AUT Journal of Civil Engineering

AUT Journal of Civil Engineering

Moving Towards the 3D Seismic Design of Structures: A Review

Document Type : Review Article

Authors
Department of Civil Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran.
Abstract
There is a common simplification in seismic design codes that independently computes the seismic force in the two orthogonal directions. Then, individual frames are designed based on the distributed lateral forces. The 3D effects, including the interaction of adjacent and orthogonal frames, are omitted in this process, while research shows that the design results differ between 2D and 3D methods. Although most seismic assessment procedures and philosophies have been developed for 2D frames, there is no standard prescription for adopting them to assess 3D structures. The progress in the computational capability of computers makes the 2D design philosophy not acceptable anymore, and the engineering community needs to move toward a 3D point of view in assessing and designing structures. Many works have investigated the 3D behavior of structures or proposed 3D design strategies for different issues. There is a need to clarify the importance of the problem as an independent research field and urge the researchers to shed light on other aspects of the 3D structural behavior. This paper reviews the research in which the 3D structural design or behavior is addressed and shows weaknesses and future research paths. The study includes four main parts: modeling, assessment, design, and optimization of 3D structures. Finally, the main results and recommendations are presented.
Keywords
Subjects

[1] S.S. Gill, A. Kumar, H. Singh, M. Singh, K. Kaur, M. Usman, R. Buyya, Quantum computing: A taxonomy, systematic review and future directions, Softw.-Pract. Exp., 52(1) (2022) 66-114.
[2] B.G. Simpson, M. Zhu, A. Seki, M. Scott, Challenges in GPU-Accelerated Nonlinear Dynamic Analysis for Structural Systems, Journal of Structural Engineering, 149(3) (2023) 04022253.
[3] M. Baravalle, Risk and Reliability Based Calibration of Structural Design Codes: Principles and Applications, Norwegian University of Science and Technology, Norway, 2017.
[4] R. Fahrni, G. De Sanctis, A. Frangi, Comparison of reliability- and design-based code calibrations, Structural Safety, 88 (2021) 102005.
[5] T.V. Galambos, Load and resistance factor design, Engineering Journal,  (1981).
[6] N.C. Lind, Consistent Partial Safety Factors, Journal of the Structural Division, 97(6) (1971) 1651-1669.
[7] R.E. Melchers, A.T. Beck, Structural Reliability Analysis and Prediction, 3 ed., John Wiley & Sons, 2018.
[8] ASCE 7, Minimum design loads for buildings and other structures, in, American Society of Civil Engineers: Structural Engineering Institute, Reston, Va., 2022.
[9] Eurocode 8: Design of structures for earthquake resistance-Part 1: General rules, seismic actions and rules for buildings, in European Committee for Standardization, 2004.
[10] H. Maranhão, H. Varum, J. Melo, Seismic design challenges: investigating bending moments, shear actions, and design parameters in RC walls according to the second generation of Eurocode 8, Bulletin of Earthquake Engineering, 23(13) (2025) 5587-5623.
[11] S.A. Ashrafi, Nonlinear dynamic analysis as a tool for more optimal seismic design of tall buildings, Struct Eng Int J Int Assoc Bridge Struct Eng, 23(2) (2013) 141-147.
[12] G. Dong, R. Garcia, K. Pilakoutas, I. Hajirasouliha, A review of optimum seismic design of RC frames: State-of-the-art, challenges and future directions, Eng. Struct., 315 (2024) 118455.
[13] L. Velasco, H. Guerrero, A. Hospitaler, A. Teran, V. Rodriguez, What is the cost of permissible damage in seismic design of steel frames? Insights from surrogate model metaheuristic optimization and seismic loss assessment, Journal of Building Engineering, 113 (2025) 114058.
[14] h. Road, and urban development research center, Iranian code of practice for seismic resistant design of buildings (the draft of the fifth edition), in Tehran, Iran, 2025.
[15] J. Wang, H.V. Burton, K. Dai, Combination Rules Used to Account for Orthogonal Seismic Effects: State-of-the-Art Review, Journal of Structural Engineering, 145(11) (2019).
[16] J.W. Baker, Conditional Mean Spectrum: Tool for Ground-Motion Selection, J. Struct. Eng.-ASCE, 137(3) (2011) 322-331.
[17] J.W. Baker, C. Allin Cornell, Spectral shape, epsilon and record selection, Earthquake Engineering & Structural Dynamics, 35(9) (2006) 1077-1095.
[18] N. Jayaram, T. Lin, J.W. Baker, A Computationally Efficient Ground-Motion Selection Algorithm for Matching a Target Response Spectrum Mean and Variance, Earthq. Spectra, 27(3) (2011) 797-815.
[19] B.A. Bradley, A generalized conditional intensity measure approach and holistic ground-motion selection, Earthquake Engineering & Structural Dynamics, 39(12) (2010) 1321-1342.
[20] B.A. Bradley, A ground motion selection algorithm based on the generalized conditional intensity measure approach, Soil Dynamics and Earthquake Engineering, 40 (2012) 48-61.
[21] P. Bazzurro, C. Cornell, Disaggregation of Seismic Hazard, Bulletin of the Seismological Society of America, 89 (1999).
[22] K. Tarbali, B.A. Bradley, J.W. Baker, Consideration and Propagation of Ground Motion Selection Epistemic Uncertainties to Seismic Performance Metrics, Earthq. Spectra, 34(2) (2018) 587-610.
[23] Selecting and Scaling Earthquake Ground Motions for Performing Response-History Analyses, NIST GCR 11-917-15, National Institute of Standards and Technology, U.S.A, 2011.
