Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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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Chapter 10, Problem 1P

Within the range of recommended values of the spring index, C, determine the maximum and minimum percentage difference between the Bergsträsser factor, KB, and the Wahl factor, KW.

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To determine

The maximum percentage difference between Bergstrasser factor and Wahl factor.

The minimum percentage difference between Bergstrasser factor, KB and Wahl factor, KW.

Answer to Problem 1P

The maximum percentage difference between KB and KW is 1.36.

The minimum percentage difference between KB and KW is 0.741.

Explanation of Solution

Write the expression for Bergstrasser factor.

KB=4C+24C3 (I)

Here, Bergstrasser factor is KB and the spring index is C.

Write the expression for Wahl factor KW.

KW=4C14C4+0.615C (II)

Here, the Wahl factor is KW.

Write the expression for the minimum percentage difference between KB and KW.

Min=(KWKBKW)×100 (III)

Write the expression for Maximum percentage difference between KB and KW.

Max=(KWKBKW)×100 (IV)

Conclusion:

Substitute 12 for C in Equation (I).

KB=4×12+24×123=5045=1.1111

Substitute 12 for C in Equation (II).

KW=4×1214×124+0.61512=4744+0.05125=1.068+0.05125=1.1194

Substitute 1.1111 for KB and 1.1194 for KW in Equation (III).

Min=(1.11941.11111.1194)×100=0.0083×1001.1194=0.741%

Thus, the minimum percentage difference between KB and KW is 0.741.

Substitute 4 for C in the Equation (I)

KB=4×4+24×43=1813=1.3846

Substitute 4 for C in the Equation (II).

KW=4×414×44+0.6154=1512+0.1537=1.25+0.1537=1.4037

Substitute 1.3846 for KB and 1.4037 for KC in the Equation (IV).

Max=(1.40371.38461.4037)×100=0.0191×1001.4037=1.36

Thus, the maximum percentage difference between KB and KW is 1.36

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Chapter 10 Solutions

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

Ch. 10 - 10-9 to 10-19 Listed in the tables are six springs...Ch. 10 - Prob. 12PCh. 10 - 10-9 to 10-19 Listed in the tables are six springs...Ch. 10 - 10-9 to 10-19 Listed in the tables are six springs...Ch. 10 - 10-9 to 10-19 Listed in the tables are six springs...Ch. 10 - 10-9 to 10-19 Listed in the tables are six springs...Ch. 10 - Prob. 17PCh. 10 - 10-9 to 10-19 Listed in the tables are six springs...Ch. 10 - 10-9 to 10-19 Listed in the tables are six springs...Ch. 10 - Consider the steel spring in the illustration. (a)...Ch. 10 - A static service music wire helical compression...Ch. 10 - Solve Prob. 1021 by iterating with an initial...Ch. 10 - A holding fixture for a workpiece 37.5 mm thick at...Ch. 10 - Solve Prob. 10-23 by iterating with an initial...Ch. 10 - A compression spring is needed to fit over a...Ch. 10 - A compression spring is needed to fit within a...Ch. 10 - A helical compression spring is to be cycled...Ch. 10 - The figure shows a conical compression helical...Ch. 10 - A helical coil compression spring is needed for...Ch. 10 - Solve Prob. 10-30 using the Goodman-Zimmerli...Ch. 10 - Solve Prob. 10-30 using the Sines-Zimmerli...Ch. 10 - Design the spring of Ex. 10-5 using the...Ch. 10 - Solve Prob. 10-33 using the Goodman-Zimmerli...Ch. 10 - A hard-drawn spring steel extension spring is to...Ch. 10 - The extension spring shown in the figure has...Ch. 10 - Design an infinite-life helical coil extension...Ch. 10 - Prove Eq. (10-40). Hint: Using Castigliunos...Ch. 10 - The figure shows a finger exerciser used by...Ch. 10 - The rat trap shown in the figure uses two...Ch. 10 - Prob. 41PCh. 10 - Prob. 42PCh. 10 - Figure 10-13b shows a spring of constant thickness...
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