Bending Moment

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

Presented By-Summiaya KhatoonID:10.01.03.122 Year:4TH

Section: C Semester:2ND

Department of Civil Engineering

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

Thank You …