AISC-LRFD Specification Research Articles

Buckling behavior of slender square concrete filled steel tubular columns strengthened with CFRP profile under combined compression and bending

An innovative stub composite column consisting of square concrete-filled steel tubular (SCFST) column internally strengthened with a I-shaped pultruded CFRP profile, referred to as SCFST-CFRP column, has been developed. Research studies have demonstrated that this new stub column has the higher axial load capacity and ductility with the less weight in comparison to the SCFST column. Considering the use of slender column in the engineered systems, this study investigated resistance and behavior of slender SCFST-CFRP columns under the combined compression and bending. In the experimental program, the combined loading tests were completed on nine groups of specimens with varied slenderness ratios and load eccentricities. The column buckling behavior was analyzed in terms of failure modes, moment-curvature response, peak loads, longitudinal strain response, and strength reduction factors. The results addressed the differences in buckling behavior between SCFST-CFRP column and SCFST column. Finite element models were created and validated to evaluate influences of critical structural parameters on column resistance and provide supplementary numerical data. In addition, the tested and simulated results were utilized to assess the applicability of existing design approaches, as suggested in the AISC-LRFD specification, the GB50936 code, and empirical equations provided by Han, for the SCFST-CFRP slender column under the combined compression and bending. Validation results identified that the GB50936 code provided relatively accurate predictions of the slender column capacities under the combined loads, while the predicted capacity was not safe for the column with a large slenderness ratio. An improvement in the GB50936 design method was conducted using the test and simulation data for the SCFST-CFRP column under the combined compression and bending.

High-dimensional optimization of large-scale steel truss structures using guided stochastic search

Despite a plethora of truss optimization algorithms devised in the recent literature of structural optimization, still high-dimensional large-scale truss optimization problems have not been properly tackled basically due to the excessive computational effort required to handle the foregoing instances. In this study, application of a recently developed design-driven heuristic, namely guided stochastic search (GSS), is extended to a more challenging class of truss optimization problems having thousands of design variables. Two variants of the algorithm, namely GSSA and GSSB, have been employed for sizing optimization of four high-dimensional examples of steel trusses, i.e., a 2075-member single-layer onion dome, a 2688-member double-layer open dome, a 6000-member double-layer scallop dome, and a 15048-member double-layer grid as per AISC-LRFD specification. The numerical results obtained indicate the efficiency of GSSA and GSSB in handling high-dimensional instances of large-scale steel trusses with up to 15048 discrete design variables.

An improved constrained differential evolution for optimal design of steel frames with discrete variables

New metaheuristic algorithms have been shown to be robust and effective for engineering optimization problems. Differential Evolution (DE), which is one of the most famous optimization approaches developed for optimal design problems with continuous design variables, is, in fact, inappropriate for constrained problems containing discrete design variables. In this article, an improved constrained differential evolution (iCDE) algorithm is proposed for optimization of steel frames with discrete design variables, followed by comprehensive testing of iCDE to validate the results. In order to make iCDE more efficient, two novel mutation approaches are proposed and tested. Three benchmark structural optimization problems are evaluated by the algorithm and compared against those reported in the literature obtained by GA, ACO, IACO, ICA, HS, and SBO. The total weight of the frame is considered as the objective function and the cross sections of the elements are taken as design variables. Constraints are based on the stress and displacement requirements conforming to the AISC-LRFD specifications. Moreover, to demonstrate the robustness of the algorithm, eight benchmark test functions of CEC-2017 are evaluated. The results show that the iCDE algorithm is computationally efficient and robust enough to find the global optima.

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

This paper performs for the first time a simultaneous optimization for members sections along with semi-rigid beam-to-column connections for space steel frames with fixed, semi-rigid, and hinged bases using a biogeography-based optimization algorithm (BBO) and a genetic algorithm (GA). Furthermore, a member\'s sections optimization for a fully fixed space frame is carried out. A real and accurate simulation of semi-rigid connection behavior is considered in this study, where the semi-rigid base connections are simulated using Kanvinde and Grilli (2012) nonlinear model, which considers deformations in different base connection components under the applied loads, while beam-to-column connections are modeled using the familiar Frye and Morris (1975) nonlinear polynomial model. Moreover, the P-∆ effect and geometric nonlinearity are considered. AISC-LRFD (2016) specification constraints of the stress and displacement are considered as well as section size fitting constraints. The optimization is applied to two benchmark space frame examples to inspect the effect of semi-rigidity on frame weight and drift using BBO and GA algorithms.

