Joint shear strength models for exterior RC beam-column connections exposed to biaxial and uniaxial cyclic loading

Journal Pre-proof Joint shear strength models for exterior RC beam-column connections exposed to biaxial and uniaxial cyclic loading Yasmin Murad PII:

S2352-7102(19)31066-6

DOI:

https://doi.org/10.1016/j.jobe.2020.101225

Reference:

JOBE 101225

To appear in:

Journal of Building Engineering

Received Date: 27 June 2019 Revised Date:

27 January 2020

Accepted Date: 27 January 2020

Please cite this article as: Y. Murad, Joint shear strength models for exterior RC beam-column connections exposed to biaxial and uniaxial cyclic loading, Journal of Building Engineering (2020), doi: https://doi.org/10.1016/j.jobe.2020.101225. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Joint Shear Strength Models for Exterior RC Beam-Column Connections Exposed to Biaxial and Uniaxial Cyclic Loading

First Author: Yasmin Murad, Ph.D., DIC. PhD in Structural Engineering at Imperial College London, 2016 Assistant Professor Civil Engineering Department The University of Jordan Amman, Jordan 11942 Phone Number: + 962-79- 6666802 E-mail: [email protected] ORCID: 0000-0002-7845-5633

Joint Shear Strength Models for Exterior RC Beam-Column Connections Exposed to Biaxial and Uniaxial Cyclic Loading Abstract Joint shear strength models available in the literature can predict the shear strength for reinforced concrete (RC) beam-column connections exposed to uniaxial cyclic loading, while an accurate biaxial joint shear strength model is still lacking. Gene expression programming (GEP) is used in this research to develop uniaxial and biaxial joint shear strength models for exterior RC beam-to-column connections exposed to uniaxial and biaxial cyclic loading respectively. The GEP models are developed based on an experimental database available in the literature, where the models are randomly trained and tested. Uniaxial joint shear strength is also predicted using the ACI 352 and ASCE 41 formulations for connections exposed to uniaxial cyclic loading. The performance of the GEP models is statistically evaluated using the coefficient of determination R-squared. The R-squared values are 79%, 79%, 95% and 93 % for the ACI, ASCE, uniaxial GEP and biaxial GEP models, respectively. The R-squared values of the GEP models are high, which confirms their accuracy and indicates that they are more fitting to the experimental results than the ACI and ASCE formulations. Keywords Joint shear strength; biaxial cyclic loading; uniaxial cyclic loading; exterior RC beam-column connections; ACI 352; ASCE 41; gene expression programming.

Introduction Reinforced concrete (RC) buildings are 3D structural systems, where RC beam-column connections are subjected to complex stress state that can cause building collapse under severe loading conditions. The 3D behaviour of RC beam-column connections under seismic loading is limited in the literature. Few experimental studies have been conducted to investigate the behaviour of 3D RC beam-column connections exposed to biaxial cyclic loading. Most of these studies have shown that biaxial connections exposed to biaxial cyclic loading is severely damaged and have less strength than similar joints exposed to uniaxial cyclic loading. Hassan (1) has shown that joint shear strength of biaxial connections is almost 25% less than that measured in the uniaxial connections. Akguzel (2) has shown that joint shear strength of RC beam-column connection exposed to biaxial cyclic loading is remarkably less than that measured in uniaxial connections. Engindeniz (3) has confirmed that corner connections exposed to biaxial loading have suffered from rapid degradation in strength and stiffness at relatively low drift levels. Hertanto (4) has shown that joint shear strength has reduced around 33% for RC beam-column connections exposed to biaxial cyclic loading. There are many analytical and empirical models, available in the literature, which can predict the shear strength of RC beam-to-column connections under cyclic and monotonic loading. Most of these models focus on the behaviour of uniaxial 2D RC beam-column connections in framed structures. Strut and tie models are analytical models with mechanical basis but they depend on the diagonal strut area that is not easy to define. Empirical models are usually built on the basis of experimental test results and they are simple and less computational demanding. An accurate biaxial joint model that can predict joint shear strength of 3D RC beam-column connection in 3D structural system is still lacking. An elliptical interaction curve, which overestimates the bidirectional joint shear strength, is suggested by several researchers and is adopted in the ACI 352 (5). Hassan (1) confirmed the validity of the elliptical interaction model in unreinforced concrete joints exposed to biaxial cyclic loading. Murad (6) proposed a biaxial hysteresis joint model that considers the effect of variations in the angle of loading between the corner connection framing beams. Hassan and Moehle (7) have proposed that the reduction in biaxial strength is simply the vectorial resolution effect, which is a widely accepted interpretation in columns and even in nonlinear analysis of many structural components.

