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Predictive Formulation for the Ultimate Combinations of Axial Force and Bending Moment Attainable by Steel Members

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Abstract

This paper is devoted to quantitative safety assessment of steel beam-columns, and delivers a plain analytical formulation for predicting the ultimate combinations of axial force and bending moment, allowing for material and geometric non-linearities. The formulation easily permits the ultimate interaction diagram of a steel member to be accurately constructed, as well as the structure to be checked for combined axial force and lateral load. It applies specifically to columns but can be used for any members. The formulation is also configured as a tool for straightforward design and construction. To that end, the structure is converted from an imperfect geometrically non-linear system into a geometrically linear system without imperfections, which allows the structure to be designed and dimensioned referring to the first order moments. The paper gives a detailed account of the mathematical developments and the final expressions, including some illustrative examples.

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References

  • American Institute of Steel Construction – AISC. (2016). Specification for Structural Steel Buildings. ANSI/AISC 360-16, An American National Standard, July 7.

  • ASCE. (2003). Seismic evaluation of existing buildings, ASCE/SEI 31-03. Reston, VA: American Society of Civil Engineers.

    Book  Google Scholar 

  • Ashraf, M., Gardner, L., & Nethercot, D. A. (2005). Strength enhancement of the corner regions of stainless steel cross-sections. Journal of Constructional Steel Research,61(1), 37–52.

    Article  Google Scholar 

  • Barg, S., Flager, F., & Fischer, M. (2018). An analytical method to estimate the total installed cost of structural steel building frames during early design. Journal of Building Engineering,15(January), 41–50.

    Article  Google Scholar 

  • Biolzi, L., & Labuz, J. F. (1993). Global instability and bifurcation in beams composed of rock-like materials. International Journal of Solids and Structures,30(3), 359–370.

    Article  Google Scholar 

  • Bu, Y., & Gardner, L. (2019). Finite element modelling and design of welded stainless steel I-section columns. Journal of Constructional Steel Research,152, 57–67.

    Article  Google Scholar 

  • CEN. (2005). Eurocode 3: Design of steel structures. Brussels: Comite Européen de Normalisation, European Standard, EN 1993-1-1.

    Google Scholar 

  • Chen, Z., Li, J., Sun, L., & Li, L. (2019). Flexural buckling of sandwich beams with thermal-induced non-uniform sectional properties. Journal of Building Engineering, 25, 100782.

  • Chen, W. F., & Lui, E. M. (1987). Structural stability: Theory and implementation. New York: Elsevier.

    Google Scholar 

  • Daneshvar, H., & Driver, R. G. (2018). Modelling benchmarks for steel shear connections in column removal scenario. Journal of Building Engineering,16(March), 199–212.

    Article  Google Scholar 

  • Dundu, M. (2011). Design approach of cold-formed steel portal frames. International Journal of Steel Structures,11(September), 259.

    Article  Google Scholar 

  • Fajoui, J., Kchaou, M., Sellami, A., Branchu, S., & Jacquemin, F. (2018). Impact of residual stresses on mechanical behaviour of hot work steels. Engineering Failure Analysis,94(December), 33–40.

    Article  Google Scholar 

  • Faridmehr, I., Osman, M. H., & Tahi, M. M. (2016). Behaviour and design of cold-formed steel C-sections with cover plates under bending. International Journal of Steel Structures,16(2), 587–600.

    Article  Google Scholar 

  • FEMA. (2000). Steel moment-frame buildings: Design criteria for new buildings, FEMA350, Prepared by the SAC Joint Venture for the Federal Emergency Management Agency, Washington, DC.

  • Focacci, F., Foraboschi, P., & De Stefano, M. (2015). Composite beam generally connected: analytical model. Composite Structures,133(December), 1237–1248.

    Article  Google Scholar 

  • Foraboschi, P. (2014). Experimental characterization of non-linear behavior of monolithic glass. International Journal of Non-Linear Mechanics,67(December), 352–370.

    Article  Google Scholar 

  • Foraboschi, P. (2016a). Versatility of steel in correcting construction deficiencies and in seismic retrofitting of RC buildings. Journal of Building Engineering,8(December), 107–122.

    Article  Google Scholar 

  • Foraboschi, P. (2016b). Effectiveness of novel methods to increase the FRP-masonry bond capacity. Composites Part B Engineering,107(December), 214–232.

    Article  Google Scholar 

  • Foraboschi, P. (2019). Lateral load-carrying capacity of steel columns with fixed-roller end supports. Journal of Building Engineering, 26, 100879.

  • Gardner, L., & Nethercot, D. A. (2004). Numerical modeling of stainless steel structural components—A consistent approach. Journal of Structural Engineering – ASCE,130(10), 1586–1601.

    Article  Google Scholar 

  • Ghannam, M. (2019). Bending moment capacity of cold-formed steel built-up beams. International Journal of Steel Structures,19(2), 660–671.

