Performance of rocking frames with friction tension-only devices
DOI:
https://doi.org/10.5459/bnzsee.1583Abstract
The implementation of a new friction tension-only “GripNGrab” device attached to a rocking steel frame is described. The device, when subject to significant tension dissipates energy via sliding in the frictional component. When the device is loaded in the compression direction, almost no compressive force is carried, but displacement occurs in the ratchetting component. This absence of any significant compressive force within the dissipative system means that the rocking frame will always recentre after uplift from earthquake shaking. A 9 m tall 4.75m wide 3-storey steel concentrically braced rocking frame is designed for low-damage seismic performance. Restoring forces are provided by (i) gravity, (ii) friction “GripNGrab” (GNG) tension-only dissipation devices at the base, and (iii) beam-slab effects. The initial fundamental period of the structure was 0.16s. The initial structure used a 10mm GNG ratchet pitch, and had a GNG strength to not slide under serviceability level shaking. Elastic, pushover, cyclic pushover, as well as time history analyses, with different shaking intensities are conducted using OpenSEES software. The scope of work is limited to a single building and a single ground motion. Parameters varied included the presence of beam-slab effects, and the GNG device stiffness, strength and tooth pitch.
It is shown that the full behaviour of the frame could be understood considering cyclic pushover analysis. The peak uplift displacement was conservatively estimated from the peak roof displacement using rigid body mechanics and the tension-only device provided no resistance to full frame recentring. For the frames considered, cumulative uplift displacements, necessary to determine the inelastic displacement capacity of the tension only device, were up to 28 times the peak uplift displacement, not necessarily occurring at the maximum shaking intensity. Maximum frame base shear force demands were up to 1.43 times that from pushover analysis. When the beam-slab, connecting the rocking frame to the rest of the structure, increased the lateral force resistance, the base shear increased significantly, reduced peak roof displacements, and increased the effective number of peak uplift displacement cycles (NPUDc). For large shaking intensities, yielding of the beam-slab occurred resulting in permanent peak roof and uplift displacements. The GNG device strength, stiffness and tooth pitch variations for the cases studied did not significantly affect the response. Initial stiffness, and secant stiffness, based methods to predict the response of rocking frames were non-conservative for these short-period structures with small energy dissipation, and a simple improvement to match the behaviour was developed for the case studied based on the R-T-m relationship for a range of shaking intensity.
References
Housner GW (1963). “The behavior of inverted pendulum structures during earthquakes”. Bulletin of the Seismological Society of America, 53(2): 403-417. https://doi.org/10.1785/BSSA0530020403 DOI: https://doi.org/10.1785/BSSA0530020403
Clough RW and Huckelbridge AA (1977). “Preliminary Experimental Study of Seismic Uplift of a Steel Frame”. Report No. UCB/EERC-77/22, Earthquake Engineering Research Center, University of California, Berkeley.
Priestley MJN, Evison RJ and Carr AJ (1978). “Seismic response of structures free to rock on their foundations”. Bulletin of the New Zealand Society for Earthquake Engineering, 11(3): 141-150. https://doi.org/10.5459/bnzsee.11.3.141-150 DOI: https://doi.org/10.5459/bnzsee.11.3.141-150
Tilby C (1981). “South Rangitikei Railway Bridge Construction”. IPENZ Transactions, 8(2).
Frost G and Tilby C (2014). “South Rangitikei Railway Bridge - Construction engineering”. The New Zealand Concrete Steel Conference. 9-11 October, Taupo, NZ.
Xiao Y, MacRae G, Hamada N, Priestley MJN and Seible F (1992). “Rocking and Capacity Test of Model Bridge Pier”. Structural Systems Research Project, Report No. SSRP 92/06, Department of Applied Mechanics and Engineering Sciences, University of California, San Diego.
Gledhill SM, Sidwell GK and Bell DK (2008). “The damage avoidance design of tall steel frame buildings - Fairlie Terrace Student Accommodation Project, Victoria University of Wellington”. Annual Conference of the New Zealand Society for Earthquake Engineering, Paper # 63.
Bruneau M and MacRae G (2017). “Reconstructing Christchurch: A Seismic Shift in Building Structural Systems”. QuakeCentre, University of Canterbury, NZ. https://resources.quakecentre.co.nz/reconstructing-christchurch/ DOI: https://doi.org/10.4028/www.scientific.net/KEM.763.11
Bruneau M and MacRae G (2019). “Building structural systems in Christchurch’s post-earthquake reconstruction”. Earthquake Spectra, 35(4): 1953–1978. https://doi.org/10.1193/052818EQS126O DOI: https://doi.org/10.1193/052818EQS126O
Deierlein G, Ma X, Hajjar F, Eatherton M, Krawinkler H, Takeuchi T, Midorikawa M, Hikino T and Kasai K (2010). “Seismic resilience of self-centering steel braced frames with replaceable energy-dissipating fuses; Part 2: E-Defense shake table test”. 7th International Conference on Urban Earthquake Engineering & 5th International Conference on Earthquake Engineering Joint Conference, 3-5 March, Tokyo.
Deierlein G, Ma X, Eatherton M, Hajjar JF, Krawinkler H, Takeuchi T, Kasai K and Midorikawa M (2011). “Earthquake resilient steel braced frames with controlled rocking and energy dissipating fuses”. Steel Construction Design and Research, 4(3): 171-175. https://doi.org/10.1002/stco.201110023 DOI: https://doi.org/10.1002/stco.201110023
MacRae G (2013). “Low damage construction – Some system issues”. 10th International Conference on Urban Earthquake Engineering, 1-2 March, Tokyo Institute of Technology, Japan.
Wiebe L, Sidwell G and Gledhill S (2015). “SCNZ: Design Guideline for Controlled Rocking Steel Braced Frames”. SCNZ Report 110. Prepared by Aurecon New Zealand Limited for SCNZ, NZ. https://www.scnz.org/wp-content/uploads/2020/11/P4_A-PRACTIONERS-GUIDE-TO-DESIGN-AND-DELIVERY-OF-CONTROLLED-ROCKING-STEEL-BRACED_Gledhill-min.pdf
Wiebe L (2015). “Controlled rocking steel braced frames: Connecting research and practice”. Steel Innovations Conference, 3-4 September, Auckland, NZ.
Kordani R, Rodgers GW and MacRae GA (2017). “Effect of post-tensioning loss due to relaxation in structural rocking walls”. Annual Conference of the New Zealand Society for Earthquake Engineering, 27-29 April, Wellington, NZ. https://www.nzsee.org.nz/db/2017/P1.31_Kordani.pdf
Rangwani K, MacRae GA, Rodgers GW, Soleimankhani H and J Cook (2020). “Tension-only device for a steel rocking frame system”. Proceedings of the New Zealand Society for Earthquake Engineering Annual Conference, 22-24 April, Wellington, NZ.
Gledhill S (2015). “A practitioner’s guide to design and delivery of controlled rocking steel braced frame structures”. Steel Innovations Conference, Auckland, NZ.
Eatherton M, Hajjar J, Ma X, Krawinkler H and Deierlein G (2010). “Seismic design and behavior of steel frames with controlled rocking—Part I: Concepts and quasi-static subassembly testing”. NASCC and Structures Congress, 12-15 May, Orlando, USA, pp.1523-1533. https://doi.org/10.1061/41130(369)138 DOI: https://doi.org/10.1061/41130(369)138
Ma X, Krawinkler H and Deierlein GG (2011). “Seismic design and behavior of self-centering braced frame with controlled rocking and energy dissipating fuses”. Report No. 174, The John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CA.
Royal Society Te Apārangi (2017). “Buildings that better survive earthquakes”. Royal Society, Wellington, NZ. https://www.rnz.co.nz/national/programmes/ourchangingworld/audio/2018629110/buildings-that-better-survive-earthquakes
Rodgers GW, Chase JG and Mander JB (2019). “Repeatability and high-speed validation of supplemental lead-extrusion energy dissipation devices”. Advances in Civil Engineering, 1–13. https://doi.org/10.1155/2019/7935026 DOI: https://doi.org/10.1155/2019/7935026
Xie R, Chanchi GJ, MacRae GA, Chase G, Rodgers G and Clifton C (2015). “Hysteretic behaviour of a frame using a brace equipped with an asymmetrical friction connection (AFC)”. Steel Innovations Conference, 3-4 September, Auckland, NZ.
MacRae GA and Clifton C (2015). “Research on seismic performance of steel structures in seismic areas”. STESSA Conference, Tongji University, Shanghai, China.
MacRae GA (2020). “Advanced Steel Structures”. ENEQ650 Lecture Notes, University of Canterbury, NZ.
Midorikawa M, Azuhata T, Ishihara T, Matsuba Y, Matsushima Y and Wada A (2002). “Earthquake response reduction of buildings by rocking structural systems”. Smart Structures and Materials 2002: Smart Systems for Bridges, Structures, and Highways. 28 June, International Society for Optics and Photonics. 4696: 265-272. https://doi.org/10.1117/12.472562 DOI: https://doi.org/10.1117/12.472562
Midorikawa M, Azuhata T, Ishihara T and Wada A (2006). “Shaking table tests on seismic response of steel braced frames with column uplift”. Earthquake Engineering and Structural Dynamics, 35(14): 1767-1785. https://doi.org/10.1002/eqe.603 DOI: https://doi.org/10.1002/eqe.603
Wada A, Yamada S, Fukuta O and Tanigawa M (2001). “Passive controlled slender structures having special devices at column connections”. Seventh International Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures, 2-5 October, Assisi, Italy. http://akira-wada.com/00_img/article/2001/0102s01_7thInterSeminar200110Assisi.pdf
Tremblay R, Poirier LP, Bouaanani N, Leclerc M, Rene V, Fronteddu L and Rivest S (2008). “Innovative viscously damped rocking braced steel frames”. Proceedings of the 14th World Conference on Earthquake Engineering, 12-17 October, Beijing, China.
Roke D, Sause R, Ricles J M and Gonner N (2009). “Damage-free seismic-resistant self-centering steel concentrically-braced frames”. STESSA2009: Proceedings of the 6th International Conference on Behaviour of Steel Structures in Seismic Areas, 16-20 August, Philadelphia, Pennsylvania, USA. ISBN 10: 0203861590 DOI: https://doi.org/10.1061/41031(341)155
Sause R, Ricles JM, Lin Y-C, Seo C-Y, Roke D and Chancellor B (2010). “Self-centring damage-free seismic-resistant steel frame systems”. 7th International Conference on Urban Earthquake Engineering & 5th International Conference on Earthquake Engineering Joint Conference, 3-5 March, Tokyo, Japan.
Eatherton M and Hajjar J (2011). “Residual drifts of self-centering systems including effects of ambient building resistance”. Earthquake Spectra, 27(3): 719-744. http://dx.doi.org/10.1193/1.3605318. DOI: https://doi.org/10.1193/1.3605318
Wiebe L (2008). “Mitigation of Higher Mode Effects in Self-Centring Walls by Using Multiple Rocking Sections”. Master of Earthquake Engineering Thesis, University Institute for Advanced Studies, University of Pavia, Italy.
Wiebe L (2013). “Design of Controlled Rocking Steel Frames to Limit Higher Mode Effects”. PhD Thesis, University of Toronto, Toronto, Ontario, Canada.
Wiebe L, Christopoulos C, Tremblay R and Leclerc M (2013a). “Mechanisms to limit higher mode effects in a controlled rocking steel frame. 1: Concept, modelling, and low amplitude shake table testing”. Earthquake Engineering and Structural Dynamics, 42(7): 1053-1068. https://doi.org/10.1002/eqe.2259 DOI: https://doi.org/10.1002/eqe.2259
Wiebe L, Christopoulos C, Tremblay R and Leclerc M (2013b). “Mechanisms to limit higher mode effects in a controlled rocking steel frame. 2: Large amplitude shake table testing”. Earthquake Engineering and Structural Dynamics, 42(7): 1069-1086. https://doi.org/10.1002/eqe.2258 DOI: https://doi.org/10.1002/eqe.2258
Wiebe L and Christopoulos C (2014). “Performance-based seismic design of controlled rocking steel braced frames. I: Methodological framework and design of base rocking joint”. Journal of Structural Engineering, 4014226. http://doi.org/10.1061/(ASCE)ST.1943-541X.0001202 DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0001202
MacRae G (1994). “P-Δ effects on single-degree-of-freedom structures”. Earthquake Spectra, 10(3): 539-568. http://dx.doi.org/10.1193/1.1585788 DOI: https://doi.org/10.1193/1.1585788
Gultom R and Ma QT (2015). “Biaxial pseudo dynamic tests of a post-tensioned rocking column with externally mounted energy dissipaters”. Proceedings of the NZSEE Annual Conference, pp.429-436. Rotorua, NZ. http://hdl.handle.net/2292/26824.
Bagheri H, Hashemi A, Quenneville P, Yousef-beik SMM and Zarnani P (2019). “Experimental test of a new self-centring tension-only brace using the Resilient Slip Friction Joint”. 11th Pacific Conference on Earthquake Engineering (PCEE), 4-9 April, Auckland, NZ. http://db.nzsee.org.nz/2019/Oral/4B.08%20Bagheri.pdf
Gunning M and Weston D (2013). “Assessment of Design Methodology for Rocking Systems”. ENCN493 Project Report, Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, NZ.
Cook J, Rodgers GW, MacRae GA and Chase JG (2015). “Experimentation with tension-only devices for use with seismic energy dissipation systems”. Proceedings of the Tenth Pacific Conference on Earthquake Engineering, Sydney, Australia.
Cook J, Rodgers GW, MacRae GA and Chase JG (2015). “Development of a ratcheting, tension only fuse mechanism for seismic energy dissipation.” Proceedings of the New Zealand Society for Earthquake Engineering Annual Conference, Rotorua, NZ.
Cook J, Rodgers GW, MacRae GA and Chase JG (2016). “Assessment of the structural response and cumulative displacement demand of Grip n’ Grab tension-only bracing system”. Proceedings of the New Zealand Society for Earthquake Engineering Annual Conference, Christchurch, NZ.
Cook J, Rodgers GW, MacRae GA and Chase JG (2017). “Testing and modelling of prototype tension-only seismic energy dissipation devices”. 16th World Conference on Earthquake Engineering (16WCEE), Santiago, Chile.
Cook J, Rodgers GW and MacRae GA (2018). “Design and testing of ratcheting, tension-only devices for seismic energy dissipation systems”. Journal of Earthquake Engineering, 24: 1-22. http://doi.org/10.1080/13632469.2018.1441765
Cook J (2018). “Design, Testing and Simulation of Grip ‘n’ Grab Ratcheting, Tension-only Devices for Seismic Energy Dissipation Systems”. PhD Thesis, University of Canterbury, Christchurch, NZ. DOI: https://doi.org/10.1080/13632469.2018.1441765
Cook J, Rodgers GW and MacRae GA (2019). “Assessment of cumulative inelastic displacement demand in energy dissipation systems using the Grip ‘n’ Grab tension-only mechanism”. Pacific Conference on Earthquake Engineering (PCEE), 4-6 April Auckland, NZ.
Rad A and MacRae G (2017). “Dynamically straightening of low-damage steel buildings after earthquakes”. 16th World Conference on Earthquake Engineering (16WCEE), Santiago, Chile. https://www.wcee.nicee.org/wcee/article/16WCEE/WCEE2017-529.pdf
Anderson PM and Simcock DM (2015). “Displacement Sensor”. Final Year Project, University of Canterbury, Christchurch, NZ.
MacRae GA (2010). “Some steel seismic research issues”. Proceedings of the Steel Structures Workshop on Research Directions for Steel Structures, University of Canterbury, Christchurch, NZ.
Livia E, Yoo J and MacRae GA (2019). “Development of a tension-only friction dissipater for rocking wall”. Pacific Conference on Earthquake Engineering (PCEE), 4-6 April Auckland, NZ.
Gu Z, Lu W and Ga Y (2022). “Asymmetrical friction damper to improve seismic behaviour of tension-only braces: An experimental and analytical study”. Engineering Structures, 256. https://doi.org/10.1016/j.engstruct.2022.114029 DOI: https://doi.org/10.1016/j.engstruct.2022.114029
Chanchi GJ, Xie R, MacRae GA, Chase G, Rodgers G and Clifton GC (2015). “Low damage brace using a symmetrical friction connection (SFC) detail”. New Zealand Society of Earthquake Engineering Annual Conference, April, Rotorua, NZ.
Pall AS and Marsh C (1982). “Response of friction damped braced frames”. Journal of the Structural Division, 108(6): 1313–1323. http://palldynamics.com/pdf/40Pall_doc1.pdf DOI: https://doi.org/10.1061/JSDEAG.0005968
Grigorian CE and Popov EP (1994). “Experimental and Analytical Studies of Steel Connections and Energy Dissipaters”. Report UCB/EERC-95/13, Engineering Research Centre. San Francisco, USA.
