Plane Steel Frames Research Articles

Hybrid tabu search algorithm for weight optimization of planar steel frames

In this study, a hybrid metaheuristic algorithm called Hybrid Tabu Search (HTS) is proposed for the weight optimization of planar steel structures. The effectiveness of HTS lies in improving the initial conditions of a tabu search algorithm with a greedy search algorithm and a swap operator used in the phase of section selection. The effectiveness of the proposed method is tested and validated on three different benchmark examples. C♯ software is developed to perform the structural analyses. Numerical results obtained by using HTS showed that the proposed method achieved significantly lighter frame weights in most of the benchmark examples. When the method was examined in terms of computational efficiency, HTS was at a level that can compete with other algorithms examined within this study, although it did not provide a significant advantage.

Gaussian mixture model for robust design optimization of planar steel frames

A new method is presented for an application of the Gaussian mixture model (GMM) to a multi-objective robust design optimization (RDO) of planar steel frame structures under aleatory (stochastic) uncertainty in material properties, external loads, and discrete design variables. Uncertainty in the discrete design variables is modeled in the wide range between the smallest and largest values in the catalog of the cross-sectional areas. A weighted sum of Gaussians is statistically trained based on the sampled training data to capture an underlying joint probability distribution function (PDF) of random input variables and the corresponding structural response. A simple regression function for predicting the structural response can be found by extracting the information from a conditional PDF, which is directly derived from the captured joint PDF. A multi-objective RDO problem is formulated with three objective functions, namely, the total mass of the structure, and the mean and variance values of the maximum inter-story drift under some constraints on design strength and serviceability requirements. The optimization problem is solved using a multi-objective genetic algorithm utilizing the trained GMM for calculating the statistical values of objective and constraint functions to obtain Pareto-optimal solutions. Since the three objective functions are highly conflicting, the best trade-off solution is desired and found from the obtained Pareto-optimal solutions by performing fuzzy-based compromise programming. The robustness and feasibility of the proposed method for finding the RDO of planar steel frame structures with discrete variables are demonstrated through two design examples.

Improving anti-collapse performance of steel frame with RBS connection

In this study, a novel RBS connection that adds “V”-type reinforcing plates to the reduced section of the upper and lower flanges of a beam is introduced. Based on validated nonlinear numerical models, the anti-progressive collapse and seismic performance of a steel frame with the novel RBS connection are discussed. When the catenary action in the beams is fully developed, adding “V”-type reinforcing plates can effectively improve the bearing capacity and corresponding displacement of the subassembly by 180.9% and 85.8%, respectively. The addition of a “V”-type reinforcing plate does not weaken the seismic performance of the RBS connection; on the contrary, it will slightly improve. Through numerical parameter analysis, the design method for the reinforcing plate and application examples against progressive collapse are given. When “V”-type reinforcing plates are applied to a plane steel frame, the maximum resistance reserve can be improved, especially when the bottom middle column fails.

Macroscopic modelling of steel frames equipped with bolt-connected reinforced concrete panel wall

This paper proposes a macroscopic numerical model for simulating the seismic behavior of steel frames equipped with bolt-connected reinforcement concrete panel wall (RPWF). The RPWF is a new type of lateral-resisting system, which was proposed by the authors. The RC panel wall is connected with steel beams by high-strength bolts. In the proposed numerical model, a RPW is modeled by Multiple-Vertical-Line-Element-Model (MVLEM) elements; the wall-to-frame bolt connection is modeled by two nonlinear springs, and a four-phase mechanical model is proposed to simulate the these springs; the deterioration effects of the steel components and the shear deformation of the panel zones are considered; the plastic hinge model is used to simulate the nonlinear behavior of the beam-column connections and the connections at column bases. Two RPWF specimens were tested to validate the proposed model, the results show that: the predicted results of the proposed model generally correlate well with the test results, the maximum error on ultimate capacity is 7.9% in the positive loading direction. Finally, nonlinear dynamic analyses are conducted on a 6-story planar steel frame and two RPWF structures, the maximum inter-story drift ratio of the planar steel frame is dramatically reduced by using the RPW. The results indicate that the RPW with the wall-to-frame bolt connections is good choice to strengthen steel frame structures.

