ASSIGNMENT 2 STRUCTURE

DCC20053
MECHANICS OF CIVIL

ENGINEERING
STRUCTURE

CHAPTER 6 : SLOPE AND DEFLECTION OF
BEAM DUE TO SYMMETRICAL BENDING

STUDENT’S NAME: NIK ROSSMALLISA BINTI KELIMAL
REGISTRATION NUMBER: 04DKA20F2083

LECTURER NAME: PUAN NORHAIZAH BINTI AMBIAH

CONTENT

SUBTOPIC PAGE
INTRODUCTION 3-5
6-7
DEFINITION 8-17
EXAMPLE QUESTION
18-19
CONCLUSION 20
REFERENCES

INTRODUCTION

The slope deflection method is a structural analysis method for beams
and beams and frames introduced in 1915 by George A. Maney. The
slope deflection method was widely used for more than a decade until
the moment distribution method was developed.
 The magnitude of the load
 The stiffness of the member
Deflection of beam means a clear bending observably in beam is not
function well. It also define as a deformation of the beam when
subjected to the laod.
The deflection diagram of the longitudinal axis that passes through the
centroid of each cross-sectional area of the beam is called the Elastic
Curve.

y y = deflection
dy @ θ = slope of deflection curve
dy @ θ dx
dx

Building codes (such as the IBC) require that deflections in beams be
held to a minimum for occupancy comfort as well as to reduce likelihood
of cracking ceiling finishes such as plaster. It is considered to be a
“serviceability” check. Allowable deflection limits are dictated by the
codes, such as L/360 of the span

Original Beam
Deflected Beam

Column Max. Deflected

Beam Span

DEFINITION OF
MACAULAY’S METHOD

AND MOMENT AREA

METHOD

Macaulay Method Moment Area Method

1. It is a simple method based on the 1. Moment area method is used to
double integration concept. In this determine the slope and
method, bending moment at any section deflection at a particular point in
is expressed in the systematic order. determine and indeterminate
structure.
2. The section x is to be taken in last
portion of the beam. In this method, 2. Theorems of moment are method
bending moment due to each force or suggested by Mohr and thus,
UDL is separated by compartment lines. these theorems are called Mohr
theorem.
3. Slope is obtained by integrating bending
moment and then deflection is obtained
by integrating of slope equation

EXAMPLE
QUESTION

SLOPE
DEFLECTION IN

MACAULAY
METHOD

Get the slope and deflection at the end of cantilever beam as below.







SLOPE
DEFLECTION IN
MOMENT AREA

METHOD

Get the slope and deflection at the of hanging beam (point D)
as below in term of EI.





CONCLUSION

In conclusion, after the first
integration of the original
differential equation, we get the
slope value at any point and
also at the next integration, we
get the deflection value at any
bridge. it is thus obvious, that
the Macaulay method and the
moment area method are used
to find the gradients and
deflections that occur as a
result of symmetrical bending
on the beam.

REFERENCES

 https://www.ques10.com/p/25425/define-macaulays-
method-and-moment-area-method/

 CIDOS 5.3
 MECHANICS OF CIVIL ENGINEERING STRUCTURE

NOTE ( CHAPTER 6: SLOPE AND DEFLECTION OF
BEAM DUE TO SYMMETRICAL BENDING