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Optimization of structural patterns for tall buildings: The case of diagrid
... In the last few decades, a great attention has been paid to sustainability and efficiency in the architecture, engineering, and construction (AEC) industry. In the field of structural engineering, design strategies based on optimization techniques are being widely utilized by designers [1][2][3][4][5][6] and studied by researchers [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Often, structural optimization processes are thought to minimize the weight, the compliance, or in a more complex way, the cost, by fixing a given amount of material and boundary conditions, while ensuring that the constraint conditions imposed on structural performance are respected. ...
... Diagrid tall buildings are constituted by a triangulated pattern covering the whole building façades; the grid of diagonal members is characterized by inherently high rigidity, particularly important since tall buildings' design is often governed by the limitation of the lateral drift and building motion. Recent works have highlighted the major role of the diagonal slope on the structural performances of diagrid tall buildings, suggesting that the optimal angle value increases with the building slenderness [7,[46][47][48] and that design solutions with variable angles along the elevation and/or the width are more efficient than uniform-angle configurations for very slender buildings [46,47]. This trend turns out to be intuitive by considering the analogy between the tall building and the vertical cantilever beam under lateral load [3,7,9]. ...
... Recent works have highlighted the major role of the diagonal slope on the structural performances of diagrid tall buildings, suggesting that the optimal angle value increases with the building slenderness [7,[46][47][48] and that design solutions with variable angles along the elevation and/or the width are more efficient than uniform-angle configurations for very slender buildings [46,47]. This trend turns out to be intuitive by considering the analogy between the tall building and the vertical cantilever beam under lateral load [3,7,9]. However, in the case of buildings with low slenderness, the stiffness capacity provided by the triangulated pattern may exceed the stiffness demand, and the member sizing may be governed strength demand [8,16]. ...
A great attention has been recently paid to sustainability and efficiency in the field of civil engineering. In this context, structural optimization processes combined with shape grammar constitute an important tool to support the design phase of large scale structures. This paper proposes shape grammars for the topology optimization of grid shells and diagrid tall buildings characterized by triangulated patterns, with the aim to minimize the structural weight. The structural feasibility of the generated solutions is assessed through numerical analyses, while the optimized patterns are identified by means of optimization processes based on genetic algorithm. The results are provided in terms of optimal geometrical patterns, structural weight, stiffness/strength checks. The approach is helpful to support the investigation of lightweight structural patterns and structurally efficient solutions. The method could be expanded and improved by considering the minimization of different objective functions that take into account both the weight and construction aspects.
... In these patterns, steep diagonals are employed at the bottom of the building, while shallow diagonals are placed at the top [20,21,32]. Additional patterns were suggested afterwards, such as variable-density patterns [33,34], layouts inspired to the principal stress lines [35,36], and configurations based on topological optimization [37][38][39]. Some studies also focused the attention on the influence of the floor shape on the diagrid structural response [29,40,41]. ...
... The majority of research works mentioned above generally selected the optimal geometry as the one employing the least amount of structural material and leading to the lowest lateral displacements, while complying with all strength requirements under vertical and lateral loads [33][34][35][36][37][38][39][40][41]. However, other than the weight and lateral flexibility, other variables can affect the suitability of a certain D. Scaramozzino et al. ...
... The torsional flexibility of the building under eccentric loads should be minimized, to avoid serviceability issues [29,30]. The construction complexity of the structure should also be limited, in order for the building to be feasible from a constructability perspective [35,39]. For this purpose, a complexity index (CI) was proposed by Tomei et al. [35], to quantify the complexity of the diagonal pattern depending on its geometric parameters. ...
Diagrids are efficient structural systems for tall building design and construction due to their high lateral stiffness. Their structural response can be optimized by changing the geometrical pattern of external diagonals. This has usually been carried out by looking for the diagonal pattern that employs the minimum amount of structural material, while complying with strength and stiffness requirements. However, other responses can be significant for the selection of the optimal pattern, such as the torsional flexibility and construction complexity of the building. In this work, the desirability function approach has been used for selecting the optimal diagonal pattern for diagrid tall buildings in a multi-response framework. The most desirable diagonal layout has been selected based on its overall desirability to minimize: (i) the wind-induced lateral displacement, (ii) the torsional rotation, (iii) the diagrid structural weight, and (iv) the construction complexity. The application of this methodology straightforwardly provides the optimal diagrid pattern considering the four responses simultaneously. The method has been applied initially to a limited set of uniform-angle patterns, and afterwards to a wider population of varying-angle geometries. Four different floor plan shapes were also taken into account. The outcomes of the analysis revealed that the specific plan shape plays only a minor role in the definition of the optimal structure, whereas the diagonal layout affects greatly the efficiency of the solution. Uniform-angle diagrids are generally the most desirable, even for taller buildings, due to their higher performance in terms of torsional rigidity and construction complexity. Among these, the patterns in which the diagrid triangular module spans over two-three floors, corresponding to diagonal inclinations of about 55°-65°, have the highest desirability. Notably, because of the competition between the different responses, this optimal inclination is not found to increase as the building becomes taller.
... Used with permission from Montuori et al. [133]. [134]: uniform-angle patterns (60°, 70°, 80°), varying-angle pattern according to Zhang approach (VA) [132], double-density pattern (DD), variable-density pattern (VD), stress lines pattern (ISO). (b) Unit structural weight (blue bars) and complexity index (red curve) for the investigated diagrid patterns. ...
... VA_IDR, VD_1, VD_15, ISO_15, ISO_9, ISO_5, ISO_5* refer to additional subsets of the corresponding patterns, as reported in [134]. Used with permission from Tomei et al. [134]. 16. Results for the 252-meter tall building: (a) surface representation of the OD obtained with # & = # " = # ' = # () = 1; (b) optimal diagrid geometry based on 4096 simulations with different exponents ri. ...
... Conversely, the solutions involving a more uniform VD pattern ( Figure 5.3c,d), where the diagonal concentration rarefies towards the top of the building, turn out to be appropriate solutions for limiting the lateral displacements, while obtaining notable material savings [108]. The previous work of Montuori et al. [133] was subsequently developed by Tomei et al. [134], who proposed additional diagonal patterns for the 90-story tall diagrid building (Figure 5.4a). Besides considering the usual uniform-and varying-angle patterns, the authors also suggested a double-density pattern (DD) (where the diagonal layout is doubled and mirrored over the diagrid façade), a variable-density pattern (VD) (generated by starting from the DD pattern with further topology optimization), and a diagrid-like pattern (ISO) (where the diagonals follow the principal stress lines obtained from the equivalent building cantilever). ...
What do proteins and diagrid tall buildings have in common? Apparently nothing. The former are nanoscopic biological systems, functioning in a complex chemo-physical environment, whose activity is pivotal to carry out a variety of physiological processes. The latter are macroscopic structural systems that are employed nowadays for the design and construction of tall buildings. Nevertheless, in this Thesis, it will be shown that both proteins and diagrid tall buildings can be investigated and modeled by means of the same structural system, the Elastic Lattice Model (ELM). ELMs are spatial structures usually made of springs or bars connected in correspondence of nodes, that can be treated as spherical hinges. In this Thesis, we will use the ELMs to explore a variety of behaviors and features of proteins and diagrids.
