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A circular section rod with a diameter 2D and a length L and a square section L length with a side length of 2D transmit the same magnitude of torsion moment.




A circular section rod with a diameter 2D and a length L and a square section L length with a side length of 2D transmit the same magnitude of torsion moment.what geometry the rod is more appropriate to use in the specified dimensions and operating conditions, why?








Solution :

Given,

diameter od rod, d = 2D

Each side of square section ,a = 2D

Now, we know that

shear stress, Ï„ = Torque(T)/Section Modulus(z)

Now, Section modulus of rod is 

Z_r= π d^3/16 = π (2D)^3/16 = 1.57D^3


Now, Section modulus of square section is

Z_s = a^3/6 = (2D)^3/6 = 1.33D^3


Since, the section modulus of rod is more than the section modulus of square section so, for same torque applied the shear stress induced in the rod will be less than that of square section.

Hence, rod geometry will be more appropriate.





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