ANALYSIS OF CORNER BEAM-COLUMN JUNCTION WITH INCLUSION OF THE EFFECT OF CONSTRUCTION JOINTS

ABSTRUCT This paper describes a comparison between beam-column junctions with and without construction joint, also, a parametric study deals with construction joint is presented by taking various conditions of the junction. These include the various positions of the construction joint, the axial load on the column, strength of concrete in the second cast and the amount of dowels crossing the joint. By developing a computer program which was originally written by Dr. Ihsan Al-Shaarbaf (1990), (P3DNFEA, program of three dimensional nonlinear finite element analysis), to consider the effect of construction joint depending on the fact that the shear force can be transmitted across the shear plane either by interlocking of the aggregate particles protruding from each face or by dowel action of the reinforcement crossing the cracks by using Fronteddu’s and Millard’s models, respectively. It is concluded that the construction joints existed in the beam-column junctions result in a significant reduction in the in-plane shear stiffness and it would affect only on the rotation and shear strains of the joint.


INTRODUCTION
The junctions studied are made of two pours, this results in a cold joint.The existence of a cold joint means that the specimens simulate construction practice.In addition to the overall behaviour of the beam-column junction during each stage of loading, it is important to note the mode of failure in this region.Five different modes of failure are possible in the beam-column connection, these include the following:

1)
Hinging of the beams at the connection,

MATERIAL MODELLING
In addition to the original three-dimensional computational model of P3DNFEA, the models used in the present study and incorporated in the present developed program are as follows: 1) Theoretical Aggregate Interlock Models 2) Theoretical Dowel Action Models

ORIGINAL THREE-DIMENSIONAL COMPUTATIONAL MODEL
The 3-D computational model of original computer program, P3DNFEA is now described.
The behaviour of concrete is simulated by using 20-noded brick elements.An elasto-plastic work hardening model followed by a perfectly plastic response, which is terminated at the onset of crushing is adopted for concrete in compression.The plasticity model was illustrated in terms of the following constituents: 1) The yield criterion of two stress invariants (Cervenka (1985)).
In tension, a smeared crack model with fixed orthogonal cracks is used (Rashid (1968)).The reinforcing bars are idealized as axial members embedded within the brick elements, the elasticperfectly plastic relation which ignores the strain-hardening region is used.

THEORETICAL AGGREGATE INTERLOCK MODELS
Several models have been proposed to explain or predict the aggregate interlock behaviour.The twophase model by Walraven and Reinhardt (1981) where µ b = 0.950 -0.220 σ n for σ n ≤ 0.5 Mpa

THEORETICAL DOWEL ACTION MODELS
Shearing forces can be transmitted across a crack in the reinforced concrete by the reinforcement crossing the crack.If the reinforcement is normal to the plane of cracking, dowel action (shearing and flexure of the bars) will contribute to the overall shear stiffness.
It has been suggested (Paulay et al. (1974)) that there are three mechanisms of shear transfer through the dowel action in cracked reinforced concrete, i.e. direct shear, kinking and flexure of the bars.If the concrete supporting each bar were considered to be rigid, the first two mechanisms would predominate.However, it has been recognized (Mills (1975)) that significant deformation of the concrete does occur, so that flexure of the dowel bar within the concrete is a principal action.This has been modelled (Millard (1984)) by considering the dowel bar as a beam on elastic foundation.This model is adopted, according to this model the dowel force, F d is given by: where the constant term is dimensionless Gf: foundation modulus for concrete, A typical value for 35 MPa concrete has been found to be 750 N/mm 3 (ACI Committee 325).For the high strength mix, it has been assumed that Gf α f cu 0.5 .
Φ: diameter of the bar.
E s : elastic modulus of steel.
∆ t : slip or relative displacement across the crack.
Only the initial dowel stiffness can be predicted using this equation.The nonlinear shear stiffness of the dowel action may be attributed to one or both of the following two causes.
1) Crushing or splitting of the concrete supporting the bar.
2) Plastic yielding of the reinforcement.
A good prediction of the ultimate shearing force in a bar with an axial stress of αf y is given by: where Fdu is the ultimate dowel force.
An exponential function was used to describe the overall dowel action behaviour.The dowel force, F d , is as follows: where ki is the initial dowel stiffness given by Eq.( 3).By simplifying Eq.( 5), the shear stiffness of the dowel action which is used in the present study as a relationship between the shearing stress and shear strain can be found as follows: where t is the effective thickness of the Gaussian point of the interface element (next section), A c is the contact area.

FINITE ELEMENT IDEALIZATION OF INTERFACE REGION
An isoparametric finite element formulation, which is treated essentially like a solid element, can be used in the present study to represent the behaviour of the interface region (Desai and Zaman (1984)), Fig.
(3).Since the element is treated essentially like any other solid element, its incremental stressstrain relationship is expressed as: where [D] i is the constitutive matrix for the interface region.The behaviour of the interface material is assumed to be like the concrete of the softer material properties for all stages of loading except the shear component which represents the shear behaviour specified for the interface region, (G t , is the shear component represents the combination effects of aggregate interlock and dowel action), the constitutive matrix for the interface element can be written as: The interface behaviour depends on the properties of the surrounding media.However, it also depends on the thickness of the thin-layer element.If the thickness is too large in comparison with the average contact dimension (B), of the surrounding element, the thin-layer element will behave essentially as a solid element.On the other hand, if it is too small, computational difficulties may arise.Based on the available experimental results, the satisfactory simulation of the interface behaviour can be obtained for (t / B) ratios in the range from (0.01) to (0.1).This conclusion may need modification if the nonlinear behaviour of solids and interfaces were simulated.The 20-noded isoparametric brick element is used.

