Book cover for Mechanics of Materials

Mechanics of Materials

Ferdinand P. Beer, E. Russell Johnston, Jr., John T. DeWolf

ISBN #9781260113273

8th Edition

1,507 Questions

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Summary

Learning Objectives

Key Concepts

Example Problems

Explanations

Common Mistakes

Summary

This section integrates the fundamental concepts of bending, shear, and torsion to analyze stresses in beams and shafts. It demonstrates how to calculate normal and shear stresses using basic formulas, combine these effects through stress transformation (Mohr’s circle) to obtain principal stresses, and apply these methods in practical design scenarios such as selecting appropriate beam sections and designing transmission shafts. The methods rely on proper usage of superposition and assumptions consistent with linear elastic behavior, and they highlight the importance of checking stress concentrations at critical points.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

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Example Problems

Example 1

A $\mathrm{W} 10 \times 39$ rolled-steel beam supports a load $\mathbf{P}$ as shown. Knowing that $P=45$ kips, $a=10$ in., and $\sigma_{\text {all }}=18$ ksi, determine (a) the maximum value of the normal stress $\sigma_{m}$ in the beam, ( $b$ ) the maximum value of the principal stress $\sigma_{\max }$ at the junction of the flange and web, ( $c$ ) whether the specified shape is acceptable as far as these two stresses are concerned.

Example 2

Solve Prob. $8.1,$ assuming that $P=22.5$ kips and $a=20$ in.

Example 3

An overhanging $\mathrm{W} 920 \times 449$ rolled-steel beam supports a load $\mathbf{P}$ as shown. Knowing that $P=700 \mathrm{kN}, a=2.5 \mathrm{m},$ and $\sigma_{\text {all }}=100 \mathrm{MPa}$ determine $(a)$ the maximum value of the normal stress $\sigma_{m}$ in the beam, (b) the maximum value of the principal stress $\sigma_{\max }$ at the junction of the flange and web, (c) whether the specified shape is acceptable as far as these two stresses are concerned.

Example 4

Solve Prob. $8.3,$ assuming that $P=850 \mathrm{kN}$ and $a=2.0 \mathrm{m}$

Example 5

(a) Knowing that $\sigma_{\mathrm{all}}=160 \mathrm{MPa}$ and $\tau_{\mathrm{all}}=100 \mathrm{MPa}$, select the most economical metric wide-flange shape that should be used to support the loading shown. ( $b$ ) Determine the values to be expected for $\sigma_{m}, \tau_{m},$ and the principal stress $\sigma_{\max }$ at the junction of a flange and the web of the selected beam.

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Step-by-Step Explanations

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Common Mistakes

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