Plastic-zone advanced analysis – Formulation including semi-rigid connection

A new numerical formulation includes the behavior of the semi-rigid connection into plastic-zone finite element model for steel plane frames. This Bernoulli-Euler formulation is an expansion and generalization of the slice technique with updated Lagrangian co-rotational system, presented before. Only one spring is placed in the finite element end node to allow the study of plasticity inside the member. The connection semi-flexibility factor eta controls this spring. It is defined for the beam length and can classify the connection as rigid or flexible. The eta effects on the vertical displacement function, the generality of the proposed model and the corresponding stiffness matrices are shown. The usage of another eta based on the finite element length is also explained. The advantages of semi-rigid connection behavior are discussed. Several answers were obtained, considering the connection stiffness and the inelastic behavior. This technique is applied to solve three benchmarked examples, applying connections of constant stiffness and semi-rigid curves from an existing data bank. The semi-rigid connection economy on beams, its appearing improvement of columns capacity, and the reduction of portal frame limit load justify this research. These examples are minimum requirements to develop the advanced direct analysis, which power is explored in the last one.

Reliability Assessment of Steel Plane Frame's Buckling Strength Considering Semi-rigid Connections

Reliability Assessment of Steel Plane Frame's Buckling Strength Considering Semi-rigid Connections

Reliability Assessment of Steel Plane Frame's Buckling Strength Considering Semi-rigid Connections

The buckling strength of a structure depends hugely on material properties, geometry dimensions, and boundary conditions that are potentially random. This paper presents an assessment of the safety of buckling strength of steel plane frame semi-rigid beam-column connections. The Newton-Raphson method is used to solve the nonlinear equation for the buckling limit of the column. The reliability of the structure is evaluated by the Monte Carlo simulation method. The effects of input parameters are also investigated.

Advancements in the stability design of steel frames considering general non‐prismatic members

AbstractThis paper discusses an innovative approach to the design of planar steel frames composed of prismatic and/or non‐prismatic members. The method evaluates the member stability limit states using an inelastic eigenvalue buckling analysis configured with column, beam and beam‐column inelastic stiffness reduction factors derived from the ANSI/AISC 360‐16 Specification. The resulting procedure provides a relatively rigorous evaluation of all member strength limits accounting for moment and axial force variations along the member lengths, non‐prismatic geometry effects, general out‐of‐plane bracing conditions and beneficial end restraint from less‐critical adjacent, unbraced segments and/or from end conditions. The approach uses a geometric non‐linear pre‐buckling analysis based on the AISC direct analysis method to estimate the in‐plane internal forces. Given these forces, an eigenvalue buckling solution is conducted to evaluate the overall member stability. Other limit states are addressed through cross‐section strength checks using the internal forces determined from the geometric non‐linear load‐displacement analysis. Calculations using this approach are compared with results from recent experimental tests.

Robustness assessment of planar steel frames caused by failure of a side column under localized fire

SummaryProgressive collapse of a building structure under fire is a disaster that may cause heavy casualties and serious economic loss. However, there is a lack of codified method to assess fire‐induced progressive collapse of building structures. A global–local analysis method (GLAM) has recently been proposed by the authors and their colleagues to assess progressive collapse of steel buildings under localized fire, and its application on fire scenarios that causes one inner column to fail has been verified. This paper extends the application of GLAM to fire scenarios that causes a side column to fail in a planar steel frame. The predictions of the GLAM were validated against the results obtained from nonlinear dynamic analysis of the whole frame model. Besides, effects of location of the heated column at different storeys and load level of the frame were also studied. The results show that GLAM gives the same collapse predictions to the case studies with detailed nonlinear dynamic analysis. The differences between the critical load obtained from GLAM and that provided by the nonlinear dynamic analysis is within 7%. Therefore, GLAM has good applicability on robustness assessment of planar steel frames caused by failure of a side column under localized fire.

A comparison of three performance-based seismic design methods for plane steel braced frames

This work presents a comparison of three performance-based seismic design methods (PBSD) as applied to plane steel frames having eccentric braces (EBFs) and buckling restrained braces (BRBFs). The first method uses equivalent modal damping ratios (�k)referring to an equivalent multi-degree-of-freedom (MDOF) linear system, which retains the mass, the elastic stiffness and responds in the same way as the original non-linear MDOF system. The second method employs modal strength reduction factors (�𝑘) resulting from the corresponding modal damping ratios. Contrary to the behavior factors of code based design methods, both �k and �k account for the first few modes of significance and incorporate target deformation metrics like inter-storey drift ratio (IDR) and local ductility as well as structural characteristics like structural natural period, and soil types. Explicit empirical expressions of �k and �k, recently presented by the present authors elsewhere, are also provided here for reasons of completeness and easy reference. The third method, developed here by the authors, is based on a hybrid force/displacement (HFD) seismic design scheme, since it combines the force-base design (FBD) method with the displacement-based design (DBD) method. According to this method, seismic design is accomplished by using a behavior factor (qh), empirically expressed in terms of the global ductility of the frame, which takes into account both non-structural and structural deformation metrics. These expressions for qh are obtained through extensive parametric studies involving non-linear dynamic analysis (NLDA) of 98 frames, subjected to 100 far-fault ground motions that correspond to four soil types of Eurocode 8. Furthermore, these factors can be used in conjunction with an elastic acceleration design spectrum for seismic design purposes. Finally, a comparison among the above three seismic design methods and the Eurocode 8 method is conducted with the aid of non-linear dynamic analyses via representative numerical examples, involving plane steel EBFs and BRBFs.