SARSAM'S SPECIMENS
Nine specimens of beam-column joints (5 exterior, and 4 interior) were tested by Sarsam (1983), the plane exterior ones-EX series were made of two pours.The first pour was made on the first day.This (3), (4), respectively.The column was first loaded to a predetermined value of (Nc), prior to any beam loading, the next stage involved loading the beam up to ultimate load.The numerical analysis is done using KT2a method, with a tolerance of 5% on the displacement convergence criterion.

1473
The concrete of specimens EX1 and EX3 are idealized by using 58 20-noded brick elements (including 1 interface element at the top level of the joint), and 37 20-noded brick elements (including 1 interface element at the top level of the joint), respectively (for half of these specimens), Fig.
(5).To simulate the procedure of loading that occurred during the experimental test, the column axial load has been firstly applied in equal increments of 10% of the maximum column load for two specimens.
Later, for EX1 two different sizes of increments have been used for beam loading.The beam was loaded initially by increments of 3.75kN up to 75% of the expected collapse load (40kN).Then reduced increments of 1.43kN each were applied until the failure load has been reached.While for EX3 the beam load has been applied in equal increments of 12.5% of the expected collapse load (80 kN).Both the initial and post-cracking stiffness are reasonably predicted for two specimens, Table (3), Table

Analysis of the Specimens
In order to analyze the two specimens, the effect of the thickness of interface element must be examined.For EX1 specimen, numerical tests with values of the thickness (t) equal to 0.014mm, 0.14mm, and 1.4mm have been carried out.The results show that the type of failure of the specimen EX1 is beam hinging in the range of (0.014-0.14)mm for thickness of interface element, Fig.( 6).A response stiffer than the experimental results was obtained when the thickness is reduced within the range, and the best fit to the experimental results was obtained at t=0.14mm with effective thickness of Gaussian point of 0.038mm, in which the effect of non-linearities along the loading stages is clear.
The failure load of numerical results is 37.5kN while the failure load of experimental results is 36.04kN,so that the error ratio is 3.9%.While for EX3 specimen, numerical tests with values of the thickness (t) equal to 0.0014mm, 0.014mm, and 0.14mm have been carried out.The results show that the type of failure of the specimen EX3 is beam hinging in the range of (0.0014-0.014)mm for thickness of interface element, Fig.( 7).A stiffer response was obtained when the thickness is reduced, and the best fit to the experimental results was obtained at t=0.0014mm with effective thickness of Gaussian point of 0.00038mm.The failure load of numerical results is 80kN while the failure load of experimental results is 78.7kN, so that the error ratio is 1.6%.In the present study the value of thickness of the interface element equal to 0.14mm is fixed for EX1 specimen to present a parametric study.

PARAMETRIC STUDY
A parametric study deals with construction joint is presented by taking various conditions of the junction.These include the various positions of the construction joint, the axial load on the column, strength of concrete in the second cast and the amount of dowels crossing the joint as follows:

THE EFFECT OF POSITION OF CONSTRUCTION JOINT
In order to study the effect of the position of construction joint (c.j.), a numerical study on four cases       13) and ( 14) that the shear and normal strains in the joint for Nc=0.0 are less than the strains for Nc=292.6kN.A possible explanation of this feature may be the following: Higher compressive stresses (at Nc=292.6kN), in spite of the more intimate interlocking they secure, produce a shortening of the protruding asperities and subsequently reduce overriding resistance.This mechanism does not happen at Nc=0.0.On the contrary, due to loss of the confinement for Nc=0.0, the response of the specimen is softer than the response for Nc=292.

Fig
Fig. (2) Adopted shearing stress-slip relationship Shearing stress (MPa) τ u Fig.(4).Material properties and additional material parameters of these specimens are shown in Tables

Fig
Fig.(6) Comparison between experimental and analytical response of different interface thickness values for EX1 have been carried out, Fig.(8), case (a) without c.j., case (b) with c.j. at the top level of the joint, case (c) with c.j. at the bottom level of the joint, and case (d) with 2 c.j. one at the top level and the other at the bottom level of the joint.These cases were made of three pours (1,2,3) of material properties shown in Table (5).Fig.(9) represents load-tip deflection of these cases.As a result of comparison between curves, a soft response occurred for cases with c.j., the response of case (c) is softer than the response of case (b), and a softer response of all is observed for case (d).It is worth noting that the mode of failure in all cases is beam hinging.

Fig.( 7 )
Fig.(7) Comparison between experimental and analytical response of different thickness value for EX3 specimen.

Fig
Fig.(8) Cases of construction joints of beam-column joint

Fig.( 11 )
Fig.(11) Normal strains distribution in joint for case a(monolithic) and case b (construction joint at the top level of joint) 6kN, Fig.(15)  .

Fig.( 12 )Fig.( 13 )
Fig.(12) Normal strains distribution in beam for case a(monolithic) and case b (construction joint at the top level of -0.002 0.000 0.002 0.004 0.006 Normal strain in beam (mm/mm) 0 Fronteddu et al. (1998) utilized their experimental results from displacement controlled shear tests on concrete lift joint specimens with different surface preparations, to propose an empirical interface

Table ( 3
) Material properties and additional material parameters of

Husain Analysis of Corner Beam-Column Junction With Inclusion D..M. Hamza The Effect of Construction Joints
H. M.

Table ( 5
) Material properties and additional material parameters of Sarsam's specimen EX1