus From Torsion Test
A torsion test measures how a specimen twists under load. The shear modulus shows the elastic stiffness in shear. It is also called the modulus of rigidity. A higher value means the material resists angular deformation better. This calculator uses torque, specimen length, polar moment, and twist angle to estimate that value.
Why the Test Matters
Many shafts, springs, fasteners, and structural parts work in torsion. Their design depends on reliable stiffness data. A torsion test gives a direct way to study that behavior. It is useful for metals, polymers, composites, and educational lab samples. The result can support quality checks and material comparisons.
Using Single Trial Data
For one trial, enter torque and angle of twist. You can also enter force and lever arm. The tool converts them into torque. Then it calculates the polar moment from the selected cross section. The shear modulus is found from the elastic torsion relation. Use consistent dimensions and small elastic angles.
Using Multiple Readings
Multiple readings usually give a stronger result. The regression option fits torque against twist angle. The slope of that line is torsional stiffness. The calculator then converts that stiffness into shear modulus. It also reports residual error and coefficient of determination. These values help judge data quality.
Reading the Results
The main result is shown in pascals, megapascals, and gigapascals. The table also lists polar moment, maximum shear stress, shear strain, and torsional stiffness. Uncertainty estimates are useful when measurements have known instrument limits. Large uncertainty warns that diameter, angle, or torque should be measured more carefully.
Best Practices
Measure diameter at several points. Average the readings before entry. Keep the specimen straight and centered. Record angles in the elastic range only. Avoid readings after yielding, slipping, or visible damage. Check that torque increases nearly linearly with angle. A curved plot may mean plastic behavior or fixture error. Export the results for lab notes and later review.
Common Sources of Error
Small angle readings can create large percentage errors. Diameter errors are even more important because polar moment uses the fourth power. Loose grips reduce apparent stiffness. Temperature, surface defects, and uneven loading can also shift measured values during repeated laboratory torsion tests.