Mechanics of Materials chap-4

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MECHANICS OF

MATERIALS

Third Edition

Ferdinand

P. Beer

E. Russell

Johnston, Jr.

John T. DeWolf

CHAPTER

4


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MECHANICS OF MATERIALS Beer Johnston DeWolf

In the preceding chapters you studied how to determine the

stresses in prismatic members subjected to axial loads or totwisting couples. In this chapter and in the following two you

will analyze the stresses and strains in prismatic members

subjected to bending. Bending is a major concept used in the

design of many machine and structural components, such as

beams and girders.

This chapter will be devoted to the analysis of prismatic

members subjected to equal and opposite couples M and M

acting in the same longitudinal plane. Such members are said to

be inpure bending.

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Pure Bending
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Pure Bending

MECHANICS OF MATERIA S


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Pure Bending


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MECHANICS OF MATERIALS


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Pure Bending



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Pure Bending



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Pure Bending



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Pure Bending



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Pure Bending



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Pure Bending



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Pure Bending



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Centroids



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Centroids for Composite Shapes



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Moment of Inertia



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Beam Section Properties

The maximum normal stress due to bending,

modulussection

inertiaofmomentsection

c

IS

I

S

M

I

Mc

m

A beam section with a larger section modulus

will have a lower maximum stress

Consider a rectangular beam cross section,

Ahbhh

bh

c

IS

6

13

6

1

3

12

1

2

Between two beams with the same crosssectional area, the beam with the greater depth

will be more effective in resisting bending.



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Elastic Flexural Formula for Bending

IM

cE

EIM

I

Mc

EcEcc

m

mm

11

the above relation is called flexural formula for bending



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MECHANICS OF MATERIALS Beer Johnston DeWolfPure Bending Example

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MECHANICS OF MATERIALS Beer Johnston DeWolfPure Bending Example

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MECHANICS OF MATERIALS Beer Johnston DeWolfPure Bending Sample Problem 4.1

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Assignment # II

Problems: 4.1-4.15

Due Date: 24-11-2014

Before 1030 am

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Pure Bending

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Mechanics of Materials chap-4