1

Based on the experimental tests and analytical models available in the literature, joint shear is mainly controlled by concrete compressive strength, joint geometry, joint transverse reinforcement, beam reinforcement ratio, and column axial load. Previous studies have shown that the increase in joint shear strength is proportional to the increase in concrete compressive strength (8)(6)(9), and joint transverse reinforcement (10). Joint shear strength increases by the decrease in joint aspect ratio (8). In the BJ failure mode, hinges are formed in the beam followed by joint shear failure. Karaynnis (11) showed that the reinforcement configuration within the joint has a significant effect on the joint behaviour, where the rectangular spiral reinforcement has shown a better response than the ordinary stirrups. Kim and LaFave (12) (13) have investigated the behaviour of RC beam-to-column connections exposed to cyclic loading and they proposed a generalized Bayesian-based model for predicting the uniaxial joint shear strength. This research focuses on the behaviour of exterior connections exposed to cyclic loading since they are more vulnerable than interior connections, which are partially confined by beams framing in from all four sides. Joint shear strength models available in the literature can predict the shear strength for RC beamcolumn connections exposed to uniaxial cyclic loading, while an accurate biaxial joint shear strength model is still lacking. Therefore, the current research develops empirical models using Gene Expression Programming (GEP) that can predict joint shear strength of exterior connections exposed to uniaxial and biaxial cyclic loading. The aim of this research is to clarify the biaxial cyclic loading effect on corner RC beam-column connections. To compare between the uniaxial and biaxial joint shear strength, a GEP model that can predict the uniaxial shear strength is also developed in this research. Although there are several models available in the literature that can predict the uniaxial joint shear strength, a GEP model that can predict the uniaxial joint shear strength is lacking in the literature. Furthermore, GEP is used to develop a uniaxial joint model in order to create a consistent comparison between it and the biaxial joint model, which is also constructed using GEP. A comparison is also made between joint shear strength values obtained using the developed GEP models and the uniaxial joint shear expressions proposed by ACI 352 (5), and ASCE 41 (14).

Experimental database Gene expression programming is used in this research to develop two empirical models that can predict uniaxial and biaxial shear strengths of exterior connections exposed to cyclic loading. Large database is found for exterior connections exposed to uniaxial cyclic loading, while only few experimental programs are carried out for exterior connection exposed to biaxial cyclic loading. Uniaxial joint shear strength model is trained and tested using 200 data test points that collected from different experimental programs (1)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39) (40)(41)(42)(43)(44), while the biaxial joint shear strength is trained and tested using 8 data test points that collected from different biaxial joint tests (1) (3)(2)(4)(45)(46). Six biaxial specimens failed due to pure joint shear, while the other two specimens tested by Engindeniz (3) suffered from a mixed mode of bond failure in bottom bars, column yielding, and some cracking in the joint area. However, it is not confirmed that this mixed mode of failure triggered the full shear capacity of the joint, which may have failure prematurely, in one direction because of anchorage loss and in the other direction because of penetration of column bar yielding into the joint. Due to the scarcity in test data in the biaxial model, these specimens are considered in the biaxial joint shear strength model. The data used for training is 75% of the total database, while that used for validation is 25% of the total database for the uniaxial model, while 65% of the biaxial database is used for training the biaxial model and 35% of the database is used for validating the biaxial GEP model. Table A-1 and Table A-2 in the appendix summarise the database that used to develop the biaxial and uniaxial joint shear strength models respectively, where the training and testing data points are randomly selected from the database. The mode of failure is joint shear for the collected database shown in Table A-1 and Table A-2. The GEP models are developed using the square root concrete compressive strength, joint transverse reinforcement, column depth, joint panel width, beam reinforcement ratio, and column axial load.

Analytical background The ACI 352R-02 (5), and other current codes propose design formulations to predict the uniaxial joint shear strength for RC beam-column connections exposed to uniaxial cyclic loading but an accurate 2

expression that can predict the biaxial joint shear strength for RC beam-column connections exposed to biaxial cyclic loading is still lacking. The ACI 352R-02 (5) design equation, illustrated in Equation1, can predict the uniaxial joint shear strength of exterior RC beam-column connections exposed to uniaxial cyclic loading. The constant γ for exterior connections under cyclic loading is 12, the effective joint width, is the column depth, and is the concrete compressive strength. Equation 1 can also be applied to predict the uniaxial joint shear strength using the ASCE 41 (14) and ACI 369 (47), where the constant γ is considered 6 for joints without hoops. = 0.083 ℎ



(1)

