Axial Force and Biaxial Bending Interaction for I-Shaped Cross Section
Publication: Practice Periodical on Structural Design and Construction
Volume 26, Issue 4
Abstract
This paper presents new formulae for the determination of the plastic strengths of steel I-sections subjected to uniaxial bending about major or minor axis combined with an axial compression force. Moreover, new formulae are developed to describe the plastic yield surfaces of steel I-sections under biaxial bending moments combined with an axial force. The proposed formulae are obtained by performing large data regression analysis on the exact I-section strength results. In addition, the proposed formulae are simple and valid for any standard or general steel I-section, with conditions dependent on dimension ratios. These formulae are compared with the exact analytical solutions and with previous analysis methods and show very good correlations. New modified simple formulae are derived to predict the yield surface of I-sections. These formulae are more practical and easier for design purposes and lead to very good results compared to existing standards and exact solutions.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. The items are as follows:
•
any additional mathematical equations;
•
the computer code; and
•
any additional curves that are needed.
References
Ahmad, S. H., and S. L. Weekoon. 1995. “Model for behavior of slender reinforced concrete columns under biaxial bending.” ACI Struct. J. 92 (2): 188–198. https://doi.org/10.14359/1151.
AISC. 2010. Specifications for structural steel buildings. AISC 360-10. Chicago: AISC.
Baptista, A. M. 2012. “Resistance of steel I-sections under axial force and biaxial bending.” J. Constr. Steel Res. 72 (May): 1–11. https://doi.org/10.1016/j.jcsr.2011.07.013.
Belingardi, G., and L. Peroni. 2007. “Experimental investigation of plastic collapse of aluminium extrusions in biaxial bending.” Int. J. Mech. Sci. 49 (5): 554–566. https://doi.org/10.1016/j.ijmecsci.2006.09.025.
Bresler, B. 1960. “Design criteria for reinforced columns under axial load and biaxial bending.” ACI Proc. J. 57 (5): 481–490.
CEN (European Committee for Standardization). 2005. Design of steel structures—Part 1-1: General rules and rules for buildings. Brussels, Belgium: CEN.
Chen, W. F., and T. Atsuta. 1977. Theory of beam-columns: Space behavior and design. New York: McGraw–Hill.
Cheng, X., and Y. Chen. 2018. “Ultimate strength of H-sections under combined compression and uniaxial bending considering plate interaction.” J. Constr. Steel Res. 143 (Apr): 196–207. https://doi.org/10.1016/j.jcsr.2017.12.019.
Duan, L., and W.-F. Chen. 1989. “Design interaction equation for steel beam-columns.” J. Struct. Eng. 115 (5): 1225–1243. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:5(1225).
Duan, L., and W.-F. Chen. 1990. “A yield surface equation for doubly symmetrical sections.” Eng. Struct. 12 (2): 114–119. https://doi.org/10.1016/0141-0296(90)90016-L.
Guerrero, N., M. E. Marante, R. Picón, and J. Flórez-López. 2007. “Model of local buckling in steel hollow structural elements subjected to biaxial bending.” J. Constr. Steel Res. 63 (6): 779–790. https://doi.org/10.1016/j.jcsr.2006.08.006.
Kim, J.-K., and S.-S. Lee. 2000. “The behavior of reinforced concrete columns subjected to axial force and biaxial bending.” Eng. Struct. 22 (11): 1518–1528. https://doi.org/10.1016/S0141-0296(99)00090-5.
Meas, O. 2012. “Modeling yield surfaces of various structural shapes.” Honors thesis, Dept. of Civil and Environmental Engineering, Bucknell Univ.
Orbison, J. G., W. McGuire, and J. F. Abel. 1982. “Yield surface applications in nonlinear steel frame analysis.” Comput. Methods Appl. Mech. Eng. 33 (1–3): 557–573. https://doi.org/10.1016/0045-7825(82)90122-0.
Parme, A. L., J. M. Nieves, and A. Gouwens. 1966. “Capacity of reinforced rectangular columns subject to biaxial bending.” ACI Proc. J. 63 (9): 911–924.
Rodriguez, J. A., and J. D. Aristizabal-Ochoa. 1999. “Biaxial interaction diagrams for short RC columns of any cross section.” J. Struct. Eng. 125 (6): 672–683. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:6(672).
Santathadaporn, S., and W. F. Chen. 1970. Interaction curves for sections under combined biaxial bending and axial force. Bethlehem, PA: Lehigh Univ.
Trahair, N. S. 2002. “Moment capacities of steel angle sections.” J. Struct. Eng. 128 (11): 1387–1393. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:11(1387).
Wsu, C.-T. T. 1985. “Biaxially loaded L-shaped reinforced concrete columns.” J. Struct. Eng. 111 (12): 2576–2595. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:12(2576).
Yun, X., L. Gardner, and N. Boissonnade. 2018a. “Ultimate capacity of I-sections under combined loading—Part 1: Experiments and FE model validation.” J. Constr. Steel Res. 147 (Aug): 408–421. https://doi.org/10.1016/j.jcsr.2018.04.016.
Yun, X., L. Gardner, and N. Boissonnade. 2018b. “Ultimate capacity of I-sections under combined loading—Part 2: Parametric studies and CSM design.” J. Constr. Steel Res. 148 (Sep): 265–274. https://doi.org/10.1016/j.jcsr.2018.05.024.
Zubydan, A. H. 2010. “A simplified model for inelastic second order analysis of planar frames.” Eng. Struct. 32 (10): 3258–3268. https://doi.org/10.1016/j.engstruct.2010.06.015.
Zubydan, A. H. 2011. “Inelastic second order analysis of steel frame elements flexed about minor axis.” Eng. Struct. 33 (4): 1240–1250. https://doi.org/10.1016/j.engstruct.2010.12.046.
Zubydan, A. H. 2013. “Inelastic large deflection analysis of space steel frames including H-shaped cross sectional members.” Eng. Struct. 48 (Mar): 155–165. https://doi.org/10.1016/j.engstruct.2012.09.024.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 23, 2020
Accepted: Apr 28, 2021
Published online: Aug 5, 2021
Published in print: Nov 1, 2021
Discussion open until: Jan 5, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.