[24] V. Gioncu, F. Mazzolani, Earthquake Engineering for Structural Design, Spon Press, London, 2011.
[25] Web of Science, in Clarivate.
[26] Y. Alashker, H. Li, S. El-Tawil, Approximations in Progressive Collapse Modeling, Journal of Structural Engineering, 137(9) (2011) 914-924.
[27] H.A. Mociran, A.G. Popa, Influence of 2D versus 3D modeling on the seismic performance of dual eccentrically braced steel frames, in:  6th International Conference on Structural Engineering, Mechanics and Computation (SEMC), CRC Press-Balkema, Cape Town, South Africa, 2016, pp. 338-341.
[28] H. Semsarha, P. Tehrani, B. Behnam, A Comparative Study on Pre- and Post-Earthquake Progressive Collapse Resistance of 2D and 3D Steel Structures, Int. J. Civ. Eng.,  (2023) 17.
[29] R. Palhares, K. Medeiros, G. Parsekian, N. Shrive, R. Marques, A unified modeling approach for concrete masonry shear walls: Conception, validation and insights, Eng. Struct., 321 (2024) 25.
[30] X. Huang, A. Brodsky, Multi-platform simulation of infilled shear-critical reinforced concrete frames subjected to earthquake excitations, Bulletin of Earthquake Engineering, 20(10) (2022) 5323-5348.
[31] G. Blasi, F. De Luca, M. Aiello, Hybrid Micro-Modeling Approach for the Analysis of the Cyclic Behavior of RC Frames, Front. Built Environ., 4 (2018) 12.
[32] S. Tanaka, M. Hori, T. Ichimura, Hybrid Finite Element Modeling for Seismic Structural Response Analysis of a Reinforced Concrete Structure, Journal of Earthquake and Tsunami, 10(05) (2016) 1640015.
[33] B. Sun, Q. Gu, P. Zhang, J. Ou, A Practical Multi-cross-line Model for Simulating Nonlinear Cyclic Behavior of Reinforced Concrete Shear Wall in Super High-Rise Buildings, in:  International Conference on Experimental Vibration Analysis for Civil Engineering Structures (EVACES), Springer International Publishing AG, Univ California San Diego, San Diego, CA, 2017, pp. 364-375.
[34] B. Sun, Q. Gu, P. Zhang, Y. Li, J. Ou, Efficient Simulation of RC Shear Walls in High-Rise Buildings Using a Practical Multi-Cross-Line-Model, J. Earthqu. Eng., 25(9) (2021) 1732-1761.
[35] O. Mishra, A.N.R. Chowdhury, P. Haldar, A concurrent multi-scale framework for performance assessment of moment resisting reinforced concrete frame, Eng. Struct., 330 (2025) 23.
[36] A. Boukham, V. Venzal, T. Parent, S. Morel, F. Dubois, B. Solbes, 3D hybrid modeling approach combining the finite and discrete element methods: Validation based on masonry shear wall tests, Int. J. Solids Struct., 289 (2024) 20.
[37] F. Tedesco, A. Bilotta, E. Turco, Multiscale 3D mixed FEM analysis of historical masonry constructions, Eur. J. Environ. Civ. Eng., 21(7-8) (2017) 772-797.
[38] A. Al-Fakih, Finite Element Modeling and Construction Aspects of Masonry Walls: An Overview, Rev. Int. Metod. Numer. Calc. Dise., 41(3) (2025) 41.
[39] Y.W. Liu, B. Sun, T. Guo, Z.X. Li, Multiscale damage analysis of engineering structures from material level to structural level: a systematic review, Int. J. Struct. Integr., 16(2) (2025) 275-310.
[40] G. Deierlein, A. Reinhorn, M. Willford, NEHRP Seismic Design Technical Brief No. 4: Nonlinear Structural Analysis for Seismic Design: A Guide for Practicing Engineers, NIST GCR 10-917-5, National Institute of Standards and Technology, U.S.A, 2010.
[41] B.H.H. Peng, G.A. MacRae, W.R. Walpole, P. Moss, R.P. Dhakal, C. Clifton, C. Hyland, Location of plastic hinges in axially loaded steel members, J. Constr. Steel. Res., 64(3) (2008) 344-351.
[42] F.M. Mazzolani, V. Piluso, Plastic design of seismic resistant steel frames, Earthquake Engineering & Structural Dynamics, 26(2) (1997) 167-191.
[43] M. Vafaei, S.C. Alih, A. Fallah, The accuracy of the lumped plasticity model for estimating nonlinear behavior of reinforced concrete frames under gradually increasing vertical loads, Struct. Concr., 21(1) (2020) 65-80.
[44] X.M. Zhao, Y.F. Wu, A.Y. Leung, H.F. Lam, Plastic Hinge Length in Reinforced Concrete Flexural Members, in:  12th East Asia-Pacific Conference on Structural Engineering and Construction (EASEC), Elsevier Science Bv, Hong Kong, Peoples R China, 2011, pp. 1266-1274.
[45] Y.C. Ou, R.A. Kurniawan, D.P. Kurniawan, N.D. Nguyen, Plastic hinge length of circular reinforced concrete columns, Comput. Concr., 10(6) (2012) 663-681.
[46] A. Elkady, D.G. Lignos, Analytical investigation of the cyclic behavior and plastic hinge formation in deep wide-flange steel beam-columns, Bulletin of Earthquake Engineering, 13(4) (2015) 1097-1118.
[47] A.M.A. Elkady, D. Lignos, Dynamic Stability of Deep and Slender Wide-Flange Steel Columns – Full Scale Experiments, in Structural Stability Research Council, 2016.