Gene expression programming Overview of gene expression programming Gene expression programming (GEP) is an extension to gene programming and gene algorithm. GEP was developed by Ferreira and it has an advantage of solving complex problems with small database (48) without the need of any predefined equations (49). The developed gene expression is expressed into an expression tree that encoded in the chromosomes (48) (50) (51) (52) (53). The GEP expression can also be expressed using karva language and several programming languages (c++, VBA, Matlab, etc). The GEP expression is developed by adding or deleting various parameters to best fit the experimental results (49)(54). Empirical expressions can be developed using GEP for the cases, where the analytical expressions are not available. The GEP expression can contain one or more genes, where each gene has a head and tail. The gene’s tail has terminal symbols (constants and variables) such as (1,a, b, c), while the gene’s head has the functions and terminal symbols including constants, variables, functions and mathematical operators such as (1,a, b, √, cos ,*,−, /) (55). Complex functions (56) are usually resulted by increasing the number of genes (56). Furthermore, increasing the number of chromosomes has resulted in increasing the running time (56). Simplified procedures are usually adopted to create a new GEP model by choosing the fitness function and then selecting the terminals and functions that are required to build the chromosomes. The number of genes, the head length, and the number of chromosomes are then determined. The genetic operators and the linking functions are finally selected (48). Gene expression programming has become an efficient tool in predicting the behaviour of structural elements in civil engineering applications (57)(58)(59)(60)(56)(51)(61)(62)(63) based on the experimental database. Researchers have used GEP to predict the tensile strength of concrete (52), the compressive strength of high performance concrete (HPC) mixes (57), etc. Model Development Gene expression programming is applied in this research using GeneXproTools (64) software in order to develop biaxial and uniaxial joint shear strength models for exterior connections exposed to biaxial and uniaxial cyclic loading respectively. Several GEP models are developed by changing the number of genes, chromosomes, head size, and linking function. The selected GEP model is the one that best fit the experimental results. The selected parameters for the GEP models that best fit the experimental results are shown in Table 1. The genome of gene expression programming includes a linear, symbolic string or chromosome of fixed length. Each chromosome consists of one or more genes with a fixed length. The genes form the expression trees of different sizes and shapes. The function set includes all the functions and mathematical operators such as (+ ,* ,− , / ,x2 ,x3, √, cos, sin etc) that can be used in the development of the GEP equation. The developed GEP equation consists of one or multiple of genes, where increasing the number of genes generates complex GEP equations. The linking function such as (+ ,* ,− , / ) is the mathematical operator that links the genes together. The constants per gene determine the number of constants that can be used in the mathematical equation for each gene. The mutation rate can create diversity and change genomes by changing an element by another. For example, functions can be replaced by another function or terminal. Recombination rate incorporates the creation of new chromosomes by combining different parts from the parent chromosomes.

3

Transposition incorporates the introduction of an insertion sequence somewhere in a chromosome, while the inversion rate consists of a small sequence within a chromosome. Two genes are used to develop each GEP model in order to obtain simplified uniaxial and biaxial joint shear strength expressions. The genes are linked together using a multiplication linking function. Simplified functional set is used including addition, subtraction, multiplication, division, square root, and square functions. Two constants are used per gene for the uniaxial and biaxial GEP models. The constants of the uniaxial model are c0 = -7.4, c1= -12.75 for the first gene, while the second gene has only one constant that equals to c0 = -126.7. Biaxial joint model has 2 constants per gene. The constants of the first gene are (c0 = -2.49, c1= 6.18) and the constants of the second gene are (c0 = 4.98, c1= 45.81). The parameters that control the uniaxial shear strength in the GEP model are concrete compressive strength, joint transverse reinforcement, column depth, joint panel width, beam longitudinal reinforcement ratio, and column axial load. Biaxial GEP model is simple and it depends on the concrete compressive strength, joint transverse reinforcement, column depth, and joint panel width. The collected database is used to develop the GEP models, where the data points of the biaxial model are limited due to the scarcity of the biaxial database. The development of the GEP models normally requires 65% to 75% of the database to be used as a training database and the rest is to be used as a validating database. Thus, five points, which are randomly selected, are used to develop the biaxial GEP model, while the other three points, which are also randomly selected are used to verify the model. The validation and training points are randomly varied during the development process of the GEP model. The validation points shown in Figure 3 (c) are selected from Akguzel (2), Hertanto (4), and Chen (46) test results. Both GEP models are expressed mathematically in Equation 4 and 5 and using the expression tree format that shown in Figure 1 and Figure 2 for the uniaxial and biaxial joint shear strength models respectively. In the expression tree do, d1, d2, d3, d4 and d5 are square root concrete compressive strength ( ), joint transverse reinforcement ( ), column depth (ℎ ), joint panel width ( ), beam longitudinal reinforcement ratio ( ) , and column axial load ( ), respectively, while c0 and c1 are constants. It should be noted that the proposed biaxial joint model that best fit the experimental results is not influenced by column axial load and beam longitudinal reinforcement ratio but all the selected parameters are used to develop the uniaxial joint shear strength model. Thus, the column axial load and beam longitudinal reinforcement ratio are excluded from the biaxial joint shear strength expression and tree. Both GEP models can predict the biaxial and uniaxial joint shear strength of exterior RC connections exposed to cyclic loading with an acceptable accuracy. Table 1 Gep setting parameter GEP Function set +, -, *, /,√ , Genes 2 Chromosomes 30 Head Size 8 Linking Function Multiplication Constant per gene 2 Mutation rate 0.05 Inversion rate 0.1 Transposition rate 0.1 One point recombination rate 0.3 Two point recombination rate 0.3 Gene recombination rate 0.1 Gene transportation rate 0.1 The performance of the GEP models is then statistically evaluated using the coefficient of determination (R2) that defined in equation 2. The predicted joint shear strength values are compared to the experimental joint shear strength values that collected from the literature and it is found that the distribution of points is close to the ideal fit as shown in Figure 3 and Figure 4. This confirms that the proposed GEP models have an acceptable capacity in predicting the uniaxial and biaxial joint shear strengths. The mean absolute error (MAE) is also calculated in order to further validate the model. The MAE values for the uniaxial and 4

biaxial joint shear strengths are 41.68% and 9.67% respectively for all data. The MAE values, which indicate to the error, are low. -

' ' "∑) %*+($% &$)((% &( ), ($% &$' )- ∑) ((% &(' )-

! = ∑)

%*+

. /=

0

1

(2)

%*+

∑1 470|34 − 64 |

(3)