Design optimization of semi-rigid plane steel frames with semi-rigid bases using biogeography-based optimization and genetic algorithms

This paper performs optimization for plane steel frames with semi-rigid beam-to-column connections, in a company with fixed, semi-rigid and hinged base connections using a biogeography-based optimization algorithm (BBO), along with a genetic algorithm (GA). In this paper, Kanvinde and Grilli [1] nonlinear model is used for simulating semi-rigid base connections, where this model considers all deformations in different base connection components under the applied loads to determine the relative spring rotation for the sake of getting accurate base rotational stiffness value. In addition, Frye and Morris [2] nonlinear model is used for simulating semi-rigid beam-to-column connections. The P-∆ effect and geometric nonlinearity are considered. The stress and displacement constraints of AISC-LRFD [3] specifications, together with size adjustment constraints, are considered in the design procedure.

Refined second-order plastic-hinge dynamic analysis for planar steel frames

The paper presents the method of the refined second-order plastic hinge analysis for planar steel frames subjected to dynamic loads. The material model used is the generalized Clough model in consideration of effects of axial and shear force on plastic limit state of cross-sections. Geometric nonlinearities of member and frame are taken into account by the use of stability functions in framed stiffness matrix formulation. Non-linear motional equation of structures was established by finite element method and solved by Newmark method combined with the modified Newton-Raphson method. Based on the obtained algorithms, the author has programmed a computational program and calculated the planar steel frames. From the calculated results, discussions and conclusions are presented.

Seismic design of plane steel braced frames using equivalent modal damping ratios

A force-based seismic design method for eccentrically braced and buckling-restrained braced plane steel frames is proposed. The method makes use of equivalent modal damping ratios that play the role of the behavior (strength reduction) factor. A comparison of the proposed design method with the EC 8 design method is presented herein and conclusions are drawn.

Concept and development of a steel\u2013bamboo SI (skeleton\u2013infill) system: experimental and theoretical analysis

A steel–bamboo SI (skeleton–infill) system with steel frame as the skeleton and bamboo box as the filler is proposed, which realizes the requirements of building assembly and sustainable development. As a first step in studying the seismic behavior of the steel–bamboo SI (skeleton–infill) system, a simplified plane steel frame–bamboo infilled wall structure is tested under low-cycle reversed loading in this paper. The deformation mode, failure mode, hysteretic behavior and energy dissipation performance of the system are discussed. The test showed that the steel frame and the bamboo infilled wall were well connected and could work together. Then, the formulas for calculating the lateral stiffness of the system and the axial stiffness of the equivalent diagonal brace which replaced the infilled wall are obtained by theoretical analysis. The error between theoretical calculation and test results was about 1.3%, which proved the correctness of the proposed formula.

Large displacement elastic analysis of planar steel frames with flexible beam-to-column connections under static loads by corotational beam-column element

This paper presents the elastic large-displacement analysis of planar steel frames with flexible connections under static loads. A corotational beam-column element is established to derive the element stiffness matrix considering the effects of axial force on bending moment (P-Δ effect), the additional axial strain caused by end rotations and the nonlinear moment – rotation relationship of beam-to-column connections. A structural nonlinear analysis program is developed by MATLAB programming language based on the modified spherical arc-length algorithm in combination with the sign of displacement internal product to automate the analysis process. The obtained numerical results are compared with those from previous studies to prove the effectiveness and reliability of the proposed element and program.

