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Cyclic response and modelling of special moment resisting beams exhibiting fixed-end rotation

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Abstract

Rebar slippage in reinforced concrete (RC) elements results in concrete expansion, large cracks, and consequently, early deterioration of strength as well as premature stiffness degradation, particularly in the inelastic energy dissipating zones. Although design standards prescribe different minimum concrete compressive strength, seismic evaluation and retrofit standards, and guidelines permit the use of provisions regarding bond strength and bar slippage issues regardless of the minimum specified concrete strength postulated in design standards. To better understand the seismic behavior of special moment-resisting (SMR) beams exhibiting fixed-end rotation resulting from the rebars inelastic elongation and slip, quasi-static cyclic tests were performed on eight full-scale SMR beams. The chosen beams have longitudinal reinforcement ratios of 0.84% (Type-1) and 1.26% (Type-2) with a shear-span to depth ratio of 6.14 and detailed following the provisions of ACI-318-19. Two specimens were prepared for each reinforcement ratio using concrete with compressive strengths equal to 2000 psi (14 MPa, M14) and 3000 psi (21 MPa, M21). The specimens were tested under cyclic displacement protocols, exhibiting flexure yielding that was followed by diagonal shear cracking and, ultimately, bond failure at the beam–block interface. It is even though the beams fulfill the requirements of ACI 318-19 for steel bars embedment and end hooks for anchorage. Force–displacement hysteretic response curves were obtained revealing pinching behavior in the cyclic response. Both types of beams deformed up to maximum chord rotations of 5.22% and 5.73% in case of beams with M14 and M21 concrete, respectively, and experienced cover concrete crushing at the compressed toe. Representative numerical models were assembled implementing fiber-section force-based inelastic beam elements. Additionally, lumped inelastic rotational springs were added to the model for fixed-end rotation. A tri-linear moment-rotation hysteretic response curve has pinching behavior was used to simulate the reduction in re-loading stiffness. This was verified with the measured response of tested beams; excellently simulates the hysteretic response. Moreover, to examine the seismic response of a total structural system regarding these findings, several response history analyses were performed on capacity-designed five-story frames to demonstrate the importance of modeling beam element fixed-end rotation for predicting the story drift demands subjected to different earthquake ground motions. It was found that despite the bar-slip phenomenon the beams developed their yield capacities; however, the response of the frame was subjective depending on the characteristics of input motions, particularly the valleys and hills of the spectral shape.

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References

  • ACI 318-19 (2019) Building code requirements for structural concrete, ACI 318-19. American Concrete Institute, Farmington Hills, MI, USA

  • ACI-ASCE Committee 352 (2002) Recommendations for design of beam-column connections in monolithic meinforced concrete structures (ACI 352R–02). American Concrete Institute, Farmington Hills, MI

  • Ahmad N, Shahzad A, Rizwan M, Khan AN, Ali SM, Ashraf M, Naseer A, Ali Q, Alam B (2019) Seismic performance assessment of non-compliant SMRF reinforced concrete frame: shake-table test study. J Earthquake Eng 23(3):444–462

    Article  Google Scholar 

  • Alavi-Dehkordi S, Mostofinejad D, Alaee P (2019) Effects of high-strength reinforcing bars and concrete on seismic behavior of RC beam-column joints. Eng Struct 183:702–719

    Article  Google Scholar 

  • American Society of Civil Engineers (2017) Seismic evaluation and retrofit of existing buildings, ASCE/SEI 41–17. American Society of Civil Engineers, Reston. https://doi.org/10.1061/9780784414859

  • Balázs GL (1989) Bond softening under reversed load cycles. Studie Ricerche, Politecnico di Milano, Milano, No 11:503–524

  • Braga F, Gigliotti R, Laterza M (2009) R/C existing structures with smooth reinforcing bars: experimental behaviour of beam-column joints subject to cyclic lateral loads. Open Constr Build Technol J 3:52–67

    Article  Google Scholar 

  • Calabrese A, Almeida JP, Pinho R (2010) Numerical issues in distributed inelasticity modelling of RC frame elements for seismic analysis. J Earthquake Eng 14(S1):38–68

    Article  Google Scholar 

  • CEB (1993) CEB-FIP Model Code 1990, Bulletin d’Information, CEB, 213/214, Lausanne.

