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#### Modulus of Rupture

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Torsion formula, *T*/*J* = *Gθ*/*L* = *τ*/*R*, has been derived on the assumption that shear stress is proportional to shear strain but when a specimen is tested in torsion, it fails by fracture and stress developed in this material goes beyond the proportional limit, that is, in the plastic stage. If shear stress and shear strain is drawn along radius of the *shaft, shear strain at any point remains proportional to radius but shear stress at any point is no longer proportional to its radius*,rather the curve becomes non-linear as shown in Fig. 12.4. A torsion test piece is continuously twisted, that is,*θ* is increased gradually till the shaft breaks. Say, *T*_{max} is the maximum torque at which shaft fails by fracture.

**Figure 12.4** Shear stress-shear strain curves