The Open Civil Engineering Journal




ISSN: 1874-1495 ― Volume 13, 2019
RESEARCH ARTICLE

Shear Strength Prediction of RC Beam-column Sandwich Interior Joints Based on Simplified Softened Strut-and-Tie



Liqun Hou*, Weiming Yan, Shicai Chen, Ruiyun Zhang, Yue Qi
Beijing Key Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Beijing 100124, China

Abstract

Introduction:

The sandwich joints casted core area with weaker strength concrete of beam, has more advantages than the traditional joints casted core area with higher strength concrete of column, such as the simple construction and quality assurance, while China design codes are too simple about the sandwich joints and have no clear calculation methods.

Methods:

Due to the scarcity of rational models for predicting the strength of RC beam-column sandwich joints, a modified simplified softened strut-and-tie model suggests a more rational calculation method for the effective compressive strength and the height of the joint concrete based on the simplified softened strut-and-tie. The shear strength of existing tested 15 sandwich interior joints is calculated by using the modified simplified softened strut-and-tie model. Furthermore, the theory results are compared with those of the code method and those of the simplified softened strut-and-tie model.

Results and Conclusion:

The results indicate that the code method is more conservative, and the modified simplified softened strut-and-tie can more precisely predict the joint shear strength than that of the softened strut-and-tie model and more secure than that of the code method. Thus, the modified simplified softened strut-and-tie model can reasonable reveal the failure mechanism of RC beam-column sandwich interior joints.

Keywords: Sandwich joints, Shear strength, Interior joints, Softened strut-and-tie, RC beam-column, Interior.


Article Information


Identifiers and Pagination:

Year: 2017
Volume: 11
Issue: Suppl-4, M2
First Page: 933
Last Page: 939
Publisher Id: TOCIEJ-11-933
DOI: 10.2174/1874149501711010933

Article History:

Received Date: 08/04/2017
Revision Received Date: 20/05/2017
Acceptance Date: 03/06/2017
Electronic publication date: 20/12/2017
Collection year: 2017

Article Metrics:

CrossRef Citations:
0

Total Statistics:

Full-Text HTML Views: 1106
Abstract HTML Views: 726
PDF Downloads: 713
ePub Downloads: 593
Total Views/Downloads: 3138

Unique Statistics:

Full-Text HTML Views: 644
Abstract HTML Views: 396
PDF Downloads: 283
ePub Downloads: 181
Total Views/Downloads: 1504
Geographical View

© Hou et al.; Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/legalcode), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.


* Address correspondence to this author at Beijing Key Laboratory of Earthquake Engineering and Structural Retrofit, The College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China; Tel: (+86)13718375216; Fax: 010-67391649; E-mail: hearthlq@emails.bjut.edu




1. INTRODUCTION

The strength of concrete columns is higher than the beams’ in the multi-high building structure. The column strength is cast continuous through the core area of joints in order to ensure continuity of the columns. In construction, the separate measures to the non-equal-strength junctions in the beam need to be taken [1"Ministry of Housing and Urban-Rural Development of the People's Republic of China", In: Technical specification for concrete structure of tall building GB50011-2010., China Architecture & Building: Peking, 2010.], the columns and the core area of joints with higher strength are pouring first, then turns to the beam and slab concrete (called traditional joints) with lower strength. The construction becomes more difficult, and the fluidity of concrete is high which cannot guarantee the strength of joint core area for the vibration deficiency. The joint core area, beam and slab are simultaneously poured in construction in recent years. This construction method is series of experimental and more and more widely concerned for its advantages, such as simple, quick and easy to ensure construction quality. Theoretical researches on the sandwich joints have been studied since the 1960s. The researches out of China have carried out mainly in the way of monotonic static load experiments which chiefly focus on the calculation of the effective compressive strength fce of the joint concrete in the joint core area [2"CSA Technical Committee", In: Design of concrete structures, 2004.-7J.H. Lee, and Y.S. Yoon, "Prediction of effective compressive strength of corner columns composing weaker slab-column joint", Mag. Concr. Res., vol. 64, no. 12, pp. 1113-1121, 2012.
[http://dx.doi.org/10.1680/macr.11.00196]
]. Researches in China mainly performed low frequency cyclic static load tests which focus on the seismic response analysis and the sandwich joints feasibility validation, and variations of shear semi-empirical formula are given based on the experimental results but lack of reasonable theory models’ support [8Q. Li, and S.M. Yu, "Research on frame’s joint that concrete strength of core is inferior to that of column", J. Tongji Univ., vol. 32, no. 12, pp. 1583-1588, 2004. [Natural science].-11Z.H. Yan, "Seismic Behavior and Design Method of RC Sandwich Beam-column Joints", Ph.D Thesis, Chongqing University, Chong Qing, China, 2010].

