Torsion in Hollow Shaft || Derivation || strength of material

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Torsion of Hollow Shaft | Derivation, Formula, Shear Stress & Angle of Twist | Strength of Materials



In this lecture of Strength of Materials (SOM), we derive the torsion equation for a hollow circular shaft, an important topic for B.Tech Mechanical, Civil, Production, Diploma, SSC JE, and GATE exams.

Hollow shafts are widely used in mechanical systems because they offer higher strength-to-weight ratio, and understanding their torsional behavior is essential for design engineers.

In this video, we explain the torque–shear stress relationship, polar moment of inertia for hollow shafts, and the formula for angle of twist, along with the comparison between solid and hollow shafts.


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Lecture – Torsion Equation for Solid Shaft:
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📌 Topics Covered in This Lecture:

– What is a Hollow Shaft?
– Difference Between Solid and Hollow Shafts
– Stress Distribution in Hollow Shafts
– Polar Moment of Inertia (J) for Hollow Shaft

J = \frac{\pi}{2}(R_o^4 - R_i^4)

\frac{T}{J} = \frac{\tau}{R_o} = \frac{G\theta}{L}

– Maximum & Minimum Shear Stress
– Strength & Weight Advantages
– Numerical Example (If included)
– Comparison with Solid Shaft

This lecture is helpful for:
➡️ B.Tech Mechanical / Civil / Production
➡️ Diploma Mechanical
➡️ SSC JE / RRB JE / GATE Aspirants
➡️ Strength of Materials & Machine Design Students
➡️ University Exam Preparation


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📚 Recommended Books (Engineering Standard):

✔ Strength of Materials – R.K. Bansal
✔ Strength of Materials – S.S. Bhavikatti
✔ Strength of Materials – S. Ramamrutham
✔ Mechanics of Materials – Beer & Johnston
✔ Engineering Mechanics of Solids – Egor Popov


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