Nonlinear Inelastic Analysis of 2D Steel Frames
An Improvement of the Plastic Hinge Method
Abstract
In this study, a new method for nonlinear analysis of 2D steel frames, by improving the conventional plastic hinge method, is presented. The beam-column element is established and formulated in detail using a fiber plastic hinge approach. Residual stresses of I-shape sections are declared at the two ends through fibers. Gradual yielding by residual stresses along the member length due to axial force is accounted for by the tangent elastic modulus concept. The P-δ effect is captured by stability functions, whereas the P-Δ effect is estimated by the geometric stiffness matrix. A nonlinear algorithm is established for solving nonlinear problems. The present study predicts the strength and behavior of 2D steel frames as efficiently and accurately as the plastic zone method did.
Keywords:
fiber plastic hinge, nonlinear algorithm, residual stress, stability functions, steel framesDownloads
References
J. G. Orbison, "Nonlinear static analysis of three-dimensional steel frames," Ph.D. dissertation, Cornell University, Ithaca, NY, USA, 1982.
"Ultimate limit state calculations of sway frames with rigid joints," ECCS General Secretariat, Brussels, Belgium, 1984.
U. Vogel, "Calibrating frames", Stahlbau, Vol. 10, pp. 295-301, Oct. 1985
S.-H. Hsieh and G. G. Deierlein, "Nonlinear analysis of three-dimensional steel frames with semi-rigid connections," Computers & Structures, vol. 41, no. 5, pp. 995-1009, Jan. 1991. DOI: https://doi.org/10.1016/0045-7949(91)90293-U
W. S. King, D. W. White, and W. F. Chen, "Second‐Order Inelastic Analysis Methods for Steel‐Frame Design," Journal of Structural Engineering, vol. 118, no. 2, pp. 408-428, Feb. 1992. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1992)118:2(408)
S.-L. Chan and P. P.-T. Chui, "A generalized design-based elastoplastic analysis of steel frames by section assemblage concept," Engineering Structures, vol. 19, no. 8, pp. 628-636, Aug. 1997.
S. L. Chan and P. K. Chui, Non-Linear Static and Cyclic Analysis of Steel Frames with Semi-Rigid Connections. Amsterdam, Netherlands: Elsevier Science, 2000.
R. D. Ziemian and W. McGuire, "Modified Tangent Modulus Approach, A Contribution to Plastic Hinge Analysis," Journal of Structural Engineering, vol. 128, no. 10, pp. 1301-1307, Oct. 2002. DOI: https://doi.org/10.1061/(ASCE)0733-9445(2002)128:10(1301)
S. L. Chan and Z. H. Zhou, "Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member. II: Three Hinges along Member," Journal of Structural Engineering, vol. 130, no. 4, pp. 545-553, Apr. 2004. DOI: https://doi.org/10.1061/(ASCE)0733-9445(2004)130:4(545)
Z. H. Zhou and S. L. Chan, "Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member. I: One Hinge along Member," Journal of Structural Engineering, vol. 130, no. 4, pp. 538-544, Apr. 2004. DOI: https://doi.org/10.1061/(ASCE)0733-9445(2004)130:4(538)
H. Van Long and N. Dang Hung, "Second-order plastic-hinge analysis of 3-D steel frames including strain hardening effects," Engineering Structures, vol. 30, no. 12, pp. 3505-3512, Dec. 2008. DOI: https://doi.org/10.1016/j.engstruct.2008.05.013
C. Ngo-Huu, P.-C. Nguyen, and S.-E. Kim, "Second-order plastic-hinge analysis of space semi-rigid steel frames," Thin-Walled Structures, vol. 60, pp. 98-104, Nov. 2012 DOI: https://doi.org/10.1016/j.tws.2012.06.019
S.-W. Liu, Y.-P. Liu, and S.-L. Chan, "Direct analysis by an arbitrarily-located-plastic-hinge element - Part 1: Planar analysis," Journal of Constructional Steel Research, vol. 103, pp. 303-315, Dec. 2014. DOI: https://doi.org/10.1016/j.jcsr.2014.07.009
P.-C. Nguyen and S.-E. Kim, "Nonlinear inelastic time-history analysis of three-dimensional semi-rigid steel frames," Journal of Constructional Steel Research, vol. 101, pp. 192-206, Oct. 2014. DOI: https://doi.org/10.1016/j.jcsr.2014.05.009
P.-C. Nguyen and S.-E. Kim, "Investigating effects of various base restraints on the nonlinear inelastic static and seismic responses of steel frames," International Journal of Non-Linear Mechanics, vol. 89, pp. 151-167, Mar. 2017. DOI: https://doi.org/10.1016/j.ijnonlinmec.2016.12.011
