What is the maximum torque transmitted by a hollow shaft of external radius ‘R’, internal radius ‘r’ and maximum allowable shear stress τ?

\frac{π}{16} (R^{3} - r^{3}) τ

\frac{π}{2 R} (R^{4} - r^{4}) τ

\frac{π}{8 R} (R^{4} - r^{4}) τ

\frac{π}{32} (R^{4} - r^{4}) τ

$\frac{π}{2 R} (R^{4} - r^{4}) τ$

Explanation:

Torque transmission by a hollow shaft:

Torsion equation = $\frac{T}{J} = \frac{τ_{m a x}}{R} = \frac{G θ}{L}$

Torque transmission $T = \frac{τ_{m a x} J}{R} = τ_{m a x} \times Z_{p}$

where, T = Torque, J = polar moment of inertia , R = Outer radius of shaft , r = internal radius of shaft

Z_p = Polar modulus of the section

F1 Ateeb 21.1.21 Pallavi D1

For hollow shaft

J = I_xx + I_yy = $\frac{π}{32} \times (D^{4} - d^{4}) = \frac{π}{2} \times (R^{4} - r^{4})$

Z_p = $\frac{J}{R} = \frac{\frac{π}{2} \times (R^{4} - r^{4})}{R}$

$T = τ_{m a x} \times Z_{p} = \frac{π}{2 R} \times (R^{4} - r^{4}) \times τ_{m a x}$

$T = \frac{π}{2 R} (R^{4} - r^{4}) τ_{m a x}$

Hint Answer

Previous Question Next Question

🔗

What is the maximum torque transmitted by a hollow shaft of external radius ‘R’, internal radius ‘r’ and maximum allowable shear stress τ?

$\frac{π}{2 R} (R^{4} - r^{4}) τ$

All Chapters — Structural Engineering

Simple Stress and Strain

Stresses in Members

Strain Energy and Resilience

Center of Gravity and Moment of Inertia

Shear Force and Bending Moment

Pure Bending

Shear Stress

Direct and Bending Stress

Slope and Deflection

Indeterminate Beams

Torsion

Plastic and Local Buckling Behaviour of Steel

Cables and Arches

Influence Lines and Approximate Analysis for Statically Determinate Structures

Deflections

Deflections Using Energy Methods

Displacement Method of Analysis: Slope-Deflection Equations

Displacement Method of Analysis: Moment Distribution

Influence line diagram mcqs

Structural engineering important exam questions

Structural engineering important exam questions II

Structural engineering important exam questions III

Plastic Analysis

Structural Engineering Loksewa Questions

Similar Questions

What is the maximum torque transmitted by a hollow shaft of external radius ‘R’, internal radius ‘r’ and maximum allowable shear stress τ?

π2R(R4−r4)τ

All Chapters — Structural Engineering

Simple Stress and Strain

Stresses in Members

Strain Energy and Resilience

Center of Gravity and Moment of Inertia

Shear Force and Bending Moment

Pure Bending

Shear Stress

Direct and Bending Stress

Slope and Deflection

Indeterminate Beams

Torsion

Plastic and Local Buckling Behaviour of Steel

Cables and Arches

Influence Lines and Approximate Analysis for Statically Determinate Structures

Deflections

Deflections Using Energy Methods

Displacement Method of Analysis: Slope-Deflection Equations

Displacement Method of Analysis: Moment Distribution

Influence line diagram mcqs

Structural engineering important exam questions

Structural engineering important exam questions II

Structural engineering important exam questions III

Plastic Analysis

Structural Engineering Loksewa Questions

Similar Questions

$\frac{π}{2 R} (R^{4} - r^{4}) τ$