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Engineering and Tech / Mechanics of Materials 9 / Chapter 4 / Problem 4-3

Mechanics of Materials | 9th Edition | ISBN: 9780133254426 | Authors: R.C. Hibbeler

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The composite shaft, consisting of aluminum, copper, and

Chapter 4, Problem 4-3

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QUESTION:

The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown. Determine the displacement of end A with respect to end D and the normal stress in each section. The cross sectional area and modulus of elasticity for each section are shown in the figure. Neglect the size of the collars at B and C.

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QUESTION:

The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown. Determine the displacement of end A with respect to end D and the normal stress in each section. The cross sectional area and modulus of elasticity for each section are shown in the figure. Neglect the size of the collars at B and C.

ANSWER:

Problem 4-3

The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown. Determine the displacement of end A with respect to end D and the normal stress in each section. The cross sectional area and modulus of elasticity for each section are shown in the figure. Neglect the size of the collars at B and C .

Step by Step Solution

Step 1 of 4

Calculate the normal stress in the section AB,

$\sigma _{AB}= \frac{P_{AB}}{A_{AB}}$

Here, the load acting on the section AB is and the cross sectional area of AB is .

Substitute 2 kip for (Consider the tensile load as possible) and 0.09 for .

$\sigma _{AB}= \frac{P_{AB}}{A_{AB}}$

$=\frac{2}{0.09}$

= 22.2 ksi (Tensile)

Therefore, the normal stress in the section AB is

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