3. 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.
4. 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.
4
5. 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.
5
6. Sign Convention
Bending which
produces compression
in top fiber and tension
in bottom fiber is taken
as positive bending.
Also called Sagging
Bending.
6
7. Sign Convention
Bending which
produces compression
in bottom fiber and
tension in top fiber is
taken as Negative
bending.
Also called Hogging
beam.
7
11. 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.
11
12. 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.
12
13. Bending moment Diagram
A bending moment
diagram is simply a
graph of bending
moment plotted
vertically against the
distance from left.
13
14. Some Bending Moment formulas
Beam
Bending
Moment Diagram
Maximum
Bending Moment
p
PL
L
w
WL^2/8
L
w
WL^2/2
L
P
PL/4
L
14
15. Example Problem
For a simply supported beam, calculate
bending moment and draw Bending moment
diagram.
20N
Ra
0.4 m
0.6 m
Rb
15
16. Solution
At first we have to calculate the reaction.
From equilibrium equation,we findRa+Rb=20
By taking moment at point Ra, assuming
clockwise direction as +ve,
-Rb*1+20*0.4=0
so, Rb=8N
& Ra=12N
16