  • CEN, TC250 (2004) EN 1992-1-1, Eurocode 2: Design of concrete structures – Par 1–1: General rules and rules for buildings. European Committee for Standardization, Brussels

  • Dwairi HM, Kowalsky MJ, Nau JM (2007) Equivalent viscous damping in support of direct displacement-based design. J Earthquake Eng 11(4):512–530

    Article  Google Scholar 

  • Eligehausen R, Popov EP, Bertero VV (1983) Local bond stress-slip relationships of deformed bars under generalized excitations. Report EERC-83/23, University of California, Berkeley, CA.

  • Fanella DA (2011) Reinforced concrete structures—analysis and design. McGraw Hill, New York

    Google Scholar 

  • Fardis MN (2009) Seismic design. Assessment and retrofitting of concrete buildings, Springer, Heidelberg

    Book  Google Scholar 

  • Filippou FC, Issa A (1988) Nonlinear analysis of reinforced concrete frames under cyclic load reversals. EERC Report 88/12, Earthquake Engineering and Research Center, University of California, Berkeley, CA.

  • Grant DN, Blandon CA, Priestley MJN (2005) Modelling inelastic response in direct displacement-based design. Report 2005/03, IUSS Press, Pavia.

  • Izzuddin BA (2001) Conceptual issues in geometrically nonlinear analysis of 3D framed structures. Comput Methods Appl Mech Eng 191(8):1029–1053

    Article  Google Scholar 

  • Liu B, Bai G, Xu Z, Ma J, Han Y (2019) Experimental study and finite element modeling of bond behavior between recycled aggregate concrete and the shaped steel. Eng Struct 201. https://doi.org/10.1016/j.engstruct.2019.109840

  • Liu B, Bai G (2019) Finite element modeling of bond-slip performance of section steel reinforced concrete. Comput Concrete24(3):237–247

    Google Scholar 

  • MacGregor JG, Wight JK (2004) Reinforced concrete, mechanics and design, 4th edn. Prentice Hall, New Jersey

  • Mander JB, Priestley MJN, Park R (1988) Theoretical stress-strain model for confined concrete. J Struct Eng ASCE 114(ST8):1804–1826

    Article  Google Scholar 

  • Masoudi M, Khajevand S (2020) Revisiting flexural overstrength in RC beam-and-slab floor systems for seismic design and evaluation. Bull Earthq Eng. https://doi.org/10.1007/s10518-020-00907-y

    Article  Google Scholar 

  • Mazza F (2019) A plastic-damage hysteretic model to reproduce strength stiffness degradation. Bull Earthq Eng. https://doi.org/10.1007/s10518-019-00606-3

    Article  Google Scholar 

  • Mazza F, Labernarda R (2017) Structural and non-structural intensity measures for the assessment of base-isolated structures subjected to pulse-like near-fault earthquakes. Soil Dyn Earthquake Eng 96:115–127

    Article  Google Scholar 

  • Mazza F (2014) A distributed plasticity model to simulate the biaxial behaviour in the nonlinear analysis of spatial framed structures. Computer and Structures 135:141–154

    Article  Google Scholar 

  • McKenna F, Fenves GL, Scott MH (2000) Object oriented program, OpenSees; open system for earthquake engineering simulation. http://www.opensees.berkeley.edu.

  • Menegotto M, Pinto PE (1973) Method of analysis for cyclically loaded R.C. plane frames including changes in geometry and non-elastic behaviour of elements under combined normal force and bending. In: Symposium on the resistance and ultimate deformability of structures acted on by well defined repeated loads, international association for bridge and structural engineering, Zurich, Switzerland, pp 15–22.

  • Moehle JP (2015) Seismic design of reinforced concrete buildings. McGraw Hill Education, New York

    Google Scholar 

  • NZS (2017) 3101.1&2:2006 A3 concrete structures standard: amendment 3. Standards New Zealand

  • Palios X, Strepelias E, Stathas N, Fardis M, Bousias S (2020) Experimental study of a three-storey concrete frame structure with smooth bars under cyclic lateral loading. Bull Earthq Eng. https://doi.org/10.1007/s10518-020-00900-5

    Article  Google Scholar 

  • Panagiotakos TB, Fardis MN (2001) Deformations of reinforced concrete members at yielding and ultimate. ACI Struct J 98(2):135–148

    Google Scholar 

  • Paulay T, Priestley MJN (1992) Seismic design of reinforced concrete and Masonry buildings. Wiley, New York

    Book  Google Scholar 

  • Penelis GG, Kappos AJ (1997) Earthquake-resistant concrete structures. Taylors and Francis, London

