Review Advanced inelastic analysis of steel structures at elevated temperatures by SCM/RPHM coupling Rafael C. Barros a, ⁎, Dalilah Pires a,b , Ricardo A.M. Silveira a , Ígor J.M. Lemes a , Paulo A.S. Rocha a a Department of Civil Engineering, Scholl of Mines, Federal University of Ouro Preto, Campus Universitário s/n, Morro do Cruzeiro, 35400-000 Ouro Preto, MG, Brazil b Federal University of São João del-Rei, DTECH, Campus Alto do Paraopeba, Rod. MG 443, KM 7, 36420-000 Ouro Branco, MG, Brazil abstract article info Article history: Received 10 January 2018 Received in revised form 14 February 2018 Accepted 2 March 2018 Available online xxxx When exposed to high temperatures, the structural members and frames have their bearing capacity compromised because the physical characteristics and material resistance used in the structures deteriorate during exposure to fire, resulting in a considerable loss of strength and stiffness. In this context, the present work carries out a whole thermomechanical analysis of steel members and frames using the Finite Element Method (FEM) inelastic formulation based on the Refined Plastic Hinge Method (RPHM) coupled with the Strain Compatibility Method (SCM). The use of SCM allows for a more realistic analysis against the design codes prescriptions. So even under high temperatures, SCM is used for both evaluation of bearing capacity and stiffness parameters. To do this, the steel behavior used in the structure numerical modeling must be described in a consistent manner through its constitutive relationship. A comparison of the results obtained here with the numerical and experimental results available in the literature suggest the effectiveness of coupling SCM/RPHM and that such a methodology can provide reliable analyses of steel members and frames subjected to high temperatures. © 2017 Elsevier Ltd. All rights reserved. Keywords: Thermal analysis Interaction diagrams Thermal-structural analysis Refined plastic hinge method (RPHM) Strain compatibility method (SCM) Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 2. Fundamentals of fire structural analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 2.1. Heating curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 2.2. Steel thermomechanical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 3. Thermal analysis via FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 3.1. Thermal equilibrium equation by FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 3.2. Solution of the heat transfer transient problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 3.3. Simple incremental algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 3.4. Incremental-iterative algorithm: Picard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 3.5. Incremental-iterative algorithm: Newton-Raphson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 4. Inelastic analysis of steel structures under high temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 4.1. Strain compatibility method (SCM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 4.2. Stress-strain relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 4.3. Moment-curvature relationship and yield curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 4.4. Full yield curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 4.5. Finite element formulation via RPHM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 4.6. Solution of thermo-structural problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 5. Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 5.1. Beam simply supported subject to uniform temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 5.2. Isolated pinned column subject to fire conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 5.3. Vogel portal frame under fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 5.4. Scaled steel frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Journal of Constructional Steel Research 145 (2018) 368–385 ⁎ Corresponding author at: Department of Civil Engineering, School of Mines, UFOP, Campus Universitário, Morro do Cruzeiro, s/No., 35400-000 Ouro Preto, MG, Brazil. E-mail addresses: rafaelcesario@hotmail.com (R.C. Barros), dalilah@ufsj.edu.br (D. Pires), ricardo@em.ufop.br (R.A.M. Silveira), igor@em.ufop.br (Í.J.M. Lemes), paulorocha@em.ufop.br (P.A.S. Rocha). https://doi.org/10.1016/j.jcsr.2018.03.001 0143-974X/© 2017 Elsevier Ltd. All rights reserved. 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