A developed design optimization model for semi-rigid steel frames using teaching-learning-based optimization and genetic algorithms

This paper proposes a developed optimization model for steel frames with semi-rigid beam-to-column connections and fixed bases using teaching-learning-based optimization (TLBO) and genetic algorithm (GA) techniques. This method uses rotational deformations of frame members ends as an optimization variable to simultaneously obtain the optimum cross-sections and the most suitable beam-to-column connection type. The total cost of members plus connections cost of the frame are minimized. Frye and Morris (1975) polynomial model is used for modeling nonlinearity of semi-rigid connections, and the P-∆ effect and geometric nonlinearity are considered through a stepped analysis process. The stress and displacement constraints of AISC-LRFD (2016) specifications, along with size fitting constraints, are considered in the design procedure. The developed model is applied to three benchmark steel frames, and the results are compared with previous literature results. The comparisons show that developed model using both LTBO and GA achieves better results than previous approaches in the literature.

Multi-objective optimization of structural steel buildings under earthquake loads using NSGA-II and PSO

The aim of this study is to illustrate and compares the use of Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) for multi-objective optimization of two and three dimensional moment resisting steel structures subjected to earthquake loads. For this purpose, steel buildings with different characteristics are designed under earthquakes using the Non-dominated Sorting Genetic Algorithm (NSGA-II) and PSO as a tool to achieve the best structure in terms of: minimize the total structural weight (which is directly related with the costs), control of the maximum inter-story drift, and to satisfy the strength requirements of the AISC-LRFD specification. It is considered that all the steel structures are constituted by elements with W section (256 in total) taken from the LRFD-AISC Database. Although, the GAs and PSO are applied for moment resisting steel structures, the concepts can be extended for other structural systems. It is concluded that the use of NSGA-II and PSO reduce the structural weight and they are a very useful tools to improve the structural performance of the buildings. Finally, the structural buildings obtained via PSO are in general better solutions in comparison with the NSGA-II approach.

Enhanced hybrid metaheuristic algorithms for optimal sizing of steel truss structures with numerous discrete variables

The advent of modern computing technologies paved the way for development of numerous efficient structural design optimization tools in the recent decades. In the present study sizing optimization problem of steel truss structures having numerous discrete variables is tackled using combined forms of recently proposed metaheuristic techniques. Three guided, and three guided hybrid metaheuristic algorithms are developed by integrating a design oriented strategy to the stochastic search properties of three recently proposed metaheuristic optimization techniques, namely adaptive dimensional search, modified big bang-big crunch, and exponential big bang-big crunch algorithms. The performances of the proposed guided, and guided hybrid metaheuristic algorithms are compared to those of standard variants through optimum design of real-size steel truss structures with up to 728 design variables according to AISC-LRFD specification. The numerical results reveal that the hybrid form of adaptive dimensional search and exponential big bang-big crunch algorithm is the most promising algorithm amongst the other investigated techniques.

Size and Geometry Optimization of Double-Layer Grids Using CBO and ECBO Algorithms

In this paper, the optimum design procedure based on colliding bodies optimization method and its enhanced version are applied to optimal design of two commonly used configurations of double-layer grids, and optimum span–depth ratios are determined. Two ranges of spans as small and large sizes with certain bays of equal lengths in two directions and different types of element groupings are considered for each type of square grids. These algorithms obtain minimum weight grid through appropriate selection of tube sections available in AISC load and resistance factor design (LRFD). Strength constraints of AISC-LRFD specifications and displacement constraints are imposed on these grids. The comparison is aimed at finding the depth at which each of the different configurations shows its advantages. Finally, the effect of support locations on the weight of the double-layer grids is investigated. The results are graphically presented from which the optimum depth can easily be estimated for each type, while the influence of element grouping can also be realized at the same time.

Nonlinear analysis based optimal design of double-layer grids using enhanced colliding bodies optimization method

In this paper an efficient approach is introduced for design and analysis of double-layer grids including both geometrical and material nonlinearities, while the results are compared with those considering material nonlinearity. Optimum design procedure based on Enhanced Colliding Bodies Optimization method (ECBO) is applied to optimal design of two commonly used configurations of doublelayer grids. Two ranges of spans as small and big sizes with certain bays of equal length in two directions are considered for each type of square grids. ECBO algorithm obtains minimum weight grid through appropriate selection of tube sections available in AISC Load and Resistance Factor Design (LRFD). Strength constraints of AISC-LRFD specifications and displacement constraints are imposed on these grids.

