10.01.03.034
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AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY
Name: Susmita Bhowmik
ID: 10.01.03.034
Department of Civil Engineering
Pre-stressed Concrete Lab
4 th Year; 2nd Semester
Sec : A
PRESENTATION ON• Bullet point• Bullet point
BENDING MOMENT STRESS (UNIAXIAL & BIAXIAL)
STRESS
The components of the
intensity of force per
unit area- that is stress.
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.
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)
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)
Types of bending moment stress
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FollowedHyperlink UNIAXIAL BENDING STRESS
BIAXIAL BENDING STRESS
TWO TYPES OF BENDING STRESS-
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.
Uniaxial Bending Stress (Cont.)
Bending stress is distributed through a beam as seen in the diagram below:
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.
Uniaxial Bending Stress (Cont.)
A beam under only a
bending load will be in a
uniaxial.
Stress (force) distribution in a bent beam
EXAMPLES:
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.
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.
Variation of tension and compression due to bending moment:
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.
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.
Biaxial Bending Stress (Unsymmetric Bending)
A biaxial stress
system has a stress
state in two
direction. . It is also
known as
unsymmetrical
(skew) bending.
Biaxial bending stress(Unsymmetric Bending)
The formula of the biaxial bending stress is given by-
σx = -(Mz Y/Iz ) + (MyZ/Iy)
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.
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:
Biaxial bending stress (Cont.)
Loading at footing base and stress distribution
Thank You………..