Analytical simulation of seismic collapse of RC frame buildings


Application of a fibre-element nonlinear modelling technique for seismic collapse capacity assessment of RC frame buildings in comparison with conventional lumped plasticity models is investigated in this paper. Constitutive material models of concrete and steel for fibre elements are adopted to enable simulation of the loss in vertical load carrying capacity of structural columns. Inclusion of the nonlinear second order P−Δ effects accelerated by degrading behaviour of steel and concrete materials in the fibre model allows prediction of the sidesway mode of collapse. The model is compared with nonlinear lumped plasticity models in which stiffness and strength degradation is replicated through degrading parameters in structural components. Static cyclic analyses of an example cantilever column and a portal frame indicate that the variation of axial loads in columns may result in accelerated degradation and failure of structural components which is not taken into account by lumped plasticity models. Moreover, incremental dynamic analysis of a ten-storey RC frame shows that the lumped plasticity model may overestimate building collapse capacity when vertical failure of structural components occurs prior to sidesway instability.


FEMA (2012). "Seismic Performance Assessment of Buildings, Volume 1 – Methodology”. FEMA P-58-1, Applied Technology Council for the Federal Emergency Management Agency, Washington, D.C.

Ibarra LF and Krawinkler H (2005). “Global Collapse of Frame Structures under Seismic Excitations”, Report No. TB 152, The John A Blume Earthquake Engineering Center, Stanford University, Stanford California.

Krawinkler H, Zareian F, Medina RA and Ibarra LF (2006). “Decision Support for Conceptual Performance‐Based Design”. Earthquake engineering & structural dynamics, 35(1): 115-133. DOI:

Zareian F and Krawinkler H (2007). “Assessment of Probability of Collapse and Design for Collapse Safety”. Earthquake Engineering & Structural Dynamics, 36(13): 1901-1914. DOI:

Lingos DG and Krawinkler H (2012). “Sidesway Collapse of Deteriorating Structural Systems under Seismic Excitations”. Rep. No. TB 177, The John A. Blume Earthquake Engineering Research Center, Stanford University, Stanford, CA.

Burton H and Deierlein G (2014). “Simulation of Seismic Collapse in Nonductile Reinforced Concrete Frame Buildings with Masonry Infills." Journal of Structural Engineering. 140, SPECIAL ISSUE: Computational Simulation in Structural Engineering, A4014016.

Eads L, Miranda E, Krawinkler H, and Lingos L (2013). “An Efficient Method for Estimating the Collapse Risk of Structures in Seismic Regions”. Earthquake Engineering & Structural Dynamics, 42(1): 25-40. DOI:

Zareian F, Krawinkler H, Ibarra LF and Lingos D (2010). “Basic Concepts and Performance Measures in Prediction of Collapse of Buildings under Earthquake Ground Motions”. Structural Design of Tall and Special Buildings, 19(1-2): 167-181.

Lignos D and Krawinkler H (2007). “A Database in Support of Modeling of Component Deterioration for Collapse Prediction of Steel Frame Structures”. Structural Engineering Research Frontiers, 249(31): 1-12. DOI:

Lignos DG and Krawinkler H (2010). “Deterioration Modeling of Steel Components in Support of Collapse Prediction of Steel Moment Frames under Earthquake Loading”. Journal of Structural Engineering, 137(11): 1291-1302. DOI:

Lignos DG and Krawinkler H (2012). “Development and Utilization of Structural Component Databases for Performance-Based Earthquake Engineering”. Journal of Structural Engineering, 139, SPECIAL ISSUE: NEES 2: Advances in Earthquake Engineering, 1382–1394.

Ibarra LF, Medina RA and Krawinkler H (2002). “Collapse Assessment of Deteriorating SDOF Systems”. Proceedings of 12th European Conference on Earthquake Engineering, Elsevier Science Ltd., London, September 2002, Paper No 665. 669-613.

Ibarra LF, Medina RA and Krawinkler H (2005). “Hysteretic Models that Incorporate Strength and Stiffness Deterioration”. Earthquake Engineering & Structural Dynamics, 34(12): 1489-1511. DOI:

Zareian F, and Krawinkler H (2006). “Simplified Performance-Based Earthquake Engineering." Report No. 162, The John A Blume Earthquake Engineering Center, Stanford University, Stanford, California.

Berry M, Parrish M and Eberhard M (2004). “PEER Structural Performance Database User’s Manual (Version 1.0)”. Pacific Earthquake Engineering Research Center, University of California, Berkeley, California.

FEMA-356 (2000). “Prestandard and Commentary for the Seismic Rehabilitation of Buildings”. Federal Emergency Management Agency, Washington, D.C.