Based on strut-and-tie model, a softened strut-and-tie model which considers concrete softening is developed by

Hwang et al [12S.J. Hwang, and H.J. Lee, "Analytical model for predicting shear strengths of interior reinforced concrete beam-column joints for seismic resistance", ACI Struct. J., vol. 97, no. 1, pp. 35-44, 2000.]. The applicability of this model to shear calculation is confirmed for many researches in discontinuity regions where plane hypothesis is not suitable [13S.J. Hwang, and H.J. Lee, "Strength prediction for discontinuity regions by softened strut-and-tie model", J. Struct. Eng., vol. 128, no. 12, pp. 1519-1526, 2002.
[http://dx.doi.org/10.1061/(ASCE)0733-9445(2002)128:12(1519)]
, 14G.H. Xing, "B.Q. LIU and D.T Niu, “Shear strength of reinforced concrete frame joints using modified softened strut-and-tie model", Engineering Mechanics, vol. 30, no. 8, pp. 60-66, 2013.].

This paper investigates the accordance of the calculated formulas for the simplified softened strut-and-tie model and that for the shear strength of frame joints in China code with sandwich experimental data, then improves the simplified softened strut-and-tie model.

2. INTRODUCTION TO THE SIMPLIFIED SOFTENED STRUT-AND-TIE MODEL

According to the paper [12S.J. Hwang, and H.J. Lee, "Analytical model for predicting shear strengths of interior reinforced concrete beam-column joints for seismic resistance", ACI Struct. J., vol. 97, no. 1, pp. 35-44, 2000.], the simplified softened strut-and-tie model satisfies the static equilibrium, the softened biaxial constitutive laws of concrete and the deformable coordination condition. It comprises diagonal mechanism constituted by diagonal strut, horizontal mechanism composed of flat strut and horizontal tie and vertical mechanism composed by steep strut and vertical tie. Strut-and-tie model is a statically indeterminate structure, the joints still hold a capacity to bear load after the tie yielding, and isn’t considered failure until the concrete in the core area reaches the compressive strength. The stress of the concrete is the sum of compressive stress for diagonal strut, flat strut and steep strut. The shear strength of the core area of joints is obtained when the acting stress exceeds the concrete strength.

The paper [12S.J. Hwang, and H.J. Lee, "Analytical model for predicting shear strengths of interior reinforced concrete beam-column joints for seismic resistance", ACI Struct. J., vol. 97, no. 1, pp. 35-44, 2000.] gives a simplified calculating method for softened strut-and-tie model, as shown in Fig. (1) the formula for shear strength follows:

Fig. (1)
Simplified softened strut-and-tie model [13S.J. Hwang, and H.J. Lee, "Strength prediction for discontinuity regions by softened strut-and-tie model", J. Struct. Eng., vol. 128, no. 12, pp. 1519-1526, 2002.
[http://dx.doi.org/10.1061/(ASCE)0733-9445(2002)128:12(1519)]
].


(1)

Where Ø=the strength reduction ratio in value of 0.85; K= the Strut-and-Tie index; = the compressive strength of a standard concrete cylinder in units of Mpa; = the softening coefficient of the concrete which is approximated as; =3.35/0.52; bs= the effective width of the diagonal strut which is taken the depth of the column’s section; as= the effective depth of the diagonal strut estimated by , cb= the depth of compression area of the beam obtained by taking cb=hb/5, hb=the beam depth, cc=the depth of compression area in the column obtained by taking cc=[0.25+0.85N/(Ac)]hc, N=the axial force acting on the column, Ac=the gross cross-sectional area of the column and hc=the thickness of the column in the direction of loading; θ=the angle between the diagonal strut and horizontal axial assumed that θ=arctan(/), and =the distance between the extreme longitudinal reinforcement in the beam and the column section respectively.