In particular, it will be shown that proteins can be efficiently modeled as a network of springs and point masses. Within the framework of modal analysis, these ELMs will be very useful to obtain accurate information regarding protein dynamics and vibrations. Specifically, the low-frequency vibrations extracted from the protein ELMs will be shown to correlate truthfully with the protein biological mechanisms and conformational changes, as well as to provide correct insights on the protein experimental flexibility, as obtained from the experimental B-factors. For this purpose, various modeling approaches will be presented and analyzed. Furthermore, we will see that applying point forces on the protein ELM also provides remarkable insights on protein flexibility. Two novel force application patterns will be reported for this purpose and the results will show that the protein ELMs coupled with the traditional linear static analysis can lead to correct predictions of the protein deformability. Finally, the possible role of geometrical non-linearities will also be investigated within the large-scale conformational changes, which are usually known to exhibit fairly large displacements. From the analyses, it will be shown that these conformational changes often imply curvilinear pathways and possible mechanical non-linearities in the structural response.
Switching to the subject of diagrid tall buildings, the ELMs will then be used to develop a matrix-based method (MBM) for the structural analysis of generic three-dimensional diagrid systems. Based on matrix calculus and the displacements method, the MBM will be applied to perform the structural analysis of diagrids, both alone and coupled with internal cores. The force distribution and the interaction of the external diagrid with the internal resisting element will be studied by inserting the MBM within the General Algorithm (GA), a semi- analytical framework developed few decades ago for the investigation of complex three-dimensional buildings. Furthermore, the MBM will be deeply exploited to investigate the influence of the diagrid geometry on the structural response. Namely, geometrical parameters such as the diagonal inclination, floor shape and building aspect ratio, will be changed in order to obtain information on the lateral and torsional flexibility of the diagrid. From these analysis, it will be shown that different diagrid geometries have a marked effect on the structural response and often a unique solution that allows to optimize all the responses does not exist. For this reason, a novel multi-response optimization will be presented, which makes use, for the first time in this field, of the desirability function approach. Based on the results of the MBM structural analyses, the desirability function will be applied to evaluate the optimal diagrid geometry that simultaneously optimizes the lateral and torsional rigidity, the amount of used material as well as the construction complexity. The outcomes will show that the desirability approach, coupled with the ELM-based MBM, is a simple yet valuable and robust tool for the selection of the optimal diagrid geometry.
... Despite their inherent efficiency, diagrid structures can be further improved. In fact, the analogy between tall building and vertical cantilever beam under lateral load [20,26,27] clearly suggests that the structural pattern should not be uniform for accommodating the variation of bending and shear stiffness demands along elevation, with diagonals gradually steeper going from the top to the base of building. As first contributions in this direction, design procedures for the generation and preliminary sizing of diagrids with variable angle have been proposed in the literature [28][29][30]. ...
... The GD strategy is applied to tall building models characterised by different slenderness ratios and the optimal patterns are obtained. The comparison to diagrid patterns analysed in previous works by the authors [27,[31][32][33] in terms of structural weight and performance parameters highlights the effectiveness of the design strategy and the efficiency of the generated patterns. ...
... In this study, the fitness function is the structural weight of the diagrid pattern. Concerning the choice of the fitness function, it is well known that minimising the weight of the structure does not necessarily minimize the overall construction cost [27], and, more importantly, other constructional, architectural, even haptic considerations can strongly affect the final design choice. However, the structural weight is an index of structural efficiency, since it gives a measure of the material consumption for satisfying a required performance level, and in the context of tall building design, it represents an item of great interest for ranking and selecting the different structural options. ...
An innovative generative design strategy, based on shape grammar, is proposed for the minimum‐weight design of diagrid tall buildings. By considering the building as a three‐dimensional vertical cantilever beam with a tubular section under horizontal load, it is evident that bending and shear stiffness demands vary along the width and elevation of the building. Further, while the structural design of tall buildings is usually governed by stiffness, the predominant design criterion for diagrids could be the local strength demand, especially for low slenderness values, thanks to the inherent rigidity of the triangular pattern. Starting from these considerations, in this paper, a generative design strategy is proposed, able to find diagrid patterns that accommodate the differentiated stiffness demand along width/elevation and satisfy the predominant design criterion, stiffness or strength. The design strategy is applied to tall building models characterised by different slenderness values. The comparison to diagrid patterns analysed in previous literature works in terms of structural weight and performance parameters highlights the effectiveness of the design strategy and the efficiency of the generated patterns.
... Within the studies recently carried out on diagrid structures, several authors [1][2][3][4] have underlined the major role of the diagonals angle, suggesting that optimal values should increase with the building slenderness [5]. Furthermore, design solutions with variable angle along the elevation have been proposed as more efficient than uniform-angle configurations for very slender buildings [1,2]. ...
... The PDI patterns are geometrically generated according to the procedure outlined in Section 5. Different regular and variable-angle diagrid are also considered for comparison, in order to assess the potential of efficiency improvement expected from the PDI patterns. The diagonal angles adopted for the diagrid patterns designed for comparative purposes are chosen by observing that, as the building slenderness H/B increases, the bending behaviour becomes more dominant than the shear one, thus steeper diagonals should be assigned to slender buildings [1][2][3][4] The height of each building model is slightly changed to make sure that each module covers an integer number of floors, by changing the diagonal angles, as reported in Table 2. All patterns are divided along height into modules, M, each containing two triangular units. ...
... Finally, for H/B = 3, the best solution in terms of weight is provided by the pattern VA 50 • . This result should be interpreted in the light of the governing role of stiffness vs. strength in the design process [4,45], as discussed in the following section. ...
In this paper, an innovative diagrid-like pattern for tall building structures is proposed. Based on the concept of principal stress trajectories, the pattern is characterized by triangular units with angle varying along width and elevation, and, being the expression of forces flow arising in the building façades, it is expected to be highly efficient and visually appealing. The idea is to model the building as a three-dimensional vertical cantilever beam with tubular section under horizontal load, and to derive the relevant principal stress lines. Then, the stress analysis results are processed, and geometrical rules are derived for generating structural grids that also satisfy constructability constraints. For this purpose, a framework for implementing and managing the stress lines concept in the preliminary structural design of tall buildings is proposed. The efficacy of the generation procedure and the efficiency of the obtained structural patterns are then verified by means of the application to tall building models characterised by different slenderness ratios, and by means of comparisons with the performance and steel weight of conventional diagrid structures.
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... Montuori et al. [15] analyzed the structural performance of diagrid square tubes with different diagonal patterns along the building, namely uniform-angle, variable-angle and variable-density patterns. Tomei et al. [16] also examined other pattern configurations, like the double-density pattern and the diagrid-like pattern, where the diagonals follow the principal stress lines obtained from an equivalent cantilever building. Angelucci and Mollaioli [17] investigated the response of diagrid structures with non-uniform pattern configurations, also simulating the presence of outriggers inducing a local increase in the density of the diagonals. ...
... The latter is minimum when the diagonals are very shallow, whereas the former gets minimized when the diagonal inclination lies in an intermediate range that depends on the building aspect ratio [20]. Furthermore, Tomei et al. [16] pointed out that each diagrid pattern has its own complexity, that needs to be minimized in order for the structure to be achievable from a construction perspective. Based on these considerations, it follows that multiple responses (lateral deflection, torsional rotation, structural mass and construction complexity) need to be minimized simultaneously in order to reach the optimal stiff, light and feasible diagrid geometry. ...
... In this paper, we apply for the first time the desirability function approach to the problem of finding the optimal geometry of diagrid systems. Different diagonal inclinations and floor shapes are considered for the diagrid tall building, that represent the different combination of input parameters, and four response variables are obtained for each geometry, namely the lateral deflection and torsional rotation at the top of the building under horizontal loads, the mass of the external diagrid tube and the diagrid complexity as suggested by Tomei et al. [16]. Based on these four response variables, each diagrid geometry is assigned an individual desirability value based on the minimization of each response. ...
