A hollow circular shaft made of 304 stainless steel uniformly tapers from an outer diameter of 3.0 cm to an outer diameter of 4.0 cm over a length of 2 meters. The inner diameter of 1.0 cm is constant over the length of the shaft. The shaft is subjected to an applied torque of 500 Nm. Determine the maximum shear stress in the shaft.

maximum shear stress = τ(max) = 95.49 × 10⁶N/m²

Explanation:

given

outer diameter at one end(D₁) = 3.0cm

outer diameter at the other end(D₂) = 4.0cm

inner diameter(d₁) = 1.0cm

torque applied(T) = 500Nm

maximum shear stress will occur at lower outer diameter

the formula is τ/r = T/J

τ= T × r/J

where r is radius

T is the torque

J is the polar 2nd M of area

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explanation: