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Pinching in Steel Rack Joints: Numerical Modelling and Effects on Structural Response

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Abstract

The structural behaviour of beam-to-column joints plays a key role in the seismic response of frame structures. Regarding to steel storage pallet racks, experimental tests have highlighted that the hysteresis loop of their joints is characterized by the pinching, with the consequence of a reduction of the dissipated hysteretic energy and load carrying capacity. In this paper the authors propose a simplified numerical pinching model capable to simulate the mechanical response of beam-to-column joints under cyclic loads. To develop and check this model, several comparisons are performed with both literature data and experimental results of laboratory tests. The proposed model is characterised by three links placed in parallel: two “composed links” describe the non-linear bending moment-rotation curve of the joint, and a linear elastic link transfers the axial and shear force from the beam to the column. The model is appropriate for predicting the down-aisle seismic response of rack systems and it can be easily implemented in commercial software packages, commonly used for non-linear seismic vulnerability analyses. Moreover, features of the model can be estimated from a few structural data and it does not require to perform expensive cyclic experimental tests. For a deeper understanding of the effects of pinching in the seismic response and to highlight the potentiality of the proposed model a case-study example is also considered. The case-study concerns a rack system, whose beam-to-column joints are modelled using two numerical approaches which differ in the deterioration of the rotational stiffness of joints. Non-linear dynamic analyses, with simulated ground acceleration time-histories, have been carried.

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References

  • Abdel-Jaber, M., Beale, R. G., & Godley, M. H. R. (2005). Numerical study on semi-rigid racking frames under sway. Computers & Structures, 83, 2463–2475.

    Article  Google Scholar 

  • Aguirre, C. (2005). Seismic behavior of rack structures. Journal of Constructional Steel Research, 61, 607–624.

    Article  Google Scholar 

  • Alath, S., & Kunnath, S. K. (1995). Modeling inelastic shear deformation in RC beam-column joints. In Proceedings of tenth conference on engineering mechanics (pp. 822–825). Boulder: University of Colorado.

  • André, F., Bachman, R. E., & Mahoney, M. G. (2006). Performance-based seismic design of pallet-type steel storage racks. Earthquake Spectra, 22(1), 47–64.

    Article  Google Scholar 

  • ATC-24. (1992). Guidelines for cyclic seismic testing of components of steel structures for buildings. Report No. ATC-24, Applied Technology Council, Redwood City, CA.

  • Bajoria, K. M., & Talikoti, R. S. (2016). Determination of flexibility of beam-to-column connectors used in thin walled cold-formed steel pallet racking systems. Thin-Walled Structures, 44, 372–380.

    Article  Google Scholar 

  • Baldassino, N., & Bernuzzi, C. (2000). Analysis and behaviour of steel storage pallet racks. Thin-Walled Structures, 37, 277–304.

    Article  Google Scholar 

  • Bernuzzi, C., & Castiglioni, C. A. (2001). Experimental analysis on the cyclic behavior of beam-to-column joints in steel storage pallet racks. Thin-Walled Structures, 39, 841–859.

    Article  Google Scholar 

  • Bernuzzi, C., Chesi, C., & Parisi, M. A. (2004). Seismic behaviour and design of steel storage racks. In 13th World Conference on Earthquake Engineering. Vancouver, B.C., Canada 1-6, Paper No. 481.

  • Bernuzzi, C., & Simoncelli, M. (2016). An advanced design procedure for the safe use of steel storage pallet racks in seismic zones. Thin-Walled Structures, 109, 73–87.

    Article  Google Scholar 

  • Bertocci, L., Comparini, D., Lavacchini, G., Orlando, M., Salvatori, L., & Spinelli. P. (2017). Experimental, numerical, and regulatory P-Mx-My domains for cold-formed perforated steel uprights of pallet-racks. Thin-Walled Structures, 119, 151–165. ISSN:0263-8231.

  • Birely, A. C., Lowes, L. N., & Lehman, D. E. (2012). A model for the practical nonlinear analysis of reinforced-concrete frames including joint flexibility. Engineering Structures, 34, 455–465.

    Article  Google Scholar 

  • Borghini, A., Gusella, F., & Vignoli, A. (2017). Seismic vulnerability of existing R.C. buildings: A simplified numerical model to analyse the influence of the beam-column joints collapse. Engineering Structures, 121, 19–29.

    Article  Google Scholar 

  • Brambilla, G., et al. (2015). Seisracks2: Progetto di ricerca EU-RECCS Reasearch Project, Comportamento sismico di scaffalature metalliche porta pallet. Costruzioni Metalliche.

  • Castiglioni, C. A., Kanyilmaz, A., Angeretti, M., Brambilla, G., Chiarelli, G. P., & Bernuzzi, C. (2014). Experimental results of full scale pushover tests of project SEISRACK2 (seismic behaviour of steel storage pallet racking systems). In Proceedings of 2nd European Conference on Earthquake Engineering, Istanbul 25–29.

  • Díaz, C., Martí, P., Victoria, M., & Querin, O. M. (2011). Review on the modelling of joint behaviour in steel frames. Journal of Constructional Steel Research, 67, 741–758.