Biaxial and uniaxial joint shear strength models have high R-squared values for validation, training, and all data, which confirms that both GEP models have an excellent correlation between the predicted and experimental values and hence can predict the experimental joint shear strength with acceptable accuracy. A comparison is made between the experimental and predicted joint shear strengths for exterior connections exposed to biaxial and uniaxial cyclic loading in Figure 3 and Figure 4 respectively. Each figure illustrates the experimental vs predicted joint shear strength for the training, validation, and all data. The R-squared values for the biaxial GEP model are 98 %, 90 %, and 93% for the validation, training, and all data, respectively as shown in Figure 3. The R-squared values for the uniaxial GEP model are 94%, 98%, and 95% for the validation, training, and all data, respectively as shown in Figure 4. The ACI formulation and the GEP models have the same trends, where the shear strength, in all models, increases by the increase of concrete compressive strength, column depth, and joint panel width as shown in equation 1, 4, and 5. This confirms the consistency of the proposed GEP models with the analytical code formulation. The proposed biaxial joint model can predict the shear strength of RC beam to column connections exposed to biaxial cyclic loading with acceptable accuracy. It should be noted that the GEP model is built based on limited database thus it needs further verification with many more tests to be considered accurate. Existing models that can predict the biaxial joint shear strength are limited in the literature. Therefore, the proposed biaxial GEP model is a novel model that can easily predict the biaxial shear strength for RC beam-to-column connections exposed to biaxial cyclic loading.

5

Figure 1 Expression tree of the developed uniaxial GEP model

Figure 2 Expression tree of the developed biaxial GEP model The following expression predicts the uniaxial joint shear strength: = 89:"

+ 7.42, −

0@ ? A × "−7.42

× (

+ 12.75),E + F × G

× H(−126.72

−

0@ L

(4)

),W

(5)

) − (ℎ + )JK

The following expression predicts the biaxial joint shear strength: = GH−15.37"6.18 −

,J × H"−2.49 +

, + (ℎ −

)JK × N O

(a)

0

PQRS &?.TU

−(

+

)V − "91.6 − (

(b)

6

−

(c) Figure 3 Comparison between the predicted and experimental values of validating data using biaxial GEP model

(a)

(b)

(c) Figure 4 Comparison between the predicted and experimental values of training data using uniaxial GEP model

Comparison between the GEP models, the ACI 352, and ASCE 41, expressions As mentioned earlier, the ACI 352R-02 (5) design formulation can predict the uniaxial joint shear strength for RC beam-column connections exposed to uniaxial cyclic loading but an expression that can predict the biaxial joint shear strength for RC beam-column connections exposed to biaxial cyclic loading is still lacking. The ASCE 41 (14) is also used to calculate the shear strength of existing joints without hoops, which is the typical practice in the industry. Thus, the comparison is made between the biaxial GEP and uniaxial GEP models, the ACI 352, and the ASCE 41, expressions for the uniaxial joint shear strength as shown in Figure 5. The R-square values for both GEP models are higher than that obtained using the ACI expression, where the R-squared values are 79%, 79%, 95%, and 93 % for the ACI, ASCE, uniaxial GEP 7

Predicted Joint Shear Strength (kN)

and biaxial GEP models, respectively. Equation 1 is used to predict the uniaxial joint shear strength using the ACI 352 and ASCE 41 codes, where the constant γ is the only difference between the two codes as explained earlier. Although the joint shear strength values predicted using the ASCE 41 are lower than that values predicted using the ACI 352, the R-squared values for both codes is the same and equals to 79% because both codes have the same formulation with different values for the constant γ. Joint shear strength values predicted using the GEP models are more fitting to the experimental results than that obtained using the ACI 352 and ASCE 41 expressions. The trend of the GEP models in agreement with the trend of the ACI 352, ASCE 41, expressions and the experimental results. This confirms the consistency of the GEP models.

2500 2000

R² = 0.7899 uni-GEP

1500 R² = 0.9487

uni-ACI

1000 ASCE-41 R² = 0.7899

500

Bi-GEP R² = 0.9288

0 0

500

1000

1500

2000

2500

Experimental Joint Shear Strength (kN)

Figure 5 Comparison between the ACI, ASCE, and GEP models

Conclusion Joint shear strength models available in the literature can predict the shear strength for RC beam-column connections exposed to uniaxial cyclic loading, while an accurate biaxial joint shear strength model is still lacking. Biaxial and uniaxial joint shear strength models are developed in this research using gene expression programming for exterior RC beam-to-column connections exposed to uniaxial and biaxial cyclic loading respectively. Uniaxial and biaxial GEP models are randomly trained and tested using 200 and 8 data test points respectively. Uniaxial GEP model is developed using six main parameters including square root concrete compressive strength, joint transverse reinforcement, column depth, joint panel width, beam reinforcement ratio, and column axial load. Biaxial GEP model is developed using four main parameters including square root concrete compressive strength, joint transverse reinforcement, column depth, and joint panel width. Uniaxial joint shear strength is also predicted using the ACI 352 and ASCE 41 formulations. The coefficient of determination R-squared is used to evaluate the performance of the models. The values of R-squared are 79%, 79%, 95%, and 93 % for the ACI, ASCE, uniaxial GEP and biaxial GEP models, respectively. The high R-square value of the GEP models confirms their accuracy and indicates that they are more fitting to the experimental results than the ACI and ASCE formulations.