Performance-based multi-objective collaborative optimization of steel frames with fuse-oriented buckling-restrained braces

A multi-objective collaborative optimal design procedure for steel frames equipped with buckling-restrained braces (BRBs) is proposed under the framework of performance-based seismic design (PBSD) in order to minimize the damage of the primary structure as well as the material cost. For this purpose, a so-called BRB energy dissipation ratio is defined and introduced in the optimization to characterize the involvement of fuse-type BRBs in hysteretic energy dissipation in building stories. Three groups of constraints obtained from the rules on geometrical and conceptual design, the requirements regarding strength and stability, and the PBSD-based story drift limits are considered. To address the discrete-continuous hybrid design variables, a hybrid coding scheme is proposed to modify the non-dominated sorting genetic algorithm II (NSGA-II). The rationality of the proposed procedure is demonstrated by a case study on a seven-story planar steel frame with BRBs. The demonstration indicates that the proposed optimization procedure can make BRBs play the role of a structural fuse successfully in steel frames. The BRB energy dissipation ratios of case C are distributed nearly uniformly along the structural height. The weak-beam-strong-column design principle can be satisfactorily achieved through the maximization of the story BRB energy dissipation ratios. Additionally, the modified hybrid coding NSGA-II algorithm is computationally efficient and stable.

Meta-heuristic design optimization of steel moment resisting frames subjected to natural frequency constraints

Natural frequencies of a structure play a key role for finding underlying structural properties. Therefore, structural design considering natural frequencies is a very important issue for engineers. While there are many studies on optimization of truss structures under multiple frequency constraints, just a few studies have been published on steel frames for which only gradient based methods were applied. In this paper, meta-heuristic algorithms are applied for the first time ever to optimal design of steel frame structures with frequency constraints. Several benchmark design examples are solved with five algorithms including particle swarm optimization (PSO), charged system search (CSS), teaching-learning based optimization (TLBO), grey wolf optimizer (GWO) and a recently developed improved grey wolf optimizer (IGWO). Optimization results of these algorithms are compared in terms of statistical indices, convergence and optimum solutions. Various types of planar and space steel frames ranging from small to large scale cases are considered for illustrating merits and applicability of meta-heuristic algorithms to these sizing optimization problems wherein the large scale cases are studied in both continuous and discrete forms.

Large displacement elastic static analysis of semi-rigid planar steel frames by corotational Euler--Bernoulli finite element

A corotational finite element for large-displacement elastic analysis of semi-rigid planar steel frames is proposed in this paper. Two zero-length rotational springs are attached to the ends of the Euler-Bernoulli element formulated in corotational context to simulate the flexibility of the beam-to-column connections and then the equilibrium equations of the hybrid element, including the stiffness matrix which contains the stiffness terms of the rotational springs, are established based on the static condensation procedure. The linear and Kishi-Chen three-parameter power models are applied in modelling the moment-rotation relation of beam-column connections. The arc-length nonlinear algorithm combined with the sign of displacement internal product are used to predict the equilibrium paths of the system under static load. The analysis results are compared to previous studies to verify the accuracy and effectiveness of the proposed element and the applied nonlinear procedure.
 Keywords: corotational context; Euler-Bernoulli element; large displacement; semi-rigid connection; steel frame; static analysis.

Improved steel frame performance against progressive collapse with infill panels

Local failure of one or more components due to abnormal loading can induce progressive collapse of a building structure. Herein, improved structural robustness is targeted to improve steel frame performance against progressive collapse. A multi-scale analysis model is constructed; then, the anti-collapse performance of a plane steel frame structure with a flush end plate connection is comprehensively analyzed using nonlinear static analysis. To enhance the anti-collapse capability of the steel frame structure, reasonable addition of infill panels in indirect- and direct-influence areas is proposed. Infill panels properly arranged in direct influence area can give full play to the Vierendeel mechanism, and effectively improve combined ability of the remaining structure. And then 1/8–1/6 of the net span is recommended as the length of the infill steel panel for the steel frame structure with flush end plate connection.

A Distributed Plasticity Approach for Steel Frames Analysis Including Strain Hardening Effects

This paper focuses on the creation and numerical application of physically nonlinear plane steel frames analysis problems. The frames are analysed using finite elements with axial and bending deformations taken into account. Two nonlinear physical models are used and compared – linear hardening and ideal elastic-plastic. In the first model, distributions of plastic deformations along the elements and across the sections are taken into account. The proposed method allows for an exact determination of the stress-strain state of a rectangular section subjected to an arbitrary combination of bending moment and axial force. Development of plastic deformations in time and distribution along the length of elements are determined by dividing the structure (and loading) into the parts (increments) and determining the reduced modulus of elasticity for every part. The plastic hinge concept is used for the analysis based on the ideal elastic-plastic model. The created calculation algorithms have been fully implemented in a computer program. The numerical results of the two problems are presented in detail. Besides the stress-strain analysis, the described examples demonstrate how the accuracy of the results depends on the number of finite elements, on the number of load increments and on the physical material model. COMSOL finite element analysis software was used to compare the presented 1D FEM methodology to the 3D FEM mesh model analysis.