PRE-STRESS CONCRETE DESIGN SESSIONAL (CE 416)

DEPARTMENT OF CIVIL ENGINEERING4THYEAR AND 2nd SEMESTER

WELCOME TO THE PRESENTATION ON BENDING MOMENT.

I am Nayeem Akhter Roll : 10.01.03.010 Sec : A

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.

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.

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.

FORMULA OF BENDING MOMENT

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.

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

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.

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

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

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 foot-pounds (ft-lb).

CALCULATION OF BENDING MOMENT

Draw the shear and bending moment diagrams for the beam shown in the Figure.

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 (1)

i.e. M = 2.5 x kN.m (2)

SOLUTION CONTD.(i) Now choose another section along BC after the 5 kN load (2 m < x < 4 m)

2 m x

5 kN

V M

2.5 kN x - 2 x

x

V = 2.5 kN - 5 kN = - 2.5 kN (3)

M = 2.5 x - 5 (x –2) = (10 - 2.5x ) kN.m (4)

SHEAR FORCE AND BENDING MOMENT DIAGRAMS

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.

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.

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.

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

SOME OF THE COMMON LOADING CASES ARE SHOWN BELOW.

THANK YOU ALL