The strut-and-tie index K can be obtained as:

(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)

Where γh= the fraction of diagonal compression transferred by the horizontal tie in the absence of the vertical tie; γv=the fraction of diagonal compression carried by the vertical tie in the absence of the horizontal tie; fyh and fyv= the yielding strengths of the horizontal and vertical rebar ties, respectively; and = the equilibrium forces of the horizontal and vertical ties respectively; and = the equilibrium constants of the horizontal and vertical ties respectively.

3. APPLICABILITY OF THE SIMPLIFIED SOFTENED STRUT-AND-TIE MODEL

The experiment determined the shear strengths from the sandwich interior joints tests collected in China are compared to the shear strengths predicted by the simplified softened strut-and-tie model to examine the applicability of the simplified softened strut-and-tie model. As indicated in Table 1, the ratio of test result to the average prediction for the simplified soften Strut-and-tie is 1.413 which is more conservative. Furthermore, the dispersion of the calculation results is large which indicates that the application of the simplified softened strut-and-tie model to sandwich interior joints is not suitable. Then the model needs to be modified based on shear-bearing capacity of sandwich joints.

Table 1
Comparison of shear stress between test results and prediction results of specimens based on the simplified softened strut-and-tie model.



4. THE MODIFIED SIMPLIFIED SOFTENED STRUT-AND-TIE MODEL

4.1. The Compressive Strength of the Joints Concrete

Previous researches show that the compressive strength and ductility of the core area of sandwich joints are increased due to the confinement provided by the beam and slab, and the compressive strength can adopt the effective compressive strength fce. The results are not so much different for each fce presented in Table 2. The compressive strength of the sandwich joints concrete can be modified to the effective compressive strength which is calculated with Equation 10 given by Gamble and Klinar [4L.W. Gamble, and D.J. Klinar, "Test of high strength concrete columns with intervening floor slabs", J. Struct. Eng., vol. 117, no. 5, pp. 1462-1467, 1991.
[http://dx.doi.org/10.1061/(ASCE)0733-9445(1991)117:5(1462)]
].

Table 2
Comparison of shear stress between test results and prediction results of frame joints based on Simplified modified softened strut-and-tie model and the China code method.


(10)

4.2. The Effective Depth of the Strut

The load transferred from the compression area of the frame beam to the joint has stress diffusing in practical engineering, and the divergence angle β is 26.5 (Fig. 2).

Fig. (2)
Schematic diagram of stress dispersion.


The average strength predicted by the simplified softened strut-and-tie model is lower than experiment values since the area of the strut on the sandwich joint is greater due to the compressive dispersion deeper than that of the traditional joint in core area. To validate the above-mentioned assumptions, the finite element models for G-1 as shown in Paper [11Z.H. Yan, "Seismic Behavior and Design Method of RC Sandwich Beam-column Joints", Ph.D Thesis, Chongqing University, Chong Qing, China, 2010] and the corresponding traditional joint J-1 is established. The concrete core area of the traditional joint is made with the same strength concrete with the column which is different from the G-1. For the shear strengths predicted by different fce similar, the effective compressive strength in the core area of sandwich joints can be calculated by the formula given by Gamble and Klinar ( fce= for / <1.4 and fce=0.67 +0.47 for /≤1.4). The principal stress clouds are shown for J-1 with 113kN load and G-1with 104.2kN load on beam (the load ratio of 1.1) in Fig. (3). We can see that the compressive diffusion depth for core area of J-1 is smaller than that of G-1, so the core area of the sandwich is larger than traditional joint’s.

Fig. (3)
Stress nephogram of the joints.


Linear fitting algorithm is applied to 7 Specimens in paper [11Z.H. Yan, "Seismic Behavior and Design Method of RC Sandwich Beam-column Joints", Ph.D Thesis, Chongqing University, Chong Qing, China, 2010]. It has a relatively high computation precision when the length of the diffusion length is ,ls=0.1 in the core area. The effective height of the diagonal strut can be modified to

(11)

4.3. Prediction Steps for the Modified Simplified Softened Strut-and-Tie Model

(1). The angle between the diagonal strut and horizontal axial θ can be obtained as θ=arctan.