    Article  Google Scholar 

  • Dowell, R. K., Seible, F., & Wlson, E. L. (1998). Pivot hysteresis model for reinforced concrete members. ACI Structural Journal, 95, 607–617.

    Google Scholar 

  • El-Metwally, S., & Chen, W. F. (1988). Moment–rotation modeling of reinforced concrete beam–column connections. ACI Structural Journal, 85(4), 384–394.

    Google Scholar 

  • EN 15512. (2009). Steel static storage systems—Adjustable pallet racking systems—Principles for structural design. CEN European Committee for Standardization; 137.

  • EN16681. (2013). Steel static storage systems—Adjustable pallet racking system—Principle for seismic design. CEN European Committee for Standardization.

  • EN 1993-1-1, Eurocode 3. (2005). Design of steel structures—Part 1-1: General rules and rules for buildings.

  • EN 1993-1-8, Eurocode 3. (2005). Design of steel structures—Part 1-8: Design of joints.

  • EN 1998-1-1, Eurocode 8. (2004). Design of structures for earthquake resistance—Part 1: General rules, seismic actions and rules for buildings.

  • Faella, C., Piluso, V., & Rizzano, G. (2000). Structural semi-rigid connections—Theory, design and software. Boca Raton, FL: CRC Press.

    Google Scholar 

  • FEM 10.2.02. (2001). The design of static steel pallet racks. Federation Europeen de la Manutention, Vers. 1.02.

  • FEM 10.2.08. (2011). Recommendations for the design of static steel storage pallet racks in seismic conditions. Federation Européenne de Manutention, Vers. 1.00.

  • Gelfi, P. (2012). SIMQKE_GR developed by P. Gelfi. Version 2.7–9th.

  • Ghobarah, A., & Biddah, A. (1999). Dynamic analysis of reinforced concrete frames including joint shear deformation. Engineering Structures, 21(11), 971–987.

    Article  Google Scholar 

  • Giordano, S., Gusella, F., Lavacchini, G., Orlando, M., & Spinelli, P. (2017). Experimental tests on beam-end connectors of cold-formed steel storage pallet racks. In Proc. 8th European Conference on Steel and Composite Structures, Eurosteel 2017, Copenhagen.

  • Gusella, F., Lavacchini, G., & Orlando, M. (2018a). Monotonic and cyclic tests on beam-column joints of industrial pallet racks. Journal of Constructional Steel Research, 140, 92–107.

    Article  Google Scholar 

  • Gusella, F., Orlando, M., Vignoli, A., & Thiele, K. (2018b). Flexural capacity of steel rack connections via the component method. The Open Construction and Building Technology Journal, 12, 3–16.

    Article  Google Scholar 

  • Haque, A. B. M. R., & Alam, M. S. (2015). Preliminary investigation on the over-strength and force reduction factors for industrial racks clad buildings. In Proceedings of the 11th Canadian Conference on Earthquake Engineering.

  • Jaspart, J. P. (2000). General report: session on connections. Journal of Constructional Steel Research, 55, 69–89.

    Article  Google Scholar 

  • Kim, J. H., Ghaboussi, J., & Elnashai, A. S. (2010). Hybrid mathematical-informational modeling of beam-to-column connections. Report No. 10-02. Mid-America Eartquake Center, April 2010.

  • Krawinkler, H. (2009). Loading histories for cyclic tests in support of performance assessment of structural components. In Proceedings of 3rd international conference on advances in experimental structural engineering, San Francisco.

  • Lima, L. R. O., Silva, L. S., Vellasco, P. C. G., & Andrade, S. A. L. (2004). Experimental evaluation of extended endplate beam-to-column joints subjected to bending and axial force. Engineering Structures, 26(10), 1333–1347.

    Article  Google Scholar 

  • Markazi, F. D., Beale, R. G., & Godley, M. H. R. (1997). Experimental analysis of semi-rigid boltless connectors. Thin-Walled Structures, 28, 57–87.

    Article  Google Scholar 

  • Markazi, F. D., Beale, R. G., & Godley, M. H. R. (2001). Numerical modelling of semi-rigid boltless connectors. Computers & Structures, 79, 2391–2402.

    Article  Google Scholar 

  • McKenna, F., Fenves, G. L., Jeremic, B., & Scott, M. H. (2000). Open system for earthquake engineering simulation. http://opensees.berkely.edu.

  • Mitra N. (2012). Pinching4 model (OpenSees User Documetation). http://opensees.berkeley.edu/wiki/index.php/Pinching4_Material.

  • Moen, C. D., Tao, F., & Cole, R. (2016). Monotonic and cyclic backbone response of single shear cold-formed steel screw-fastened connections. In Proceedings of the international colloquium on stability and ductility of steel structures, SDSS2016, Timisoara, Romania.

  • NTC 2008, Ministero delle Infrastrutture. (2008). DM 14 gennaio 2008. Norme Tecniche per le Costruzioni.

  • Orlando, M., Lavacchini, G., Ortolani, B., & Spinelli, P. (2017). Experimental capacity of perforated cold-formed steel open sections under compression and bending. Journal of Steel and Composite Structures, 24, 201–211. ISSN:1229-9367.

