Inelastic Analysis and Design: Frames with Members in Minor-Axis Bending

New method of inelastic buckling analysis for steel frames

System-based design of planar steel frames, I: Reliability framework

This research presents a comprehensive investigation of the global stability of cellular steel columns, beam-columns, and frames. For the cellular steel columns, the existing equation for predicting the elastic buckling load is improved to account for the local bending deformation of the web posts. Subsequently, the column strength equation is analytically developed from the energy approach. The second-order inelastic analysis is performed using 3D finite element (FE) models and validated against the experimental results. The validated FE models are then employed to assess the developed column strength curve and examine the influence of initial imperfections on the critical strength of the columns. Equivalent geometric imperfection amplitudes are determined to implicitly incorporate the effect of residual stresses on the flexural buckling strength of cellular steel columns. The developed equation provides a conservative prediction of the strong-axis flexural buckling strength, with a mean prediction-to-FE critical strength ratio of 0.97. For the cellular steel beam-columns, the energy approach is also used to develop the axial-bending (P-M) strength interaction diagrams. Overall, the developed equation yields accurate predictions of the strength of cellular steel beam-columns, with a mean prediction-to-FE critical strength ratio of 0.98. In addition, the strength of cellular steel and its parent hot-rolled steel shapes is compared to establish the criterion for the effective utilization of cellular steel beam-columns, ensuring that the selected cellular steel shape offers greater strength compared to its parent shape (larger P-M envelope). Finally, stability analysis methods for the cellular steel members and frames are proposed based on the current AISC-LRFD specification. The equivalent cross-sectional properties of cellular steel members are derived and utilized for the beam elements to represent the global responses of cellular steel members in the second-order elastic analysis. The proposed methods using beam elements are verified with the second-order inelastic analysis using shell elements. These methods can be used to predict the strength of cellular steel members and frames within the provided limitations.

Stability study on structural systems assembled by system scaffolds

Linear structural analysis is incapable of reflecting the real behavior of a structure under abnormal or ultimate loading conditions. When deformations are large and a structure behaves nonlinearly, the stiffness of the structure changes even if the structural material shows a purely linear elastic behavior, and a geometric nonlinear analysis or a second-order elastic analysis should be performed. However, under severe environmental loading such as strong wind or earthquake, there is a need for a direct second-order inelastic analysis to calculate the ultimate strength capacity and to predict the true behavior of structures. This paper presents and compares two beam-column models, both based upon fiber-type, beam-column elements, for inelastic and large deformation analysis of planar steel structural systems. Derivations of the different stiffness matrices that are used in the new models are presented. Both models have the capacity to account for residual stress consideration. The new model satisfies the rigid-body test, while the second model does not. The accuracy of the two models is compared with benchmark problems via three examples. The results indicate that the new model is more robust and has a faster rate of convergence for problems involving inelastic behavior, high stress, and large deflections.

This paper presents a robust procedure to calibrate nonlinear formulations so as to predict first member failure in accordance with recognized design equations. The procedure accounts for residual stresses and geometrical imperfections through an equivalent out-of-straightness for each member. It is shown that, for most of the cases studied, there is excellent agreement between first member failure predictions of the (calibrated) second-order inelastic analysis and conventional design equations using budding lengths determined through refined analyses.

In this paper, the Newton-Raphson method is combined with three different algorithms. These algorithms are the generalized minimum residual (GMRES), the least squares (LSQR), and the biconjugate gradient (BCG). Of these algorithms, the most effective at reducing the number of iterations and the time required is identified. A common characteristic of these algorithms is that they replace the inversion of the tangent stiffness matrix with an iterative procedure to solve the linearized system of equations. A computer program based on three algorithms is developed to numerically solve a system of nonlinear equations. The procedure can be applied to analysis of structures with complex behaviors, including unloading, snap-through buckling, and inelastic postbuckling analyses. To demonstrate the efficiency and accuracy of the method developed here, some well-known trusses are investigated and analyzed using the various aforementioned algorithms. Results show that the biconjugate gradient algorithm is a more effective scheme to be coupled with the Newton-Raphson method when nonlinear structural problems are to be solved, having considerable savings in computational cost and time. Furthermore, the BCG algorithm is improved for solving a system of nonlinear equations. Finally, results reveal that the improved BCG method drastically reduces the computational time and the number of iterations while the accuracy of the results is maintained.

