The intensity of shear stress at any point in the cross-section o
A. directly proportional to
B. <p>not proportional to</p>
C. inversely proportional to
D. none of the above
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
The torsion equation for a circular member is
\(\frac{{\rm{\tau }}}{{\rm{r}}} = \frac{{\rm{T}}}{{\rm{j}}} = \frac{{{\rm{C\;\theta }}}}{{\rm{l}}}\)
Where τ = Torsional stress induced at the outer surface of the shaft (Maximum Shear stress), r = Radius of the shaft, T = Twisting Moment or Torque
J = Polar moment of inertia, C = Modulus of rigidity for the shaft material, l = Length of the shaft, θ = Angle of twist in radians on a length “l”
From the torsion equation,
\(\tau = \frac{T}{J} \times r\;\)
J is a constant value, so
The intensity of shear stress at any point in the cross-section of the shaft subjected to pure torsion is directly proportional to its distance from the center.
- Torsional stress: When a machine member is under the twisting force then it is said to be the shaft is subjected to torsion. Due to this torsion in the shaft, the stresses induced in the shaft are known as torsional stress.
- Twisting can be produced in the shaft when two equal and opposite couples acting in parallel planes.
- Due to torsion in the shaft, the stresses induced in the shaft are known as torsional stress. Twisting can be produced in the shaft when two equal and opposite couples acting in parallel planes.