Diagrids represent one of the emerging structural systems employed worldwide for the construction of high-rise buildings. Their potential relies on the peculiar architectural effect and their great lateral stiffness. Because of the modular nature of the diagrid triangular element, optimization processes are usually carried out to assess the best arrangement of the external diagonals in order to enhance the structural performance while using the lowest amount of structural material. In this contribution, we make use for the first time of the desirability function approach to investigate the optimal geometry of the diagrid system. A 168-meter tall building, with four different floor shapes, is analyzed, and the inclination of the external diagonals is varied between 35° and 84°. The desirability function approach is applied to find the most desirable geometry to limit both the lateral and torsional deformability, the amount of employed material as well as the construction complexity of the building. A sensitivity analysis is also carried out to investigate the influence of the individual desirability weight on the obtained optimal geometry. The effect of the building height is finally evaluated, through the investigation of sets of 124-, 210- and 252-meter tall diagrid structures.
... Conversely, the solutions involving a more uniform VD pattern (Figure 10c,d), where the diagonal concentration rarefies towards the top of the building, turn out to be appropriate solutions for limiting the lateral displacements, while obtaining notable material savings [9]. The previous work of Montuori et al. [32] has been subsequently developed by Tomei et al. [33], who propose additional diagonal patterns for the 90-story tall diagrid building (Figure 11a). ...
... The optimization procedure aims at minimizing the unit structural weight of the building, while complying with the stiffness and strength requirements. This is achieved by formulating an objective function (OF) to be minimized, and specifying the constraints of the optimization problem, as thoroughly described in [15,33]. [31], double-density pattern (DD), variable-density pattern (VD), stress lines pattern (ISO). ...
... (b) Unit structural weight (blue bars) and complexity index (red curve) for the investigated diagrid patterns. VA_IDR, VD_1, VD_15, ISO_15, ISO_9, ISO_5, ISO_5* refer to additional subsets of the corresponding patterns, as reported in [33]. Used with permission from Tomei et al. [33]. ...
Due to the increasing number of people and activities within the cities, tall buildings are exploited worldwide to address the need for new living and commercial spaces, while limiting the amount of used land. In recent decades, the design of tall buildings has undergone a remarkable improvement, thanks to the development of new computational tools and technological solutions. This has led to the realization of innovative structural systems, like diagrids, which allow the achievement of high structural performances and remarkable architectural effects. In this paper, a thorough and updated review of diagrid structural systems is provided. Simplified methodologies for the preliminary design and structural analysis are reported. Special attention is also paid to the optimization of the structural response based on the geometrical pattern. A discussion of the effect of local deformability, stability and shear-lag phenomenon is carried out. Results from nonlinear and dynamic analyses for the seismic assessment of diagrid systems are reported, and attention is also paid to the recent research on diagrid nodes. Eventually, an overview of twisted, tapered, tilted and freeform diagrid towers is carried out, with a final mention of hexagrids, another recent evolution of tubular systems for tall buildings.
... To the Authors' best knowledge, buildability performances (also known as 'fabrication-aware design') are not thoroughly and unanimously defined in literature, in spite of their paramount design role and recent excellent proposals [40,41,42]. As such, the selected DGs, the related metrics and the resulting partial metric are intended to be an intentionally not all-encompassing, although rigorous, buildability performance model. ...
... Face out-of-planarity. Face planarity is the most widespread and traditionally considered construction constraint for double curvature gridshells (e.g., [42,43]). Indeed, planar faces accommodate cheaper flat panels that are significantly less expensive than molded or cold bent doubly curved panels. ...
Gridshell structures require an intricate design activity that shall comply with several design goals of diversenature. This design phase can be approached with different methods and strategies and usually requires multiple competencies from different scientific fields. In this context, a common benchmark, called FreeGrid, is proposed to the scientific and practitioners’ communities in order to test and compare different approaches to the design and optimization of steel gridshells on the bases of ad-hoc defined performance metrics. FreeGrid sets three design baseline problems: a barrel vault, a parabolic dome, and a hyperbolic paraboloid, having their spring line partially not constrained (free-edge) and subjected to uniform and piecewise uniform load conditions. Participants are called to modify the baseline gridshell(s), observing a limited number of design constraints (related to geometry, external constraints and material), in order to improve their structural, buildability, and sustainability performances through the maximization of a bulk quantitative performance metric. Specifically, the structural performance metric accounts for both ultimate and serviceability behavior, through the calculation of the critical Load Factor and maximum vertical displacement; the buildability performance metric includes the evaluation of face planarity, uniformity of structural joints and members; the sustainability performance metric is based on thestructure embodied carbon. This paper describes the baseline gridshells setups, the proposed performance metrics and the recommended method for performance assessment. The complete data of the baseline structures are made available according to an Open Data policy, together with post processing utilities intended to align the procedure to obtain the performance metrics.
... To improve design efficiency and quality, researchers have exploited optimization techniques and their applications to create excellent structural designs for building engineering [16][17][18][19][20] and multiphysics problems [21][22][23][24]. In terms of optimizing the distribution of interstory drift ratios, researchers [16][17][18][19][20] have primarily performed the formulation, where interstory drift ratios are limited via a series of constraint functions and the structural weight or material consumption is minimized. ...
... To improve design efficiency and quality, researchers have exploited optimization techniques and their applications to create excellent structural designs for building engineering [16][17][18][19][20] and multiphysics problems [21][22][23][24]. In terms of optimizing the distribution of interstory drift ratios, researchers [16][17][18][19][20] have primarily performed the formulation, where interstory drift ratios are limited via a series of constraint functions and the structural weight or material consumption is minimized. Although this formulation enforces optimized interstory drift ratios that are lower than or equal to the prescribed limits, it does not theoretically guarantee that the resulting interstory drift ratios exhibit a certain pattern. ...
An approach to control the profiles of interstory drift ratios along the height of building structures via topology optimization is proposed herein. The theoretical foundation of the proposed approach involves solving a min—max optimization problem to suppress the maximum interstory drift ratio among all stories. Two formulations are suggested: one inherits the bound formulation and the other utilizes a p-norm function to aggregate all individual interstory drift ratios. The proposed methodology can shape the interstory drift ratio profiles into inverted triangular or quadratic patterns because it realizes profile control using a group of shape weight coefficients. The proposed formulations are validated via a series of numerical examples. The disparity between the two formulations is clear. The optimization results show the optimal structural features for controlling the interstory drift ratios under different requirements.
... A key role in the performance of tall buildings is played by the conceptual design of the structure, which can be tackled at different and interrelated levels, as well described in Tomei et al. (2018): at the global level, for designing the shape and establishing a specific macroscopic behavior; at the intermediate level, for defining the organization of the elements, their relationships, and fulfill local stiffness/strength demands; and at the detail level. The present work is focused on the intermediate-level conceptual design of tube structure tessellations. ...
... Asadi and Adeli (2018) investigate the performance of steel diagrid structures with different building heights and aspect ratios to evaluate their key seismic performance factors. Tomei et al. (2018) included the cross-section sizing in a more complex optimization method that also considers nonuniform patterns, which cannot be simplified into reduced models. Similarly, Angelucci and Mollaioli (2017) proposed a strength optimization method for stiffness-designed patterns. ...
