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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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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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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Assignment # II
Problems: 4.1-4.15
Due Date: 24-11-2014
Before 1030 am
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