Improved accuracy for the Cm factor of steel beam-columns

The Cm factor acting originally as equivalent moment factor for stability checking of beam-columns, assumes an additional function as part of the magnification factor B1 since the AISC–LRFD specification adopted a single equation for beam-column strength calculation. This article first clarifies the difference between the two roles of Cm for in-plane instability checking and section yielding checking and establishes the relationship between the two Cm. As there is no distinction between the two Cm, some confusion occurs in the current AISC specification, and Cm as equivalent moment factor is not accurately evaluated in many cases. In the present study, the ratio P/Pe is introduced into the Cm formula for beam-columns subject to end moments to enhance its precision. For members subject to transverse loading, formulas based on rational analysis are given in order to avoid the use of conservative value of 1.0. By making use of the principle of superposition, simple and accurate formulas are obtained for the case of transverse loading combined with end moments. The proposed formulas are compared with the calculation by finite element method to ensure their feasibility for designing elastic–plastic members with initial imperfections. The results are satisfactory.

Computationally efficient discrete sizing of steel frames via guided stochastic search heuristic

Recently a design-driven heuristic approach named guided stochastic search (GSS) technique has been developed by the authors as a computationally efficient method for discrete sizing optimization of steel trusses. In this study, an extension and reformulation of the GSS technique are proposed for its application to problems from discrete sizing optimization of steel frames. In the GSS, the well-known principle of virtual work as well as the information attained in the structural analysis and design stages are used together to guide the optimization process. A design wise strategy is employed in the technique where resizing of members is performed with respect to their role in satisfying strength and displacement constraints. The performance of the GSS is investigated through optimum design of four steel frame structures according to AISC-LRFD specifications. The numerical results obtained demonstrate that the GSS can be employed as a computationally efficient design optimization tool for practical sizing optimization of steel frames.

Design of intermediate transverse stiffeners for shear web panels

The function of intermediate transverse stiffeners attached on plate girder web panels is to provide simple supports so as to reduce the panel aspect ratio, thereby increasing the shear buckling strength. This study investigates the moments of inertia of the transverse stiffeners required to maintain the simple support condition not just for elastic buckling but also for postbuckling through linear buckling and nonlinear finite element analyses. From nonlinear regression analyses of the FEA results, a set of design equations are formulated and compared with the current provisions in AISC and AASHTO LRFD specifications. It is found that the design equation for elastic buckling in AISC and AASHTO LRFD specifications is too conservative especially when the aspect ratio is greater than 1.0. Also, the design equation for postbuckling in AISC and AASHTO specifications results in designs that are too conservative due to oversimplification.

Guided stochastic search technique for discrete sizing optimization of steel trusses: A design-driven heuristic approach

This study presents a design-driven heuristic approach named guided stochastic search (GSS) technique for discrete sizing optimization of steel trusses. The method works on the basis of guiding the optimization process using the well-known principle of virtual work as well as the information collected during the structural analysis and design stages. The performance of the proposed technique is investigated through a benchmark truss instance as well as four real-size trusses sized for minimum weight according to AISC-LRFD specifications. A comparison of the numerical results obtained using the GSS with those of other available algorithms indicates that the proposed technique is capable of locating promising solutions using lesser computational effort.

Flexure and Shear Interaction in Steel I-Girders

AASHTO LRFD and AISC specifications have adopted Basler’s interaction equation, which was formulated for noncompact sections without considering shear buckling. AASHTO LRFD specifications, however, have completely neglected the interaction effect of bending on shear strength since the 3rd edition in 2004. AISC LRFD specifications followed suit with the 2005 edition. This study was aimed at investigating interaction behaviors in noncomposite I-girders and developing new interaction equations without considering shear buckling. Also, a simple and universally applicable methodology was proposed for web panels whose failures were associated with shear buckling. The interaction should not be ignored when web failures are governed by yielding because of combined bending and shear. Otherwise, the shear capacity of the web panel could be grossly overestimated, thereby compromising the safety of the girder.

