How Many Steel Strands Are Needed to Safely Lower a Lift into a Mine?

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SUMMARY

The discussion focuses on calculating the number of high strength steel strands required to safely lower a lift into a mine at a depth of 4000m. Each steel strand has a diameter of 3mm, an ultimate stress of 1200MPa, and an allowable stress of 600MPa. The empty lift weighs 15kN, with a capacity for 20 persons, each weighing 800N. To determine the number of strands, one must calculate the total load, including the weight of the cable, and ensure that the stress in each strand does not exceed the allowable limit.

PREREQUISITES
  • Understanding of axial stress (P/A) calculations
  • Familiarity with basic physics concepts related to force and weight
  • Knowledge of material properties, specifically steel density (77kN/m³)
  • Ability to perform calculations involving stress and load distribution
NEXT STEPS
  • Calculate the total weight of the lift including the cable using its density
  • Determine the cross-sectional area of a single steel strand
  • Learn about safety factors in engineering design
  • Explore the implications of material failure and stress limits in structural engineering
USEFUL FOR

Engineers, particularly those in structural and mechanical fields, students studying engineering mechanics, and professionals involved in mining operations will benefit from this discussion.

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A lift is used to lower miners 4000m into a mine. The lift is supported by many high strength steel strands of 3mm diameter each. The ultimate stress for the steel strands is 1200MPa and the allowable stress is 600MPa. The empty lift weighs 15kN. It has a capacity of 20 persons. The density of steel is 77kN/m3 and each person weighs 800N.
1)Calculate the number of strands required.
2)What is the maximum depth to which the lift can be lowered before the cable snaps?
I am assuming we have to use \epsilon = \sigma/E
I am not sure how to start this question. The biggest problem I have is that I don't know how to use that equation (what each variable stands for), (and for this course we have no textbook, so I can't find any sample problems). Any help is appreciated.
 
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The equation you have noted is for the stress-strain relationship. That is not needed for this problem.. What you need to find out is the force (P) and stress (P/A) in each strand under the given loads to be sure that there are a sufficient number of strands such that the stress does not exceed 600 MPa. You must include the weight of the cable itself, based on the given density and calculated volume... you have enough information given to calculate it's weight, and it's cross section area. You need a basic understanding of P/A axial stress.
 

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