Ramhormozian S, Clifton C and MacRae GA (2014). “The asymmetric friction connection with Belleville springs in the sliding hinge joint”. Proceedings of the New Zealand Society for Earthquake Engineering Annual Conference, 21 April, Auckland, NZ. P27. http://db.nzsee.org.nz/2014/poster/27_Ramhormozian.pdf
Ramhormozian S, Clifton C, MacRae GA and Davet GP (2017). “Stiffness-based approach for Belleville springs use in friction sliding structural connections”. Journal of Constructional Steel Research, 138: 340-356. https://dx.doi.org/10.1016/j.jcsr.2017.07.009 DOI: https://doi.org/10.1016/j.jcsr.2017.07.009
Chanchi JG, MacRae GA, Chase JG, Rodgers GW and Clifton GC (2016). “Effects of the bolt grip length on the behaviour of asymmetrical friction connections (AFC)”. Proceedings of the New Zealand Society for Earthquake Engineering Annual Conference, NZ.
Chanchi JG, MacRae GA, Chase JG, Rodgers GW and Clifton GC (2020). “Asymmetric friction connection bolt lever arm effects on hysteretic behaviour”. Journal of Earthquake Engineering, 1-22. http://dx.doi.org/10.1080/13632469.2020.1733136. DOI: https://doi.org/10.1080/13632469.2020.1733136
Hatami M, MacRae GA, Rodgers GW and Clifton C (2019). “Steel shim hardness effects on asymmetric friction connection performance”. 12th Canadian Conference on Earthquake Engineering, 17-20 June, Quebec, Canada.
Zhang R, Xie J-Y, Chouery K-E, Liu J-R, Jia L-J, Xiang P, Zhao X-Z, MacRae GA, Clifton GC, Dhakal RP, Ramhormozian S and Yan Z-D (2022). “Strong axis low-damage performance of rocking column-base joints with asymmetric friction connections”. Journal of Constructional Steel Research 191(2022): 107175. https://doi.org/10.1016/j.jcsr.2022.107175 DOI: https://doi.org/10.1016/j.jcsr.2022.107175
Rangwani K, MacRae GA, Rodgers GW and Soleimankhani H (2021). “Rocking frame behaviour with tension only device – Numerical study”. Proceedings of the New Zealand Society for Earthquake Engineering (NZSEE) Annual Conference, 12-16 April, Christchurch, NZ.
Soleimankhani H, MacRae G and Sullivan T (2021). “The oscillation resistance ratio (ORR) for understanding inelastic response”. Bulletin of the New Zealand Society for Earthquake Engineering, 54(3): 299-312. https://doi.org/10.5459/bnzsee.54.4.299-312 DOI: https://doi.org/10.5459/bnzsee.54.4.299-312
Newmark NM et al. (1948). “Tentative Provisions for the Development of Seismic Regulations for Buildings”. Applied Technology Council Report ATC 3-06, NBS Special Publication 510, NSF Publication 78-8.
Berrill JB, Priestley MJN and Chapman HE (1980). “Section 2 - Design earthquake loading and ductility demand”. Bulletin of the New Zealand Society for Earthquake Engineering, 13(3): 232-241. https://doi.org/10.5459/bnzsee.13.3.232-241 DOI: https://doi.org/10.5459/bnzsee.13.3.232-241
Standards New Zealand (2016). “NZS1170.5: Structural Design Actions - Part 5: Earthquake Actions - New Zealand Incorporating Amendment No. 1”. Standards New Zealand, Wellington, NZ. https://www.standards.govt.nz/shop/nzs-1170-52004
Vidic T, Fajfar P and Fischinger M (1994) “Consistent inelastic design spectra: Strength and displacement”. Earthquake Engineering and Structural Dynamics, 23(5): 507-521. https://doi.org/10.1002/eqe.4290230504 DOI: https://doi.org/10.1002/eqe.4290230504
Rahgozar N, Moghadam A and Aziminejad A (2016). “Inelastic displacement ratios of fully self-centering-controlled rocking systems subjected to near-source pulse-like ground motions”. Engineering Structures, 108: 113-133. https://doi.org/10.1016/j.engstruct.2015.11.030 DOI: https://doi.org/10.1016/j.engstruct.2015.11.030
Joo A, Zsarnoczay A, Opoldusz M and Kollar L (2016). “Applicability of modal response spectrum analysis on rocking structures”. Proceedings of the 16th World Conference on Earthquake Engineering, Santiago, Chile.