(2). Use equation (10) to calculate the effective compressive strength fce in the core area.

(3). The softening coefficient of the concrete is approximated as .

(4). The effective depth of the diagonal strut as is estimated by equation (11).

(5). The effective width of the diagonal strut bs is obtained as bs=hc.

(6). The strut-and-tie index K is gotten by Equation (2) to (9).

(7). The shear strength V for Sandwich joints can be calculated by equation (1).

5. APPLICABILITY OF THE MODIFIED SIMPLIFIED SOFTENED STRUT-AND-TIE MODEL

According to the data of accomplished experiment in China, the comparison of shear strength between prediction of results based on the simplified modified softened strut-and-tie model and test values are shown in Table 2. As indicated in Fig. (4) and Table 2, the results based on the modified simplified softened strut-and-tie model are in better agreement with experimental results than those of the simplified softened strut-and-tie model, and the difference of calculated value for each fce is similar. The results obtained by the semi-empirical formula of China current standard are smaller than test results while the prediction values gotten by the current standard formula are more closer to the test results when the compressive strength of the concrete is taken by the effective compressive strength, but not as good as prediction values by the modified simplified softened strut-and-tie model.

Fig. (4)
Comparison diagram of two calculation.


Description: V1 to V5 is in the table are the shear strength calculated by the modified simplified softened strut-and-tie model, and fce is calculated by the formula from CSAA23.3-04 [2"CSA Technical Committee", In: Design of concrete structures, 2004.], ACI318-2008 [3"ACI Committee 318", In: Building code requirements for structural concrete (ACI318-08) and commentary., American Concrete Institute: Farington Hills, MI, 2008.], Gamble and Klinar [4L.W. Gamble, and D.J. Klinar, "Test of high strength concrete columns with intervening floor slabs", J. Struct. Eng., vol. 117, no. 5, pp. 1462-1467, 1991.
[http://dx.doi.org/10.1061/(ASCE)0733-9445(1991)117:5(1462)]
], Kayani [5M.K. Kayani, "Load transfer from high strength concrete columns through lower strength concrete slabs", PhD thesis, University of Illinois, Illinois, US, 1992.], Ospina and Alexander [6C.E. Ospina, and S.D. Alexander, "Transmission of interior Concrete Column Loads through floors", J. Struct. Eng., vol. 124, no. 6, pp. 602-610, 1998.
[http://dx.doi.org/10.1061/(ASCE)0733-9445(1998)124:6(602)]
] respectively; V6 is obtained by Equation 11.6.4-2 [15"Ministry of Housing and Urban-Rural Development of the People's Republic of China", In: Code for design of concrete structures (GB50011-2010)., China Architecture & Building: Peking, 2010.] of Code for design of concrete structures(China), V7 is also obtained by Equation 11.6.4-2 [15"Ministry of Housing and Urban-Rural Development of the People's Republic of China", In: Code for design of concrete structures (GB50011-2010)., China Architecture & Building: Peking, 2010.], but the compressive strength of the concrete is taken by the effective compressive strength given by Gamble and Klina.

CONCLUSION

  1. The predictions of shear strength for Sandwich joints according to China current concrete structure design criterion standards are smaller and uneconomic, but the prediction values obtained by the current standard formula are more similar with the test results when the effective compressive strength is taken in the joints’ core area.
  2. The prediction results of the sandwich joints’ shear strength calculated by the modified simplified softened strut-and-tie model agree better with the experiment results than the prediction results obtained by the simplified softened strut-and-tie model, and are even smaller than the predictions by the China standard formula when the effective compressive strength is taken for the same joints’ core area.
  3. The application of the Sandwich joints is restricted because China design codes are too simple about the sandwich joints and have no clear calculation methods. The modified simplified soften strut-and-tie has a definite mechanical model which can reveal reasonable force-mechanism of RC beam-column sandwich joints and can be used to calculated the shear strength.

CONSENT FOR PUBLICATION

Not applicable.

