Imagine that a long steel wire hangs vertically from a high-altitude balloon. (a) What is the greatest length (feet) it can have without yielding if the steel yields at 44) ksi? (b) If the in wire hangs from a ship at sea, what is the greatest length? (Obtain the weight densities of steel and seawater from Table I-I. Appendix I.)

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 1, Problem 1.5.1P
Textbook Problem
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Imagine that a long steel wire hangs vertically from a high-altitude balloon. (a) What is the greatest length (feet) it can have without yielding if the steel yields at 44) ksi? (b) If the in wire hangs from a ship at sea, what is the greatest length? (Obtain the weight densities of steel and seawater from Table I-I. Appendix I.)

(a)

To determine

Greatest length of steel wire

Explanation of Solution

Given Information:

A vertically hanging steel wire is given. Steel has yield point 40 ksi and weight density 490 lb/ft3.

Calculation:

Consider the free body diagram of wire as,

The maximum stress in vertically hanging wire occurs at point A and is calculated as,

σmax=Weight of wirecross sectional area=Weight density×L×AA=Weight density×L

Now since steel has yield stress equal to 40 ksi, hence to prevent yielding,

(b)

To determine

Greatest length of steel wire

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