1. DEPARTMENT OF CIVIL ENGINEERING
4THYEAR AND 2nd SEMESTER
PRE-STRESS CONCRETE DESIGN SESSIONAL (CE 416)

2. WELCOME TO
THE PRESENTATION ON
BENDING MOMENT.
I am Nayeem Akhter
 Roll : 10.01.03.010
 Sec : A

3. WHAT IS A BENDING MOMENT?
A BENDING MOMENT IS A MEASURE OF THE BENDING
EFFECT DUE TO FORCES ACTING ON A BEAM. IT IS
MEASURED IN TERMS OF FORCE AND DISTANCE.

4. SHEAR AND MOMENT DIAGRAMS


Members with support loadings applied
perpendicular to their longitudinal axis are called
beams.
Beams classified according to the way they are
supported.

5. SHEAR AND MOMENT DIAGRAMS


Shear and moment functions can be plotted in graphs called
shear and moment diagrams.
Positive directions indicate the distributed load acting
downward on the beam and clockwise rotation of the beam
segment on which it acts.

6. FORMULA OF BENDING MOMENT

7. BENDING MOMENT AT A SECTION OF A BEAM

Bending moment at a section of a beam is
defined as the algebraic sum of the moment
of all the forces acting on one side of the
section.

8. A graphical representation of the bending
moment equation along the span of the
beam is known as bending moment
diagram(BMD).

9. SIGN CONVENTION FOR BENDING MOMENT
It is very important to define the sign convention
for bending moment before calculating the values.
The possible bending of a beam is shown in the
following figure.

10. Sagging bending moment is taken as +ve. It
results in developing tension in the bottom fibres
and compression in top fibres of the beam.

11. Hogging bending moment is taken as –ve. And
it develops compression in the bottom fibres
and tension in the top fibres.

12. UNIT OF BANDING MOMENT

A bending moment is a measure of the
bending effect due to forces acting on a
beam. It is a type of stress and is measured
in terms of force and distance. so they have
as unit Newton-metres (N-m) , or footpounds (ft-lb).

13. CALCULATION OF BENDING MOMENT

Draw the shear and bending moment
diagrams for the beam shown in the Figure.

14. SOLUTION
(i)
First determine the reactions at A and B. These are equal to 2.5 kN
each.
(ii)
Cut the beam at an arbitrary section x after A but before B
2.5 kN
V
M
x
The unknown forces V and M are assumed to act in the positive sense on the right hand
face of the segment according to the sign convention:
V = 2.5 kN
i.e.
(1)
M = 2.5 x kN.m
(2)

15. SOLUTION CONTD.
(i)
Now choose another section along BC after the 5 kN load (2 m < x < 4 m)
2m
x
5 kN
V
2.5 kN
x-2
M
x
x
V =
M=
2.5 kN - 5 kN = - 2.5 kN
2.5 x - 5 (x –2) =
(3)
(10 - 2.5x ) kN.m
(4)

16. SHEAR FORCE AND BENDING MOMENT DIAGRAMS

17. ASSUMPTIONS IN SIMPLE BENDING THEORY





Beams are initially straight
The material is homogenous and isotropic i.e. it has
a uniform composition and its mechanical
properties are the same in all directions.
Young’s Modulus is the same in tension as in
compression.
Sections are symmetrical about the plane of
bending.
Sections which are plane before bending remain
plane after bending.

18. ASSUMPTIONS IN SIMPLE BENDING CONTD.



The last assumption implies that each section
rotates during bending about a neutral axis, so that
the distribution of strain across the section is linear,
with zero strain at the neutral axis.
The beam is thus divided into tensile and
compressive zones separated by a neutral surface.
The theory gives very accurate results for stresses
and deformations for most practical beams
provided that deformations are small.

19. DIFFERENCE BETWEEN MOMENT AND BENDING
MOMENT?

Take a beam as an example. Moment is
responsible for a beam to rotate about some axis.
Whereas bending moment are a pair of moments
which will not rotate the beam but it will deflect it.

20. DIFFERENCE BETWEEN SHEAR FORCE AND BENDING
MOMENT?

shear force is maximum at support and zero at centre
Bending moment maximum at centre and zero at support
for all simply supported beams.


shear force acts on a place and it induce on a direct
place where the loads are transfered.
Bending moment act with reference to lever arm
distance. (B.M = force X Distance)
unit for shear force is KN
unit for mending moment is Kn.m

21. SOME OF THE COMMON LOADING CASES ARE
SHOWN BELOW.

22. THANK YOU ALL