CONFLICT OF INTEREST

The author(s) confirm that this article content has no conflicts of interest.

ACKNOWLEDGEMENTS

The writer gratefully acknowledges the support from National Natural Science Foundation of China (no.91315301-03, no.51378039, no.51378037) for this study.

REFERENCES

[1] "Ministry of Housing and Urban-Rural Development of the People's Republic of China", In: Technical specification for concrete structure of tall building GB50011-2010., China Architecture & Building: Peking, 2010.
[2] "CSA Technical Committee", In: Design of concrete structures, 2004.
[3] "ACI Committee 318", In: Building code requirements for structural concrete (ACI318-08) and commentary., American Concrete Institute: Farington Hills, MI, 2008.
[4] L.W. Gamble, and D.J. Klinar, "Test of high strength concrete columns with intervening floor slabs", J. Struct. Eng., vol. 117, no. 5, pp. 1462-1467, 1991.
[http://dx.doi.org/10.1061/(ASCE)0733-9445(1991)117:5(1462)]
[5] M.K. Kayani, "Load transfer from high strength concrete columns through lower strength concrete slabs", PhD thesis, University of Illinois, Illinois, US, 1992.
[6] C.E. Ospina, and S.D. Alexander, "Transmission of interior Concrete Column Loads through floors", J. Struct. Eng., vol. 124, no. 6, pp. 602-610, 1998.
[http://dx.doi.org/10.1061/(ASCE)0733-9445(1998)124:6(602)]
[7] J.H. Lee, and Y.S. Yoon, "Prediction of effective compressive strength of corner columns composing weaker slab-column joint", Mag. Concr. Res., vol. 64, no. 12, pp. 1113-1121, 2012.
[http://dx.doi.org/10.1680/macr.11.00196]
[8] Q. Li, and S.M. Yu, "Research on frame’s joint that concrete strength of core is inferior to that of column", J. Tongji Univ., vol. 32, no. 12, pp. 1583-1588, 2004. [Natural science].
[9] "M.L. Zhang and J.R. Qian. “Experimental study on behavior of reinforced concrete beam-column joint with lower core concrete", Ind. Constr., vol. 36, no. 6, pp. 18-22, 2006.
[10] Z. Jiang, Experimental research on the seismic behavior of reinforced concrete beam-column joints constructed with beam concrete by improved measures, 2007.
[11] Z.H. Yan, "Seismic Behavior and Design Method of RC Sandwich Beam-column Joints", Ph.D Thesis, Chongqing University, Chong Qing, China, 2010
[12] S.J. Hwang, and H.J. Lee, "Analytical model for predicting shear strengths of interior reinforced concrete beam-column joints for seismic resistance", ACI Struct. J., vol. 97, no. 1, pp. 35-44, 2000.
[13] S.J. Hwang, and H.J. Lee, "Strength prediction for discontinuity regions by softened strut-and-tie model", J. Struct. Eng., vol. 128, no. 12, pp. 1519-1526, 2002.
[http://dx.doi.org/10.1061/(ASCE)0733-9445(2002)128:12(1519)]
[14] G.H. Xing, "B.Q. LIU and D.T Niu, “Shear strength of reinforced concrete frame joints using modified softened strut-and-tie model", Engineering Mechanics, vol. 30, no. 8, pp. 60-66, 2013.
[15] "Ministry of Housing and Urban-Rural Development of the People's Republic of China", In: Code for design of concrete structures (GB50011-2010)., China Architecture & Building: Peking, 2010.

Endorsements



"Open access will revolutionize 21st century knowledge work and accelerate the diffusion of ideas and evidence that support just in time learning and the evolution of thinking in a number of disciplines."


Daniel Pesut
(Indiana University School of Nursing, USA)

"It is important that students and researchers from all over the world can have easy access to relevant, high-standard and timely scientific information. This is exactly what Open Access Journals provide and this is the reason why I support this endeavor."


Jacques Descotes
(Centre Antipoison-Centre de Pharmacovigilance, France)

"Publishing research articles is the key for future scientific progress. Open Access publishing is therefore of utmost importance for wider dissemination of information, and will help serving the best interest of the scientific community."