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14

Appendix Table A-1 Biaxial joint shear database Authors and year

Specimen name

cylinder Concrete compressive strength (MPa)

Joint shear reinforcement area (mm2)

column depth (mm)

Joint width (mm)

joint aspect ratio

beam reinforcement ratio

Column axial load (N)

Number of cycles used in each displacement amplitude

Joint shear strength (N)

TDP-1 TDP-2 TDD-2

22.9 25 24.7

56.5487 56.5487 0

230 230 230

215 215 215

1.434 1.434 1.434

0.0196 0.0196 0.0220

0 0 0

4 4 4

97000 117000 141000

3D1

17.4

0

230

230

1.434

0.0191

115000

2

18820

specimen 1 specimen 2

34.12

0

356

330.5

1.43

0.0128

0

3

51000

34.54

0

356

330.5

1.43

0.0128

0

3

53000

B-J-1

30.43

0

457.2

431.8

1

0.0221

2862

2

765056

DD1

28.9

0

230

215

1

0.0224

200000

4

82200

Eric Hertanto 2005

Umut akguzel 2011 Engindeniz 2008

Hassan 2011 Chen 2006

*Joint width is calculated according to ACI-352

Table A-2 Uniaxial joint shear database

Authors and year

Specimen name

cylinder Concrete compressive strength (MPa)

Binbhu & Jaya 2008

A1 T1

Joint shear reinforcement Area

column depth

Joint width joint aspect ratio

beam reinforcement ratio

Column axial load (N)

Joint shear strength (N)

Joint shear strength predicted using ACI-352 (N)

Joint shear strength predicted using ASCE-41 (N)

(mm2)

(mm)

(mm)