Behavior of thin-walled circular hollow section tubes subjected to bending

Thin-walled steel circular hollow sections (CHSs) are widely used in wind turbine towers. The tower tubes are mainly subjected to bending. There have been a few experimental studies on the bending behavior of thin-walled CHS steel tubes. This paper describes a series of bending tests to examine the influence of section slenderness on the inelastic and elastic bending properties of thin-walled CHS. In addition, the influence of stiffeners welded in the steel tube is considered. Sixteen bending tests were performed up to failure on different sizes of CHS with diameter-to-thickness ratio (D/t) varying from 75 to 300. The experimental results showed that the specimens with small diameter-to-thickness ratios failed by extensive plastification on the central part of the tube. With the increase of diameter-to-thickness ratio, the local buckling phenomena became more pronounced. The stiffeners in the steel tubes increased the load carrying capacity and improved the ductility of the specimens. The experimental results were compared with current design guidelines on thin-walled steel members in AISC-LRFD, AS4100 and European Specification. It was found that the test results agreed well with the results based on AS4100 design code.

Advanced Design for The Bolted Clip-Angle Connection

The main focus of this study is to investigate the clip-angle connections are described the section based on ideal limit states. The connection components are designed in accordance with the 2001 AISC-LRFD Specifications and the 2005 AISC Seismic Provisions. In the suggested clip-angle connection, the structural beam can be connected to the column using six high-strength bolts. The slippage on the shear faying surface contributes to increasing energy dissipated capacity in the connection behavior. The design of the clip-angle connection should include these mechanical characteristics. Therefore, this study presents new design methodology that can be applied to bolted clip-angle connections. Besides, step-by-step procedures for design will be treated herein.

On the performance of a modified multiple-deme genetic algorithm in LRFD design of steel frames

This paper investigates the performance of a multiple-deme genetic algorithm (GA) with modified reproduction operators, in optimal design of planar steel frames according to the AISC-LRFD specification. The design objective is to minimise the weight of frame subject to strength, displacement and constructability constraints. A number of new crossover and mutation operators, used alongside the standard operators are utilised in optimum design of a number of steel frames subjected to the constraints of the AISC-LRFD specification, with and without considering the second order effects, as set out by the code requirements. This modified GA (MGA) is shown to have a very fast convergence and to produce relatively high-quality designs. This paper also utilizes the concept of multiple-deme in the GA, as it has been used successfully for other metaheuristic population-based methods. The multiple-deme GA is used alongside the modified GA operators and the algorithm is named the modified multiple-deme GA (MMDGA). The modified GA (MGA) and modified multiple-deme GA (MMDGA) are applied to three benchmark problems and the results are compared to those obtained by other metaheuristic methods. In the majority of cases, the results of comparisons suggest the superiority of the MMDGA in terms of the quality of final design and the total number of performed finite elements analyses.

Performance of the PR connections under combined Axial-tension and moment loading

The inherent moment capacity of bolted top-seat angle connections with double web angles (TSDW), categorized as partially restrained (PR) connections according to AISC-LRFD specifications, can be considered in analyses of semi-rigid connections especially when an accurate analysis of such fames is desired. However, in some cases, developed internal forces in the frame elements may affect the connection behavior, considerably. Axial tension force is one of such internal forces that may be imposed on frame connections in some cases such as construction imperfections, seismic loading or under large deflections of the catenary action during the progressive collapse of the semi-rigid frames. This study aims at the effects of the axial tension force on the performance of the bolted TSDW angle connections using nonlinear finite element method (FEM). The obtained results show that the axial tension force reduces the connection moment capacity and stiffness, considerably. Based on the obtained moment-rotation curves, affected by this particular loading type, equations are proposed to estimate the reduction rate of the connection stiffness and moment capacity.

A hybrid tabu-simulated annealing heuristic algorithm for optimum design of steel frames

A hybrid tabu-simulated annealing algorithm is proposed for the optimum design of steel frames. The special character of the hybrid algorithm is that it exploits both tabu search and simulated annealing algorithms simultaneously to obtain near optimum. The objective of optimum design problem is to minimize the weight of steel frames under the actual design constraints of AISC-LRFD specification. The performance and reliability of the hybrid algorithm were compared with other algorithms such as tabu search, simulated annealing and genetic algorithm using benchmark examples. The comparisons showed that the hybrid algorithm results in lighter structures for the presented examples.

Advanced analysis for structural steel building design

The 2005 AISC LRFD Specifications for Structural Steel Buildings are making it possible for designers to recognize explicitly the structural resistance provided within the elastic and inelastic ranges of behavior and up to the maximum load limit state. There is an increasing awareness of the need for practical second-order analysis approaches for a direct determination of overall structural system response. This paper attempts to present a simple, concise and reasonably comprehensive introduction to some of the theoretical and practical approaches which have been used in the traditional and modern processes of design of steel building structures.