[48] F. Yuan, Y.F. Wu, Effect of load cycling on plastic hinge length in RC columns, Eng. Struct., 147 (2017) 90-102.
[49] L. Ren, B.W. Fang, K. Wang, F. Yuan, Numerical Investigation on Plastic Hinge Length of Ultra-high Performance Concrete Column under Cyclic Load, J. Earthqu. Eng.,  (2020) 19.
[50] S. Alacali, G. Arslan, A prediction model for plastic hinge length of rectangular RC columns using gene expression programming, Neural Comput. Appl.,  (2024) 21.
[51] J.A. Almeida, M.J. Bandelt, Plastic hinge length in reinforced HPFRCC beams and columns, Eng. Struct., 315 (2024) 13.
[52] P. Li, L. Jin, W.S. Chen, H. Hao, X.L. Du, Numerical investigation on plastic hinge behavior of hybrid steel-FRP reinforced concrete columns, Eng. Struct., 322 (2025) 14.
[53] L.L. Fan, L. Jin, O. Zhao, J. Liang, P. Li, X.L. Du, Plastic hinge behavior of rectangular CFRP-confined RC columns: Meso-scale modelling and formulation, Eng. Struct., 307 (2024) 16.
[54] A.S.o.C. Engineers, Seismic Evaluation and Retrofit of Existing Buildings, in American Society of Civil Engineers, U.S.A, 2017.
[55] A.T. Council, Guidelines for Nonlinear Structural Analysis for Design of Buildings, NIST GCR 17-917-46v2, National Institute of Standards and Technology, 2017.
[56] A.T. Council, Guidelines for Nonlinear Structural Analysis for Design of Buildings: Part IIb – Reinforced Concrete Moment  Frames, NIST GCR 17-917-46v3, National Institute of Standards and Technology 2017.
[57] A.T. Council, Guidelines for Nonlinear Structural Analysis for Design of Buildings, NIST GCR 17-917-46v1, National Institute of Standards and Technology, 2017.
[58] A. Maity, A. Kanvinde, D.I.H. Rosa, A.d.C.e. Sousa, D.G. Lignos, A Displacement-Based Fiber Element to Simulate Interactive Lateral Torsional and Local Buckling in Steel Members, Journal of Structural Engineering, 149(5) (2023) 04023045.
[59] A.R.T. Wayghan, V. Sadeghian, Consideration of Shear Behavior in Macromodeling of Deep Reinforced Concrete Members, Journal of Structural Engineering, 149(5) (2023) 04023037.
[60] A. Alghossoon, A.H. Varma, Fiber-based model for simulating strength and stiffness deterioration of high-strength steel beams, Thin-Walled Structures, 183 (2023) 14.
[61] M.P. Kassab, E.D.B. Campello, A. Ibrahimbegovic, A geometrically exact thin-walled rod model with warping and stress-resultant-based plasticity obtained with a two-level computational approach, Comput. Meth. Appl. Mech. Eng., 433 (2025) 18.
[62] A. Ghezelbash, A.M. D'Altri, S. Sharma, P.B. Lourenço, J.G. Rots, F. Messali, A block-based numerical strategy for modeling the dynamic out-of-plane behavior of unreinforced brick masonry walls, Meccanica,  (2024) 37.
[63] H. Garcia, J. Jimenez-Pacheco, J. Ulloa, Effective properties of masonry structures and macro-model analysis with experimental verification, Results Eng., 23 (2024) 20.
[64] D. Decret, Y. Malecot, Y. Sieffert, F. Vieux-Champagne, L. Daudeville, Extending a Macro-Element Approach for the Modeling of 3D Masonry Structures Under Transient Dynamic Loading, Appl. Sci.-Basel, 14(23) (2024) 25.
[65] P. Kesavan, A. Menon, A macro-element with bidirectional interaction for seismic analysis of unreinforced masonry walls, Earthquake Engineering & Structural Dynamics, 52(6) (2023) 1740-1761.
[66] F. Vanin, A. Penna, K. Beyer, A three-dimensional macroelement for modelling the in-plane and out-of-plane response of masonry walls, Earthquake Engineering & Structural Dynamics, 49(14) (2020) 1365-1387.
[67] B. Pantò, F. Cannizzaro, I. Caliò, P.B. Lourenço, Numerical and Experimental Validation of a 3D Macro-Model for the In-Plane and Out-Of-Plane Behavior of Unreinforced Masonry Walls, Int. J. Archit. Herit., 11(7) (2017) 946-964.
[68] I. Tistel, G. Grimstad, A macro model description of the non-linear anchor block foundation behavior, in:  6th International Conference on Structural Engineering, Mechanics and Computation (SEMC), CRC Press-Balkema, Cape Town, SOUTH AFRICA, 2016, pp. 2078-2084.
[69] B. Pantò, I. Caliò, P.B. Lourenço, A 3D discrete macro-element for modelling the out-of-plane behaviour of infilled frame structures, Eng. Struct., 175 (2018) 371-385.
[70] L.S. da Silva, S. Oliveia, R. Costa, F. Gentili, Design and analysis of steel structures considering the 3D behavior of the joints, Advanced Steel Construction, 16(2) (2020) 137-145.
[71] S. Sistla, R. Chandramohan, T.J. Sullivan, A Macro-Model for Simulating Gusset Plate Buckling in Buckling-Restrained Braced Frame Buildings, Earthquake Engineering & Structural Dynamics, 54(11) (2025) 2711-2726.