  • Peterman, K. D., Nakata, N., & Schafer, B. W. (2014). Hysteretic characterization of cold-formed steel stud-to-sheathing connections. Journal of Constructional Steel Research, 101, 254–264.

    Article  Google Scholar 

  • Peterman, K. D., Stehman, M. J. J., Madsen, R. L., Buonopane, S. G., Nakata, N., & Schafer, B. W. (2016). Experimental seismic response of a full-scale cold-formed steel-framed building. I: System-level response. Journal of Structural Engineering, 142(12), 04016127.

    Article  Google Scholar 

  • Prabha, P., Marimuthu, V., Saravanan, M., & Arul Jayachandran, S. (2010). Evaluation of connection flexibility in cold formed steel racks. Journal of Constructional Steel Research, 66, 863–872.

    Article  Google Scholar 

  • Rodgers, J. E., & Mahin, S. A. (2011). Effects of connection deformation softening on behavior of steel moment frames subjected to earthquakes. International Journal of Steel Structures, 11(1), 29–37.

    Article  Google Scholar 

  • Rosin, I., Calado, L., Proença, J., Carydis, P., Mouzakis, H., Castiglioni, C., et al. (2009). Storage racks in seismic areas. Final report. Research Fund for Coal and Steel, European Commission.

  • SAP 2000. (2016). CSI Analysis Reference Manual for SAP 2000. Berkeley, CA: Computers and Structures Inc.

    Google Scholar 

  • Saws Model. (OpenSees User Documentation). 2010. http://opensees.berkeley.edu/wiki/index.php/SAWS_Material.

  • Shah, S. N. R., Ramli Sulong, N. H., Khan, R., Jumaat, M. Z., & Shariati, M. (2016). Behavior of Industrial Steel Rack Connections. Mechanical Systems and Signal Processing, 70–71, 72–740.

    Google Scholar 

  • Shen, Y. L., Schneider, J., Tesfamariam, S., Stiemer, S. F., & Mu, Z. G. (2013). Hysteresis behavior of bracket connection in cross-laminated-timber shear walls. Construction and Building Materials, 48, 980–991.

    Article  Google Scholar 

  • Silva, L. S., Lima, L. R. O., Vellasco, P. C. G., & Andrade, S. A. L. (2004). Behaviour of flush end-plate beam-to-column joints under bending and axial force. Steel and Composite Structures, 4(2), 77–94.

    Article  Google Scholar 

  • Silva, L. S., Santiago, A., & Real, P. V. (2002). Post-limit stiffness and ductility of end-plate beam-to-column steel joints. Computers & Structures, 80, 515–531.

    Article  Google Scholar 

  • Ślęczka, L., & Kozłowski, A. (2007). Experimental and theoretical investigations of pallet racks connections. Advanced Steel Construction, 3(2), 607–627.

    Google Scholar 

  • Takeda, T., Sozen, M. A., & Nielsen, N. N. (1970). Reinforced concrete response to simulated earthquakes. Journal, Structural Division, ASCE, 96(ST12), 2557–2573.

    Google Scholar 

  • Tao, F., Cole, R., & Moen, C. D. (2016). Monotonic and cyclic backbone response of single shear sheathing-to-cold-formed steel screw-fastened connections. In Wei-Wen Yu International Specialty Conference on Cold-Formed Steel Structures 2016—Recent Research and Developments in Cold-Formed Steel Design and Construction, Baltimore, Maryland.

  • Tilburgs, I. K. (2013). Those peculiar structures in cold formed steel: “Racking and shelving”. Steel Construction, 6(2), 95–106.

    Article  Google Scholar 

  • Tsai, K. C., Shiun, Wu, & Popov, E. P. (1995). Cyclic performance of steel beam-column moment joints. Engineering Structures, 8, 596–602.

    Article  Google Scholar 

  • Yin, L., Tang, G., Zhang, M., Wang, B., & Feng, B. (2016). Monotonic and cyclic response of speed-lock connections with bolts in storage racks. Engineering Structures, 116, 40–55.

    Article  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the Italian Rack Manufacturing Company ROSSS SpA, Scarperia and San Piero, Florence (IT), especially the President Stefano Bettini and Engineer Giovanni Lavacchini, for supporting this research work and kindly supplying specimens and hosting the experimental setup. Moreover, the authors greatly appreciate the skillful work of Mr. S. Giordano, Mr. F. Bruni and Mr. E. Barlacchi of the SMTL of the Department of Civil and Environmental Engineering of Florence for their assistance in the experimental work.

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  1. Department of Civil and Environmental Engineering, University of Florence, Via di S. Marta 3, 50139, Florence, Italy

    Federico Gusella, Maurizio Orlando & Paolo Spinelli

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  1. Federico Gusella
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Correspondence to Federico Gusella.

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Gusella, F., Orlando, M. & Spinelli, P. Pinching in Steel Rack Joints: Numerical Modelling and Effects on Structural Response. Int J Steel Struct 19, 131–146 (2019). https://doi.org/10.1007/s13296-018-0095-x

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