Problem 1 Based on Torsion | Summary and Q&A

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April 11, 2022
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Problem 1 Based on Torsion

TL;DR

Calculate the diameter of a solid steel shaft based on power transmitted, permissible shear stress, and angle of twist.

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Key Insights

  • ✊ The problem involves determining the diameter of a solid steel shaft based on power transmitted, permissible shear stress, and angle of twist.
  • 📶 The strength criteria and rigidity criteria are used to calculate the diameter.
  • 💬 The diameter is found to be 124.83 mm based on the strength criteria.
  • ☺️ The modulus of rigidity is given as 1 x 10^5 newton per mm square.
  • 🇦🇪 Converting units and using appropriate formulas are crucial in solving the problem accurately.
  • 🐻‍❄️ The calculation involves torque values, polar moment of inertia, shear stress, radius, and angle of twist.
  • 🌥️ Selecting a larger diameter helps decrease stress and increase the area of the shaft.

Questions & Answers

Q: What are the given parameters for the problem?

The given parameters are the power transmitted (300 kilowatts), speed (250 rpm), permissible shear stress (30 newton per mm square), angle of twist (1 degree), and the length of the shaft (2 meters).

Q: How is power transmitted calculated in this problem?

Power transmitted is calculated using the formula p = 2πnt/60, where p is power in watts, n is speed in rpm, and t is torque in newton meters.

Q: What are the two criteria used to determine the diameter of the solid shaft?

The two criteria used are the strength criteria and the rigidity criteria.

Q: How is the diameter calculated using the strength criteria?

The diameter is calculated using the formula t/j = fs/r, where t is torque, j is polar moment of inertia, fs is shear stress, and r is radius.

Q: How is the diameter calculated using the rigidity criteria?

The diameter is calculated using the formula t/j = gθ/l, where g is modulus of rigidity, θ is angle of twist in radians, and l is length of the shaft.

Q: Why is the greater value for diameter selected in this problem?

The greater diameter is selected to ensure a larger area and lower stress value in the shaft.

Summary & Key Takeaways

  • A circular solid steel shaft transmits 300 kilowatts at 250 rpm, with a permissible shear stress of 30 newton per mm square and an angle of twist of 1 degree in a length of 2 meters.

  • The problem is to determine the diameter of the shaft using modulus of rigidity as 1 x 10^5 newton per mm square.

  • By using both the strength and rigidity criteria, the diameter is calculated to be 124.83 mm.

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