In the context of tall building design, the tube concept represents one of the most performing systems. The diagrid is the widespread type of tube system and consists of a diagonal grid of beams that wraps the building, forming a diamond pattern. It performs as lateral bracing and is additionally able to sustain vertical loading through axial forces. Despite its efficiency, a growing interest is recently observed in alternative geometries to replace the diagrid pattern and improve the architectural impact conferred by the building skin aesthetics on the urban environment. The paper pursues the use of a Voronoi mesh, in which the geometry of the cells is steered to known schemes for the structural design of a cantilever tube structure. The objective is to mimic a macroscopic structural behavior through a topology and size modification of the Voronoi mesh that increases the density for creating resisting paths with higher stiffness. The paper proposes a novel method Vorogrid for designing a new class of tall buildings equipped with an organic‐looking and mechanically sound tube structure, which makes them a valuable alternative to competitors (diagrid, hexagrid, random Voronoi). Diagrids and hexagrids still remain more efficient in terms of forces and displacements but are characterized by a more usual appearance, instead Vorogrid offers more design control and better performances on average with respect to random Voronoi structures. This method is streamed into a pipeline that includes grid initialization strategies, geometric and structural optimization to mitigate the effects of the grid randomness, and structural sizing.
... Fig 4 illustrates the powerful tool of parametric design for generating several alternatives shapes and configuration for tall buildings with different vertical and horizontal profile constrains [1]. The driving factors in building design are efficiency and sustainability [9]. These become even more important when considering large-scale building, because it is difficult to obtain the desired performance with the least amount of structural materials, and it is becoming more difficult with modem architecture, where complexity of forms is becoming the norm. ...
... These become even more important when considering large-scale building, because it is difficult to obtain the desired performance with the least amount of structural materials, and it is becoming more difficult with modem architecture, where complexity of forms is becoming the norm. That is especially evident in tall buildings, where people increasingly attempt to create unique tall building geometric forms as a symbol for key projects [9]. Overcoming such challenges will be firstly by investigating the key concerns and main parameters that have a significant impact on the design process and output of tall building conceptual design. ...
... Design strategies for diagrids and Voronoi-like tall buildings that are based on size optimization can be found e.g., in Mollaioli (2017, 2018) and Tomei et al. (2018). Advances in optimization of high-rise building structures are reviewed in Aldwaik and Adeli (2016). ...
... While most of the existing approaches of multi-scale analysis of tall buildings employ homogenization to derive the macroscopic elastic modula for a cantilever beam model, see in particular Montuori et al. (2014), the macroscopic in-plane elastic constants are used in this contribution to address a shell model of the box-shaped grid. Hence, instead of using size or parametric optimization for truss/beam models, see in particular Zegard and Paulino (2015) and Tomei et al. (2018), or SIMP-based topology optimization, see in particular Stromberg et al. (2011), a multi-material topology optimization approach is conceived to handle the distribution of a discrete set of lattices throughout the shell model. ...
The conceptual design of grid systems in tall buildings is addressed by combining optimization and multiscale analysis of lattice structures. Macroscopic properties of lattices with given cross-section are available in the literature for different cell topologies. A multi-material optimization problem is formulated to find the distribution of a prescribed discrete set of candidate cross-sections and shapes such that the structural weight of the grid is minimized under constraints on the lateral displacements of the building. Preliminary numerical simulations are shown, addressing the design of tall buildings that employ diagrids and hexagrids.
... Gerasimidis [36] proposed a simple approach to optimize size of diagonal members in tall buildings subject to lateral stiffness and deflection constraints. Tomei [37] utilized an encoding scheme for minimal weight design of irregular diagrid structures by genetic algorithms imposing constraints on the lateral stiffness. A lattice-based algorithm is offered by [38] for conceptual design of diagrids. ...
... Gerasimidis [36] proposed a simple approach to optimize size of diagonal members in tall buildings subject to lateral stiffness and deflection constraints. Tomei [37] utilized an encoding scheme for minimal weight design of irregular diagrid structures by genetic algorithms imposing constraints on the lateral stiffness. A lattice-based algorithm is offered by [38] for conceptual design of diagrids. ...
Diagrids are of practical interest in high-rise buildings due to their architectural configuration and efficiency in withstanding lateral loads by exterior diagonal members. In the present work, diagrid models are screened based on a sizing optimization approach. Section index of each member group is treated as a discrete design variable in the optimization problem to be solved. The structural constraints are evaluated due to Load and Resistant Design Factor regulations under both gravitational and wind loadings. The research is threefold: first, falcon optimization algorithm is utilized as a meta-heuristic paradigm for such a large-scale and highly constrained discrete problem. Second, the effect of geometry variation in diagrids on minimal structural weight is studied for 18 diagrid models via three different heights (12, 20 and 30 stories) and three diagrid angles. Third, distinct cases of rigid and flexible bases are compared to study the effect of such boundary conditions on the results. The effect of soil flexibility beneath the foundation on the optimal design was found highly dependent on the diagrid geometry. The best weight and performance in most of the treated examples belong to the geometry that covers two stories by every grid line on the flexible-base.
... On the first point, a single FE is adopted per structural member in most of the published studies, e.g. [12,21,81]. Some authors [68,71] discretize each structural member into 4 FEs. ...
... This period saw a revolutionary change in manufacturing due to improvements in steel production and building methods. From an aerial perspective, these inventions not only made it easier to build skyscrapers but also completely changed the urban environments of big cities like New York, Chicago, and London (Tomei et al., (2018)). ...
... To the authors' best knowledge, buildability performances (also known as 'fabrication-aware design') are not thoroughly and unanimously defined in literature, in spite of their paramount design role and recent excellent proposals [14][15] [16]. As such, the selected DGs, the related metrics and the resulting partial metric are intended to be an intentionally not all-encompassing, although rigorous, buildability performance model. ...
FreeGrid is meant to offer a common benchmark to test and compare different approaches to the design and optimization of steel gridshells, from man-based heuristic design to AI-based one. FreeGrid sets three design baseline problems: a barrel vault, a paraboloidal dome, and a hyperbolic paraboloid, having their spring line partially not constrained (free-edge) and subjected to symmetric and asymmetric load conditions. Participants are called to modify the baseline gridshell(s) in order to improve their structural performances, buildability, and sustainability, all three of them weighted in a single, bulk quantitative performance metric. Participants shall comply with a limited number of design constraints, while any other design solution is allowed. Baseline setups, performance metrics and design constraints will be fully detailed in technical specifications made publicly available. The full data of the baseline structures will be offered to participants according to an Open Data policy, together with postprocessing utilities intended to align the procedure to obtain the performance metrics. The FreeGrid benchmark will be launched within the IASS Symposium 2023 in Melbourne.
... From the point of view of the structural design, optimization techniques are currently widespread in the world of both practitioners [18]- [23] and researchers [24]- [32], and the current literature also provides examples of design strategies for grid shell structures that combine optimization techniques with form finding approaches [33]- [42]. ...
... Asadi et al. [6] studied the behavior of steel diagrid structures against seismic loading and performed a complete investigation on the nonlinear performance of diagrid systems using static, time-history dynamic, and incremental dynamic analyses. Tomei et al. [10] proposed a new design method that depends on sizing optimization to improve the preliminary design method to deal with complex and non-conventional patterns of diagrid structures. Devansh et al. [3] performed a parametric study on diagrid structures against earthquake loads by changing parameters such as diagrid angle, cross-sectional shape, and column location. ...