[72] A. Skiadopoulos, D.G. Lignos, Development of Inelastic Panel Zone Database, Journal of Structural Engineering, 147(4) (2021) 04721001.
[73] PEER, Open System for Earthquake Engineering Simulation (OpenSees), in Pacific Earthquake Engineering Research Center, University of California, Berkeley, 2023.
[74] A. Skiadopoulos, A. Elkady, D. Lignos, Improved panel zone model for seismic design of steel moment resisting frames, in:  The 17th World Conference on Earthquake Engineering, Sendai, Japan, 2020.
[75] A. Skiadopoulos, A. Elkady, D.G. Lignos, Proposed Panel Zone Model for Seismic Design of Steel Moment-Resisting Frames, Journal of Structural Engineering, 147(4) (2021) 04021006.
[76] R. Mata, E. Nunez, Parametric study of 3D steel moment connections with built-up box column subjected to biaxial cyclic loads, J. Constr. Steel. Res., 197 (2022) 35.
[77] D.A. Abdoh, Three-dimensional peridynamic modeling of deformations and fractures in steel beam-column welded connections, Eng. Fail. Anal., 160 (2024) 18.
[78] A. Dooshabi, M.A. Najafgholipour, Nonlinear finite element analysis of shear defective reinforced concrete beam to column connections strengthened with three practical techniques, Eng. Fail. Anal., 163 (2024) 36.
[79] E. Golias, P. Touratzidis, C.G. Karayannis, Seismic Response of RC Beam-Column Joints Strengthened with FRP ROPES, Using 3D Finite Element: Verification with Real Scale Tests, CivilEng, 5(2) (2024) 395-419.
[80] E. Nuñez, R. Mata, Strong column-weak beam relationship of 3D steel joints with tubular columns: Assessment, Validation and Design proposal, Journal of Building Engineering, 82 (2024) 18.
[81] K.V.A. Pham, Y.N. Kim, S. Woo, S.J. Kim, G. Lee, K. Lee, Experimental-FEA investigation of the structural performance of steel box connector in precast concrete connection, Journal of Building Engineering, 95 (2024) 23.
[82] J. Wu, Experimental study and numerical simulation of RHS column-to-I beam bolted connections with external diaphragms, Cogent Eng., 11(1) (2024) 16.
[83] W. Wang, Y. Chen, W. Li, R.T. Leon, Bidirectional seismic performance of steel beam to circular tubular column connections with outer diaphragm, Earthquake Engineering & Structural Dynamics, 40(10) (2011) 1063-1081.
[84] J. Fan, C. Liu, Y. Yang, Y. Bai, C. Wu, Shear capacity of 3D composite CFT joints subjected to symmetric loading condition, J. Constr. Steel. Res., 112 (2015) 242-251.
[85] I. Chan, Y. Koetaka, Numerical model for 3D steel moment frames with H-shaped beams and hollow-section columns under multi-directional seismic ground motions, Eng. Struct., 246 (2021) 112730.
[86] L.S. da Silva, S. Oliveira, R. Costa, F. Gentili, Design and analysis of steel structures considering the 3D behaviour of the joints, Advanced Steel Construction, 16(2) (2020) 137-145.
[87] Y. Bai, S. Wang, B. Mou, Y. Wang, K.A. Skalomenos, Bi-directional seismic behavior of steel beam-column connections with outer annular stiffener, Eng. Struct., 227 (2021) 111443.
[88] R. Mata, E. Nuñez, Cyclic Behavior of Concrete-Filled Tube Columns with Bidirectional Moment Connections Considering the Local Slenderness Effect, Buildings, 14(7) (2024) 48.
[89] F.P. Moncayo-Matute, D.F. Chicaiza-Machuca, I.S. Vélez-Sisalima, P.B. Torres-Jara, E. Vázquez-Silva, Seismic Behavior of Flange-Web Welded Plate Connections in Tubular and Concrete-Filled Columns Using Finite Element Analysis, Appl. Sci.-Basel, 14(15) (2024) 21.
[90] S. Jeyarajan, J.Y.R. Liew, Robustness analysis of 3D Composite buildings with semi-rigid joints and floor slab, Structures, 6 (2016) 20-29.
[91] M.N. Kataoka, A.L.H.C. El Debs, Parametric study of composite beam-column connections using 3D finite element modelling, J. Constr. Steel. Res., 102 (2014) 136-149.
[92] A. Ataei, M.A. Bradford, H.R. Valipour, Moment-Rotation Model for Blind-Bolted Flush End-Plate Connections in Composite Frame Structures, Journal of Structural Engineering, 141(9) (2015) 04014211.
[93] B. Mou, F. Zhao, F.Y. Wang, W. Pan, Effect of reinforced concrete slab on the flexural behavior of composite beam to column joints: Parameter study and evaluation formulae, J. Constr. Steel. Res., 176 (2021) 16.
[94] C. Amadio, C. Bedon, M. Fasan, Numerical assessment of slab-interaction effects on the behaviour of steel-concrete composite joints, J. Constr. Steel. Res., 139 (2017) 397-410.
[95] A. Braconi, A. Elamary, W. Salvatore, Seismic behaviour of beam-to-column partial-strength joints for steel-concrete composite frames, J. Constr. Steel. Res., 66(12) (2010) 1431-1444.
[96] T.C.H. Liu, Moment-rotation-temperature characteristic of steel/composite connections, J. Struct. Eng.-ASCE, 125(10) (1999) 1188-1197.
[97] L. Misini, J. Ristic, V. Hristovski, D. Ristic, Performance testing of roof beam-column connections for precast N-system, Mag. Concr. Res., 76(5) (2023) 261-271.