    Article  Google Scholar 

  • Giżejowski, M., Szczerba, R., & Gajewsk, M. (2019). Buckling resistance criteria of prismatic beams under biaxial moment gradient. International Journal of Steel Structures,19(2), 559–576.

    Article  Google Scholar 

  • Guarracino, F. (2003). On the analysis of cylindrical tubes under flexure: theoretical formulations, experimental data and finite element analyses. Thin-Walled Structures,41(2–3), 127–147.

    Article  Google Scholar 

  • Gusella, F., Arwade, S. R., Orlando, M., & Peterman, K. D. (2019a). Influence of mechanical and geometric uncertainty on rack connection structural response. Journal of Constructional Steel Research,153, 343–355.

    Article  Google Scholar 

  • Gusella, F., Lavacchini, G., & Orlando, M. (2018a). Monotonic and cyclic tests on beam-column joints of industrial pallet racks. Journal of Constructional Steel Research,140(January), 92–107.

    Article  Google Scholar 

  • Gusella, F., Orlando, M., & Peterman, K. D. (2019b). On the required ductility in beams and connections to allow a redistribution of moments in steel frame structures. Engineering Structures,179(January), 595–610.

    Article  Google Scholar 

  • Gusella, F., Orlando, M., & Thiele, K. (2018b). Evaluation of rack connection mechanical properties by means of the Component Method. Journal of Constructional Steel Research,149(October), 207–224.

    Article  Google Scholar 

  • Javed, M. F., Hafizah, N., Memon, S. A., Jameel, M., & Aslam, M. (2017). Recent research on cold-formed steel beams and columns subjected to elevated temperature: A review. Construction and Building Materials,144(July), 686–701.

    Article  Google Scholar 

  • Kaehler, R. C., White, D. W., & Kim Y. D. (2010). Frame design using web-tapered members. Design Guide 25, Chicago, IL: MBMA and AISC.

  • Kim, S., Han, T. H., Won, D. H., & Kang, Y. J. (2014). Tangent moduli of hot-rolled I-shaped axial members considering various residual stress distributions. Thin-Walled Structures,76(March), 77–91.

    Article  Google Scholar 

  • Lacey, A. W., Chen, W., Hao, H., & Bi, K. (2019). Review of bolted inter-module connections in modular steel buildings. Journal of Building Engineering,23(May), 207–219.

    Article  Google Scholar 

  • Law, K. H., & Gardner, L. (2013a). Global instability of elliptical hollow section beam-columns under compression and biaxial bending. International Journal of Steel Structures,13(4), 745–759.

    Article  Google Scholar 

  • Law, K. H., & Gardner, L. (2013b). Buckling of elliptical hollow section members under combined compression and uniaxial bending. Journal of Constructional Steel Research,86, 1–16.

    Article  Google Scholar 

  • Li, L.-L., & Li, G.-Q. (2016). The internal force relationship of rectangular and I-section for bi-linear hardening material with limit strain. International Journal of Steel Structures,16(1), 243–255.

    Article  Google Scholar 

  • Maleki, S., & Mehretehran, A. M. (2018). 3D wind buckling analysis of long steel corrugated silos with vertical stiffeners. Engineering Failure Analysis,90(August), 156–167.

    Article  Google Scholar 

  • Maraveas, C., & Tsavdaridis, K. D. (2019). Assessment and retrofitting of an existing steel structure subjected to wind-induced failure analysis. Journal of Building Engineering,23(May), 53–67.

    Article  Google Scholar 

  • McGuire, W., Gallagher, R. H., & Ziemian, R. D. (2000). Matrix structural analysis (2nd ed.). New York: Wiley.

    Google Scholar 

  • Mohammadi, E., Hosseini, S. S., & Asgari, Marnani J. (2018). An interactive solution for lateral-torsional buckling of the mono-symmetric beam-columns with discrete lateral bracings. Structures,14(June), 164–177.

    Article  Google Scholar 

  • Multipurpose Finite Element package ABAQUS, ABAQUS/Standard user’s Manual Volumes I–III and ABAQUS CAE Manual, Dassault Systemes.

  • Naghavi, M., Rahnavard, R., Thomas, R. J., & Malekinejad, M. (2019). Numerical evaluation of the hysteretic behavior of concentrically braced frames and buckling restrained brace frame systems. Journal of Building Engineering,22(March), 415–428.

    Article  Google Scholar 

  • Omidian, P., & Saffari, H. (2018). Comparative analysis of seismic behavior of RC buildings with Shape Memory Alloy rebar in regular, torsional irregularity and extreme torsional irregularity cases. Journal of Building Engineering,20(November), 723–735.

    Article  Google Scholar 

  • Piluso, V., Pisapia, A., Castaldo, P., & Nastri, E. (2019). Probabilistic theory of plastic mechanism control for steel moment resisting frames. Structural Safety,76(January), 95–107.

    Article  Google Scholar 

  • Rezaiee-Pajand, M., & Masoodi, A. R. (2019). Stability analysis of frame having FG tapered beam-column. International Journal of Steel Structures,19(2), 446–468.