... Structural optimization is one of the most prominent methods for design (Bendsoe and Kikuchi 1988;Li et al. 2015;Zhu et al. 2015), being utilized to solve problems in a wide range of fields, including automotive (Chen et al. 2017;Fonseca et al. 2021), aviation (Munk et al. 2019), and civil engineering (Tomei et al. 2018). Composite materials and plastic/metal hybrid (PMH) structures present particular properties such as anisotropy, material interface, and different manufacturing constraints for dissimilar materials. ...
The integration of metal and injection-molded composite materials has the potential to achieve numerous benefits in the design of structural components. However, due to the nature of plastics and the plastic injection molding (PIM), it becomes difficult to conciliate structural performance and part quality criteria. To obtain an optimal balance between the criteria, it is necessary an efficient design approach that can handle even complex models present in the real-world. In this study, the design enhancement of a recycled carbon fiber-reinforced plastic/metal hybrid automotive structure is realized via a novel manufacturability-constrained optimization with focus on part quality and PIM suitability. Multilayer size optimization is carried out by referring thickness design guidelines (TDGs) in order to optimize material distribution with composite material properties considered. Thickness-dependent properties are correlated with design variables and updated at each iteration. Part quality indicators and functional criteria are adopted to evaluate the optimized structures. The design procedure is shown to be superior to standard optimization methods and efficiently enable a satisfactory balance between performance and part quality by considering major injection-molded part design constraints. Reduction in cycle time, injection pressure, and warpage by 27, 63, and 7% were achieved along with 4% mass reduction. Moreover, statistical analyses showed that TDGs have a strong correlation with mass and stiffness while wall thickness has major effects in part quality and suitability with a confidence level of 95%. The results contribute to the advancement of lightweight and high-quality structural components produced by fast-manufacturing processes in the auto industry.
... However, research on the damage mechanism of the diagrid structure under earthquake lags behind the practice in engineering, and the existing seismic design methods are limited to elastic design [1][2][3], which is relatively conservative. Combined with specific engineering practices, Scholars [4][5][6][7][8][9][10][11][12] have carried out elastic-plastic analysis on diagrid structure, studied the internal force distribution of diagrid structure under horizontal and vertical loads, and pointed out that the inclined concrete filled steel tubular (CFST) columns mainly bear axial tension and compression cyclic loads. Specifically, the inclined columns at the bottom of the structure all bear the axial pressure, whereas the inclined column experiences tension force in the upper floor of the high intensity zone [12][13][14]. ...
The mechanical performance of the diagrid concrete filled steel tubular (CFST) columns is significantly different from that of the traditional bending components, and very few research has been conducted on their hysteretic performance. In this study, the axial cyclic test results of eight CFST columns were presented. Based on the experimental results, the degenerate trilinear model was used to establish the dimensionless skeleton curve model, and the calculation formulas for the peak bearing capacity and the corresponding displacement of the CFST columns were proposed. On account of the observed damage characteristics of the CFST columns, different hysteretic rules were selected to establish the unloading stiffness functions in the tension and compression directions. Thus, a hysteretic model suitable for CFST columns under axial cyclic loading was proposed, and the rationality of the hysteretic model was verified by comparison with the test results. Afterwards a refined finite element model of the diagrid structure was established using the proposed hysteretic model of the CFST columns. Through elastic–plastic time history analysis, the energy distribution of the diagrid structure was studied, and the interlayer distribution of the inclined CFST columns under rare earthquakes was analyzed. The results shown that the energy had an obvious mutation at the junction between the bottom module and the secondary node layer, so it is necessary to avoid large stiffness mutations in the design of the diagrid structure.
... In the last two decades, gridshell structures are often adopted in large span systems thanks to their peculiarity to combine aesthetic qualities and optimal structural performances, which are completely merged since the shape is itself the structure. Design strategies based on optimization techniques, currently spreading in the world of both practitioners [1][2][3][4][5][6] and researchers [7][8][9][10][11][12][13][14][15], are always more often applied also to gridshell structures because of their capacity to deal with the complex process of searching competitive solutions in terms of structural weight, cost and structural/ functional requirements [16][17][18][19][20][21][22][23][24][25][26]. ...
Structural optimization techniques are becoming popular and effective approaches for the design of constructions, able to support architects and structural designers in the complex process of searching competitive solutions, usually in terms of structural weight, cost and accounting for specific structural/functional requirements. In case of gridshells, the structural weight is strictly related to the susceptibility of the structure to global buckling, which is often the governing design criterion. The susceptibility to global buckling is mainly due to the global stiffness of the structures, primarily related to the stiffness of the joints, to the boundary conditions, and to the presence of imperfections. In this context, the paper presents design strategies based on optimization techniques that specifically take into accounts the presence of semi-rigid, rigid and hinged joints in order to guarantee light solutions safe from global buckling phenomena. In particular, two approaches are proposed: the joint stiffness approach, which considers the gridshell composed by semi-rigid joints, all characterized by the same rotational stiffness, and the rigid/hinged approach, which considers the gridshell composed by most hinged joints, and by a low number of rigid joints arranged in optimal positions. The approaches have been applied to a case study characterized by different boundary conditions, different rise-to-span ratios and also considering both perfect and imperfect shapes. The results of the proposed optimization processes highlight the beneficial effect of a finite value of the rotational stiffness of the joints in the susceptibility of the gridshell to global buckling phenomena, leading to light structural solutions.
... In the last two decades the diagrid emerged as the most efficient solution for tall buildings with tube configurations (Ali & Moon 2007, Mele et al. 2014; it is constituted by triangulated pattern of the building façades composed by a uniform grid of diagonal members, that confers to the diagrid an inherent rigidity. The efficiency of the diagrid could be further improved by optimizing the topology of the triangulated pattern; indeed, by considering the analogy with a vertical cantilever beam under lateral load (Beghini & Sarkisian 2014, Cascone et al. 2021a, Tomei et al. 2018), the structural pattern should be not uniform to accommodate the variation of bending and shear stiffness demands along elevation and base, with diagonals gradually steeper going from the top to the base of building, and from the inside out along the base. In this context, the proposed structural grammar aims to find the optimized pattern by changing the number and slope of diagonals both along elevation and base. ...
A great attention has been recently paid to sustainability and efficiency in the field of civil engineering. In this context, structural optimization processes combined with generative design constitute an important tool to support the design phase and to guarantee the exploration of a wide space of solutions. A generative approach recently re-evaluated is related to shape grammars, i.e. algorithms composed by intertwined rules able to define a theoretically infinite number of solutions, unexpected during the algorithm writing. The combination of a shape grammar and structural optimization is a structural grammar. This paper proposes structural grammars for the topology optimization of large structures made of triangulated patterns; in particular, grid shells and diagrid tall buildings are considered, being paradigmatic examples where the structural pattern also affects architectural, functional and constructive aspects.
... On the other hand, design strategies based on optimization techniques are being widely spread nowadays among practitioners [27-32] and researchers [11,[33][34][35][36][37][38][39][40][41]. In this context, structural optimization strategies are mainly divided into three approaches [42]: sizing optimization, shape optimization and topology optimization. ...