[98] J. Jin, T. Yan, T. Nagae, T. Okazaki, T. Matsumiya, N. Takahashi, Effect of composite slab and connection detail on cyclic behavior of steel beam-to-HSS column moment connections, Journal of Building Engineering, 95 (2024) 24.
[99] B. Gil, R. Goni, E. Bayo, Experimental Research and Finite Element Modeling of 3-D Semi-Rigid Composite Joints under Proportional Loads, in:  9th International Conference on Steel-Concrete Composite and Hybrid Structures, Res Publ Serv, Leeds, England, 2009, pp. 613-618.
[100] J.S. Fan, Q.W. Li, J.G. Nie, H. Zhou, Experimental Study on the Seismic Performance of 3D Joints between Concrete-Filled Square Steel Tubular Columns and Composite Beams, Journal of Structural Engineering, 140(12) (2014) 13.
[101] J.J. Xu, Z.P. Chen, Y.L. Chen, J.Y. Xue, Earthquake Damage Evaluation of T-Shaped SRC Composite Column-Steel Beams in 3D Connection Joints, Adv. Struct. Eng., 18(5) (2015) 701-713.
[102] M. Tonidis, A. Sharma, V. Birtel, Experimental and numerical investigations on the influence of transverse beams and slab on the seismic behavior of non-seismically designed exterior beam-column joints, Earthquake Engineering & Structural Dynamics, 53(14) (2024) 4451-4476.
[103] S. Singhal, A. Chourasia, S. Chellappa, J. Parashar, Precast reinforced concrete shear walls: State of the art review, Struct. Concr., 20(3) (2019) 886-898.
[104] M. Bruneau, J.W. Berman, D. Lopez-Garcia, D. Vian, A review of steel plate shear wall design requirements and research, Eng. J.-Amer. Inst. Steel Constr., 44(1) (2007) 27-34.
[105] J. Mo, B. Uy, D.X. Li, H.T. Thai, H. Tran, A review of the behaviour and design of steel-concrete composite shear walls, Structures, 31 (2021) 1230-1253.
[106] L. Pozza, R. Scotta, D. Trutalli, M. Pinna, A. Polastri, P. Bertoni, Experimental and Numerical Analyses of New Massive Wooden Shear-Wall Systems, Buildings, 4(3) (2014) 355-374.
[107] K. Kolozvari, C. Arteta, M. Fischinger, S. Gavridou, M. Hube, T. Isakovic, L. Lowes, K. Orakcal, J. Vásquez, J. Wallace, Comparative Study of State-of-the-Art Macroscopic Models for Planar Reinforced Concrete Walls, ACI Structural Journal, 115(6) (2018).
[108] K. Kolozvari, L. Biscombe, F. Dashti, R.P. Dhakal, A. Gogus, M.F. Gullu, R.S. Henry, L.M. Massone, K. Orakcal, F. Rojas, A. Shegay, J. Wallace, State-of-the-art in nonlinear finite element modeling of isolated planar reinforced concrete walls, Eng. Struct., 194 (2019) 46-65.
[109] M. Fischinger, T. Isakovic, K. Kolozvari, J. Wallace, Guest editorial: Nonlinear modelling of reinforced concrete structural walls, Bulletin of Earthquake Engineering, 17(12) (2019) 6359-6368.
[110] M. Fischinger, K. Rejec, T. Isakovic, Modeling Inelastic Shear Response of RC Walls, in:  15th World Conference on Earthquake Engineering, Lisbon, Portugal, 2012.
[111] Y. Lu, M. Panagiotou, Three-Dimensional Cyclic Beam-Truss Model for Nonplanar Reinforced Concrete Walls, Journal of Structural Engineering, 140(3) (2014) 04013071.
[112] Y. Lu, M. Panagiotou, I. Koutromanos, Three-dimensional beam-truss model for reinforced concrete walls and slabs – part 1: modeling approach, validation, and parametric study for individual reinforced concrete walls, Earthquake Engineering & Structural Dynamics, 45(9) (2016) 1495-1513.
[113] K. Kolozvari, K. Kalbasi, K. Orakcal, J. Wallace, Three-dimensional shear-flexure interaction model for analysis of non-planar reinforced concrete walls, Journal of Building Engineering, 44 (2021) 102946.
[114] K. Kolozvari, M.F. Gullu, K. Orakcal, Finite Element Modeling of Reinforced Concrete Walls Under Uni- and Multi-Directional Loading Using Opensees, J. Earthqu. Eng.,  (2021) 1-24.
[115] Q.B. To, J. Shin, S.J. Kim, H.W. Kim, K. Lee, Effective Prediction of Concrete Constitutive Models for Reinforced Concrete Shear Walls under Cyclic Loading, Materials, 17(8) (2024) 24.
[116] L.A.S. Kouris, S.P. Triantafyllou, D.A. Bournas, F.A. Kariou, Empirical Equations for Modelling Yarn-Mortar Debonding in TRM-Strengthened Masonry Walls Subjected to Out-of-Plane Loading, Buildings, 14(1) (2024) 22.
[117] L. Latha, S.R. Chaudhuri, Improving In-Plane Behavior of Weak Brick Masonry Walls Through Assimilation of Partially Confining RC Bands, J. Earthqu. Eng., 28(9) (2024) 2577-2599.
[118] Y. Nie, T.Y. Xie, X.Y. Zhao, A 3D pilot simulation of masonry walls retrofitted with steel strips using a novel meso-scale damage-plasticity interface model, Structures, 65 (2024) 21.
