Mathematical Modeling of Column-Base Connections under Monotonic Loading

Document Type : Research Papers


1 Assistant Professor, Department of Civil Engineering, Babol University of Technology, Babol, Iran

2 M.Sc. Student, Department of Civil Engineering, Shomal University of Amol, Amol, Iran.


Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1) analysis methods of semi-rigid joints; (2) prediction methods for the mechanical behavior of joints; (3) mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.


Benoit, P.G. and Kim J.R. (2011). “Determination of the base plate stiffness and strength of steel storage racks”, Journal of Constructional Steel Research, 67(6), 1031-1041.
Chisala, M.L. (1999). “Modeling M–f curves for standard beam to column connections”, Engineering Structures, 21(2), 1066–1075.
Ermopoulos, J. and Stamatopoulos, G. (1996). “Mathematical modeling of column base plate connection”, Journal of Constructional Steel Research, 36(2), 79–100.
Ermopoulos, J. and Stamatopoulos, G. (2011). “Experimental and analytical investigation of steel column bases”, Journal of Constructional Steel Research, 67(9), 1341-1357.
Eurocode 3. (2003). “Design of steel structures, part 1.8: design of joints”, European Committee for Standardization, Brussels.
Hamizi, M., Ait-Aider, H. and Aliche, A. (2011). “Finite element method for evaluating rising and slip of column–base plate for usual connections”, Strength of Materials, 43(6), 662-672.
Hashemi, M.J. and Mofid, M. (2010). “Evaluation of energy-based modal pushover analysis in reinforced concrete frames with elevation irregularity”, Scientia Iranica, 17(2), 96–106.
Hoseok, C. and Judy, L. (2012). “Seismic behavior of post-tensioned column base for steel self-centering moment resisting frame”, Journal of Constructional Steel Reasearch, 78(1), 117–130.
Jae-Hyouk, C. and Yeol, C. (2013). “An experimental study on inelastic behavior for exposed-type column bases under three-dimensional loadings”, Journal of Mechanical Science and Technology, 27(3), 747-759.
James, M. and Lawrence, A. (2010). Steel design guide 1: base plate and anchor rod design, 2nd Edition, AISC.
Kishi, N. and Chen, W.F. (1990). “Moment-rotation relations of semi-rigid connections with angles”, Journal of Structural Engineering, ASCE, 116(7), 1813–1834.
Krishnamurthy, N. and Thambiratham, D.P. (1990). “Finite element analysis of column base plates”, Computers and Structures, 34(2), 215–23.
Latour, M., Piluso, V. and Rizzano G. (2014). “Rotational behavior of column base plate connections: Experimental analysis and modeling”, Engineering Structures, 68(1), 14-23.
Lee, D. and Goel, S.C. (2001). “Seismic behavior of column-base plate connections bending about weak axis”, Report No. UMCEE 01-09, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, Michigan.
Lorenz, R.F., Kato, B. and Chen, W.F. (1993). “Semi-rigid connections in steel frames”, Proceedings of Council on TallBuildings and Urban Habitat, McGraw-Hill, Inc., New York, NY.
Mofid, M. and Mohamadi, M.R. (2011). “New modeling for moment–rotation behavior of bolted endplate connections”, Scientia Iranica, 18(4), 827–834.
Mofid, M., Ghorbani, M. and McCabe, S.L. (2001). “On the analytical model of beam-to-column semi-rigid connections, using plate theory”, Thin-Walled Structures, 39(4), 307–325.
Mofid, M., Mohamadi, M.R. and McCabe, S.L. (2005). “Analytical approach on end plate connection: ultimate and yielding moment”, Journal of Structural Engineering, ASCE, 131(3), 449–456.
Mohamadi Shoore, M.R. (2008). “Parametric analysis on nonlinear behavior of bolted end plate connection”, Ph.D. Thesis, Civil Engineering Department, Sharif University of Technology, Tehran, Iran.
Ramberg, W. and Osgood, W.R. (1943). “Description of stress–strain curves by three parameters”, Technical Note No. 902, National Advisory Committee for Aeronautics, Washington, DC.
Riahi, A. and Curran, J.H. (2010). “Comparison of the cosserat continuum approach with the finite element interface models in the simulation of layered materials”, Scientia Iranica, 17(1), 39–52.
Richard, R.M., Hisa, W.K. and Chrnielowiec, M. (1998). “Derived moment–rotation curves for double framing angles”, Journal of Computers and Structures, 30(3), 485–494.
Shen, J. and Astaneh-Asl, A. (2000). “Hysteresis model of bolted-angle connections”, Journal of Constructional Steel Research, 54(3), 317- 43.
Shi, Y.J., Chan, S.L. and Wong, Y.L. (1996). “Modeling for moment–rotation characteristics for end plate connections’’, Journal of Structural Engineering, ASCE, 122(11), 1300–1306.
Wald, F. and Baniotopoulos, Ch.C. (1999). “Numerical modeling of column base connection”, In: COST C1 Conference (Liege 1998), ISBN: 92-828-6337-9. pp. 497–507.
Yee, Y.L. and Melchers, R.E. (1986). “Moment-rotation curves for bolted connections”, Journal of Structural Engineering, ASCE, 112(3), 615–635.
Yun, G.J., Ghaboussi, J. and Elnashai A.S. (2010). “Mechanical and informational modeling of steel beam-to-column connections”, Engineering Structures, 32(2), 449-458.
Volume 47, Issue 2 - Serial Number 2
December 2014
Pages 255-272
  • Receive Date: 23 December 2012
  • Revise Date: 23 September 2013
  • Accept Date: 30 September 2013
  • First Publish Date: 01 December 2014