AHSANULLAH UNIVERSITY OFSCIENCE AND TECHNOLOGY.

DEPARTMENT OF CIVIL ENGINEERING4THYEAR AND 2nd SEMESTER

Pre-stress concrete design sessional (CE 416)

WELCOME TOTHE PRESENTATION ON BENDING MOMENT.

THIS IS IMRAN ISLAM.ROLL: 10.01.03.066Section : B

Bending moment

A bending moment is a moment whose rotational force is resisted.

when a force is applied on a body far away from the fixed point, then the body will tends to bend with the support of the fixed end. this type of force is called bending moment.

Considering free body

Bending moment is an important factor to be consider while designing any structural component. For example we consider the following which shows the free body diagram

Of a simply supported beam

Based on these sign conventions we can write the equation of bending moment at section X-X as given below;Considering forces on the left of the section X-XMX = RALA - F 1X1 – F2 X2

Considering forces to the right section of X-X.MX = RB LB - F 3X3 – F4 X4.

The above expression is called as banding moment equation which can be written depending upon the loading on the beam. A graphical representation of the bending moment equation along the span of the beam is known as bending moment diagram(BMD).

‘’It is also defined as the algebraic sum of the moments about a section of the beam concerned of all the forces acting on one side of the section’’. 

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 (Ne-cm) , or foot-pounds force (ft-lb).

Sign convention for bending moment

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.

Importance of bending moment

Positive and Negative are just directions. The main concern is whether there exist a bending moment or not. Sagging and hogging moments are important to differentiate. This is of great importance in designing reinforced concrete members as we have to provide steel rebar in the zone of beam having tensile stress as concrete is weak in tension.

Calculation of bending moment

2m 3m 3m 2m

5kN 10kN

2kN/m

A B C D E

5kN

Calculation of reaction

Solution: Calculation of Reactions: Due to symmetry of the beam, loading

and boundary conditions, reactions at both supports are equal.

.`. RA = RB = ½(5+10+5+2 × 6) = 16 kN

Shear Force Calculation: V0-0 = 0 V1-1 = - 5kN V6-6 = - 5 – 6 = -

11kN V2-2 = - 5kN V7-7 = - 11 + 16

= 5kN V3-3 = - 5 + 16 = 11 kN V8-8 = 5 kN V4-4 = 11 – 2 × 3 = +5 kN V9-9 = 5 – 5 =

0(check) V5-5 = 5 – 10 = - 5kN

2m 3m 3m 2m

10kN2kN/m

1

1 3

4

2

32

4 6

6

5

5

9

98

7

7

8

RA=16kN RB = 16kN

2m 3m 3m 2m

5kN 10kN 5kN2kN/m

A BC D E

++

5kN 5kN

5kN 5kN 5kN11kN

11kNSFD

2m 3m 3m 2m

5kN 10kN 5kN2kN/m

A BC D E

RA=16k RB = 16kN

Bending Moment Calculation: MC = ME = 0 [Because Bending moment at free end is zero]MA = MB = - 5 × 2 = - 10 kNmMD = - 5 × 5 + 16 × 3 – 2 × 3 × 1.5 = +14 kNm

2m 3m 3m 2m

5kN 10kN 5kN2kN/m

A BC D E

10kNm 10kNm

14kNm

BMD

Points of contra flexure

Point of contra flexure [inflection point]

It is the point on the bending moment diagram where bending moment changes the sign from positive to negative or vice versa.

It is also known as ‘inflection point’. At the point of inflection point or contra flexure the bending moment is zero.

formula for maximum bending moment

This depends on the arrangement of a beam or column. for a simply supported beam with a point load in the centre of the beam

Mmax = WL/4 and will occur at centre span

W is the load in kNL is the span in m

Moment is given in kNm

for a uniformly distributed load w given in kN/m

Mmax = wL^2/8 and will occur at centre span.

Different shapes of bending moment due to varying loading

significance of bending moment in a structure

the points where bending moments are maximum are points of maximum stress , therefore these points require more reinforcement with steel to counter the stresses , Where as at points where stresses are less , curtailment of steel can be done . 

To avoid the bending of member reinforcement is used.

bending moment is required for design of any structural component and also for the calculation of slope and deflection of structure

THANK YOU