[119] Y.H. Zhao, X. Yan, Y.M. Zhang, Damage Analysis of 3D Masonry Structures under Explosion Shock Waves Based on the CDEM, KSCE J. Civ. Eng.,  (2024) 12.
[120] P. Fajfar, D. Marusic, I. Perus, Torsional effects in the pushover-based seismic analysis of buildings, J. Earthqu. Eng., 9(6) (2005) 831-854.
[121] M. De Stefano, B. Pintucchi, Predicting torsion-induced lateral displacements for pushover analysis: Influence of torsional system characteristics, Earthquake Engineering & Structural Dynamics, 39(12) (2010) 1369-1394.
[122] N. Li, C.H. Zhai, Z.X. Li, J.J. Hu, L.L. Xie, Energy-Based Modal Pushover Procedure for Asymmetric Structures, Adv. Struct. Eng., 13(6) (2010) 1129-1138.
[123] F. Khoshnoudian, M. Kiani, T.Y. Yang, A new pushover procedure for two-way asymmetric-plan tall buildings under bidirectional earthquakes, The Structural Design of Tall and Special Buildings, 23(14) (2014) 1097-1117.
[124] K. Shakeri, K. Tarbali, M. Mohebbi, Pushover analysis of asymmetric-plan buildings based on distribution of the combined modal story shear and torsional moment, Earthq. Eng. Eng. Vib., 13(4) (2014) 707-716.
[125] G. Manoukas, I. Avramidis, Improved multimode pushover procedure for asymmetric in plan buildings under biaxial seismic excitation—application to tall buildings, The Structural Design of Tall and Special Buildings, 24(6) (2015) 397-420.
[126] R.Z. Bidoki, M. Shayanfar, An energy-based pushover-analysis with torque-effects in assessment of the structures with asymmetric plan, Soil Dynamics and Earthquake Engineering, 108 (2018) 58-68.
[127] A. Rooshenas, Comparing pushover methods for irregular high-rise structures, partially infilled with masonry panels, Structures, 28 (2020) 337-353.
[128] M. Ghamari, M. Shooshtari, Application of Performance-Based Plastic Design (PBPD) method for 3D steel structures, Eng. Struct., 199 (2019) 109649.
[129] M. Ghamari, M. Shooshtari, H. Homaei, 3D design of steel structures with considering nonlinear base shear distribution and seismic energy, Structures, 37 (2022) 82-94.
[130] B. Daee, A.A. Aghakouchak, Assessment of Nonlinear Static Procedures for Determination of Target Displacement in Asymmetric Buildings, Adv. Struct. Eng., 15(8) (2012) 1265-1277.
[131] D. Mejía-Pérez, J. Valdés-González, J. De-la-Colina, Assessment of the inelastic structural response of building models that consider the combination of orthogonal seismic effects, Eng. Struct., 234 (2021).
[132] A.K. Chopra, R.K. Goel, Capacity-Demand-Diagram Methods Based on Inelastic Design Spectrum, Earthq. Spectra, 15(4) (1999) 637-656.
[133] P. Fajfar, Capacity spectrum method based on inelastic demand spectra, Earthquake Engineering & Structural Dynamics, 28(9) (1999) 979-993.
[134] T. Ucar, O. Merter, M. Duzgun, A study on determination of target displacement of RC frames using PSV spectrum and energy-balance concept, Struct. Eng. Mech., 41(6) (2012) 759-773.
[135] A. Habibi, E. Jami, Correlation Between Ground Motion Parameters and Target Displacement of Steel Structures, Int. J. Civ. Eng., 15(2A) (2017) 163-174.
[136] N.L. Sinkovic, M. Dolsek, J. Zizmond, Impact of the type of the target response spectrum for ground motion selection and of the number of ground motions on the pushover-based seismic performance assessment of buildings, Eng. Struct., 175 (2018) 731-742.
[137] A.K. Chopra, R.K. Goel, A modal pushover analysis procedure for estimating seismic demands for buildings, Earthquake Engineering & Structural Dynamics, 31(3) (2002) 561-582.
[138] M. Kreslin, P. Fajfar, The extended N2 method considering higher mode effects in both plan and elevation, Bulletin of Earthquake Engineering, 10(2) (2012) 695-715.
[139] M. Ferraioli, Multi-mode pushover procedure for deformation demand estimates of steel moment-resisting frames, International Journal of Steel Structures, 17(2) (2017) 653-676.
[140] M. Ferraioli, A. Lavino, A. Mandara, An adaptive capacity spectrum method for estimating seismic response of steel moment-resisting frames, Ing. Sismica, 33(1-2) (2016) 47-+.
[141] B. Gupta, S.K. Kunnath, Adaptive Spectra-Based Pushover Procedure for Seismic Evaluation of Structures, Earthq. Spectra, 16(2) (2000) 367-391.
[142] S. Antoniou, R. Pinho, Development of a displacement-based pushover procedure, J. Earthqu. Eng., 8(5) (2004) 643-661.
[143] M. Jalilkhani, S.H. Ghasemi, M. Danesh, A multi-mode adaptive pushover analysis procedure for estimating the seismic demands of RC moment-resisting frames, Eng. Struct., 213 (2020) 18.
[144] A.Y. Rahmani, N. Bourahla, R. Bento, M. Badaoui, Adaptive upper-bound pushover analysis for high-rise moment steel frames, Structures, 20 (2019) 912-923.
[145] F. Barbagallo, M. Bosco, A. Ghersi, E.M. Marino, An over-damped multimodal adaptive nonlinear static analysis for seismic assessment of infilled RC buildings, Eng. Struct., 229 (2021) 16.