The advantage of second-order nonlinear analysis lies on its capacity to model actual structural response instead of making assumption on the structural behavior such as the arbitrary assumption of effective length factor. Considering the construction process of a structure, it may become a sway frame from a non-sway frame when a story is added or, on the contrary, to convert to a non-sway frame from a sway frame when bracings or infill walls are constructed and this makes the first-order linear analysis extremely inconvenient to use. Further, the deformation and load distributions of the structures considering the construction sequence can be much different from those obtained by assuming all structural elements share loads simultaneously. This paper proposes an advanced simulation-based design using an improved second-order analysis for structures accounting for both local and global imperfections, sequential loads and construction process. The technique for such an analysis is described and the error for ignoring the effects of sequential loads and construction procedure is quantified. Both the elastic and the plastic second-order analyses are used for comparison.

This paper discusses the evaluation criteria for alternating loads utilizing partial inelastic analyses and free from the stress classification. As finite element analysis becomes popular, it has been noticed by designers that in some cases the conventional stress classification does not work well. The stress classification itself had been engineered as a practical tool to evaluate the integrity of a structure by elastic analyses, which actually could have inelastic behavior. For example, primary stress limits were determined reflecting the stress level at collapse. Therefore, the problem concerning the stress classification can be solved recalling how it had been engineered. In other words, the key to solve the problem is the inelastic evaluation method corresponding to each stress category. From this point of the view, the application of the inelastic analyses becomes widely studied. Consequently, as for primary loads, it has been proven that the collapse load evaluation by Limit or Plastic Analysis is effective and practical for design analyses. On the other hand, as for the alternating loads, it is not sufficiently discussed how the alternative criteria should be without stress classification. In this paper, the following are discussed based on the calculation results in the Committee on Three Dimensional Finite Element Stress Evaluation in JPVRC. 1. Prerequisite of the elastic-plastic analysis for shakedown evaluation, and the evaluation criteria based on plastic strain increment and its distribution. 2. The advantage to use simplified elastic-plastic analysis method than to perform fully elastic-plastic analyses, and the calculation procedure for Ke factors to be used with. The associated code rules are proposed.

Applicable design codes for power plant components and pressure vessels demand for a design check against progressive plastic deformation. In the simplest case, this demand is satisfied by compliance with shakedown rules in connection with elastic analyses. The possible noncompliance implicates the requirement of ratcheting analyses on elastic–plastic basis. In this case, criteria are specified on maximum allowable accumulated growth strain without clear guidance on what material models for cyclic plasticity are to be used. This is a considerable gap and a challenge for the practicing computer-aided engineering engineer. As a follow-up to two independent previous papers PVP2013-98150 ASME (Kalnins et al., 2013, “Using the Nonlinear Kinematic Hardening Material Model of Chaboche for Elastic-Plastic Ratcheting Analysis,” ASME Paper No. PVP2013-98150.) and PVP2014-28772 (Weitze and Gilman, 2014, “Additional Guidance for Inelastic Ratcheting Analysis Using the Chaboche Model,” ASME Paper No. PVP2014-28772.), it is the aim of this paper to close this gap by giving further detailed recommendation on the appropriate application of the nonlinear kinematic material model of Chaboche on an engineering scale and based on implementations already available within commercial finite element codes such as ANSYS® and ABAQUS®. Consistency of temperature-dependent runs in ANSYS® and ABAQUS® is to be checked. All three papers together constitute a comprehensive guideline for elastoplastic ratcheting analysis. The following issues are examined and/or referenced: (1) application of monotonic or cyclic material data for ratcheting analysis based on the Chaboche material model, (2) discussion of using monotonic and cyclic data for assessment of the (nonstabilized) cyclic deformation behavior, (3) number of backstress terms to be applied for consistent ratcheting results, (4) consideration of the temperature dependency (TD) of the relevant material parameters, (5) consistency of temperature-dependent runs in ANSYS® and ABAQUS®, (6) identification of material parameters dependent on the number of backstress terms, (7) identification of material data for different types of material (carbon steel, austenitic stainless steel) including the appropriate determination of the elastic limit, (8) quantification of conservatism of simple elastic-perfectly plastic (EPP) behavior, (9) application of engineering versus true stress–strain data, (10) visual checks of data input consistency, and (11) appropriate type of allowable accumulated growth strain. This way, a more accurate inelastic analysis methodology for direct practical application to real world examples in the framework of the design code conforming elastoplastic ratcheting check is proposed.

