Problem on Calculation of Diameter of Shaft

TL;DR

A question is presented regarding the diameter of a solid shaft and the percentage saving in weight if it is replaced by a hollow shaft.

Transcript

hello students let us take a new question in the topic of torsion i am marking this question let's read what is given here a solid circular shaft is to transmit 300 kilowatts at 100 rpm if shear stress is not to exceed 80 newton per mm square find the diameter of shaft what percentage saving in weight would be obtained if this shaft is replaced by ... Read More

Key Insights

• 🚄 The torque transmitted by a shaft can be calculated using the equation 2πnt/60, where n is the speed in rpm.
• 📶 The diameter of a solid shaft can be determined using the strength criteria formula, considering the torque, shear stress, and the equation relating torque to diameter.
• ⭕ The torque of a solid shaft can be equated to the torque of a hollow shaft, allowing the calculation of the outer and inner diameters of the hollow shaft.

Questions & Answers

Q: What is the main objective of the given question?

The main objective is to find the diameter of a solid shaft and calculate the percentage saving in weight if it is replaced by a hollow shaft.

Q: How is the diameter of the solid shaft calculated?

The diameter of the solid shaft is calculated using the strength criteria formula, considering the given torque, shear stress, and the equation relating torque to diameter.

Q: How is the percentage saving in weight determined?

The percentage saving in weight is determined by calculating the areas of the solid and hollow shafts and comparing them, taking into account the outer and inner diameters of the hollow shaft.

Q: What factors are assumed to be the same for both the solid and hollow shafts?

The material, length, and maximum shear stress are assumed to be the same for both the solid and hollow shafts.

Summary & Key Takeaways

• The question involves finding the diameter of a solid shaft that can transmit a given power while not exceeding a given shear stress.

• The question also asks for the percentage saving in weight if the solid shaft is replaced by a hollow one, with the internal diameter being 0.6 times the external diameter.

• Torque calculations are used to determine the diameter of the solid shaft and to equate the torque of the solid and hollow shafts, leading to the calculation of the outer and inner diameters of the hollow shaft.

• The percentage saving in weight is then calculated using the areas of the solid and hollow shafts.