[146] A. Daei, M. Poursha, On the accuracy of enhanced pushover procedures for seismic performance evaluation of code-conforming RC moment-resisting frame buildings subjected to pulse-like and non-pulse-like excitations, Structures, 32 (2021) 929-945.
[147] A.G. Sextos, Selection of Ground Motions for Response History Analysis, in: M. Beer, I.A. Kougioumtzoglou, E. Patelli, I.S.-K. Au (Eds.) Encyclopedia of Earthquake Engineering, Springer Berlin Heidelberg, Berlin, Heidelberg, 2015, pp. 1-10.
[148] B. Li, W.-C. Xie, M.D. Pandey, Generate tri-directional spectra-compatible time histories using HHT method, Nuclear Engineering and Design, 308 (2016) 73-85.
[149] S.-H. Ni, W.-C. Xie, M.D. Pandey, Tri-directional spectrum-compatible earthquake time-histories for nuclear energy facilities, Nuclear Engineering and Design, 241(8) (2011) 2732-2743.
[150] A.G. Langroudi, M. Davoodi, Spatially varying earthquake ground motion: artificial generation and effects on earth-fill dam behavior, Aust. J. Civ. Eng.,  (2022) 12.
[151] D. Huang, Z. Wang, Wavelet‐Based Stochastic Model for Jointly Simulating Three‐Component Ground Motions, Bulletin of the Seismological Society of America, 112(3) (2022) 1483-1501.
[152] K. Kostinakis, A. Athanatopoulou, K. Morfidis, Correlation between ground motion intensity measures and seismic damage of 3D R/C buildings, Eng. Struct., 82 (2015) 151-167.
[153] K. Kostinakis, A. Athanatopoulou, Incremental dynamic analysis applied to assessment of structure-specific earthquake IMs in 3D R/C buildings, Eng. Struct., 125 (2016) 300-312.
[154] Y. Zhou, P. Ge, M. Li, J. Han, An area-based intensity measure for incremental dynamic analysis under two-dimensional ground motion input, Struct. Des. Tall Spec. Build., 26(12) (2017).
[155] H. Rajabnejad, H. Hamidi, S.A. Naseri, M.A. Abbaszadeh, Effect of intensity measures on the response of a 3D-structure under different ground motion duration, International Journal of Engineering, 34(10) (2021) -.
[156] M. Ghamari, M. Shooshtari, Suitable intensity measures for 3D steel structures, Soil Dynamics and Earthquake Engineering, 175 (2023) 108230.
[157] C. Cantagallo, R. De Risi, M. Terrenzi, G. Camata, E. Spacone, Sufficiency assessment of intensity measures for natural and spectral-matched ground motion records, Bulletin of Earthquake Engineering, 22(13) (2024) 6305-6326.
[158] W. Zhen, Y. Qiu, Y. Zhang, W. Li, Ground-Motion Intensity Measures for the Seismic Response of the Roof-Isolated Large-Span Structure, Buildings, 14(2) (2024) 411.
[159] A.H. Ayabakan, A.F. Ugur, A.A. Dindar, Quantification of Ground Motion Intensity Using 3-Dimensional Input Energy Spectrum, in:  3rd International Workshop on Energy Based Seismic Engineering-IWEBSE, Springer International Publishing AG, Istanbul, TURKIYE, 2025, pp. 107-116.
[160] L. Simões da Silva, Towards a consistent design approach for steel joints under generalized loading, J. Constr. Steel. Res., 64(9) (2008) 1059-1075.
[161] B. Gil, R. Goñi, E. Bayo, Experimental and numerical validation of a new design for three-dimensional semi-rigid composite joints, Eng. Struct., 48 (2013) 55-69.
[162] H.-H. Khoo, K.-C. Tsai, C.-Y. Tsai, C.-Y. Tsai, K.-J. Wang, Bidirectional substructure pseudo-dynamic tests and analysis of a full-scale two-story buckling-restrained braced frame, Earthquake Engineering & Structural Dynamics, 45(7) (2016) 1085-1107.
[163] S.R. Bhardwaj, A.H. Varma, Design of Wall Structures for In-Plane and Out-of-Plane Forces: An Exploratory Evaluation, in:  Structures Congress, American Society of Civil Engineers, U.S.A, 2017, pp. 546-557.
[164] X. Wei, M. Bruneau, Experimental Performance of Buckling Restrained Braces Subjected to Bidirectional Displacement Histories, in:  16th World Conference on Earthquake Engineering, Santiago, Chile, 2017.
[165] X. Wei, M. Bruneau, Buckling Restrained Braces Applications for Superstructure and Substructure Protection in Bridges MCEER-16-0009, The University of Buffalo, Buffalo, U.S.A, 2016.
[166] J. Bleyer, P. de Buhan, Yield surface approximation for lower and upper bound yield design of 3D composite frame structures, Computers & Structures, 129 (2013) 86-98.
[167] J. Shen, B. Akbas, Seismic Energy Demand in Steel Moment Frames, J. Earthqu. Eng., 3(4) (1999) 519-559.
[168] E.M. Hernandez, G. May, Dissipated Energy Ratio as a Feature for Earthquake-Induced Damage Detection of Instrumented Structures, J. Eng. Mech., 139(11) (2013) 1521-1529.
[169] T. Rodriguez-Nikl, M.E. Rodriguez, Effect of Displacement and Hysteretic Energy on Earthquake Damage in Reinforced Concrete Structures, Journal of Structural Engineering, 147(7) (2021) 04021083.
