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In this paper, the problem of layout optimization for X-bracing of steel frames is studied using the ant system (AS). A new design method is employed to share the gravity and the lateral loads between the main frame and the bracings according to the requirements of the IBC2006 code. An algorithm is developed which is called optimum steel designer (OSD). An optimization method based on an approximate analysis is also developed for layout optimization of braced frames. This method is called the approximate optimum steel designer (AOSD) and uses a simple deterministic optimization algorithm leading to the optimum patterns and it is much faster than the OSD. Several numerical examples are treated by the proposed methods. Efficiency and accuracy of the methods are then discussed. A comparison is also made with Genetic algorithm for one of the frames.

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 From the time that civil engineers have used steel in building structures, they tried to increase its strength so as to produce more economic and lighter structures by using more elegant sections. Increase of steel strength is not always useful for all members of a steel structure. In some members under certain conditions, it is needed to reduce the strength as much as possible to improve the behavior of structure. By using very low strength steel according to the Easy-Going Steel (EGS) concept in this research, it is shown that the performance of diagonal Eccentrically Braced Frames (EBFs) improves substantially. For this purpose, a finite element analysis was used to simulate diagonal eccentrically braced frames. Fifteen diagonal eccentrically braced frames were designed through AISC2005. By substitutingvery low strength steelinstead of carbon steel with equal strength in the links, their performance improve fundamentally without any global or local instability in their links.

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Inelastic deformation of structural components is generally acceptable in seismic design. In such behavior, the strength of structures increases while plastic hinges are formed in members frequently. The strength revealed during the formation of plastic hinges is called "overstrength". Overstrength is one of the important parameters in the seismic design of structures. The present study tries to evaluate the overstrength of the concentrically steel braced frames (CBFs), considering reserved strength, because of members post-buckling. As such, a static nonlinear (pushover) analysis has been performed on the model buildings with single and double bracing bays, different stories and brace configurations (chevron V, invert Vand X-bracing). It has been realized that the number of bracing bays and the height of buildings have a low effect on reserve strength due to brace post-buckling. However, these parameters have a profound effect on the overstrength factor. These results indicate that the overstrength values for CBFs, proposed in seismic design codes, need to be modified.

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An evolutionary structural optimization (ESO) method is used for plastic design of frames. Based on safe theorems some criteria are derived and made an effort to satisfy them during the optimization process. In this regard, equilibrium is checked and yield condition is gradually satisfied during the optimization process. In this method, the amount of used material and the stiffness for each element are improved, simultaneously, to impose upper bound of moment in the element. Frame analysis and optimization algorithm are implemented as PLADOF (PLAstic Design of Frames) computer code. Four examples are presented to illustrate the performance of the algorithm

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Due to the algorithmic simplicity, cellular automata (CA) models are useful and simple methods in structural optimization. In

this paper, a cellular-automaton-based algorithm is presented for simultaneous shape and topology optimization of continuum

structures, using five-step optimization procedure. Two objective functions are considered and the optimization process is

converted to the single objective optimization problem (SOOP) using weighted sum method (WSM). A novel triangle

neighborhood is proposed and the design domain is divided into small triangle elements, considering each cell as the finite

element. The finite element formulation for constant strain triangles using three-node triangular elements is developed in this

article. Topological parameters and shape of the design space are taken as the design variables, which for the purpose of this

paper are continuous variables. The paper reports the results of several design experiments, comparing them with the currently

available results obtained by CA and genetic algorithm in the literature. The outcomes of the developed scheme show the

accuracy and efficiency of the method as well as its timesaving behavior in achieving better results

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Barrel vaults are attractive space structures that cover large area without intermediate supports. In this paper, the charged

search system (CSS) optimization algorithm is employed for optimal design of barrel vaults. This method utilizes the governing

laws of Coulomb and Gauss from electrostatics and the Newtonian law of mechanics. The results demonstrate the efficiency of

the discrete CSS algorithm compared to other meta-heuristic algorithms.

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For the analysis of structures, the first step consists of configuration processing followed by data generation. This step is the most time consuming part of the analysis for large-scale structures. In this paper new graph products called triangular and circular graph products are developed for the formation of the space structures. The graph products are extensively used in graph theory and combinatorial optimization, however, the triangular and circular products defined in this paper are more suitable for the formation of practical space structural models which can not be generated easily by the previous products. The new products are employed for the configuration processing of space structures that are of triangular or a combination of triangular and rectangular shapes, and also in circular shapes as domes and some other space structural models. Cut out products are other new types of graph products which are defined to eliminate all of the connected elements to the considered node to configure the model or grid with some vacant panels inside of the model. The application of the presented graph products can be extended to the formation of finite element models.