36.7

396

150

100

1

0.1072

15920

74710

90507

45254

23.9

0

200

200

1.65

0.0163

120000

62290

194768

97384

JA-0

34

157

300

200

0.67

0.0151

102000

241230

348458

174229

Ja-S5

34

660

300

200

1

0.0151

102000

242760

348458

174229 174229

Ja-x12

34

383

300

200

1

0.0151

102000

241230

348458

JA-X14

34

465

300

200

1

0.0151

102000

24046

348458

174229

JB-0

31.6

0

300

200

1

0.0157

94800

230970

335934

167967

Calvi 2001

Chalioris 2008

JB-S1

31.6

101

300

200

1

0.0157

94800

252530

335934

167967

JB-X10

31.6

157

300

200

1

0.0157

94800

247160

335934

167967

JB-X12

31.6

226

300

200

1

0.0157

94800

245630

335934

167967

JCA-0

20.6

0

200

100

1

0.0157

41200

241230

90411

45206

JCA-X10

20.6

157

200

100

1

0.0157

41200

70470

90411

45206

JCA-S1

20.6

101

200

100

1

0.0157

41200

69370

90411

45206

JCA-S1X10

20.6

258

200

100

1

0.0157

41200

70470

90411

45206

JCA-s2

200

100

1

0.0157

41200

69010

90411

45206

20.6

201

jca-s2x10

20.6

358

200

100

1

0.0157

41200

70110

90411

45206

jcb-0

20.6

0

200

100

1

0.0236

46000

105770

90411

45206

jcb-x10

20.6

157

200

100

1

0.0236

46000

103860

90411

45206

jcb-s1

20.6

101

200

100

1

0.0236

46000

104980

90411

45206 45206

jcb-s1x10

20.6

258

200

100

1

0.0236

46000

105340

90411

jcb-s2

20.6

201

200

100

1

0.0236

46000

106080

90411

45206

jcb-s2x10

20.6

358

200

100

1

0.0236

46000

106440

90411

45206

15

Chun & kim 2004

Chun 2007

Chutarat & Aboutaha 2003

jc-2

60.1

2752

500

425

1

0.0213

490000

1343.89

1640799

820400

jm-2

60.1

2752

500

425

1

0.0213

490000

1342.22

1640799

820400

jc-2

60.1

4054

500

425

1

0.0213

0

1199900

1640799

820400

jm-2

60.1

4054

500

425

1

0.0213

0

1197600

1640799

820400

32.8

3103

520

550

0.97

0.0169

0

1125630

1631407

815703

32.8

3103

520

550

0.97

0.0169

0

1113890

1631407

815703

32.8

3103

520

550

0.97

0.0169

0

1080400

1631407

815703

27.6

1548

406

381

1.126

0.0246

0

932470

809403

404702

27.6

1548

406

381

1.126

0.0433

0

1188600

809403

404702

#2

55.7

774

457

305

0.888

0.0371

689000

1154340

1036103

518052

#4

49.4

774

457

305

0.888

0.0371

1380000

1302610

975751

487875

#5

44.6

774

457

305

0.888

0.0371

1357000

1184770

927135

463567

#6

48.3

774

457

305

0.888

0.0371

587000

1104490

964826

482413

J1

47.4

2280

305

279.5

1.249

0.0246

175000

457790

584561

292281

J2

47

2280

305

279.5

1.249

0.0246

175000

633500

582090

291045

J5

46.6

2280

305

279.5

1.249

0.0328

175000

985980

579607

289804

J7

49

2280

305

279.5

1.249

0.0382

175000

760570

594346

297173

jc-no.111 jm no. 11-1a jm -no 11-1b

I-GROUP 1 IIGROUP 1

CLYDE 2000

DURRANI & ZERBE 1987

EHSANI & ALAMEDDINE 1991

EHSANI 1987

EHSANI & WIGHT 1985 A

LL8

55.1

2294

356

337

1.427

0.0319

293700

942960

886982

443491

LH8

55.1

3054

356

337

1.427

0.0319

293700

946930

886982

443491

HL8

55.1

2533

356

337

1.427

0.0408

507300

1231020

886982

443491

HH8

55.1

3293

356

337

1.427

0.0408

507300

1230020

886982

443491

LL11

75.8

2294

356

337

1.427

0.0319

285000

929150

1040337

520168

LH11

75.8

3054

356

337

1.427

0.0319

276000

925090

1040337

520168

HL11

75.8

2533

356

337

1.427

0.0408

587000

1177460

1040337

520168

HH14

96.5

3293

356

337

1.427

0.0408

605000

1217610

1173824

586912

LL14

96.5

2294

356

337

1.427

0.0319

236000

936500

1173824

586912

LH14

96.5

3054

356

337

1.427

0.0319

222000

933530

1173824

586912

HH11

96.5

3293

356

337

1.427

0.0408

605200

1217610

1173824

586912

1

64.6

1333

340

320

1.411

0.0202

133000

676160

870973

435486

2

67.2

1333

340

320

1.411

0.0247

338000

592680

888327

444164

3

64.6

1333

300

279.5

1.463

0.0279

383000

716270

671241

335621

4

67.2

1534

300

279.5

1.463

0.0346

325000

920970

684616

342308

5

44.6

1333

300

279.5

1.463

0.0449

222000

843450

557737

278869

1S

51.4

1080

300

279.5

1.6

0.019

222000

384560

598748

299374

2S

47.6

1333

300

279.5

1.6

0.019

222000

368860

576190

288095

3S

34.9

1080

300

279.5

1.463

0.019

222000

402160

493373

246686

6S

42.3

1080

340

320

1.412

0.0201

303310

490650

704788

352394

16

EHSANI & WIGHT 1985 B

GENCOGLU & EREN 2002

HAMIL 2000

1B

40.5

1080

300

279.5

1.6

0.0449

177870

591210

531484

265742

2B

42.1

1080

300

279.5

1.463

0.0449

221870

679470

541880

270940

3B

49.3

1333

300

279.5

1.6

0.0449

221870

1053730

586389

293195

4B

53.8

1333

300

279.5

1.463

0.0449

221870

1062200

612567

306283

5B

29.3

1520

340

320

1.412

0.0402

356580

444270

586573

293286

6B

48

1080

340

320

1.412

0.03

303820

437010

750773

375387

#2

39.5

0

400

250

1.5

0.0092

150000

114040

625976

312988

C6LN0

53.1

0

150

130

1.4

0.0357

50000

113900