A refined plastic hinge analysis method, known as one of the most effective and practical second-order inelastic analysis methods for steel frames, is able to evaluate the ultimate structural behavior of steel frames by considering the geometric and material nonlinearities. However, an appropriate advanced nonlinear solution technique has to be incorporated to help structural engineers perform the rational design of steel frames by predicting the ultimate strength and post-failure structural behavior accurately. In this study, a refined plastic hinge analysis method, combined with a work-increment-control solution technique with an iterative procedure in incremental loading steps, was presented in order to overcome the shortcomings of the load-increment-control solution techniques employed in previous studies. In the work-increment-control solution technique of present study, one convergence criterion refining the problem of using two convergence criteria in the conventional increment/iteration procedure of work-increment-control solution techniques and an automatic incremental algorithm calculating the load factor and the magnitude of incremental work for next incremental loading step were employed. To verify the accuracy and appropriateness of the present approach, three representative plane steel frames employed in previous studies were analyzed, and the analysis results were compared with those by other approaches. The present approach, that evaluated fairly accurately the load-displacement relationships, ultimate loads, plastic hinge numbers and locations, and the post-critical responses up to the formation of collapse mechanism of the plane steel frames, proved to be acceptable.

A simplified model for inelastic seismic analysis of RC frame have shear hinge in beam-column joints

Current ASME Boiler and Pressure Vessel Code Section III, Division 5 rules for design and construction of high temperature nuclear reactors do not consider weld residual stresses in the design evaluations. These rules essentially assume that the selection of weld wires and welding process produce ductile welds and subsequent load cycling and creep reduce residual stresses. However, welding residual stresses have been identified as an important contributing factor for premature in-service degradation and cracking of components in various nuclear reactor fleets. One specific critical failure mode is stress relaxation cracking which occurs due to the enhanced creep crack growth in certain materials caused by relaxation of weld residual stresses in components operating in high temperatures. The UK standard R5 addresses this issue by incorporating welding residual stresses in the structural integrity assessment procedure. Consistent with Volume 2/3 of R5, this paper recommends incorporating the effects of weld residual stress in the creep-fatigue damage evaluation of ASME Section III, Division 5 rules when these stresses are non-negligible or not mitigated by post-weld heat treatment. For creep-fatigue evaluations, Section III, Division 5 and related nuclear code cases offer three analysis methods: (i) design by elastic analysis, (ii) design by elastic-perfectly plastic analysis, and (iii) design by inelastic analysis. The paper presents potential methods for integrating weld residual stress effects into creep-fatigue damage evaluations for all three analysis methods. Finite element simulation of welding residual stresses is performed on a component with available test data found in literature. Various approaches are explored to assess the effect of welding residual stresses on enhanced creep damage. The validity of these approaches is then evaluated through comparison with the base case inelastic analysis results.

An investigation of the cyclic elastic-plastic response of an Olefin plant heat exchanger subject to cyclic thermal and pressure loading is presented. The heat exchanger configuration is non-standard as the tube-sheet thickness is considerably less than that required by conventional design by formula rules. Ratchetting assessment is performed using the elastic stress analysis and stress categorization procedure, which indicates that shakedown occurs under the specified loading. The cyclic elastic-plastic response of the heat exchanger is also modeled by inelastic analysis, assuming both elastic perfectly plastic and a strain hardening material models. In the elastic-perfect plastic analysis, the vessel exhibits incremental plastic strain accumulation for 10 full load cycles, with no indication that the configuration will adapt to steady state elastic or plastic action; i.e. elastic shakedown or plastic shakedown. However, the strain increments are small and would not lead to the development of a global plastic collapse or gross plastic deformation during the specified life of the vessel. The strain hardening analysis indicates that the actual vessel will adapt to plastic shakedown after 6 load cycles.

This paper examines factors affecting the strength requirements of columns in multi-storey frames responding to seismic ground motions. The examination is carried out using an inelastic static analysis approach and the concept of an "equivalent condensed frame". In particular, the influence of higher modes and the effect of varying the pattern of beam flexural strength over the frame height are evaluated. It is suggested that the current capacity design approach of the NZ Concrete Design Code overstates the importance of higher mode effects while neglecting the potentially more important influence of the beam flexural strength pattern that is provided for a frame. Some tentative modifications to the current column design procedure are suggested for future evaluation under inelastic dynamic response conditions.