Gridshell are fascinating examples of structures able to combine aesthetic qualities and optimal structural performances thanks to a complete merging between “shape” and “structure”. To make gridshell structurally efficient is their capacity to cover large spans with light systems, exploiting the inherent strength of a double curvature shell. The design of gridshell is often the result of strategies based on both form-finding and structural-optimization techniques, sometimes combined together to obtain efficient structural solutions and architectural conception of space. Pre-tensioned rods, in some cases incorporated in the structure of gridshell, could particularly influence the structural performance of gridshell in terms of both its global deformability and stress distribution within its members. Consequently, pre-tensioned rods, when present, represent additional structural components to necessarily consider in the design optimization process of gridshell. Aim of the present paper is, first, to analyze the influence of pre-tensioned rods in the design optimization of gridshell and, then, to propose an optimization procedure for gridshell equipped with pre-tensioned rods. To this end, some simple gridshell examples and the case study of the Smithsonian Museum canopy in Washington are analyzed in the paper. The obtained results underline the importance of considering the presence of pre-tensioned rods both in the phase finalized to find the free-form shape and, moreover, in the structural optimization process.
... Previous studies have used GA-based algorithms in the optimization of diagrid structures. Tomei et al. (2018) proposed techniques using stiffness-based structural analysis for member size optimization of diagrid structures with complex patterns including varying angle along the height, varying density along the height, and patterns following stress lines of cantilever beams. Orhan and Taşkın (2021) studied the topology optimization of diagrids using SAP2000 to generate the building models and MATLAB for the size optimization based on simplified formulas for strength analysis. ...
... Moon [14] has early shown that there exists an optimal inclination of the external diagonals able to minimize the lateral building deflection under horizontal loads. Various diagonal layouts have been proposed in the following years and the corresponding building efficiency under lateral loads has been investigated [15][16][17][18]. Attention has also been paid to torsional actions and the role that these might have in the parametric investigation of the diagrid structural response [13]. ...
... In recent years, diagrid structure system has attracted the attention of many researchers because of its structural efficiency and special architectural form. Aspect ratio and diagonal angles are two important factors that affect the performance and aesthetics of diagrid structure [10,11]. There have been many studies on the preliminary design and calculation methods of diagrid structures. ...
In order to propose a simple and practical methodology for calculating the deformation of diagrid structure with polygon plane in arbitrary direction, the diagrid structure is considered to be mainly composed of “element” by geometric method. The vertical stiffness and lateral stiffness of diagrid structure with arbitrary polygon plane under vertical load and horizontal load are derived respectively. The corresponding laboratory test and numerical simulation analysis are carried out through the scale models of steel diagrid structures. The analysis results show that the calculated results of each deformation equation are in good agreement with the test results and numerical simulation results. In addition, the influence of the parameters on the stiffness of the structure is revealed theoretically. The results demonstrate that when the diagonal angle is about 55°, the variation of the diagonal angle has the greatest effect on the vertical stiffness of the diagrid structure. Moreover, the vertical stiffness of steel diagrid structure is smaller than that of traditional structure, and the vertical displacement is obviously larger. It is necessary to limit the inter-story drift ratio of vertical modules. Furthermore, current paper theoretically explains that the more edges of diagrid structure, the greater the horizontal shear stiffness of the structure.
... Due to their aesthetic appeal and mechanic performance, preliminary design and optimization on diagrid systems constitute a fertile field of research [14,15]. The works [16,17,18,19,20] introduce design strategies of sizing and optimization for different geometrical diagrid patterns. ...
Skyscrapers are among the most distinctive building types of the modern age. Since many resources are attributed to these buildings, their design should consider a proper performance-based construction economy and environmental sustainable development. This research introduces a new concept for a bundled tall building founded on the use of a multi-core-outrigger system, which is additionally enriched with diagrid structures. The concept is inspired by the bamboo plant and follows the biomimetic design principles for the structural organization and performance-based criteria for optimizing the lateral stiffness and for shaping the cross section. Particularly , the incident wind speed is maximized to exploit Vertical Axis Wind Turbines (VAWTs), which are located along the whole building height at the center of the bundled towers. The building morphogenesis is accomplished by a multistep methodology that is fully developed in a parametric environment and includes structural and computational fluid dynamic analyses. With the aim of validating the proposed concept , a case study of a 320-m-tall three-core building has been designed for the city of Pisa, Italy. The use of VAWTs results in an annual emissions reduction of about 10 kgCO 2 /m 2.
... Yüksek yapılarda kullanılan diagrid sistemlerin, optimum gridal geometriye sahip olarak tasarlanması, düğüm noktalarının doğru açılarla konfigüre edilmesi, modülasyon ve prefabrikasyonun sağlanarak kısa zamanda seri üretim yapılabilmesi ile strüktürel verimliliği sağlanabilmektedir. Ayrıca strüktürel yeterliliklerinin yanı sıra estetik görünüşleri de diagrid sistemlerin tercih edilme sebeplerinden birini teşkil etmektedir [4]. Dünya üzerinde Swiss Re (Londra), Hearst Tower (New York), Cyclone Tower (Kore), Capital Gate Tower (Abu Dabi) ve Jinling Tower (Çin) en popüler olan diagrid sistemlerdir [5]. ...
Deprem, yıkıcı özelliği en fazla olan doğal afetlerin başında gelmektedir. Bu nedenle depremde oluşacak can ve mal kayıplarını en aza indirmek amacıyla inşaat mühendisliğinde depreme dayanıklı yapı tasarımı kavramı ortaya çıkmıştır ve yapıların deprem performansları analizi önem kazanmıştır. Özellikle düzensiz geometriye sahip ve/veya çok katlı yapılar için dinamik analiz yapılması gereklidir. Bu çalışmada düzensiz geometriye sahip bir yüksek katlı yapının nümerik olarak zaman tanım alanında deprem analizi gerçekleştirilmiş ve balsa çıtalarından yapılmış yapı modeline deneysel olarak sarsma masası testi uygulanmıştır. Balsa malzemesi hafif olmasının yanı sıra uygun dayanım ve enerji sönümleme özelliğine sahiptir. Bu özellikler ise malzemenin mikro yapısında bulunan trakeler ve bu trakeleri eşit aralıklarla kesen doğrusal olarak sıralanmış parankimalardan türemektedir. Ayrıca yapı modelinde çok katlı yapılar için hem estetik hem de strüktürel yeterliliği sağlayan diagrid sistem tercih edilmiştir. Çalışmada deneysel ve nümerik analiz sonuçları ivme ve çatı deplasman parametreleriyle kıyaslanmıştır. Birinci deprem kaydı kullanıldığında deneysel sonuçlar nümerik sonuçlardan daha yüksek bulunmuştur; ancak, karakteristik özeliği birinci depremden farklı olan ikinci deprem kaydı deneysel modele uygulandığında elde edilen ivme değerinin nümerik modelden daha az olduğu görülmüştür. Diğer taraftan, ikinci deprem kaydı kullanıldığında elde edilen çatı deplasmanının deneysel ve nümerik sonuçları ise büyük bir uyum içindedir.
... This success came with several discussions as they brought up some other challenges that needed to be addressed. Today, there have been several studies in literature assessing tall structures in different aspects such as structural performance [5][6][7][8][9][10][11] ; environmental sustainability [12,13] ; and their effects on urbanism [14][15][16] . All of these topics are interconnected to each other and have been discussed widely in the built-environment platforms. ...
In architecture, interlace structural concept is considered as a new design approach for cosmopolitan cities with high density to minimize the land use and increase the interaction. With various architectural approach, land resources can be minimized by this interlace concept for residential complexes. Such buildings will eliminate the reduction of land resource problem and on the other side safety measures in structural design is incorporated by interlace concept of buildings. This new concept can be constructed steel or reinforced concrete. In this paper, an analytical approach has been presented for these buildings in architecture and structural design. In the research, design considerations were taken for interlaced structures with reinforced concrete and steel. Components of steel structure, isolated footing, and columns. This paper is presenting a step wise process for interlance structures. They are identification of project area, layout and model preparation, analysis and design of concrete interlaced structure, analysis and design of steel interlaced structure, drafting of the plans and costing and estimation of the structures. Comparison of both reinforced concrete and steel structures were carried out. The main aim of the paper is to provide a comparison between steel and concrete interlaced structure. A cost estimation was carried out to determine optimum design and construction for interlaced structures.
