bending moment
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Ahsanullah University of Science &Technology
Presentation on: BENDING MOMENT
Course No: CE-416 Course Name: Pre-stressed Concrete Lab. Course Teacher: Galib Muktadir & Sabrina Nasreen
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Presented By-Summiaya KhatoonID:10.01.03.122 Year:4TH
Section: C Semester:2ND
Department of Civil Engineering
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Contents Definition of Bending Moment. Significance of Bending Moment. Sign Convention. Sagging Beam. Hogging Beam. Unit of Bending Moment. Section of Maximum Moment. Some Bending Moment Formulas. Example Problem. Solution.
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Definition of Bending Moment
A Bending Moment is the measure of the internal stress that produced by the external force or moment causing the element to bend.
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Significance of Bending Moment
Bending Moments are maximum at the points of maximum stress, so these points require more reinforcement to counteract the stresses.
Bending moment is the main factor that decide the reinforcement detailing of a structure.
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Sign Convention
Bending which produces compression in top fiber and tension in bottom fiber is taken as positive bending.
Also called Sagging Bending.
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Sign Convention
Bending which produces compression in bottom fiber and tension in top fiber is taken as Negative bending.
Also called Hogging beam.
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Sagging Beam
Compression
Tension
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Sagging Beam
Compression
Tension
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Hogging Beam
Tension
Compression
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Unit of Bending Moment
• As, bending moment is the result of force and distance ,so the unit is Kip-ft or lb-ft or N-m or KN-m.
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Section of Maximum Moment
It can be shown mathematically, that when the shear force is zero or changes sign, the bending moment will be either a maximum or relative maximum.
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Bending moment Diagram
A bending moment diagram is simply a graph of bending moment plotted vertically against the distance from left.
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Some Bending Moment formulas Beam Bending
Moment Diagram Maximum Bending Moment
p L
PL
w
L WL^2/8
w
L WL^2/2
P
L
PL/4
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Example Problem
For a simply supported beam, calculate bending moment and draw Bending moment diagram.
20N
Ra 0.4 m 0.6 m Rb
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Solution
At first we have to calculate the reaction.From equilibrium equation,we find- Ra+Rb=20By taking moment at point Ra, assuming
clockwise direction as +ve, -Rb*1+20*0.4=0 so, Rb=8N & Ra=12N
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Solution
Now, shear force diagram- 12N
8N Fig: shear force diagram
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Solution
Finally, from shear force diagram, we can draw the bending moment diagram-
4.8 N-m
Fig: Bending Moment Diagram
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Thank You …