Analysis of Reinforced Beam-Column Joint Subjected to ... 2/Issue 10/IJEIT1412201304_30.pdf ·...

ISSN: 2277-3754

ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT)

Volume 2, Issue 10, April 2013

149

Analysis of Reinforced Beam-Column Joint

Subjected to Monotonic Loading S. S. Patil, S. S. Manekari

Abstract - The common regions of intersecting elements are

called joints. Whenever the area of these regions is limited, as in

case of linear elements (beams and columns) framing into each

other, it is essential to verify their maximum shear stress, as well

as the minimum shear stress and deformations (displacements)

of beam column joint region. The various research studies

focused on corner and exterior beam 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

different. Various graphs like load vs. displacement

(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 most 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, moderate 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

site 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 but 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 earthquakes 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 earthquake

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 Loading 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 simulation. 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. Furthermore, 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. Hegger 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 of 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 joint 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

moment 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 of 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 discussed.

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 joint, 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 configuration

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 joint 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 should 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 widths of the beam on the

face of the joint should cover at least ¾ the width of the

column.

Fig. 3 Corner joint

Type1- Static loading Strength important, Ductility secondary

A type-1 joint connects members in an ordinary structure

designed on the basis of strength, to resist the gravity and

wind load.

Type2-Earthquake 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

M1 and M2 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 M3 and M4.

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Fig.ure 3.7 (b) shows the resulting forces to be transmitted

through the joint. The joint shear on plane passing through

the center of the joint is

Vu = T1 – T2 – V3

Fig.6 Joint Loads and Resulting Forces from Lateral Forces

Above Fig.6 (a) shows the loads acing on a joint in a

structure subjected 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 within the joint. The joint shear on plane passing through the center of the joint

is

Vu = T1 + C2 – V3

Vu = T1 + T2 – V3 (C2 = T2)

Joint confinement:-

bb,x ≥ 0.75 bc,x

bb,y ≥ 0.75 bc,y

bb,y ≥ 0.75 bc,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 structures 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 behavior 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 flexibility/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 shaking 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 Relationship 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 approximate. 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 detailed

study for such kind of complex problems.

ELEMENT TYPE USED : As shown in Fig.10

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 node –

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 Reinforced 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 of plastic

deformation. The geometry and node locations for this

element type are shown in Fig.ure below.

MATERIAL PROPERTIES: Concrete: - As shown in Fig.11Development of a model for the behavior of concrete

is a challenging task. Concrete is a quasi-brittle 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

reaches the maximum compressive strength σcu

, the curve

descends into a softening region, and eventually crushing

failure occurs at an ultimate strain εcu

. 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 Properties:- In this project the structure

has been modeled using Steel Reinforced Concrete. 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 similar 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 considered: Rock Soil

General Data of Building:

• Grade of concrete : M 20 • Grade of steel considered : Fe 250, Fe 415 • Live load on roof: 2 KN/m2 (Nil for earthquake) • Live load on floors : 4 KN/m2 • Roof finish : 1.0 KN/m2 • Floor finish : 1.0 KN/m2 • Brick wall in longitudinal direction : 250 mm

thick

• Brick wall in transverse direction : 150 mm thick

• Beam in longitudinal direction : 230X300 mm • Beam in transverse direction : 230X300 mm • Column size : 300X600 mm • Density of concrete : 25 KN/m3

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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 Software

( 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. 13 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 beam 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 BEAM-COLUMN JOINTS

As shown in Fig. 14 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 located 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 generation.

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 boundary 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..15 Modeling of the 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).Accurate 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 single 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 joint 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/mm2

Maxi.

Stress

in N/mm2

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


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/mm2

Maxi. Stress

in N/mm2

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,


3. Fixed support conditions for corner beam column 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/mm2

Maxi. Stress

in N/mm2

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



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/mm2

Maxi. Stress

in N/mm2

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



5.Corner beam column joint with varying stiffness the


Case NO 1 Beam 230mm X 375mm

Column 230mm X 600mm

Stiffness of beam: KB = 252685.54 mm3

Stiffness of Column: Kc =1380000 mm3

Stiffness of Joint: Kj = KB/ Kc

= 252685.54 / 1380000

= 0.18

Table V

Load in

KN

Displacement in

mm

Mini. Stress

in N/mm2

Maxi. Stress

in N/mm2

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 3.77446

25 3.6889 -6.94422 4.6321

30 3.983 -7.60862 6.17119



6. Exterior beam column joint with varying stiffness the


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Case NO 1 Beam 230mm X 450mm

Column 230mm X 375mm

Stiffness of beam: KB = 436640.62 mm3

Stiffness of Column: Kc = 336914.06 mm3

Stiffness of Joint: Kj = KB/ Kc

= 436640.62/336914.06

= 1.29

Fig. 25 Load Vs Maximum Deformation, Minimum Stress,


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


Table VIII

Load

in KN

Mini.

Stress in

N/mm2

Mini.

Stress in

N/mm2

Mini.

Stress

In N/mm2

Mini.

Stress

In N/mm2

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


Table IX

Load

in KN

Maxi.

Stress

in N/mm2

Maxi.

Stress

in N/mm2

Maxi.

Stress

in N/mm2

Maxi.

Stress in

N/mm2

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

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Fig. 29load Vs Displacement Graph

11. .Variation in stiffness of Exterior beam column joint:-

Table XI

Load

in

KN

Mini. Stress

in N/mm2

Mini.

Stress in

N/mm2

Mini.

Stress in

N/mm2

Mini.

Stress in

N/mm2

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 XII

Load

in

KN

Maxi.

Stress in

N/mm2

Maxi.

Stress in

N/mm2

Maxi.

Stress

in N/mm2

Maxi.

Stress

in N/mm2

Sj=1.29 Sj=2.05 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 Graph

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 hinge 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 the

displacement is minimum as compare to Sj=1.29, Sj=2.05,

Sj=0.75.


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.


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.


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.


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 Non-linearly.

REFERENCES

[1] Vladimir Guilherma Haach, Ana Lucia Home De Cresce El Debs and Mounir Khalil El Debs “Evaluation of the

influence of the column axial load on the behavior of

monotonically loaded R/C exterior beam-column joints

through Numerical simulations “Engineering Structures pp

965-975. (2008).

[2] A. El-Nabawy Atta, S. El-Din Fahmy Taher, A.-H. A. Khalil and S. El-Din El-Metwally “Behavior of reinforced high-

strength concrete beam-column joint.Part1: experimental

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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

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