3.
STRESS
The components of the
intensity of force per
unit area- that is stress.
4.
Bending Moment Stress
If the stress in a beam depends on the bending moment is called
bending moment stress. It is the internal stresses caused by bending
moments acting at a given distance from the neutral axis. It is also
known as flexural stress.
5.
Bending Moment Stress (Cont.)
The formula for bending stress, σ, is as follows:
σ = My/ I
M = moment acting on beam from moment
diagram (kip-in or lb-in)
y = distance from neutral axis to extreme edge of
member (in)
I = moment of inertia about the axis (in^4)
6.
Bending Moment Stress (Cont.)
Recalling that
S = I/Y , the bending stress
formula could be re-written as:
σ = M/S
where: S = section modulus about the axis
(in³)
7.
Types of bending moment stress
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TWO TYPES OF BENDING STRESS
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UNIAXIAL BENDING STRESS
BIAXIAL BENDING STRESS
8.
Uniaxial Bending Stress
• An uniaxial bending stress system has a stress state in
one direction.
• In Diagram 1 we have shown a simply supported
beam loaded at the center. It deflects (or bends) under
the load.
9.
Uniaxial Bending Stress (Cont.)
Bending stress is distributed through a beam as
seen in the diagram below:
10.
Uniaxial Bending Stress (Cont.)
EXAMPLES:
A simply-supported
beam always has
tensile stresses at the
bottom of the beam
and compressive
stresses at the top of
the beam.
11.
Uniaxial Bending Stress (Cont.)
EXAMPLES:
A beam under only a
bending load will be in a
uniaxial.
Stress (force) distribution in a bent beam
12.
Uniaxial Bending Stress (Cont.)
Example
GIVEN: A nominal 2x10 (actual dims. 1½” x 9¼”) is used as a
simply-supported beam with loading as shown. The allowable
bending stress is 1200 psi.
REQUIRED:
a) Determine the maximum moment on the beam.
b) Determine the maximum actual bending stress on the beam
c) Determine if the beam is acceptable based upon allowable
bending stress.
13.
Uniaxial Bending Stress (Cont.)
The maximum bending moment, Mmax, on a simply-supported, uniformly
loaded beam is:
Mmax = wL2/8
or, Mmax = (140 PLF)(11') 2/8
or, Mmax = 2117.5 lb-ft
The bending stress is:
σ =M/S
=[2117.5 lb - ft(12"/ft)] / 21.39 in³
or, σ = 1187.9 PSI
Since the actual bending stress of 1187.9 PSI is less than the allowable
bending stress of 1200 PSI, THE BEAM IS ACCEPTABLE.
14.
Variation of tension and compression due
to bending moment:
With the shown sign convention, bending
about X-axis causes compression in the
top part and tension in the bottom
region, whereas bending about Y-axis
causes compression in the left hand part
and tension in the right part.
In biaxial bending (d), the top-left part
is subjected to double compression and
the bottom right part is subjected to
double tension. The remaining parts are
subjected to combined compression
and tension.
15.
Biaxial Bending Stress
(Unsymmetric Bending)
A biaxial stress
system has a stress
state in two
direction. . It is also
known as
unsymmetrical
(skew) bending.
16.
Biaxial bending stress
(Unsymmetric Bending)
The formula of the biaxial bending stress is given
by-
σx = -(Mz Y/Iz ) + (MyZ/Iy)
17.
Biaxial bending stress (Cont.)
EXAMPLES:
The column having
axial load acting in
such a way that the
load is eccentric about
both the axes in the
plane of the column
then it is called
biaxially loaded
column.
18.
Biaxial bending stress (Cont.)
EXAMPLES:
Schematic stress
distribution of a
rectangular footing
under the effect of
biaxial bending
together with vertical
load is shown in
Figure:
Loading at footing base and stress distribution
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