Concept explainers
(a) What is the minimum cross-sectional area required of a vertical steel cable from which is suspended a 270-kg chandelier? Assume a safety factor of 7.0. (b) If the cable is 7.5 m long, how much does it elongate?
Part (a)
Minimum cross-sectional area required of a vertical steel cable.
Answer to Problem 52P
Solution: Minimum cross-sectional area required of a vertical steel cable is4.72 ×10-7 m2
Explanation of Solution
Given:Mass of the steel cable,
Factor of safety= 7
Length of the cable,
Formula used:
Where,
Calculation: Force acting on the wire is
Ultimate tensile stress of steel is
From the stress equation,
The required cross section is
Conclusion:Cross-sectional area of
Part (b)
Elongation of cable.
Answer to Problem 52P
Solution: Elongation of cable is
Explanation of Solution
Given:Mass of the steel cable,
Factor of safety = 7
Length of the cable,
Cross-sectional area,
Young’s modulus of steel,
Formula used:
Calculation:
The elongation of wire when load is acting is given by
Conclusion: Steel cable will elongate 0.21m if load of 270 kg is acted on the cable.
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