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The present paper focuses on size optimization of scallop domes subjected to static loading. As this type of space structures includes a large number of the structural elements, optimum design of such structures results in efficient structural configurations. In this paper, an efficient optimization algorithm is proposed by hybridizing particle swarm optimization (PSO) algorithm and cellular automata (CA) computational strategy, denoted as enhanced particle swarm optimization (EPSO) algorithm. In the EPSO, the particles are distributed on a small dimensioned grid and the artificial evolution is evolved by a new velocity updating equation. In the new equation, the difference between the design variable vector of each site and an average vector of its neighboring sites is added to the basic velocity updating equation. This new term decreases the probability of premature convergence and therefore increases the chance of finding the global optimum or near global optima. The optimization task is achieved by taking into account linear and nonlinear responses of the structure. In the optimization process considering nonlinear behaviour, the geometrical and material nonlinearity effects are included. The numerical results demonstrate that the optimization process considering nonlinear behaviour results in more efficient structures compared with the optimization process considering linear behaviour. .

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In this research, the Charged System Search (CSS) and Enhanced Charged System Search (ECSS) algorithm are used to obtain the optimum design of irregular grillage systems with different spacing and various boundary conditions. The cross-sectional properties of the beams are selected as the design variables and the weight of structure is used as the objective function. The displacement limitations and permissible stress constraints are employed from LRFD-AISC and are considered in the formulation of the design problem. Furthermore, in obtaining the response of the grillage systems, the effect of warping is also taken into account. The comparison of the results shows that warping changes the beam spacing, and different boundary conditions have substantial effects on the optimum design of irregular grillage systems

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Damping of a full-scale cable with a pair of passive–on magnetorheological (MR) dampers was tested. A cable of 215.58m long with the first mode frequency of 0.658Hz was tensioned horizontally in cable prefabrication factory. Two MR dampers were attached to the cable in an angle in the plane perpendicularly to the cable axis in 5m length from the cable anchorage. The applied voltage level was 0V, 3V, 6V and 9V. The cable was excited manually to a certain amplitude level for the first three modes of vertical vibration. The free decay curves of the cable were then recorded. The damping of the cable was calculated from the measured anti-node vibration amplitude. The damping of the free cable was also tested for reference. It was found that the damping of the cable is still low when MR dampers were no voltage strengthened. However, the damping of the cable increased greatly for the other with MR damper cases compared to free cable. Further study showed that the damping of the cable with MR dampers were strongly depended on applied voltage level and vibration amplitude. There is an optimal damping value when MR damper is voltage strengthened. The dependence of the optimum damping on applied voltage level, vibration amplitude and vibration mode was further analyzed.

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In the process of structural analysis we often come to structures that can be analyzed with simpler methods than the standard approaches. For these structures, known as regular structures, the matrices involved are in canonical forms and their eigen-solution can be performed in a simple manner. However, by adding or removing some elements or nodes, such methods cannot be utilized. Here, an efficient method is developed for the analysis of irregular structures in the form a regular structure with additional or missing nodes or with additional or missing supports. In this method, the saving in computational time is considerable. The power of the method becomes more apparent when the analysis should be repeated very many times as it is the case in optimal design or non-linear analysis.

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In this paper, a new enhanced version of the Particle Swarm Optimization (PSO) is presented. An important modification is made by adding probabilistic functions into PSO, and it is named Probabilistic Particle Swarm Optimization (PPSO). Since the variation of the velocity of particles in PSO constitutes its search engine, it should provide two phases of optimization process which are: exploration and exploitation. However, this aim is unachievable due to the lack of balanced particles’ velocity formula in the PSO. The main feature presented in the study is the introduction of a probabilistic scheme for updating the velocity of each particle. The Probabilistic Particle Swarm Optimization (PPSO) formulation thus developed allows us to find the best sequence of the exploration and exploitation phases entailed by the optimization search process. The validity of the present approach is demonstrated by solving three classical sizing optimization problems of spatial truss structures.

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It is well known that damaged structural members may alter the behaviour of the structures considerably. Careful observation of these changes has often been viewed as a means to identify and assess the location and severity of damages in structures. Among the responses of a structure, natural frequencies and natural modes are both relatively easy to obtain and independent from external excitation, and therefore, can be used as a measure of the structural behaviour before and after an extreme event which might have led to damage in the structure. This paper applies Charged System Search algorithm to the problem of damage detection using vibration data. The objective is to identify the location and extent of multi-damage in a structure. Both natural frequencies and mode shapes are used to form the required objective function. To moderate the effect of noise on measured data, a penalty approach is applied. Varity of numerical examples including beams, frames and trusses are examined. The results show that the present methodology can reliably identify damage scenarios using noisy measurements and incomplete data.

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Formation of a suitable null basis is the main problem of finite elements analysis via force method. For an optimal analysis, the selected null basis matrices should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient method is developed for the formation of the null bases of finite element models (FEMs) consisting of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-equilibrating systems (SESs) on these subgraphs. Two examples are presented to illustrate the simplicity and effectiveness of the presented graph-algebraic method.

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In this paper, the problem of simultaneous shape and size optimization of single-layer barrel vault frames which contains both of discrete and continuous variables is addressed. In this method, the improved magnetic charged system search (IMCSS) is utilized as the optimization algorithm and the open application programming interface (OAPI) plays the role of interfacing analysis software with the programming language. A comparison between the results of the present method and some existing algorithms confirms the high ability of this approach in simultaneous shape and size optimization of the practical and large-scale spatial structures.