Patrice Talaga
(UCB S.A., Belgium)

"Open access journals are a novel concept in the medical literature. They offer accessible information to a wide variety of individuals, including physicians, medical students, clinical investigators, and the general public. They are an outstanding source of medical and scientific information."


Jeffrey M. Weinberg
(St. Luke's-Roosevelt Hospital Center, USA)

"Open access journals are extremely useful for graduate students, investigators and all other interested persons to read important scientific articles and subscribe scientific journals. Indeed, the research articles span a wide range of area and of high quality. This is specially a must for researchers belonging to institutions with limited library facility and funding to subscribe scientific journals."


Debomoy K. Lahiri
(Indiana University School of Medicine, USA)

"Open access journals represent a major break-through in publishing. They provide easy access to the latest research on a wide variety of issues. Relevant and timely articles are made available in a fraction of the time taken by more conventional publishers. Articles are of uniformly high quality and written by the world's leading authorities."


Robert Looney
(Naval Postgraduate School, USA)

"Open access journals have transformed the way scientific data is published and disseminated: particularly, whilst ensuring a high quality standard and transparency in the editorial process, they have increased the access to the scientific literature by those researchers that have limited library support or that are working on small budgets."


Richard Reithinger
(Westat, USA)

"Not only do open access journals greatly improve the access to high quality information for scientists in the developing world, it also provides extra exposure for our papers."


J. Ferwerda
(University of Oxford, UK)

"Open Access 'Chemistry' Journals allow the dissemination of knowledge at your finger tips without paying for the scientific content."


Sean L. Kitson
(Almac Sciences, Northern Ireland)

"In principle, all scientific journals should have open access, as should be science itself. Open access journals are very helpful for students, researchers and the general public including people from institutions which do not have library or cannot afford to subscribe scientific journals. The articles are high standard and cover a wide area."


Hubert Wolterbeek
(Delft University of Technology, The Netherlands)

"The widest possible diffusion of information is critical for the advancement of science. In this perspective, open access journals are instrumental in fostering researches and achievements."


Alessandro Laviano
(Sapienza - University of Rome, Italy)

"Open access journals are very useful for all scientists as they can have quick information in the different fields of science."


Philippe Hernigou
(Paris University, France)

"There are many scientists who can not afford the rather expensive subscriptions to scientific journals. Open access journals offer a good alternative for free access to good quality scientific information."


Fidel Toldrá
(Instituto de Agroquimica y Tecnologia de Alimentos, Spain)

"Open access journals have become a fundamental tool for students, researchers, patients and the general public. Many people from institutions which do not have library or cannot afford to subscribe scientific journals benefit of them on a daily basis. The articles are among the best and cover most scientific areas."


M. Bendandi
(University Clinic of Navarre, Spain)

"These journals provide researchers with a platform for rapid, open access scientific communication. The articles are of high quality and broad scope."


Peter Chiba
(University of Vienna, Austria)

"Open access journals are probably one of the most important contributions to promote and diffuse science worldwide."


Jaime Sampaio
(University of Trás-os-Montes e Alto Douro, Portugal)

"Open access journals make up a new and rather revolutionary way to scientific publication. This option opens several quite interesting possibilities to disseminate openly and freely new knowledge and even to facilitate interpersonal communication among scientists."


Eduardo A. Castro
(INIFTA, Argentina)

"Open access journals are freely available online throughout the world, for you to read, download, copy, distribute, and use. The articles published in the open access journals are high quality and cover a wide range of fields."


Kenji Hashimoto
(Chiba University, Japan)

"Open Access journals offer an innovative and efficient way of publication for academics and professionals in a wide range of disciplines. The papers published are of high quality after rigorous peer review and they are Indexed in: major international databases. I read Open Access journals to keep abreast of the recent development in my field of study."


Daniel Shek
(Chinese University of Hong Kong, Hong Kong)

"It is a modern trend for publishers to establish open access journals. Researchers, faculty members, and students will be greatly benefited by the new journals of Bentham Science Publishers Ltd. in this category."


Jih Ru Hwu
(National Central University, Taiwan)


Browse Contents



Webmaster Contact: info@benthamopen.net
Copyright © 2019 Bentham Open