[170] C.-M. Uang, V.V. Bertero, Evaluation of seismic energy in structures, Earthquake Engineering & Structural Dynamics, 19(1) (1990) 77-90.
[171] G.W. Housner, Limit design of structures to resist earthquake, in:  Proc. of 1st WCEE, 1956, pp. 5.1-5.13.
[172] S.C. Goel, W.C. Liao, M.R. Bayat, S.H. Chao, Performance-Based Plastic Design (Pbpd) Method for Earthquake-Resistant Structures: An Overview, Struct. Des. Tall Spec. Build., 19(1-2) (2010) 115-137.
[173] S. Leelataviwat, P. Doung, N. Naiyana, A Review on Performance-Based Plastic Design Method: Concept and Recent Developments in: A. Benavent-Climent, F. Mollaioli (Eds.) 1st International Workshop on Energy-Based Seismic Design, Springer, Madrid, Spain, 2021.
[174] A.J. Kappos, S. Stefanidou, A Performance-Based Seismic Design Procedure for 3D R/C Buildings, Explicitly Accounting for Deformation Control, in:  Workshop on Advances in Performances-Based Earthquake Engineering, Springer, Corfu, GREECE, 2009, pp. 149-159.
[175] A.S. Tzimas, T.L. Karavasilis, N. Bazeos, D.E. Beskos, Extension of the hybrid force/displacement (HFD) seismic design method to 3D steel moment-resisting frame buildings, Eng. Struct., 147 (2017) 486-504.
[176] A.S. Tzimas, T.L. Karavasilis, N. Bazeos, D.E. Beskos, A hybrid force/displacement seismic design method for steel building frames, Eng. Struct., 56 (2013) 1452-1463.
[177] M.N. Priestley, Direct displacement-based design of precast/prestressed concrete buildings, PCI Journal,  (2002).
[178] K. Farokhnia, M.G. Hooks, Seismic Design Provisions for 3D-Printed Buildings, J. Struct. Des. Constr. Pract., 30(4) (2025) 8.
[179] Y.N. Mu, J.T. Qu, Y. Shu, Y.B. Tan, Simplified Estimation Method of Plastic Energy Dissipation for MDOF Systems Using Force Analogy Method, Buildings, 13(5) (2023) 15.
[180] N. Gholami, S. Garivani, S.S. Askarian, I. Hajirasouliha, Estimation of hysteretic energy distribution for energy-based design of structures equipped with dampers, Journal of Building Engineering, 51 (2022) 23.
[181] G.B. Shargh, R. Barati, Estimation of inelastic seismic input energy, Soil Dynamics and Earthquake Engineering, 142 (2021) 17.
[182] U.A. Noor, Advances in Machine Learning for Structural Seismic Response Prediction: A Comprehensive Review, Arch. Comput. Method Eng.,  (2025) 84.
[183] S. He, S.Y. Wang, R.Y. Zhang, A generalizable gated graph recurrent unit (Graph-GRU) network for nonlinear response prediction of cross-structures, Computers & Structures, 318 (2025) 15.
[184] I. Choi, J. Choi, B.K. Oh, Time-frequency enhanced CNN models for nonlinear strain prediction in RC structures, Struct. Concr.,  (2025) 21.
[185] Q.Y. Zhang, M.Z. Guo, L.L. Zhao, Y. Li, X.X. Zhang, M. Han, Transformer-based structural seismic response prediction, Structures, 61 (2024) 23.
[186] P. Zakian, A. Kaveh, Multi-objective Seismic Design Optimization of Structures: A Review, Arch. Comput. Method Eng., 31(2) (2024) 579-594.
[187] A. Manguri, H. Hassan, N. Saeed, R. Jankowski, Topology, Size, and Shape Optimization in Civil Engineering Structures: A Review, CMES-Comp. Model. Eng. Sci., 142(2) (2025) 933-971.
[188] A. Kaveh, T. Bakhshpoori, M. Azimi, Seismic optimal design of 3D steel frames using cuckoo search algorithm, The Structural Design of Tall and Special Buildings, 24(3) (2015) 210-227.
[189] X.-S. Yang, Nature-Inspired Metaheuristic Algorithms, 1st ed.,    Luniver Press, United Kingdom, 2008.
[190] A. Martin, G. Deierlein, Structural topology optimization of tall buildings for dynamic seismic excitation using modal decomposition, Eng. Struct., 216 (2020) 17.
[191] A. Kaveh, S. Rezazadeh Ardebili, Optimum design of 3D reinforced concrete frames using IPGO algorithm, Structures, 48 (2023) 1848-1855.
[192] P.E. Mergos, Optimum design of 3D reinforced concrete building frames with the flower pollination algorithm, Journal of Building Engineering, 44 (2021) 102935.
[193] X.-S. Yang, Flower Pollination Algorithm for Global Optimization, in: J. Durand-Lose, N. Jonoska (Eds.) Unconventional Computation and Natural Computation, Springer Berlin Heidelberg, Berlin, Heidelberg, 2012, pp. 240-249.
[194] P.E. Mergos, Surrogate-based optimum design of 3D reinforced concrete building frames to Eurocodes, Dev. Built Environ., 11 (2022) 12.
[195] M.J.H. Mazdarani, S.R.H. Vaez, P. Hosseini, M.A. Fathali, Reliability-based layout optimization of concentrically braced in 3D steel frames, Structures, 47 (2023) 1094-1112.
[196] L.L. Xing, P. Gardoni, J.Y. Yu, Y. Zhou, P. Zhang, Multi-objective optimization of high-rise buildings with outrigger systems subject to seismic loads, Journal of Building Engineering, 111 (2025) 18.