... Previous studies by the authors have shown that for actual supertall buildings with more element types and numbers, the optimality criteria (OC) method would sometimes fail to converge to an optimal solution (Xu et al. 2016). A suitable algorithm is necessary to handle such large-scale nonlinear optimization problems (Spence and Gioffre 2012, Spence and Kareem 2013, Tomei et al. 2018. ...
Wind load is the most critical kind of loads in the structural design of supertall buildings. Performance-based wind-resistant structural optimization can effectively reduce the material cost of supertall buildings in the premise of ensuring their structural safety and serviceability. For modern supertall buildings with complex structural systems, the formulation of its structural optimization problem is highly complicated. Moreover, the optimization problem itself is also nonlinear and extensive in scale. This study first addresses the optimization formulation of complex structure system which includes concrete-filled steel tube (CFST) frame members and shear wall members. These structural members are often used in supertall buildings but are seldom discussed in existing literature of structural optimization. Then, the interior point algorithm, which is propitious for large-scale nonlinear optimization, is used to seek the optimal design solution. A real-life supertall building, the 432 m Guangzhou West Tower, is used as an example to examine the effectiveness of the proposed computer-based optimization method. The proposed method is shown to work effectively in the optimal wind-resistant design of supertall buildings with complex structural systems.
Design automation addresses the problem of manual and time-consuming design processes by streamlining and optimizing the creation of products, systems, or solutions using automated tools and workflows. The insufficient implementation of design automation technologies in the building and structural design industry has significant implications for productivity, innovation, and sustainability. This underscores an urgent need for comprehensive solutions to address this societal challenge. In this paper, a review of building and structural design automation methods is presented, covering the progression from generative design to the integration of deep generative models and optimization techniques. This review explores generative design and deep generative models, including generative adversarial network, variational autoencoder, and reinforcement learning frameworks, followed by topology optimization and their applications. This paper discusses key works that have introduced methods and techniques in generative design. Moreover, it addresses key challenges observed in generative systems across design fields. Furthermore, potential opportunities for future research are also identified, highlighting crucial areas that require strategic solutions. This study aims to establish a comprehensive reference framework to facilitate method selection and enhance existing methodologies through a systematic hybridization approach, thereby advancing the capabilities of the field.
The development in structural optimization of diagrid buildings is emerged recently due to the urgent need to fulfil environmental sustainability. Despite this, little work has so far been undertaken to optimize diagrid buildings with various heights under nonlinear seismic analysis. This paper studies the optimization of diagrid buildings using parameter space investigation (PSI) to find out the optimum size of diagonal adopting the minimization of diagonals weight. The PSI was utilized among Python script connected with ABAQUS software and visual basic program to generate the feasible and Pareto sets for the studied buildings. Optimal Pareto solutions which is extracted from the proposed method are compared with the referential stiffness-based method to evaluate the efficiency and applicability of the methods. The results concluded that the optimization of diagrid buildings using PSI is a powerful tool for structural engineers to determine the
design parameters and can achieve sustainable and resilient structures. In additions, the PSI method could decrease the tension damage in the slabs drastically.
From the standpoint of economic and ecological compatibility, the term hybrid composites are becoming increasingly important. These are composite materials that are composed two or more separate green and artificial/synthetic fibers that are reinforced with appropriate polymetric matrices to produce a composite material with qualities that are equivalent to those of manufactured composite materials. In addition, to stay up with new technological developments, it has essential to design materials that are less harmful to the environment and to protect our ecosystem for many years. This notion has prompted people to adopt hybrid composite materials in everyday engineering and non-engineering applications. These composites have several beneficial characteristics, cost, recyclability, and biodegradability, which made them an excellent option for composite polymers in a variety of applications. In this respect, a concerted effort has been adopted in this chapter to provide a summary of diverse green and artificial/synthetic fibers, their categorization, and their usage in numerous engineering applications including aerospace; the chapter begins with a discussion of composite materials and their varied features.
Earthquakes often affect buildings that did comply with regulations in force at the time of design, prompting the need for new approaches addressing the complex structural dynamics of seismic design. In this paper, we demonstrate how strucural resilience can be appraised to inform optimization pathways by utilising artificial neural networks, augmented with evolutionary computation. This involves efficient multi-layer computational models, to learn complex multi-aspects structural dynamics, through several levels of abstraction. By means of single and multi-objective optimization, an existing structural system is modelled with an accuracy in excess of 98% to simulate its structural loading behaviour, while a performance-based approach is used to determine the optimum parameter settings to maximize its earthquake resilience. We have used the 2008 Wenchuan Earthquake as a case study. Our results demonstrate that an estimated structural design cost increase of 20% can lead to a damage reduction of up to 75%, which drastically reduces the risk of fatality.
در پژوهش حاضر، تأثیر الگوی هندسی المانهای قطری بر تابآوری لرزهیی سازههای شبکهی قطری با استفاده از نمودارهای شکنندگی بررسی شده است. بدین منظور، بر روی سه سازهی ۲۴ طبقهی شبکهی قطری با زوایای پیکربندی ۴۹، ۶۷ و ۷۴ درجه به همراه یک سازهی قاب خمشی محیطی دسته شدهی مبنا، تحلیلهای تاریخچهی زمانی غیرخطی )NTHA( و دینامیکی فزاینده )IDA( تحت رکوردهای نیرومند حوزهی نزدیک انجام شده است. با پیادهسازی سطوح عملکرد کرانهی رفتار کشسان، استفادهی بیوقفه، ایمنی جانی و آستانهی فرورریزش براساس ضوابط FEMA بر روی نمودارهای شکنندگی، احتمال تجاوز از حالتهای حدی برای سازههای مطالعاتی محاسبه شده است. درنهایت، با درنظر گرفتن فرمولاسیون تابع خسارت پیشنهادی MCEER، شاخص نیرومندی تابآوری لرزهیی برای سازهها مشخص شده است. بر پایهی ارزیابی نمودارهای شکنندگی سازههای مطالعاتی ملاحظه شد که تعبیهی زوایای بزرگ برای المانهای مورب محیطی، احتمال رخداد سطوح عملکرد در مقابل زلزله را افزایش میدهد. براساس پردازشهای عددی تابآوری لرزهیی، مقادیر شاخص نیرومندی برای سازههای شبکهی قطری با زوایای ۴۹،۶۷ و ۷۴ درجه و سازهی قاب خمشی محیطی دسته شده به ترتیب 95/9، 91/7، 88/6 و 85/1 درصد محاسبه شده است. مطابق نتایج اخیر نتیجهگیری شد که ایجاد الگوی مثلثی در قابهای پیرامونی باعث کاهش افت کیفیت کارایی و بهبود پایداری دینامیکی سازهها بعد از وقوع زلزله میشود.
Background
Nowadays, a renewed momentum on the use of timber material is ensured by the development of high performing engineered wood products, which enables larger and taller structures to be built. Although the design of multi-story timber buildings is still in its early stages, the active interest shown by designers and researchers in advancing awareness and technologies in this field bodes well for the proliferation of an increasing number of tall wooden buildings.