Haselton C, Liel A, Lange ST and Deierlein G (2008). “Beam-Column Element Model Calibrated for Predicting Flexural Response Leading to Global Collapse of RC Frame Buildings”. PEER Report 2007/03, Pacific Earthquake Engineering Research Center College of Engineering University of California, Berkeley.

Bao Y, Kunnath SK, El-Tawil S and Lew H (2008). “Macromodel-Based Simulation of Progressive Collapse: RC Frame Structures”. Journal of Structural Engineering, 134(7): 1079-1091. DOI:

Khandelwal K, El-Tawil S, Kunnath SK and Lew H (2008). “Macromodel-Based Simulation of Progressive Collapse: Steel Frame Structures”. Journal of structural engineering, 134(7), 1070-1078. DOI:

Tsai M-H (2012). “Evaluation of Different Loading Simulation Approaches for Progressive Collapse Analysis of Regular Building Frames”. Structure and Infrastructure Engineering, 8(8): 765-779. DOI:

Masoero E, Darò P and Chiaia B (2013). “Progressive Collapse of 2D Framed Structures: An Analytical Model”. Engineering Structures, 54: 94-102.

Elwood KJ and Moehle JP (2008). “Dynamic Collapse Analysis for a Reinforced Concrete Frame Sustaining Shear and Axial Failures”. Earthquake Engineering & Structural Dynamics, 37(7): 991-1012. DOI:

Baradaran Shoraka M, Yang T and Elwood K (2013). “Seismic Loss Estimation of Non‐Ductile Reinforced Concrete Buildings”. Earthquake Engineering & Structural Dynamics, 42(2): 297-310. DOI:

Elwood KJ (2004). “Modelling Failures in Existing Reinforced Concrete Columns”. Canadian Journal of Civil Engineering, 31(5): 846-859. DOI:

OpenSees (2012). “Open System for Earthquake Engineering Simulation”. Pacific Earthquake Engineering Research Centre, University of California, Berkeley, California.

Popovic’s S (1973). “A Numerical Approach to the Complete Stress Strain Curve for Concrete”. Cement and Concrete Research, 3(5): 583-599. DOI:

Mander JB, Priestley MJN and Park R (1988). “Theoretical Stress‐Strain Model for Confined Concrete”. Journal of Structural Engineering, 114(8): 1804–1826. DOI:

Karthick MM, and Mander JB (2011). “Stress-Block Parameters for Unconfined and Confined Concrete Based on a Unified Stress-Strain Model”. Journal of Structural Engineering, 137(2): 270–273. DOI:

Concrete Structures Standard (2006). “NZS310: Part 1-The Design of Concrete Structures”. Standards New Zealand, Wellington,

Kunnath SK, Heo Y and Mohle JF (2009). “Nonlinear Uniaxial Material Model for Reinforcing Steel Bars”. Journal of Structural Engineering, 135(4): 335–343. DOI:

Chang G, and Mander J (1994). “Seismic Energy Based Fatigue Damage Analysis of Bridge Columns: Part I – Evaluation of Seismic Capacity”. Technical Report NCEER-94-0006, National Center for Earthquake Engineering, University of New York at Buffalo, Buffalo, NY 14261.

Dhakal RP and Maekawa K (2002). “Modeling for Postyield Buckled of Reinforcement”. Journal of Structural Engineering, 128(9): 1139-1147. DOI:

Dhakal RP and Maekawa K (2002). “Path-Dependent Cyclic Stress–Strain Relationship of Reinforcing Bar Including Buckling”. Engineering Structures, 24(11): 1383–1396. DOI:

Bull D and Brunsdon D (1998). “Examples of Concrete Structural Design to New Zealand Standards 3101". New Zealand.

Kampenhuber D and Adam C (2013). “Vulnerability of Collapse Capacity Spectra to Material Deterioration”. Proceedings of the Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics (VEESD 2013), Vienna, Austria, 28–30 August 2013.

Tsantaki S, Ibarra LF and Adam C (2013). “Effect of Modelling Uncertainty on the Seismic Collapse Capacity of Simple Systems Vulnerable to the P-delta Effect”. Proceedings of the Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics (VEESD 2013), Vienna, Austria, 28-30 August 2013.

Vamvatsikos D and Cornell A (2002). “Incremental Dynamic Analysis”. Earthquake Engineering & Structural Dynamics, 31(3): 491-514. DOI:

How to Cite
Koopaee, M. E., Dhakal, R. P., & MacRae, G. (2015). Analytical simulation of seismic collapse of RC frame buildings. Bulletin of the New Zealand Society for Earthquake Engineering, 48(3), 157-169.

Most read articles by the same author(s)

1 2 3 > >>