Materials Science And Engineering
Materials Science And Engineering
10th Edition
ISBN: 9781119405498
Author: Callister, William D., Jr, RETHWISCH, David G., Jr., 1940- Author.
Publisher: Wiley,
Question
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Chapter 6, Problem 1QAP
To determine

To derive:

The Equation 6.4a and 6.4b using mechanics of materials principles.

Expert Solution & Answer
Check Mark

Answer to Problem 1QAP

The Equation 6.4a and 6.4b using mechanics of materials principles is shown in conclusion.

Explanation of Solution

Write the expression for engineering stress.

σ=PA (I)

Here, the tensile force is P and cross-sectional area is A.

Write the expression for shear stress.

τ=VA (II)

Here, the normal force is P and shear forces is V.

Conclusion:

Show the diagram of a block element of material of cross-sectional area A that is subjected to a tensile force P, the orientations of the applied stress, the normal stress to this plane, as well as the shear stress taken parallel to this inclined plane.

Materials Science And Engineering, Chapter 6, Problem 1QAP , additional homework tip  1

Materials Science And Engineering, Chapter 6, Problem 1QAP , additional homework tip  2

Materials Science And Engineering, Chapter 6, Problem 1QAP , additional homework tip  3

For static equilibrium in the x-direction.

Fx=0

Which means that

PPcosθ=0P=Pcosθ

Write the expression for the stress σ in terms of P and A using the above expression and the relationship between A and A .

σ=PA=PcosθAcosθ=PAcos2θ=σcos2θ

Write the expression for τ .

τ=VA=PsinθAcosθ=PAsinθcosθ=σsinθcosθ

Thus, the τ value is σsinθcosθ_ .

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