Explanation Write the expression for tension due to load and acceleration. F t = ( W m + w l ) ( 1 + a g ) . (I) Write the expression for allowable fatigue tension. F f = ( p / S u ) S u D d 2 (II) Here, the specified life is p / S u , ultimate tensile strength of the wire is S u , sheave diameter is D and nominal wire rope size is d . Write the expression for equivalent bending load. F b = E r d w A m D (III) Here, the young modulus for the wire rope is E w , the diameter of the wires is d w and the metal cross sectional area is A m . Write the expression for factor of safety. n f = F f − F b F t . (IV) Write the expression for nominal area. A n o m = π 4 d 2 (V) Write the expression for ultimate wire load. F u = ( S u ) n o m A n o m . (VI). Write the expression for factor of safety on the basis of ultimate wire load. n = F u F t (VII) Conclusion: Refer table 17-24 “Wire rope data.” to obtain the weight as w = 1.60 d 2 . Substitute 5000 lbf for W , 1.60 d 2 for w , 4 ft / s 2 for a , 90 ft for l and 32.3 ft / s 2 for g in Equation (I). F t = ( 5000 lbf m + 1.60 d 2 × 90 ft ) ( 1 + 4 ft / s 2 32.2 ft / s 2 ) = ( 5000 lbf m + 144 d 2 ft ) ( 1 + 0.1242 ) = ( 5000 lbf m + 144 d 2 ft ) ( 1.1242 ) = 5621 lbf m + 161.88 d 2 ft (VIII) Refer table 17-27 “Some useful properties of 6 × 7 , 6 × 19 ,and 6 × 37 wire rope.” to obtain the rope young modulus, diameter of wire and the area of metal as E r = 12 × 10 6 psi , d w = 0.067 d in and A m = 0.40 d 2 . Substitute 12 × 10 6 psi for E r , for d w , 30 in for and 0.40 d 2 for A m in Equation (III). F b = ( 12 × 10 6 psi ) ( 0.067 d in ) ( 0.40 d 2 in 2 ) 30 in = ( 12 × 10 6 lbf / in 2 ) ( 0.0268 d 3 in 3 ) 30 in = 10720 d 3 lbf Refer Figure 17-21, “Experimentally determined relation between the fatigue life of wire rope and the sheave pressure.” To obtain the pressure strength ratio as p / S u = 0.0014 . Substitute 0.00014 for p / S u and 30 in for D and the 240 kpsi for S u in Equation (II). F f = 0.004 ( 240 kpsi ) ( 30 in ) ( d in ) 2 = 0

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

10th Edition

ISBN: 9780073398204

Author: Richard G Budynas, Keith J Nisbett

Publisher: McGraw-Hill Education

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Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

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The number of rope required.

Solution Summary: The author explains how to write the expression for tension due to load and acceleration. The young modulus for the wire rope is E_w.

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