1-27. The radius of a shaft is 12 mm. Two strain gauges are attached to the surface of the shaft as shown in the figure. The strains of  and  are measured repeatedly. From the measured results, the distribution of  is found to be , what is the estimated torque in the form of . Assume that , .

Solution:

Pure shear 

Use  in the above equation, we have

Thus

Then the torque can be given by

Thus, also follows a normal distribution with

The estimated torque  is .                                                                 Ans.