    Google Scholar 

  • Penelis GG, Penelis GG (2014) Concrete buildings in seismic regions. Taylor and Francis, London

    Book  Google Scholar 

  • Pinho R (2007a) Nonlinear dynamic analysis of structures subjected to seismic action. In: Pecker A (ed) Advanced earthquake engineering analysis. CISM, Udine, pp 63–89

    Chapter  Google Scholar 

  • Pinho R (2007b) Using pushover analysis for assessment of buildings and bridges. In: Pecker A (ed) Advanced earthquake engineering analysis. CISM, Udine, pp 91–120

    Chapter  Google Scholar 

  • Priestley MJN, Calvi GM, Kowalsky MJN (2007) Displacement based sSeismic design of structures. IUSS Press, Pavia

    Google Scholar 

  • Rizwan M, Ahmad N, Khan AN (2018) Seismic performance of compliant and noncompliant special moment-resisting reinforced concrete frames.ACI Struct J 115(4):1063–1073

    Google Scholar 

  • Rodrigues H, Varum H, Arede A, Costa A (2012) Comparative efficiency analysis of different nonlinear modelling strategies to simulate the biaxial response of RC columns. Earthq Eng Eng Vibration 11(4):553–556

    Article  Google Scholar 

  • SAP2000 (2009) Integrated software for structural analysis and design. Computer and Structures Inc., Walnut Creek

  • Saatcioglu M, Alsiwat JM, Ozcebe G (1992) Hysteretic behavior of anchorage slip in R/C members. J Struct Eng 118(9):2439–2458

    Article  Google Scholar 

  • Scott MH, Fenves GL (2006) Plastic hinge integration methods for force-based beam column elements. J Struct Eng 132:244–452

    Article  Google Scholar 

  • SeismoSoft (2016) Seismostruct—a computer program for static and dynamic analysis for framed structures. Available from URL: www.seismosoft.com (online).

  • Sezen H, Setzler EJ (2008) Reinforcement slip in reinforced concrete columns. ACI Struct J 105(3):280–289

    Google Scholar 

  • Sivaselvan M, Reinhorn AM (1999) Hysteretic models for cyclic behavior of deteriorating inelastic structures. Technical Report, No. MCEER-99-0018, University at Buffalo, SUNY, Buffalo, NY.

  • Sivaselvan M, Reinhorn AM (2001) Hysteretic models for deteriorating inelastic structures. J Eng Mech ASCE 126(6):633–640.

    Article  Google Scholar 

  • Sivaselvan M, Reinhorn AM (2002) Collapse analysis: large inelastic deformations analysis of planer frames. J Struct Eng ASCE 128(12):1575–1583

    Article  Google Scholar 

  • Soroushian P, Obasaki K, Marikunte S (1991) Analytical modelling of bonded bars under cyclic loads. J Struct Eng ASCE 117(1):48–60

    Article  Google Scholar 

  • Spacone E (2001) A module for analysis and design of segmental pre-stressed concrete bridges (CASI-TR-01-04), Final report of a CASI FY00 Technology Transfer Grant. Colorado Advanced Software Institute, Fort Collins, CO.

  • Wang Z, Li L, Zhang YX, Zheng SS (2019) Reinforcement model considering slip effect. Eng Struct 198. https://doi.org/10.1016/j.engstruct.2019.109493

Download references

Acknowledgements

The authors are grateful to the Provincial Disaster Management Authority (PDMA), Govt. of Khyber Pakhtunkhwa, for financially supporting the experimental part of the research work. The authors thank the undergraduate and postgraduate students of the Department of Civil Engineering of UET Peshawar who helped in the experimental testing of specimens. The authors are grateful to the anonymous reviewers for suggesting improvements.

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Authors and Affiliations

  1. Department of Civil Engineering, UET Peshawar, Peshawar, KP, Pakistan

    Naveed Ahmad

  2. Faculty of Civil Engineering, K. N. Toosi University of Technology, Tehran, Iran

    Mostafa Masoudi

  3. Galway Mayo Institute of Technology, GMIT, Galway, Ireland

    Suhaib Salawdeh

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  1. Naveed Ahmad
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  2. Mostafa Masoudi
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  3. Suhaib Salawdeh
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Correspondence to Naveed Ahmad.

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Ahmad, N., Masoudi, M. & Salawdeh, S. Cyclic response and modelling of special moment resisting beams exhibiting fixed-end rotation. Bull Earthquake Eng 19, 203–240 (2021). https://doi.org/10.1007/s10518-020-00987-w

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