    Article  Google Scholar 

  • Roy, K., & Lim, J. B. P. (2019). Numerical investigation into the buckling behaviour of face-to-face built-up cold-formed stainless steel channel sections under axial compression. Structures,20(August), 42–73.

    Article  Google Scholar 

  • Roy, K., Mohammadjani, C., & Lim, J. B. P. (2019a). Experimental and numerical investigation into the behaviour of face-to-face built-up cold-formed steel channel sections under compression. Thin-Walled Structures,134(January), 291–309.

    Article  Google Scholar 

  • Roy, K., Ting, T. C. H., Lau, H. H., & Lim, J. B. P. (2018a). Nonlinear behaviour of back-to-back gapped built-up cold-formed steel channel sections under compression. Journal of Constructional Steel Research,147(August), 257–276.

    Article  Google Scholar 

  • Roy, K., Ting, T. C. H., Lau, H. H., & Lim, J. B. P. (2018b). Nonlinear behavior of axially loaded back-to-back built-up cold-formed steel un-lipped channel sections. Steel and Composite Structures,28(2), 233–250.

    Google Scholar 

  • Roy, K., Ting, T. C. H., Lau, H. H., & Lim, J. B. P. (2019b). Experimental and numerical investigations on the axial capacity of cold-formed steel built-up box sections. Journal of Constructional Steel Research,160(September), 411–427.

    Article  Google Scholar 

  • Santos, P., Gonçalves, M., Martins, C., Soares, N., & Costa, J. J. (2019). Thermal transmittance of lightweight steel framed walls: Experimental versus numerical and analytical approaches. Journal of Building Engineering,25(September), 100776.

    Article  Google Scholar 

  • Saoula, A., & Meftah, S. A. (2019). Effect of shear and distortion deformations on lateral buckling resistance of box elements in the framework of Eurocode 3. International Journal of Steel Structures,19(4), 1302–1316.

    Article  Google Scholar 

  • Schafer, B. W. (2002). Local, distortional and Euler buckling of thin-walled columns. Journal of Structural Engineering, American Society of Civil Engineers,128(3), 289–299.

    Article  Google Scholar 

  • Schillo, N., & Feldmann, M. (2018). Interaction of local and global buckling of box sections made of high strength steel. Thin-Walled Structures,128(July), 126–140.

    Article  Google Scholar 

  • Seo, J., Won, D., Kim, S., & Kang, Y. J. (2019). Inelastic compressive buckling behavior of a cylindrical shell at elevated temperature: Case study. Journal of Building Engineering, 24, 100766.

  • Sepahvand, M. F., & Akbari J. (2019). Toward seismic design of tall steel moment resisting frames using the theory of plastic mechanism control. Journal of Building Engineering, 24, 100750.

  • Surovek-Maleck, A. E., & White, D. W. (2004). Alternative approaches for elastic analysis and design of steel frames. II: Verification studies. Journal of Structural Engineering – ASCE,130(8), 1197–1205.

    Article  Google Scholar 

  • Wang, J., & Gardner, L. (2017). Flexural buckling of hot-finished high-strength steel SHS and RHS columns. Journal of Structural Engineering – ASCE,143(6), 04017028.

    Article  Google Scholar 

  • White, D. W., Jeong, W. Y., & Toğay, O. (2016). Comprehensive stability design of planar steel members and framing systems via inelastic buckling analysis. International Journal of Steel Structures,16(4), 1029–1042.

    Article  Google Scholar 

  • Xie, W., Xia, J., Zheng, Y., Wang, Q., Chang, H., & Yang, S. (2019). Performance of steel frames with new lightweight composite infill walls under curvature ground deformation. Journal of Building Engineering, 25, 100805.

  • Yuan, W.-B., Bao, Z.-S., Yu, N.-T., Zhu, S.-S., & Wu, L.-P. (2017). Nonlinear bending of box section beams of finite length under uniformly distributed loading. International Journal of Steel Structures,17(2), 491–499.

    Article  Google Scholar 

  • Yuan, H. X., Wang, Y. Q., Gardner, L., Du, X. X., & Shi, Y. J. (2015). Local-overall interactive buckling behaviour of welded stainless steel I-section columns. Journal of Constructional Steel Research,111, 75–87.

    Article  Google Scholar 

  • Zhao, O., Gardner, L., & Young, B. (2016). Structural performance of stainless steel circular hollow sections under combined axial load and bending—Part 2: Parametric studies and design. Thin-Walled Structures,101(April), 240–248.

    Article  Google Scholar 

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  1. Dipartimento Culture del Progetto, Università IUAV di Venezia, Dorsoduro 2206, 30123, Venice, Italy

    Paolo Foraboschi

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  1. Paolo Foraboschi
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Correspondence to Paolo Foraboschi.

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Foraboschi, P. Predictive Formulation for the Ultimate Combinations of Axial Force and Bending Moment Attainable by Steel Members. Int J Steel Struct 20, 705–724 (2020). https://doi.org/10.1007/s13296-020-00316-6

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