C. M. Foley and S. Vinnakota, "Inelastic analysis of partially restrained unbraced steel frames," Engineering Structures, vol. 19, no. 11, pp. 891-902, Nov. 1997. DOI: https://doi.org/10.1016/S0141-0296(97)00175-2
L. H. The, M. J. Clarke, "Plastic-Zone Analysis of 3D Steel Frames Using Beam Elements," Journal of Structural Engineering, vol. 125, no. 11, pp. 1328-1337, Nov. 1999. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1999)125:11(1328)
X.-M. Jiang, H. Chen, and J. Y. R. Liew, "Spread-of-plasticity analysis of three-dimensional steel frames," Journal of Constructional Steel Research, vol. 58, no. 2, pp. 193-212, Feb. 2002. DOI: https://doi.org/10.1016/S0143-974X(01)00041-4
C. G. Chiorean, "A computer method for nonlinear inelastic analysis of 3D semi-rigid steel frameworks," Engineering Structures, vol. 31, no. 12, pp. 3016-3033, Dec. 2009. DOI: https://doi.org/10.1016/j.engstruct.2009.08.003
P.-C. Nguyen, N. T. N. Doan, C. Ngo-Huu, and S.-E. Kim, "Nonlinear inelastic response history analysis of steel frame structures using plastic-zone method," Thin-Walled Structures, vol. 85, pp. 220-233, Dec. 2014. DOI: https://doi.org/10.1016/j.tws.2014.09.002
P.-C. Nguyen and S.-E. Kim, "Distributed plasticity approach for time-history analysis of steel frames including nonlinear connections," Journal of Constructional Steel Research, vol. 100, pp. 36-49, Sep. 2014. DOI: https://doi.org/10.1016/j.jcsr.2014.04.012
P.-C. Nguyen and S.-E. Kim, "An advanced analysis method for three-dimensional steel frames with semi-rigid connections," Finite Elements in Analysis and Design, vol. 80, pp. 23-32, Mar. 2014. DOI: https://doi.org/10.1016/j.finel.2013.11.004
P.-C. Nguyen and S.-E. Kim, "Second-order spread-of-plasticity approach for nonlinear time-history analysis of space semi-rigid steel frames," Finite Elements in Analysis and Design, vol. 105, pp. 1-15, Nov. 2015. DOI: https://doi.org/10.1016/j.finel.2015.06.006
A. Saritas and A. Koseoglu, "Distributed inelasticity planar frame element with localized semi-rigid connections for nonlinear analysis of steel structures, "International Journal of Mechanical Sciences, vol. 96-97, pp. 216-231, Jun. 2015. DOI: https://doi.org/10.1016/j.ijmecsci.2015.04.005
P.-C. Nguyen and S.-E. Kim, "Advanced analysis for planar steel frames with semi-rigid connections using plastic-zone method," Steel and Composite Structures, vol. 21, no. 5, pp. 1121-1144, Jan. 2016. DOI: https://doi.org/10.12989/scs.2016.21.5.1121
P.-C. Nguyen and S.-E. Kim, "Nonlinear elastic dynamic analysis of space steel frames with semi-rigid connections," Journal of Constructional Steel Research, vol. 84, pp. 72-81, May 2013. DOI: https://doi.org/10.1016/j.jcsr.2013.02.004
N. L. Tran and T. H. Nguyen, "Reliability Assessment of Steel Plane Frame's Buckling Strength Considering Semi-rigid Connections," Engineering, Technology & Applied Science Research, vol. 10, no. 1, pp. 5099-5103, Feb. 2020. DOI: https://doi.org/10.48084/etasr.3231
N. W. Bishay-Girges, "Improved Steel Beam-Column Connections in Industrial Structures," Engineering, Technology & Applied Science Research, vol. 10, no. 1, pp. 5126-5131, Feb. 2020. DOI: https://doi.org/10.48084/etasr.3248
N. Konkong, "An Investigation on the Ultimate Strength of Cold-Formed Steel Bolted Connections," Engineering, Technology & Applied Science Research, vol. 7, no. 4, pp. 1826-1832, Aug. 2017. DOI: https://doi.org/10.48084/etasr.1243
H. Veladi and H. Najafi, "Effect of Standard No. 2800 Rules for Moment Resisting Frames on the Elastic and Inelastic Behavior of Dual Steel Systems," Engineering, Technology & Applied Science Research, vol. 7, no. 6, pp. 2139-2146, Dec. 2017. DOI: https://doi.org/10.48084/etasr.1040
W.-F. Chen, Structural Stability: Theory and Implementation. Englewood Cliffs, NJ, USA: Prentice Hall, 1987.
Y.-B. Yang and M.-S. Shieh, "Solution method for nonlinear problems with multiple critical points," AIAA Journal, vol. 28, no. 12, pp. 2110-2116, 1990. DOI: https://doi.org/10.2514/3.10529
Downloads
How to Cite
License
Copyright (c) 2020 Authors
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.