Seo CY (2005). “Influence of Ground Motion Characteristics and Structural Parameters on Seismic Responses of SDOF Systems”. PhD Thesis, Lehigh University, Bethlehem, PA.
Zhang C, Steele TC and Wiebe LDA (2018). “Design-level estimation of seismic displacements for self-centering SDOF systems on stiff soil”. Engineering Structures, 177: 431-443. https://doi.org/10.1016/j.engstruct.2018.09.067 DOI: https://doi.org/10.1016/j.engstruct.2018.09.067
Gulkan P and Sozen M (1974). “Inelastic responses of reinforced concrete structures to earthquake motions”. ACI Journal, 71(12): 604-610. https://doi.org/10.14359/7110 DOI: https://doi.org/10.14359/7110
Applied Technology Council (1996). “ATC 40 Seismic Evaluation and Retrofit of Concrete Buildings, Vol 1 & 2”. Report No. SSC 96-01. Applied Technology Council, Redwood City, California, USA. https://www.atcouncil.org/pdfs/atc40toc.pdf
Priestley MJN, Calvi MC and Kowalsky MJ (2007). “Displacement-Based Seismic Design of Structures”. Pavia, Italy: IUSS PRESS 670pp.
FEMA (2000). “FEMA356: Report on the Prestandard and Commentary for the Seismic Rehabilitation of Buildings”. Federal Emergency Management Agency, Washington, DC. https://www.nehrp.gov/pdf/fema356.pdf
Pennucci D, Sullivan TJ and Calvi GM (2011). “Displacement reduction factors for the design of medium and long period structures”. Journal of Earthquake Engineering, 15(S1): 1-29. https://doi.org/10.1080/13632469.2011.562073 DOI: https://doi.org/10.1080/13632469.2011.562073
MacRae GA, Zhao X, Clifton C, L-J Jia, Dhakal R, Xiang P, Ramhormozian S and Rodgers G (2020). “The China-NZ ROBUST friction building shaking table testing overview”. 17th World Conference on Earthquake Engineering, September, Sendai, Japan. Paper C000558.
Yan Z, Ramhormozian S, Clifton C. Bagheri H, Rangwani K, MacRae G, Quenneville P, Dhakal R, Xiang P, Jia L and Zhao X (2021). “Three-storey configurable steel framed building incorporating friction based energy dissipater: Structural configuration and instrumentation”. Proceedings of the New Zealand Society for Earthquake Engineering Annual Conference, 14 - 16 April, Christchurch, NZ.
Rangwani K, MacRae GA, Rodgers GW, Yan Z, Clifton C and Ramhormozian S (2022). “Planning and prediction of large-scale ROBUST rocking frame test”. Draft Paper for Bulletin of the New Zealand Society for Earthquake Engineering.
MacRae GA, Ahmadzadah S, Ashdown J, Soleimankhani H and McGann C (2021). “Moment frame column seismic demands”. Proceedings of the New Zealand Society for Earthquake Engineering Annual Conference, 14-16 April, Christchurch, NZ.
McKenna F, Fenves GL and Scott MH (2003). “Open System for Earthquake Engineering Simulation”. Pacific Earthquake Engineering Research Center, University of California, Berkeley, California. http://opensees.berkeley.edu
Rangwani et al (2018). “ROBUST Outputs Folders”. https://www.dropbox.com/sh/h8x4zf03m02dj7y/AADmQfVa1c1EvSSqLRCtwY57a?dl=0.
Standards New Zealand (1997). “NZS3404: Part 1. Steel Structures Standard, Part 1”. Standards Association of New Zealand, Wellington, NZ. https://www.standards.govt.nz/shop/nzs-3404-parts-1-and-21997
Carr A (2007). “Ruaumoko Theory Manual: Volume 1”. https://doi.org/10.13140/RG.2.1.1872.2728
Jury RD (1978). "Seismic Load Demands on Columns of Reinforced Concrete Multi-Storey Frames". ME Thesis, University of Canterbury, Christchurch, 129pp.
Standards New Zealand (1982). “NZS3101.1. 1982. Code of Practice for Design of Concrete Structures, Part 1”. Standards Association of New Zealand, Wellington, NZ. https://www.standards.govt.nz/shop/nzs-3101-11982/.
MacRae G and Carr A (1987). “Capacity design of steel moment resisting frames”. Pacific Conference of Earthquake Engineering (PCEE), 4-6 April Auckland, NZ.
