Background and Theory for the Torsion Test
Material Properties: Steel and Cast Iron
In this laboratory session we are going to study the material properties of Steel and Cast Iron as revealed by the
Torsion Test. The steel (A36) and cast iron (Gray-40) specimens (Figure 5) are solid cylinders 10 in
long, which have been machined in the center portion with 6 in of length and a reduced section of
0.75 in diameter. The diameter at each end is 1 in, so the machine may grip and apply a torque to
the specimens without introducing effects of stress or strain.
Torsion Definitions
The following are definitions of various torsion material properties that will be determined for both
mild steel and cast iron specimens:
(a) Shear Modulus. The shear modulus is analogous to the Modulus of Elasticity. Also known as
the modulus of rigidity, this property is represented by G. It is a proportionality
constant, which relates shear stress to shear strain. The units of G used in this lab are (psi). In
this lab, G is calculated by finding the slope of the linear elastic portion of the shear
stress vs. shear strain graph. The reference values of G are 11.5 x 10^6 psi for mild steel and
6.3 to 7.8 x 10^6 for cast iron. You may reference these values in your lab report.
(b) Torsion Yield Stress. The Torsion Yield Stress is analogous to the Tensile Yield Stress. The
Torsion Yield Stress corresponds to the maximum shear stress value in the linearelastic range. On the shear stress vs. shear strain graph, the yield limit will be the point
just before the diagram plateaus or levels-off. Similarly in tension or compression, Hooke’s
Law for shear is applicable for the material up to this point on the shear stress-strain graph.
Theory of Torsion
Torsion stresses and strains behave similarly to shear stresses and strains we have observed in class.
The primary assumption of torsion for our purposes is that plane sections remain plane – that is
horizontal lines remain horizontal and vertical lines remain vertical during twisting as shown in
Figure 1.
Shear stress and shear strain can be defined as follows:

The Lab Report will contain the following:

• Abstract
• Introduction
•  Procedure
• Data
• Results
• Calculations
•  Discussion
• Analysis
• Conclusion
• Appendices