# Numerical - Shear stress, given torque & dimensions

Q.  What is the shear stress acting on the outer surface of a hollow shaft subjected to a torque of 100 Nm?
(The inner and outer diameter of the shaft is 15 mm and 30 mm respectively.)

- Published on 21 Sep 15

a. 50.26 N/mm2
b. 40.24 N/mm2
c. 20.120 N/mm2
d. 8.74 N/mm2

#### Discussion

• Bethany Tesfaye   -Posted on 29 Aug 21
Great thanks!
• Aditya   -Posted on 17 Jan 21
How it is TR =(100×10^3×15)
• Sravanthi   -Posted on 25 Nov 15
Given: Torque acting on hollow shaft: 100 Nm = 100 x 103 N / mm , outer diameter of shaft = 30 mm, inner diameter of shaft = 15 mm

Formula: 1) Shear stress (τ) = TR / J

here, T is the torque acting on shaft, J is the polar moment of inertia, R is the radius of shaft

2) Polar moment of inertia (J) = π (D4 - d4) / 32

Solution:

1) Polar moment of inertia (J) = π (D4 - d4) / 32

= π (304 - 154) / 32

= 74551.466 mm4

2) Shear stress (τ) = TR / J

= (100 x 103 x 15 ) / 74551.466

= 20.120 N/mm2

shear stress acting on the outer surface of a hollow shaft subjected to a torque of 100 Nm is 20.120 N/mm2

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