141528

70764

C6LN1

53.1

57

150

130

1.4

0.0357

50000

118650

141528

70764

C6LN3

50.6

170

150

130

1.4

0.0357

50000

137860

138156

69078

C6LN5

38.2

283

150

130

1.4

0.0357

50000

164680

120040

60020

C6LH0

104.6

0

150

130

1.4

0.0357

100000

163860

198637

99318

C6LH1

105.4

57

150

130

1.4

0.0357

100000

169070

199395

99697

C6LH3

100.4

170

150

130

1.4

0.0357

100000

187650

194608

97304

C4ALN0

44

0

150

130

1.4

0.0357

50000

129600

128831

64415

C4ALN1

47.3

57

150

130

1.4

0.0357

50000

162260

133575

66787

C4ALN3

43.2

170

150

130

1.4

0.0357

50000

168300

127654

63827

C4ALN5

52.3

283

150

130

1.4

0.0357

50000

185170

140457

70229

C4ALH0

107.9

283

150

130

1.4

0.0357

100000

200980

201746

100873

O6

41

57

460

380

1.087

0.0107

0

434300

1114789

557395

O7

37.3

57

460

380

1.087

0.0107

0

440240

1063298

531649

RK3

57.2

1030

200

150

1.5

0.0419

500000

402000

225984

112992

RK4

51.7

1030

200

150

1.5

0.0419

500000

357000

214845

107423

RK5

54.9

1030

200

150

1.5

0.0419

500000

423000

221394

110697

RK6

86.5

1030

200

150

1.5

0.0419

500000

556000

277900

138950

RK7

54.7

1030

200

150

2

0.0419

500000

277000

220991

110495

RK8

38.9

1030

200

150

1.5

0.0419

500000

273000

186361

93181

HAKUTO 2000

HEGGER 2003

70-2T5

92.3

2431

450

385

1

0.02

196000

1276660

1657805

828902

70-1T55

84

2431

450

385

1

0.02

196000

1282170

1581511

790756

28-3T4

42.2

4028

550

465

0.909

0.0134

196000

1200810

1654745

827373

28-0T0

39.8

3278

550

465

0.909

0.0134

196000

1230620

1607002

803501

HWANG 2004

0T0

81.1

1639

420

370

1.071

0.0229

196000

1078820

1393865

696933

1B8

74.5

1639

420

370

1.071

0.0229

196000

1151020

1335945

667972

3T3

83.1

2277

420

370

1.071

0.0229

196000

1058500

1410948

705474

2T4

85.5

2146

420

370

1.071

0.0229

196000

1066320

1431177

715589

1T44

87.7

2146

420

370

1.071

0.0229

196000

1072570

1449473

724737

3T4

90.7

2779

450

385

1

0.0202

196000

1280760

1643373

821687

2T5

92.3

2431

450

385

1

0.0202

196000

1272890

1657805

828902

1T55

84

2431

450

385

1

0.0202

196000

1278400

1581511

790756

S1

36.1

0

180

165

1.67

0.0318

90000

194080

177734

88867

S2

94

0

180

165

1.67

0.0318

90000

199040

286800

143400

HUANG 2005

IDAYANI 2007

17

170

180

165

1.67

0.0318

90000

223870

177734

88867

31.6

0

200

200

1.5

0.0079

152290

82560

223956

111978

31.6

101

200

200

1.5

0.0079

126400

82930

223956

111978

A2

31.6

201

200

200

1.5

0.0079

152290

82930

223956

111978

A3

31.6

302

200

200

1.5

0.0079

152290

82200

223956

111978

B0

31.6

0

300

200

1

0.0157

228430

227810

335934

167967

B1

31.6

101

300

200

1

0.0157

228430

253290

335934

167967

C0

31.6

157

300

200

1

0.0151

228430

239700

335934

167967

C2

31.6

358

300

200

1

0.0151

228430

242760

335934

167967

C3

31.6

459

300

200

1

0.0151

228430

239700

335934

167967

C5

31.6

660

300

200

1

0.0151

228430

243530

335934

167967

AJ1S

32.8

101

200

200

1.5

0.0079

70000

84830

228169

114084

A1

36.4

0

200

200

1.5

0.0079

70000

74950

240364

120182

A2

36.4

0

200

200

1.5

0.0079

70000

76070

240364

120182

B1

36.4

402

200

200

1.5

0.0079

70000

77190

240364

120182

B2

36.4

402

200

200

1.5

0.0079

70000

77190

240364

120182

BS-OL

30.9

0

300

280

1.5

0.0209

402980

264210

465070

232535

BS-LL

30.9

0

300

280

1.5

0.0209

402980

534590

465070

232535

BS-U

30.9

0

300

280

1.5

0.0209

402980

411210

465070

232535

BS-L-LS

30.9

0

300

280

1.5

0.0209

402980

415730

465070

232535

E1

30.4

435

300

300

1

0.0268

216000

535550

494241

247120

E2

30.4

435

300

300

1

0.0268

216000

371130

494241

247120

B2

28.3

435

300

300

1

0.0177

216000

370030

476865

238432

LEE & KO 2007

W0

34.8

1402

400

450

1.125

0.0127

835200

907830

1057600

528800

LIU 2006

RC-1

18

0

230

215

1.4348

0.0178

75000

148710

208959

104480

T5

21.5

603

300

300

1.67

0.0124

290250

267900

415644

207822

T9

21.5

603

300

300

1.67

0.0124

580500

303200

415644

207822

T10

21.5

603

300

300

1.67

0.0124

290250

322500

415644

207822

T2

29.1

0

200

200

1.65

0.0164

100000

72090

214915

107457

1

39.9

0

406

406

1

0.0314

546700

1224550

1037046

518523

2

36.4

0

406

406

1

0.0314

1247000

1110450

990517

495259

3

41

0

406

406

1

0.0314

561500

1045820

1051244

525622

4

38.1

0

406

406

1

0.0314

1304800

1771780

1013384

506692

5

38.2

0

406

406

1

0.0314

523600

966870

1014713

507356

KARAYANNIS 2008

KARAYANNIS & SIRKELIS 2005

KARAYANNIS & SIRKELIS 2008

KUANG & WONG 2006

KUSHARA & SHIOHARA 2008

MASI 2009

PAMPANIN 2002

PANTELIDES 2002

S3

36.1

A0 A1

18

PARKER & BULIMAN 1997

6

37.3

0

406

406

1

0.0314

1280000

1160640

1002688