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The effect of axial deformation of shell particles on the dynamic instability (flutter) of cantilevered cylindrical shells made of functionally graded materials (FGM) under an end axial follower force is addressed. To this end, at first, results for free vibration of FGM cylindrical shells were verified with previous outcomes and they were in very good agreement. Then, the effect of axial deformation of the shell, acting like a reducing linearly-distributed follower load, on the critical circumferential mode number and the flutter load of FGM shells was accounted for. Finally, the effect of axial deformation of the shell particles on the critical circumferential mode number and the flutter load of FGM shells were investigated. In this case, three homogeneous shells with different elasticity moduli and densities and two FGM materials were considered: nickel-stainless steel and stainless steel-alumina. Results include the increasing critical circumferential mode number and the increasing value of the flutter load due to axial deformation. The increase in the flutter load occurs in proportion to the whole elasticity modulus of the material, and thus it can be derived from the formula of mixture for an FGM.

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Latticed columns are frequently used in industrial steel structures. In some countries these built-up columns might be even used in other types of steel structures such as residential and commercial buildings. Besides, latticed columns are parts of skeletons of many historic buildings all around the world. To analyze a steel structure with latticed columns a more accurate numerical model for such a column seems to be essential. The lay-out and connectivity of constructing main profiles of a latticed column leads to formation of many shear zones along the length of a column. Therefore, considering shear effects on the behavior of a lattice column is inevitable. This paper proposed a new super-element with twelve degrees of freedom to be used in finite element modeling of latticed columns. The cross sectional area, moments of inertia, shear coefficient and torsional rigidity of the developed new element are derived. To compute these parameters with less complexity a model using only beam elements is also introduced. A general purpose finite element program named LaCE is developed. This FE program is capable of performing linear and nonlinear analysis of 3D-frames with latticed columns, considering shear deformation. To show the accuracy of the proposed element, several cases are studied. The outcome of these investigations revealed that the current-in-practice model for latticed columns suffers from some major shortcomings which to some extends are resolved by the proposed super-element. The developed element showed the capability of modeling a lattice column with good accuracy and less computational cost.

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The purpose of this study is to determine the effect of vierendeel panel width and vertical truss spacing ratio in an inelastic behavior of the STF system due to earthquake loads. The STF system is applied to a six-storey building that serves as apartments [2]. The STF system is used in the building in the transverse direction (N-S direction), while in the longitudinal direction (W-E direction) the building system uses the special moment resisting frame. The structural behavior was evaluated using nonlinear pushover and time history analyses. The results showed that by increasing the ratio of vierendeel panel width and vertical truss spacing, the ductility of the structure was increased. Based on the performance evaluation, the ratio of the vierendeel panel width and vertical truss spacing on the STF buildings that provided satisfactory performance was more or equal to 1.6. The ultimate drift obtained from non-linear time history analysis was smaller than the pushover analysis. This result showed that the static nonlinear pushover analysis was quite conservative in predicting the behavior of the six-storey building in an inelastic condition.

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The linear and nonlinear responses of steel buildings with perimeter moment resisting frames (PMRFs) are estimated and compared to those of equivalent buildings with spatial moment resisting frames (SMRFs). The equivalent models with SMRFs are designed by using an approximated procedure in such a way that, not only their fundamental period, total mass and lateral stiffness are fairly the same as those of the corresponding buildings with PMRFs, but also other characteristics to make the two structural "as equivalent" as possible. The numerical study indicates that the interstory shears of the PMRFs building may be significantly larger than those of the SMRFs building. The main reasons for this are that the buildings with PMRFs are stiffer and that the dynamics properties of the two types of structural systems are different. The interstory displacements are similar for both structural systems in many cases. For some other cases, however, they are larger for the model with SMRFs, depending upon the closeness between the earthquake corner periods and the periods of the buildings. The global ductility and story ductility demands are larger for the buildings with PMRFs, implying that, since larger ductility demands are imposed, the detailing of the connections will have to be more stringent than for the buildings with SMRFs. It can be concluded, that the seismic performance of the steel buildings with SMRFs may be superior to that of steel buildings with PMRFs. The findings of this paper are for the particular models used in the study. Much more research is needed to reach more general conclusions

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The vibration of cable-stayed bridges subjected to the passage of high-speed trains is studied in this article. The moving train includes a number of wagons, each of which is modeled as a four-axle system possessing 48 degrees of freedom. The car model is nonlinear and three-dimensional and includes nonlinear springs and dampers of primary and secondary suspensions, dry friction between different parts and also clearances and mechanical stops. Two parallel rails of the track are modeled as Euler-Bernoulli beams on elastic points as rail pads. The rail irregularities are assumed to be stationary random and ergodic processes in space, with Gaussian amplitude probability densities and zero mean values. The bridge deck is modeled as a plate supported by some cables. The current model is validated using several numerical models reported in the literature of the earlier researcher.