• Structural Engineering and Mechanics
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• v.56 no.2
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• pp.169-188
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• 2015

There are two types of nonlinear analysis methods for building frameworks depending on the method of modeling the plastification of members including lumped plasticity and distributed plasticity. The lumped plasticity method assumes that plasticity is concentrated at a zero-length plastic hinge section at the ends of the elements. The distributed plasticity method discretizes the structural members into many line segments, and further subdivides the cross-section of each segment into a number of finite elements. When a reinforced concrete member experiences inelastic deformations, cracks tend to spread form the joint interface resulting in a curvature distribution. The program IDARC includes a spread plasticity formulation to capture the variation of the section flexibility, and combine them to determine the element stiffness matrix. In this formulation, the flexibility distribution in the structural elements is assumed to be the linear. The main objective of this study is to evaluate the accuracy of linear flexibility distribution assumed in the spread inelasticity model. For this purpose, nonlinear analysis of two reinforced concrete frames is carried out and the linear flexibility models used in the elements are compared with the real ones. It is shown that the linear flexibility distribution is incorrect assumption in cases of significant gravity load effects and can be lead to incorrect nonlinear responses in some situations.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.423-442
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• 2001

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.45-52
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• 2003

A finite element procedure to estimate ultimate strength of space frames considering spread of plasticity is presented. The improved displacement field is introduced based on inclusion of second order terms of finite rotations. All the nonlinear terms due to bending and torsional moment as well as axial force are precisely considered. The concept of plastic hinge is introduced and the incremental load/displacement method is applied for the elasto-plastic analysis. The initial yield surface is defined based on the residual stress and the full plastification surface is considered under the combined action of axial force, bending and torsional moments. The elasto-plastic stiffness matrices are derived using the flow rule and the normality condition of the limit function. Finite element solutions for ultimate strength of space frames are compared with available solutions and experimental results.

• Steel and Composite Structures
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• v.41 no.6
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• pp.887-898
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• 2021

This paper presents a simplified model to capture the nonlinear behavior of steel frames depending on the spread of plasticity method. New interaction formulae were derived to evaluate the plastic strength for I-shaped steel sections under uniaxial bending moment and axial compression load. Also, new empirical formulae were derived to evaluate the tangent stiffness modulus of steel I-shaped cross-sections considering the effect of the residual stresses suggested by the specifications in European Convention for Construction Steelworks (ECCS). The secant stiffness which depends on the tangent modulus is used to evaluate the internal forces. Based on stiffness matrix method, a finite element analysis program was developed for the nonlinear analysis of space steel frames using the derived formulae. Comparison between the proposed model results with those given by the fiber model shows very good agreement. Numerical examples were introduced to verify, check the accuracy, and evaluate the efficiency of the proposed model. The analysis results show that the new proposed model is accurate and able to minimize the solution time.

• Transactions of Materials Processing
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• v.23 no.3
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• pp.139-144
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• 2014

In the current study, we present a new model for predicting width spread of a slab with a dog-bone shaped cross section during rolling in the roughing train of a hot strip mill. The approach is based on the extremum principle for a rigid plastic material and a three dimensional admissible velocity field. The upper bound theorem is used for calculating the width spread of the slab. The prediction accuracy of the proposed model is examined through comparison with the predictions from 3-D finite element (FE) process simulations.

• Journal of Korean Society of Steel Construction
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• v.15 no.3
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• pp.299-311
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• 2003

This paper presents a finite element procedure to estimate the ultimate strength of space frames considering spread of plasticity. The improved displacement field is introduced based on the inclusion of second-order terms of finite rotations. All the non-linear terms due to bending moment, torsional moment, and axial force are precisely considered. The concept of plastic hinges is introduced and the incremental load/displacement method is applied for elasto-plastic analyses. The initial yield surface is defined based on the residual stress, and the full plastification surface is considered under the combined action of axial forces, bending and torsional moments. The elasto-plastic stiffness matrices are derived using the flow rule and the normality condition of the limit function. Finite element solutions for the ultimate strength of space frames are compared with available solutions and experimental results.

• Structural Engineering and Mechanics
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• v.10 no.4
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• pp.371-392
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• 2000

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. The pseudo plastic zone method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established by comparison with a comprehensive range of analytical benchmark frame solutions. The pseudo plastic zone method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

• Transactions of Materials Processing
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• v.23 no.3
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• pp.145-150
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• 2014

Precision control of the slab is crucial for product quality and production economy in hot strip mills. The current study presents a new model for predicting width spread of a slab with a rectangular cross section during roughing. The model is developed on the basis of the extremum principle for a rigid plastic material and a three dimensional admissible velocity field. This model incorporates the effect of process variables such as the shape factor and the ratio of width to thickness. We compare the results of this model to 3-D finite element (FE) process simulations and also to results from a previous study.

• Transactions of Materials Processing
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• v.28 no.2
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• pp.89-97
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• 2019

In this paper, we examine the application of a new concept - on-line FE model in various metal rolling processes. This technology allows for completion of process simulation within a tiny fraction of a second without losing the high level of prediction accuracy inherent to FEM. The procedure is systematically demonstrated through the design of actual on-line models for the prediction of the width spread in horizontal rolling of the slab using a dog bone profile and horizontal rolling of the strip with a strip profile. The validity and the prediction accuracy of the on-line FE models were analyzed and discussed.

• Journal of Korean Society of Steel Construction
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• v.18 no.6
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• pp.687-696
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• 2006

An efficient numerical method is developed to estimate the elasto-plastic post-buckling strength of space-framed structures. The inelastic ultimate strength of beam-columns and frames is evaluated by the parametric study. Applying the improved plastic hinge analysis that evaluate the gradual stiffness decrease effects due to spread of plasticity, elasto-plastic post-buckling behavior of steel frames is investigated considering the various residual stress distributions. Introducing the plastification parameter that represent pread of plasticity in the element and performing parametric study of equivalent element force and member idealization, finite-element solutions for the elasto-plastic analysis of space frames are compared with the results by plastic region analysis, shell elements and experimental results.