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Journal for Studies in Management and Planning
Available at http://edupediapublications.org/journals/index.php/JSMaP/
e-ISSN: 2395-0463
Volume 02 Issue 10
October 2016
Available online:http://edupediapublications.org/journals/index.php/JSMaP/ P a g e | 161
L Shaped Columns Subjected To Axial Load And Uniaxial Bending –
Interaction Diagrams
Gudem Venkateshwarlu
M.Tech. (Structural Engineering)
Vaagdevi college of engineering, Warangal, India
Dr. S Sunil Pratap Reddy
Professor, Department of Civil Engineering
Vaagdevi college of engineering, Warangal, India
Abstract
The IS 456-2000 code clause 25.1.1 defines the column as a ‘compression member’ the
effective length of which exceeds three times the least lateral dimension. Axially loaded
columns may fail in any one of the following three modes. Pure compressionfailure, combined
compression and bending failure, Failure by elastic instability.
INTRODUCTION
Structural concrete members in
compression are generally referred to as
columns and struts. The term ‘column’ is
associated with members transferring loads
to the ground and the term strut is applied to
compression members in any direction such
as those in a truss. The failure modes
depend primarily on the slenderness ratio of
the member which in turn depends on the
cross sectional dimensions, effective length,
and support conditions of the member. In
tied columns the main longitudinal bars are
confined within closely spaced lateral ties.
Spiral columns have main longitudinal
reinforcement enclosed within closely
spaced and continuously wound spiral
reinforcement. Composite columns have
longitudinal reinforcement in the form of
structural steel section or pipes with or
without longitudinal bars. In general tied
columns are the most commonly used
having different shapes (square, rectangular,
T, L, circular etc). Spiral columns are
adopted with circular cross sections and also
for square and octagonal sections. Columns
with uniaxial eccentric loading are generally
encountered in the case of columns rigidly
connected to beams from one side only such
as the edge columns. Columns with biaxial
eccentric loading are common in corner
columns with beam rigidly connected at
right angles on the top of the column.
Eccentrically loaded columns have to be
designed for combined axial force and
bending moments.
The design of member subjected to
combined axial load and bending will
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Journal for Studies in Management and Planning
Available at http://edupediapublications.org/journals/index.php/JSMaP/
e-ISSN: 2395-0463
Volume 02 Issue 10
October 2016
Available online:http://edupediapublications.org/journals/index.php/JSMaP/ P a g e | 162
involve lengthy calculation by trial and
error. In order to overcome these
difficulties, interaction diagram may be
used. Although the above statement refers
to design, it is equally valid in the case of
analysis. If an interaction diagram is
readily available for the given column
section, then the analysis problem simply
reduces to whether or not the point
corresponding to factored load effects (Pu,
Mu) lies within the envelope of the
interaction curve. Furthermore, the design
strength components (Pu, Mu) can be easily
read off from the interaction curve,
corresponding to any given eccentricity e,
or given Pu.
Literature Review:
The design of member subjected to
combined axial load and bending will
involve lengthy calculation by trial and
error. In order to overcome these
difficulties, interaction diagram may be
used. Although the above statement refers
to design, it is equally valid in the case of
analysis. If an interaction diagram is
readily available for the given column
section, then the analysis problem simply
reduces to whether or not the point
corresponding to factored load effects (Pu,
Mu) lies within the envelope of the
interaction curve. Furthermore, the design
strength components (Pu, Mu) can be easily
read off from the interaction curve,
corresponding to any given eccentricity e,
or given Pu. L N Rama Murthy
(1983)Their research presents two
methods to determine graphically the
ultimate loads in L shaped columns under
biaxial eccentricity. The first method is
based on the concept of failure surface in a
column and requires the determination of
the major axis interaction curve in an L- shaped column. In the second method it is
shown that the major axis interaction curve
for an L column can be obtained from an
equivalent square or rectangular column.
The second method is developed to replace
the first method which is cumbersome.
Experiments were done and it is found that
the experimental results and the theoretical
values of ‘R’ are in agreement and hence
this method can be used safely in design.
Cheng-tzu (1985): A computer analysis
model that simulate the load-deformation
and moment-curvature behavior of
reinforced concrete elements subject to
combined biaxial bending and axial load is
presented. Based on load and moment
increments, the algorithm enables
determination of ultimate strength,
interaction diagrams, load-deflection, and
moment-curvature relationships for
Page 3 of 6
Journal for Studies in Management and Planning
Available at http://edupediapublications.org/journals/index.php/JSMaP/
e-ISSN: 2395-0463
Volume 02 Issue 10
October 2016
Available online:http://edupediapublications.org/journals/index.php/JSMaP/ P a g e | 163
reinforced concrete columns with square,
rectangular, and L-shaped sections and any
material properties up to the maximum
moment capacity of the sections. Excellent
agreement was achieved between the
experimental strengths obtained from the
present tests and the analytical results
calculated using the computerprograms.
Objective of the Work:
The interaction diagrams for rectangular
and circular sections have been prepared
and published by BIS in SP: 16 “Design
aids for reinforced concrete to IS 456”. A
large number of charts have been
presented, covering various cases. The
design and analysis of non- rectangular
column sections like I, L, T and + by using
the method of analysis using basic
equations is laborious and time
consuming, hence their design and
analysis also require interaction diagrams.
SP: 16 does not provide interaction
diagrams for cross sections other than
rectangle andcircle. The objective of this
research is to develop interaction diagrams
for I and L shaped columns to serve as an
aid for their analysis and design. Another
objective is to find a relation between the
interaction values of an I section column
and L section column with the rectangular
column such that the analysis and design
are simplified because interaction
diagrams for rectangular columns are
easily available. The present investigation
can be extended to ‘T’ and ‘+’
shapedcolumns. It does not take into
account the effects of strength gain due to
confinement. Hence research can be done
on I and L shaped columns with confined
concrete.The interaction diagrams can be
extended to columns with
biaxialeccentricity.The slenderness effect
of long columns can be taken into account
and interaction diagrams can be drawn
considering the slendernesseffect.
Interaction diagrams for L shapedcolumn
Interaction charts for L shaped columns have been prepared by varying the following
parameters.
1) Cross-section of thecolumn:
2) Grade ofsteel:
3) Grade ofconcrete:
4) Coverconcrete:
