Analysis of Reinforced Beam-Column Joint Subjected to Monotonic Loading

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ISSN: 2277
-
3754


ISO 9001:2008 Certified


International Journal of Engineering and Innovative Technology (IJEIT)


Volume 2, Issue 10, April 2013



149

Analysis of
R
einforced Beam
-
C
olumn
J
oint
S
ubjected to Monotonic Loading

S. S. Patil,
S. S. Manekari


Abstract

-

The common regions of intersecti
ng elements are
called joints. W
henever the area of these regions is limited, as in
case of linear elements

(be
ams and columns) framing into each
other, it is essential to verify their
maximum shear stress
, as well
as the
minimum

shear stress and deformations (d
isplacements)

of
beam column joint
region. The various research studies
focused on corner and exterior be
am column joints and their
behavior, support conditions of beam
-
column joints i. e .both
ends hinged and fixed
, stiffness variation of the joint

.
In this
study various parameters are studied for monotonically loaded
exterior and corner reinforced concrete
beam column joint.
The

corner as well as exterior beam
-
column joint is analyzed with
varying stiffness of beam
-
column joint.
The

behavior of exterior
and corner beam
-
column joint subjected to monotonic loading is
differen
t.
Various

graphs like load vs.

dis
placement

(
deformations)
,

Maximum
stress,

Stiffness
variations i.
e
. joint
ratios of beam
-
column joints are plotted.


Index Terms

-

Corner and Exterior Joints, Joint Ratios,
Monotonic Load, Stiffness Variations.


I.
INTRODUCTION

Earthquakes are one of the m
ost feared natural
phenomena that are relatively unexpected and whose
impact is sudden due to the almost instantaneous
destruction that a major earthquake can produce.

Severity
of ground shaking at a given location during an earthquake
can be minor, modera
te and strong which relatively
speaking occur frequently, occasionally an rarely
respectively. Design and construction of a building to resist
the rare earthquake shaking that may come only once in
500 years or even once in 2000 years at a chosen project
s
ite even though life of the building itself may be only 50 to
100 years is too robust and also too expensive. Hence, the
main intention is to make building earthquake
-
resistant that
resist the effect of ground shaking although it may get
damaged severely b
ut would not collapse during even the
strong earthquake. Thus, the safety of people and contents
is assured in earthquake
-
resistant buildings. This is a major
objective of seismic design codes throughout the world.
The

performance of structures in earthqua
kes indicates that
most structures, system and components, if properly
designed and detailed, have a significant capacity to absorb
energy when deformed beyond their elastic limits.
Experience with the behavior of reinforced concrete beam
-
column joints in
actual earthquakes is limited. To fully
realize the benefits of ductile behavior of reinforced
concrete frame structures, instabilities due to large
deflections and brittle failure of structural elements must be
prevented under the most severe expected ear
thquake
ground motions.

II
.

LITERATURE REVIEW

As it is explained above the strength of beam
-
column
joint plays a very important role in the strength of the
structure, here the literature survey is carried out to have the
information about the Monotonic Lo
ading applied to the
beam
-
column joint. The literature review covers research
papers based on beam
-
column joints.

Vladmir Guilherne
Haach, Ana Lucia Home De Cresce El Debs, Mounir Khalil
El Debs
[1]

This paper investigates the influence of the
column axial
load on the joint shear strength through
numerical simulations. The numerical study is performed
through the software ABAQUS, based on Finite Element
Method. A comparison of the numerical and experimental
results is presented in order to validate the simul
ation. The
results showed that the column axial load made the joint
more stiff but also introduced stresses in the beam
longitudinal reinforcement. A more uniform stress
distribution in the joint region is obtained when the stirrup
ratio is increased. Furt
hermore, some tension from the top
beam longitudinal reinforcement is absorbed by the stirrups
located at the upper part of the joint. This paper gives the
affect of stirrup ratio to exterior beam
-
column joints where
the beam is loaded monotonically.
Hegge
r Josef,Sherif Alaa
and Roeser Wolfgang
[8]

here authors have carried out
Monotonic tests on beam
-
column joints which showed the
failure of the connection can either be in the beam(bending
failure) or inside the joint(shear and bond failures).The
behavior

o
f exterior beam
-
column joints is different from
that of interior connections. The model has been calibrated
using a database with more than 200 static load tests. The
reported test results as well as test results from the literature
were used to study the
behavior

of exterior and interior
beam
-
column connections. The shear strength of an exterior
beam
-
column connection decreases with increasing joint
slenderness.
Murty.C. V. R, Durgesh C. Rai, K. K. Bajpai,
and Sudhir K. Jain

[14]
described an experimental
study of
beam
-
column joints in frames common in pre
-
seismic
code/gravity
-
designed reinforced concrete (RC) frame
buildings. Exterior RC joint sub assemblages are studied
with four details of longitudinal beam bar anchorage and
three details of transverse j
oint reinforcement. All these
specimens showed low ductility and poor energy
dissipation with excessive shear cracking of the joint core.

Uma. S. R. and Meher Prasad
.
A

[15]

discussed

the general
behavior of common types of joints in reinforced concrete
mo
ment resisting frames. The mechanisms involved in joint
performance with respect to bond and shear transfer are
critically reviewed and discussed in detail. The factors
impacting the bond transfer within the joint appears to be
well related to the level o
f axial load and the amount of




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transverse reinforcements in the joints. The parameters that
affect the shear demand and shear strength of the joint are
explained. The design of shear reinforcement within the
joint and its detailing aspects are also discuss
ed.


III.
FRAMED JOINTS

Beam column joints can be critical regions in reinforced
concrete frames designed for inelastic response to severe
seismic attack. As a consequence of seismic moments in
columns of opposite signs immediately above and below
the joi
nt, the joint region is subjected to horizontal and
vertical shear forces whose magnitude is typically many
times higher than in the adjacent beams and columns. If not
designed for, joint shear failure can result.

DESIGN OF JOINTS


Joint types


According
to geometrical
con
figu
ration


Interior
,
Exterior
,
Corner


According to loading conditions and structural behavior

Type
-
I
,
Type
-
II

Interior joint
:
-

As shown in
Fig.
.1

An interior joint has
beams framing into all four sides of the joint. To be
classified as

an interior joint, the beam should cover at least
¾ the width of the column, and the total depth of shallowest
beam should not be less than ¾ the total depth of the
deepest beam
.


Fig.
1
Interior joint

Exterior Joint
:
-

As shown in
Fig.
.
2

An Exterior join
t has
at least two beams framing into opposite sides of the joint.
To be classified as an exterior joint, the widths of the beams
on the two opposite faces of the joint should cover at least
¾ the width of the column, and the depths of these two
beams shou
ld not be less than ¾ the total depth of deepest
beam framing in to the joint.


Fig
. 2
Exterior
Joint

Corner Joint
:
-

As shown in
Fig.
.
3
A Corner joint has at
least one beam framing into the side of the joint. To be
classified as a corner joint, the widt
hs of the beam on the
face of the joint should cover at least ¾ the width of the
column.


Fig.
3

Corner joint

Type1
-

S
tatic loading

Strength important
,

Ductility secondary

A type
-
1 joint connects members in an ordinary structure
designed on the basis of s
trength, to resist the gravity and
wind load.


Type2
-
E
arthquake and blast loading

Ductility +

strength
,
inelastic

range of deformation
,
Stress
reversal

A type
-
2 joint connects members designed to have
sustained strength under deformation reversals into the

inelastic range, such as members designed for earthquake
motions, very high wind loads, or blast effects.


Fig. 4 Typical

Beam Column Connections

Joint loads and resulting forces:

As shown in
Fig.
5
The
joint region must be designed to resist forces that
the beam
and column transfer to the joint, including axial loads,
bending moment, torsion, and shear force.
Fig.
ure3.7 (a)
shows the joint loads acting on the free body of a typical
joint of a frame subjected to gravity loads, with moments
M
1
and M
2

acting

on the opposite sides, in the opposing
sense.


Fig
. 5
Joint
Loads
and

Resulting Forces
from

Gravity Forces

These moments will be unequal, with their difference
equilibrated by the sum of column moments M
3

and M
4
.




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Fig.
ure 3.7 (b) shows the resulting for
ces to be transmitted
through the joint.

The joint shear on plane passing through
the center of the joint is

V
u
= T
1


T
2


V
3


Fig
.6
Joint
Loads and Resulting Forces from Lateral Forces

Above
Fig.
6

(a) shows the loads acing on a joint in a
structure su
bjected to sideway loading.
Fig.
6

(b) shows the
resulting internal forces. Only for heavy lateral loading,
such as from seismic forces, would the moments acting on
opposite faces of the joint acting in the same sense,
producing very high horizontal shear w
ithin the
joint
.

The

joint shear on plane passing through the center of the joint
is

V
u
= T
1
+ C
2


V
3

V
u
= T
1
+ T
2


V
3



(C
2

= T
2
)


Joint confinement
:
-


b
b,x
≥ 0.75 b
c,x


b
b,
y

≥ 0.75 b
c,
y

b
b,
y

≥ 0.75 b
c,
y


Fig
. 7
Plan
View of Interior Joint with Beams in
X
and
Y
Direction Providing Confinement


Fig
. 8
Plan

View of
Exterior
Joint with Beams in
X
and
Y
Direction Providing Confinement

IV
.

LOADING SYSTEMS

The s
tructures are being imposed by many loads e.g.
dead load, live load, imposed(wind) load, snow load,
earthquake load etc. The structures have to be designed in
such a way that they can bear these loads to overcome the
collapse or failure of the structures.
Today the earthquake
resistant structures are being designed more widely. To
understand the behavior of the structures in the earthquake,
the researchers are applying cyclic loading to the building
in the laboratory.


Types of Loading systems
:
-

The
behavio
r

of building is studied with different types of
loads
.

1)

Static
loading:
-

Static means slow loading in structural

testing.

Test of components
:
-
Beams(bending),column
(axial),beams and columns


Purpose of testing
:
-

Determine strength limits



Determine the f
lexibility/rigidity of structures

2)

Quasi
-
static loading
:
-

Very slowly applied loading in
one direction (monotonic)

3)

Quasi
-
static reversed cyclic loading
:
-
Very slowly
applied loading in both direction (cyclic)

4) Dynamic (random) loading
:
-

Shake at the
base or any
other elevation of the structure

s
haking similar to that
during earthquakes.

Monotonic Loading

The Monotonic loading can be defined as very slowly
applied loading in one direction it may be in upward or
downward direction. In Monotonic loading
for the failure of
the member the load is maximum

. Therefore, the structures
must be designed for monotonic loading. If the structures
are designed as per monotonic loading, the structures are
safe in other loading systems.


Fig
. 9
Bond
Slips Relationsh
ip of Deformed Bars






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V
.

FINITE ELEMENT ANALYSIS

The Finite Element Analysis is a numerical technique in
which all complexities of the problems varying shape,
boundary conditions and loads are maintained as they are
but the solutions obtained are approximat
e. Solutions can
be obtained for all problems by Finite Element
Analysis
.
Various steps involved in FEM are as follows.

1. Selection of field variables and the elements.

2. Discretization of structure.

3. Finding the element properties

4. Assembling element

stiffness matrix

5. Solution of nodal unknown

FINITE ELEMENT MODELING & ANALYSIS

Ansys software has been used for conducting the finite
element analysis of the Concrete Beam Column Joint.
Ansys has many features which help to carry out detail
ed
study for such kind of complex problems.


ELEMENT TYPE USED


:

As shown in
Fig.
1
0
Reinforced Concrete

An eight
-
node solid element, Solid65,
was used to model the concrete. The solid element has eight
nodes with three degrees of freedom at each nod
e


translations in the nodal x, y, and z directions. The element
is capable of plastic deformation, cracking in three
orthogonal directions, and crushing. The geometry and
node locations for this element type are shown in below.


Fig
.10
Solid65


3
-
D
Rei
nforced Concrete Solid (
ANSYS
1998)

A Link8 element is used to model the steel reinforcement.
Two nodes are required for this element. Each node has
three degrees of freedom,


translations in the nodal x, y,
and z directions. The element is also capable o
f plastic
deformation. The geometry and node locations for this
element type are shown in
Fig.
ure below.


MATERIAL
PROPERTIES:

Concrete
:
-

As shown in
Fig.
1
1
Development of a model for the behavior of concrete
is a challenging task. Concrete is a quasi
-
bri
ttle material
and has different behavior in compression and tension. The
tensile strength of concrete is typically 8
-
15% of the
compressive strength (Shah, et al. 1995).
Fig.
ure below
shows a typical stress
-
strain curve for normal weight
concrete (Bangash
1989).


Fig
.11
Typical
Uniaxial Compressive
and

Tensile Stress
-
Strain
Curve For concrete (
Bangash
1989)

In compression, the stress
-
strain curve for concrete is
linearly elastic up to about 30 percent of the maximum
compressive strength. Above this point,
the stress increases
gradually up to the maximum compressive strength. After it
re
aches the maximum compressive strength σ
cu
, the curve
descends into a softening region, and eventually crushing
failure occurs at an ultimate strain ε
cu
. In tension, the stress
-
strain curve for concrete is approximately linearly elastic up
to the maximum

tensile strength. After this point, the
concrete cracks and the strength decreases gradually to zero
(Bangash 1989).

Steel Reinforced Concrete [Smeared
Model] Material Propertie
s:
-

In this project the structure
has been modeled using Steel Reinforced Conc
rete. The
material properties mentioned below act equivalent for a
Smeared Reinforcement concrete model using solid 65
elements

in Ansys. Many research papers have been
published using similar kind of model. Broujerdian et. al
(2010) have worked using a si
milar approach. The used of
these features

enables obtaining good results with
fewer
solvers

and modeling time.



VI
.

PROBLEM STATEMENT




Problem Definition



A ground plus five Storey RC office building is
considered.



Plan dimensions
:
12 m x 12 m



Location considered
:
Zone
-
III






Soil Type cons
idered
:

Rock Soil







General Data of Building:



Grade
of concrete


:

M 20



Grade of ste
el considered



:

Fe 250, Fe 415



Live load on roof:

2 KN/m
2
(Nil for earthquake)



Live
load on floors

: 4 KN/m
2




Roof finish



: 1.0 KN/m
2





F
loor finish



: 1.0 KN/m
2



Brick wall in longitudinal direction : 250 m
m
thick



Brick wall in transverse direction

: 150 mm
thick



Beam in longitud
inal direction

: 230X300 mm



Beam in transvers
e direction

: 230X300 mm



Column size



: 300X600 mm



Density

of concrete


: 25 KN/m
3










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Density of
brick wall including plaster :


20
KN/m
3



Plinth beam(PB1)




: 350X250 mm



Plinth beam(PB2)


: 250X300 mm


Analysis:
-



1)

Ansys Sof
tware


(

Non
-
Linear finite element




Analysis
)

:



The exterior and corner beam
-
column joint to be





Analyzed

in the Ansys FEM Software.



Fig
.12
Dimensional
View Showing Exterior and Corner Beam
-
Column Joint

2
) Ansys

Analysis
: From


As shown in
Fig.

1
3

Once the reinforcement detailing of the beam and
column is known the exterior beam
-
column joint is
modeled in Ansys FEM Software. Non
-
linear analysis of
exterior and corner joint is carried out with 6 load step and
30
iterations in each load step. The mesh size of 80 mm is
taken for macro
-
elements in concrete part of the beam and
column. The exterior beam
-
column joint is modeled and a
monotonic loading of 5 KN is applied at the tip of the beam
till the failure of the be
am takes place. The application of
the monotonic loading is shown in
Fig

13.
The
behavior

of
this joint is studied with different parameters
.


Fig.

13

Application of the Monotonic loading to exterior joint


VII
.
FINITE

ELEMENT MODELLING AND

ANALYSIS

OF

BE
AM
-
COLUMN JOINTS

As shown in
Fig.

1
4

the

exterior and corner beam
-
column joint is considered to study joint behavior subjected
to monotonic loading. Preparation of FE model is carried
out based on results obtained from space frame analysis of
a building lo
cated in zone
-
III. Model construction is done
by defining geometrical joints and lines. Material definition
is carried out prior to assigning of macro elements. The
joint is fully restrained at the column ends. The load is
applied at the tip of the beam in

one direction.



Fig
. 14
Test Specimen
Arrangement

Modeling Arrangement
:
-
The test specimen arrangement
is shown in
Fig.
14

the

mesh was generated using a
preprocessor. The corner of the macro elements were user
-
defined and then filled by automatic mesh ge
neration.
These were arranged to keep the mesh as regular as
possible, with a maximum element aspect ratio of 2.The
loading and boundary constraints were then applied to the
macro element nodes as shown in
Fig.

15


Fig.

15 General

model layout showing bou
ndary conditions

Reinforcing bar anchorage
:
-
To study the effect of
reinforcing bars on joint
behavior
, smeared bars were
specified for all of the reinforcement within the model. The
anchorage of the beam tension bar is one of the main
contributors to joint

behavior
. The anchorage
behavior

is
significantly affected by the material model of the element
in which the bar is embedded, and more importantly, any
additional reinforcing bars within the element.

Boundary
conditions
:
-

As shown in
Fig.
.1
5
Modeling of t
he boundary
conditions is often the most critical aspect in achieving
sensible, reliable data from a finite element model. In the
test specimens, the critical zones (around the joint) were far
from the applied boundary constraints (edge of the
model).Accur
ate boundary constraints however, still
required.

The column connections were modeled as hinged
supports attached to a single node to allow full rotation.
Column end caps, used to support and restrain the test
specimens in the loading frame, were included
in the model
to allow the effective length of the column to be modeled
correctly. The material for the end caps had a higher
ultimate capacity, but had a similar stiffness to the concrete
to reduce restraint in the adjacent elements.
Mesh




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arrangement
:
-

A s
ingle mesh arrangement was developed
for use with the bent down bar

anchorage.







Fig.16 modeling

of corner beam

column joints in the Ansys.



Fig.17 Modeling

of Exterior beam column joints in the Ansys

VIII
.

RESULTS AND DISCUSSIONS

Parametric
Study
:
-
The exterior and corner beam
-
column
joints are studied with different parameters like i.e.
Maximum principle stress, Minimum principle stress,
Displacement, Deformation also studied end conditions of
beam column j
oint i.e. fixed end conditions, Hinge end
conditions and Stiffness variation of beam column joint i.e.
Corner and Exterior joint subjected to monotonic loading.


Fig.

18 Case

No
.(1) Corner Beam
-
column Joint.


Fig.
19
Case No.(2) Exterior Beam
-
column Joint
.

1. Corner

beam column joint
(Hinge

Condition)

the
dimensions are provided as below.



Beam size

230mm X 300mm

Column size


230mm X 600mm




Table I




Load
in KN

Displacement in
mm

Mini. Stress
in N/mm
2

Maxi.
Stres
s

in N/mm
2

5

0.613871

-
0.403609

0.34717

10

1.75262

-
7.09

4.14598

15

1.9085

-
7.46933

4.58003

20

2.0533

-
9.14242

7.79495

25

2.30366

-
9.87

7.87493

30

2.59696

-
14.9082

9.97489



Fig.20

Load Vs Maximum Deformation, Minimum Stress,
Maximum Stress Graph

2
. Exterior

beam column joint (
Hinge conditions)

the
dimensions are provided as below.

Beam


230 mm x 300 mm

Column

230 mm x 600 mm





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Table II

Load
in kN

Displacement

(mm)

Mini. Stress
N/mm
2

Maxi. Stress

in N/mm
2

5

0.792331

-
0.88596

0.432535

10

1.92308

-
4.77346

5.60122

15

2.1009

-
6.77345

5.62132

20

2.19251

-
11.7367

10.6008

25

2.38355

-
14.8968

14.405

30

2.55905

-
17.9068

17.6008



Fig.21 Load Vs Maximumdeformation, Minimum Stress,
Maximum Stress Graph

3.

Fixed support conditions for corner beam colum
n
joint
the dimensions are provided as below.




Beam 230 mm x 300 mm

Column 230 mm x 600 mm


Table III

Load in
KN

Displacement
in mm

Mini. Stress in
N/mm
2

Maxi. Stress

in N/mm
2

5

2.72677

-
1.00969

6.27466

10

2.
8003

-
2.47423

7.03936

15

2.88495

-
3.791

8.19089

20

2.9633

-
4.793

8.89089

25

3.2035

-
5.4371

9.5062

30

3.6075

-
7.951

14.9088


Fig.22

Load Vs Maximum Deformation, Minimum Stress,
Maximum Stress Graph

4. Fixed

support conditions for Exterior beam column
joint
the

dimensions are provided as below.


Beam

230mmx 300mm

Column
230mmx 600mm

Table IV

Load in
KN

Displacement
in mm

Mini. Stress
in N/mm
2

Maxi. Stress

in N/mm
2

5

0.499

-
1.7309

1.53771

10

1.205

-
1
.9875

2.47114

15

1.558

-
4.04003

2.69536

20

1.832

-
4.90289

4.74555

25

2.157

-
5.4525

5.6299

30

2.308

-
9.1298

7.47541


Fig.23 Load Vs Maximum Deformation, Minimum Stress,
Maximum Stress Graph

5.
Corner beam column joint with varying stiffness

the
dimensi
ons are provided as below.



Case NO 1

Beam 230mm X 375mm

Column 230mm X 600mm


Stiffness
of beam:

K
B
=

252685.54 mm
3


Stiffness
of Column:

Kc =1380000 mm
3


Stiffness
of Joint
: Kj = K
B
/ Kc



= 252685.54 / 1380000


= 0.18

Table V

Load in
KN

Displacement in
mm

Mini. Stress
in N/mm
2

Maxi. Stress

in N/mm
2

5

0.4172

-
0.931495

0.303477

10

0.8344

-
3.92411

2.20581

15

1.6689

-
4.00092

2.22582

20

3.3478

-
6.00393

3.774
46

25

3.6889

-
6.94422

4.6321

30

3.983

-
7.60862

6.17119


Fig.24 Load Vs Maximum Deformation, Minimum Stress,
Maximum Stress Graph

6. Exterior

beam column joint with varying stiffness

the
dimensions are provided as below.







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Case NO 1

Beam

230mm X 450mm

Column 230mm X 375mm

Stiffness of
beam:

K
B
= 436640.62 mm
3

Stiffness of
Column:

Kc = 336914.06 mm
3

Stiffness
of Joint
: Kj = K
B
/ Kc


= 436640.62/336914.06


= 1.29


Fig. 25 Load Vs Maximum Deformation, Minimum Stress,
Maximum Stress Graph

7
.
Variation in stiffness of corner beam column joint

Table VII

Load
in
KN

Displace

ment in
mm

Displace
ment in
mm

Displacem
ent in mm

Displaceme
nt in mm



Sj=0.18

Sj=1.29

Sj=2.05

Sj=
0.75

5

0.4172

0.34116

0.274849

0.5875

10

0.8344

0.68233

0.549698

1.175

15

1.6689

1.36467

1.099396

1.3512

20

3.3478

2.7293

1.319256

1.6215

25

3.6889

3.4095

1.649056

2.0268

30

3.983

4.4295

2.141056

2.6346


Fig. 26 Load Vs Maximum Deformation

8
.

Varia
tion in stiffness of corner beam column joint

Table VIII

Load
in KN

Mini.
Stress in
N/mm
2

Mini.

Stress in
N/mm
2

Mini.

Stress

In N/mm
2

Mini.

Stress

In N/mm
2


Sj=0.18

Sj=1.29

Sj=2.05

Sj=0.75

5

-
0.931495

-
0.889535

-
0.922823

-
0.035402

10

-
3.92411

-
1.21114

-
1.33809

-
0.88506

15

-
4.00092

-
2.12256

-
1.53242

-
1.77012

20

-
6.00393

-
2.13257

-
1.56506

-
2.27215

25

-
6.94422

-
2.33399

-
1.66497

-
2.30116

30

-
7.60862

-
2.34361

-
1.8868

-
3.2847


Fig. 27


Load Vs Minimum Stress Graph

9
.

Variation in stiffness of corner bea
m column joint

Table IX

Load
in KN

Maxi.
Stress


in N/mm
2

Maxi.
Stress


in N/mm
2

Maxi.
Stress

in N/mm
2

Maxi.
Stress in
N/mm
2



Sj=0.18

Sj=1.29

Sj=2.05

Sj=0.75

5

0.303477

0.3956

0.389974

0.008042

10

2.20581

1.66923

0.585308

0.201056

15

2.22582

1.67924

1.15246

0.402113

20

3.77446

1.96634

1.20463

1.21377

25

4.6321

2.93769

1.29138

1.23761

30

6.17119

6.50058

2.3821

4.01801


Fig. 28 Load Vs Maximum Stress Graph

10.

Variation in stiffness of Exterior beam column joint:
-

Table X

Loa
d in
KN

Displacem
ent
in mm

Displacem
ent in mm

Displacem
ent

in mm

Displace
ment in
mm



Sj=1.29

Sj=2.05

Sj=0.75

Sj=0.18

5

0.604115

0.60052

0.213883

0.507809

10

1.20823

1.20104

0.427767

1.0156

15

2.41646

1.38119

0.641712

1.16794

20

2.8996

1.6571

1.81128

1.40134

25

3.6244

2
.0714

2.12017

1.75134

30

3.9248

2.6927

2.60442

2.27664






ISSN: 2277
-
3754


ISO 9001:2008 Certified


International Journal of Engineering and Innovative Technology (IJEIT)


Volume 2, Issue 10, April 2013



157




Fig. 29load Vs Displacement Graph

11.

.Variation in stiffness of Exterior beam column joint:
-

Table XI

Load
in

KN

Mini. Stress
in N/mm
2

Mini.
Stress in
N/mm
2

Mini.
Stress in
N/mm
2

Mini.
Stress

in
N/mm
2



Sj=1.29

Sj=2.05

Sj=0.75

Sj=0.18

5

-
0.858169

-
2.09364

-
0.429264

-
0.88953

10

-
1.71634

-
3.06832

-
0.858527

-
2.25308

15

-
2.33399

-
4.05034

-
1.397001

-
2.68991

20

-
2.60959

-
4.899265

-
1.57095

-
2.88285

25

-
2.97925

-
5.79853

-
2.13031

-
3.91109

30

-
5.
54457

-
6.09465

-
2.83467

-
4.5792


Fig.30 Load Vs Minimum Stress Graph

12
.

Variation in stiffness of Exterior beam column joint:
-

Table XI
I

Load
in
KN

Maxi.
Stress in
N/mm
2

Maxi.

Stress in
N/mm
2

Maxi.
Stress

in N/mm
2

Maxi.
Stress

in N/mm
2



Sj=1.29

Sj=2.0
5

Sj=0.75

Sj=0.18

5

1.5166

0.67842

1.3244

2.18446

10

3.0332

3.00113

2.64879

3.8436

15

4.543

3.2643

3.55204

4.4024

20

6.5429

3.50445

7.08526

6.82696

25

8.0439

4.00889

8.40464

7.9676

30

10.0439

4.678425

9.2199

9.9624


Fig. 31 Load Vs Maximum Stress G
raph

IX.

CONCLUSION

1)
As
load


increases displacement, minimum stress and
maximum stress also increases.

2)
For fixed support condition for corner and exterior joint
the
displacement,

minimum stress and maximum stress
values
are minimum

as compare to hin
ge

support condition.

3)
The behavior of corner beam column joint is different
than that of the exterior beam column joint.

4)
For stiffness variation of corner joint for Sj=0.18 t
he
displacement is minimum as compare to Sj=1.29, Sj=2.05,
Sj=0.75
.

5)

For s
tiffness variation of corner joint for Sj=0.18 the
minimum stress is more as compare to Sj=1.29 and
Sj=2.05,

for Sj=0.75 the minimum stress is maximum as
compare to Sj=
0.18.

6)
For stiffness variation of corner joint for Sj=0.18 the

maximum stress is more
as compare to
Sj=1.29

and
Sj=2.05
, for

Sj=0.75

the maximum stress is maximum as
compare to
Sj=0.18.

7)
For stiffness variation of

Exterior joint for
Sj=1.29

the
displacement is minimum as compare to
Sj=2.05
,

for
Sj=0.75

and for
Sj=0.18

the displacement is
maximum as
compare to
Sj=1.29
.

8)
For stiffness variation of

Exterior joint for
Sj=1.29

the
minimum stress is more as compare to
Sj=2.05

and

Sj=0.75
, for

Sj=0.18

the minimum stress is more as

compare to
Sj=1.29
.

9)
For stiffness variation of

Exterior j
oint for
Sj=1.29

the
maximum stress is less as compare to
Sj=2.05
.for
remaining stiffness
Sj=0.75

and

Sj=0.18

the maximum
stress is less.


(Minimum)

10)
As stiffness of the structure changes the displacement,
minimum stress and maximum stress changes No
n
-
linearly.

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[1]

Vladimir Guilherma
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El

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ISSN: 2277
-
3754


ISO 9001:2008 Certified


International Journal of Engineering and Innovative Technology (IJEIT)


Volume 2, Issue 10, April 2013



158

[5]

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AUTHOR BIOGRAPHY





Prof.
Patil S

.S.
.

B.E. (Civil), M.E. (Civil
-

Structures)

, Phd.

ISSE( LM )

Is the professor &
Head of

civil/Structural Engineering Dept.

WIT Solapur.( M.S.) INDIA




Mr.
Manekari S.S.

B.E. (Civil), M.E. (Civil
-

Structures)
, ISSE (LM)
M .E. Student of WIT

Solapur.( M.S.) INDIA