501344

4A

49

0

300

275

1.67

4B

49

0

300

275

1.67

0.0218

0

231270

575190

287595

0.0218

300000

270470

575190

4C

46

0

300

275

287595

1.67

0.0218

570000

333190

557304

4D

49

0

300

278652

275

1.67

0.0218

0

293990

575190

287595

4E

50

0

300

275

1.67

0.0218

300000

313590

581030

290515

4F

47

0

300

275

1.67

0.0218

600000

358670

563329

281665

5A

53

679

300

275

1.67

0.0218

0

455890

598207

299103

5B

54

679

300

275

1.67

0.0218

300000

477180

603824

301912

5C

54

679

300

275

1.67

0.0218

600000

474180

603824

301912

5D

54

679

300

275

1.67

0.0357

0

454570

603824

301912

5E

56

679

300

275

1.67

0.0357

300000

593360

614904

307452

5F

54

679

300

275

1.67

0.0357

600000

647670

603824

301912

62709

C1AL

41.7

57

150

130

1.4

0.0201

50000

114650

125419

C2

61.7

57

150

130

1.4

0.0201

275000

110360

152559

76279

C3L

44.4

57

150

130

1.4

0.0201

50000

112310

129415

64708

C4

44.4

57

150

130

1.4

0.0357

275000

159630

129415

64708

C4A

55.4

57

150

130

1.4

0.0357

275000

169610

144560

72280

C4AL

44.7

57

150

130

1.4

0.0357

50000

154260

129852

64926

C5

41.3

57

150

130

1.4

0.0357

275000

75620

124816

62408

C6

49.8

57

150

130

1.4

0.0357

275000

118660

137059

68530

C6L

57.3

57

150

130

1.4

0.0357

50000

140170

147018

73509

SCOTT 1996

C7

44

57

150

130

1.4

0.0357

275000

104380

128831

64415

C8

55.6

57

150

130

1.4

0.0357

275000

89040

144821

72410

C9

44.9

57

150

130

1.4

0.0357

275000

92210

130142

65071

M1

34

444

200

200

1.5

0.0192

300000

153660

232305

116153

M2

33.5

451

200

200

1.5

0.0308

300000

282150

230591

115295

A1

35

581

200

200

1.5

0.0157

200000

157280

235697

117848

E2

35

732

200

200

1.5

0.0154

200000

152500

235697

117848

E1

26.5

732

200

200

1.5

0.0231

200000

233960

205089

102544

G1

26.5

760

200

200

1.5

0.0231

200000

239320

205089

102544

S1

44.6

918

200

200

1.5

0.0154

713600

143390

266064

133032

S2

31.3

1018

200

200

1.5

0.0153

500800

157200

222890

111445

S6

39.8

1018

200

200

1.5

0.0308

636800

225600

251340

125670

X6

32.5

616

200

200

1.5

0.0308

520000

302530

227123

113561

TSONOS 1999

TSONOS 2007

TSONOS 1992

WONG & KUANG 2008

S'6

34.9

0

200

200

1.5

0.0308

558400

303770

235360

117680

F2

28.9

0

200

200

1.5

0.0308

462400

205550

214175

107087

BS-L-300

42.6

0

300

280

1

0.0209

575100

561830

546064

273032

BS-L-450

38.6

0

300

280

1.5

0.0209

521100

377440

519795

259898

BS-L-600

45.5

0

300

280

2

0.0209

614250

340120

564345

282172

BS-L-V2

40.7

314

300

280

1.5

0.0209

549450

514180

533747

266874

VS-L-V4

35.4

628

300

280

1.5

0.0209

477900

533800

497783

248892

BS-L-H1

41.6

157

300

280

1.5

0.0209

561600

495480

539617

269808

19

ALVA 2004

BS-L-H2

52.6

314

300

280

1.5

0.0209

710100

531070

606780

303390

LVP1

40.4

1208

300

200

1.33

0.0268

360000

539500

379841

189920

LVP2

23.9

1005

300

200

1.33

0.0268

397620

514100

292152

146076

LVP3

24.6

1206

300

200

1.33

0.0268

215010

364400

296400

148200

LVP4

24.6

1005

300

200

1.33

0.0268

221580

327200

296400

148200

LVP5

25.9

1206

300

200

1.33

0.0268

233190

380400

304131

152065

2D1

17.9

0

230

230

1.4348

0.0118

115000

18250

222916

111458

2D2

18.9

0

230

230

1.4348

0.0118

115000

23890

229058

114529

2D3

18

0

230

230

1.4347

0.0119

115000

26780

223538

111769

2D4

18.7

0

230

230

1.4347

0.0119

115000

23890

227843

113922

U-J-1

29.63

0

457.2

430.9

1

0.028

97860

991950

1068090

534045

U-J-2

30.54

0

457.2

430.9

1.67

0.0221

97860

791780

1084368

542184

U-BJ-1

30.27

0

457.2

430.9

1

0.0109

97860

533570

1079564

539782

31.31

100.53

200

250

1.5

0.0201

0

257904

278658

139329

45.52

100.53

200

250

1.5

0.0201

0

368165

335993

167997

31.8

100.53

200

250

1.5

0.0201

0

372400

280830

140415

24.88

100.53

200

250

1.5

0.0201

0

330547

248402

124201

ALVA 2007

Umut Akguzel 2011

HASSAN WAEL 2011

Ridwan 2016

Sefatullah Halim 2014

BCJ-CSA BCJ-SSS4 BCJ-SSF4 BCJ-SSS8 BCJ-SSF8 BCJ-CSB

32.29

100.53

200

250

1.5

0.0201

0

358623

282985

141492

28.68

502.655

200

250

1.5

0.0201

0

336809

266697

133349

I-1

26.4

226.195

500

450

0.9

0.0155

2250000

950000

1151447

575723

I-1t

25.5

452.39

500

450

0.9

0.0219

2250000

1065000

1131650

565825

*Joint width is calculated according to ACI-352

20

Highlights •

•

Joint shear strength models available in the literature can predict the shear strength for RC beam-column connections exposed to uniaxial cyclic loading while an accurate biaxial joint shear strength model is still lacking. Gene expression programming is used in this research to develop uniaxial and biaxial joint shear strength models for exterior RC beam-column connections.