MECHANICS STRUCTURE

DCC20053:MECHANICS

OF CIVIL ENGINEERING

STRUCTURE

LECTURER NAME:PUAN NORHAIZAH BINTI AMBIAH
ASSIGMENT 2:TOPIC 4 (BENDING STRESS IN BEAM)

GROUP MEMBER

NURUL AYUNI BINTI ANUAR NOR ALISANAJWA BINTI AHMAD
04DKA20F2014 SAKRI

04DKA20F2010

CONTENTS

INTRODUCTION
DEFINITION OF BENDING STRESS
EFFECT OF BENDING STRESS IN BEAM
CALCULATE THE CENTROID AND SECOND
MOMENT AREA OF A SECTION
TYPE OF BENDING STRESS
QUESTION AND SOLUTION
CONCLUSION
REFERENCES

INRODUCTION

Bending stress is the normal stress that an object encounters when it is subjected to a
large load at a particular point the causes the object to bend and become fatigued.
Bending stress occurs when operating industrial equipment and in concreate and
metallic structures when they are subjected to a tensile load.

DEFINITION OF BENDING
STRESS

When a beam having a fixed cross sectional area undergoes transverse loads (acting perpendicular to beam axis), it
bends and this bending moment will be formed at all the sections of the beam.

Hence, the beam material offers resistance to deformation occurring in the member induced by the bending moment.
These resistance or stresses introduced by bending moment are known as bending stresses.

Consider the figure of a beam acted upon by the loading as shown in Figure.

The assumptions involved in analyzing the beam member is as below.
• Beam has uniform area throughout its length.
• All the layers are made of an identical material, which will have similar properties throughout its length.
• Beam will be symmetric about a plane in alignment with its neutral axis, and the resultant force from the applied

loading will be on the same plane.
• Primary cause leading to failure is bending.
• Elasticity modulus E is the same in both the tension and compression.
• The cross-section will plane after the beam finishes undergoing bending.

Formula used:

Bending stresses can be calculated using the relation below.

=


Here, the term s is the bending stress or normal stress on the section, M is the moment caused due to
bending, y is the distance measured from neutral axis to a point at which the moment is required, and I
is second moment of area estimated about neutral axis.

EFFECT OF BENDING STRESS IN BEAMS

- The bending moment and shearing force are set up at all section of a beam when it is loaded with some external loads.
- The bending moment at a section tends to bend or deflect the beam and the internal stresses resits it bending. The process
of bending stops, when every cross-section sets up full resistance to the bending moment.
- The resistance, offered by the internal stresses, to the bending is called as bending stress and the relevant theory is called
the theory of simple bending.
- The following assumptions are made in the theory of simple bending:

1) The material of the beam is perfectly homogeneous.
2) The beam material is stressed within its elastic limit and thus obeys Hooke’s Law.
3) The transverse section, which were plane before bending remain plane after bending also.
4) Each layer of the beam is free to expand of contract independently of the layer above or below it.
5) The value of E(Young’s Modulus of elasticity) is the same tension and compression.

CALCULATE THE SENTROID AND MOMENT AREA
OF A SECTION

 It has been established,since long that every particle of body is attracted by earth towards its centre.
 The force of attraction,which is proportional to the mass of particle,acts vertically downwards and is

known as weight of the body.
 The center of gravity (CG) is the center of an object’s weight distribution,where the force of gravity can

be considered to act.It is the point in any object about which it is in perfect balance no matter how it is
turned or rotated around the point.

 For a finite set of point masses, CG may be defined as the average of positions weighted by mass.
That is,the ( Sum of mass*position ) / ( Sum of mass).

 Table of area and centroid for basic geometrical.

How to calculate CG?

̅ = ∑
∑

� = ∑
∑

TYPE OF BENDING STRESS

SYMMETRICAL NON SYMMETRICAL

QUESTION
AND

SOLUTION…

A uniformly distributed load 17 KN/mm is supported by 3m span of beam.Calculate the
maximum bending stress of the section.

200mm

17KN/mm

10mm
3m

200mm 10mm

STEP 1 : � and �

̅ =
2

= 200 = 100mm
2

y1 = + d2 y2 =
2 2

= 10 + 200 = 200
2 2

= 205mm = 100mm

� = + Y1 (205mm) � Y2 (100mm)
+

= 200 ×10 205 +(10 ×200)(100)
(2000+2000)

= 152.5mm

STEP 2 : Second moment of Inertia

∑ = +

= 3 + Aℎ2
12

= 200 × 103 + (200 × 10)(205 − 152.5)2 H1(52.5)
12 H2(52.5)

= 16666.66667 + (2000)(2756.25)
= 5.53 × 106 4

= 3 + Aℎ2
12

= 10 × 2003 + (10 × 200)(152.5 −100)2
12

= 6666666.667 + (2000)(2756.25)
= 12.18 × 106 4

∑ = (5.53 × 106) + (12.18 × 106 )

= 17.71 × 106 4

STEP 3 : Moment maxima

STEP 4 : Bending stress

∑ = = ( ) = ( )
2 ∑ ∑

3(17) = 225 × 102 (152.5) = 225 × 102 (210−152.5)
2 17.71 ×106 17.71 × 106
=

= 25.5 −2 = 3431250 = 1293750
17710000 17710000

= 0.194 −2 = 0.073 −2

STEP 5 : Bending stress distribution

= 0.073 −2

yC=57.5mm

yT=152.5mm
= 0.194 −2

CONCLUSION

Aim of this task was to study the effect of different forces on the bending stresses in the
beam and the result show that there is a linear relationship between bending stress and
applied load. Experimental bending stress show perfect linear relationship with applied
load whereas the theoretical bending stress does not respond that much in increase of
applied load.

REFERENCES

 https://i.ytimg.com/vi/IyRZ0WIhCdU/maxresdefault.jpg
 30 MAY 2013
 BY ECUSW

THANKS!

POLITEKNIK KOTA BHARU
CIVIL ENGINEERING

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