Objective
As a consequence of the difficulties with designing a nominally all-wooden tall structure, whilst utilizing its beneficial aspects, dual timber-concrete systems are considered in this work. In detail, the study aims to investigate the contribution of a reinforced concrete core coupled to timber stability systems for the effective control of lateral drifts in multi-storey buildings subjected to severe loading scenarios.
Methods
The design of a 26-storey structural model, conceived by combining concrete cores with three design alternatives for the perimeter structure (namely a GLT frame, a CLT shear walled system and a GLT diagrid), provides the opportunity for discussing its lateral bearing capacities.
Results
The building models show high lateral stiffness in withstanding seismic and wind induced loads. This result is mainly attributable to the introduction of the rigid concrete core, which nearly supplies the demand for shear and bending stresses alone. Compared to a typical cross laminated core, the concrete tube results in a stiffness increment of 68% for the frame variant, 45% for the wall variant and 23% for the diagrid variant. Therefore, the serviceability requirements, both in terms of top displacements and inter-story drifts, are inherently satisfied and kept well below the prescriptive limitations.
Conclusion
The results confirm the excellent behavior of the diagrid systems, for which any variations of the inner core have almost insignificant impact on the global building performance. In addition, previous research works suggest that the timber member sizing is mainly governed by stiffness requirements, which materialize through monitoring of the lateral sway, while member strength demands are deemed to be implicitly satisfied. The paper demonstrates that strength and stiffness demands can be of equal significance during the sizing process of dual systems.
Background
Changes in the skyline of cities all over the world show that tall buildings are an interesting solution to accommodating growth more sustainably in today’s urban areas. Stability against lateral loading is the main issue for designing high-rise buildings. Diagrid systems or grid structures are one of these stable systems. For a long time, the only structural pattern used in this system was the triangular modulus (diagrid).
Methods
In the present study, a new pattern for grid structures was introduced, and its performance was compared with the two previous common patterns (triangular and hexagonal). The new pattern is called the Isometric Cube grid, thanks to its particular shape. The design process was performed based on a simple stiffness criterion presented in the previous research. In order to calculate the stiffness of the structure for the new pattern, two types of existing structural nodes were distinguished, and the results were combined to determine the stiffness of the unit forming the entire grid.
Results and Conclusion
From the results of analysis, it was found that the optimal angles of diagonal elements were in the range of 50-65 degrees. Although the behavior of the new pattern in terms of shear stiffness was between the two previous patterns (and closer to the hexagonal pattern), the shear stiffness ratio increased from 30° to 65° for cube pattern, while for hexagrid, it decreased over the same range of angles.
Background
Diagrid structures, widely used for the tall buildings of the third millennium, are characterized by a very effective behaviour in the elastic field due to the grid triangulation. In particular, under horizontal actions, axial forces and deformations mainly arise in the structural members of the diagrid, thus resulting in the reduction of the shear lag effect and racking deformations. The response to incremental horizontal actions beyond the plastic threshold, however, shows a poor plastic redistribution capacity, with consequent low values of global ductility, in spite of a significant design overstrength.
Objective
In this paper, it is proposed to exploit the high elastic efficiency of the diagrid type and use a vibration control system, based on mass damping mechanism with large mass ratios, to reduce a priori the inelastic demands due to seismic actions.
Methods
Starting from the analysis of the seismic behavior of archetype diagrid buildings, a case study is selected to assess the effectiveness of the proposed motion-based design approach. For this purpose, the diagrid is first transformed into a megastructure (MS) configuration by densifying the diagonal elements at the most stressed corner areas and transfer floors, suitably chosen. Then, the exterior mega-frame is detached from interior sub-structures, thus allowing for a relative motion between the two structural portions according to a “mega-sub-structure control system” (MSCS), which activates the mass damping mechanism.
Results
Time-history analyses carried out on simplified lumped-mass models confirm the effectiveness of the proposed strategy in reducing the seismic response.
Conclusion
Finally, the practical feasibility of the MSCS and engineering solutions for the relevant structural organization are discussed.
In the first decades of the 21st century, new structural systems have started to appear for the design and construction of tall buildings: the diagrids and the hexagrids.
These systems are characterized by a grid pattern of diagonals placed over the external surface of the building, which allows providing good structural performances while achieving noteworthy aesthetic and architectural effects.
The diagrid is realized through a mesh of triangles made up of megadiagonals and ring beams. The structural behavior of this system is mostly governed by the axial deformation of the diagonals, allowing to reach high levels of stiffness against lateral loads.
The hexagrid is a system composed of hexagonal beehive cells and can be of two main types: the horizontal hexagrid, which includes four diagonal members and two horizontal beams, and the vertical hexagrid, which includes four diagonal members and two vertical columns. In the case of hexagrids, the structural behavior is mostly dominated by the bending and shear deformability of the diagonals and horizontal or vertical members. This usually leads to a lower lateral stiffness performance for the hexagrid when compared to the diagrid.
Nowadays, both systems are finding continuous application in the design and construction of tall buildings worldwide, revealing an increasing interest in these structural systems by designers. Moreover, an increasing number of research groups within the academic environment are currently focusing their work on these grid solutions.
Diagrid and Hexagrid Structures: New Perspectives in Design of Tall Buildings
Domenico Scaramozzino and Giuseppe Lacidogna
Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Introduction
In the first decades of the 21st century, new structural systems have started to appear for the design and construction f tall buildings: the diagrids and the hexagrids. These systems are characterized by a grid pattern of diagonals placed over the external surface of the building, which allows providing good structural performances while achieving noteworthy aesthetic and architectural effects.
The diagrid is realized through a mesh of triangles made up of megadiagonals and ring beams. The structural behavior of this system is mostly governed by the axial deformation of the diagonals, allowing to reach high levels of stiffness against lateral loads.
The hexagrid is a system composed of hexagonal beehive cells and can be of two main types: the horizontal hexagrid, which includes four diagonal members and two horizontal beams, and the vertical hexagrid, which includes four diagonal members and two vertical columns. In the case of hexagrids, the structural behavior is mostly dominated by the bending and shear deformability of the diagonals and horizontal or vertical members. This usually leads to a lower lateral stiffness performance for the hexagrid when compared to the diagrid.
Nowadays, both systems are finding continuous application in the design and construction of tall buildings worldwide, revealing an increasing interest in these structural systems by designers. Moreover, an increasing number of research groups within the academic environment are currently focusing their work on these grid solutions.
Diagrids are the efficient systems of tube structures for tall buildings. One of the design considerations for these structures is the geometrical pattern of the system. In this paper, a new method of fuzzy-genetic algorithm based on bilinear membership functions is proposed with an improved crossover operator and penalty function. The method is applied on tall buildings with a diagrid system to find the optimum geometrical patterns and the overall structural weight. Various three-dimensional diagrid structures with 24, 36, 42, 56, and 60 stories and different slenderness ratios are analyzed under gravity and wind load. Then the effects of variation in the number of bays (4, 6, and 8) are investigated and compared with each other. The results show that by increasing the dimension of the structure, the structural weight is reduced up to 33% in some cases. However, the obtained angle of the diagrid members (range of 63 to 79 degrees) is increased by increasing the number of stories and the height of the structure. The optimum weight and geometrical pattern of the models is obtained and a formulation is extracted from the results regarding the optimum angle of a diagrid system. Considering GA, results show the merit of the accelerated fuzzy-genetic algorithm regarding the convergence and the avoidance of being trapped in local minimum.
In this study, in order to determine the outer shell geometry of high‐rise diagrid structures by means of minimum structural material utilization, simplified strength‐ and stiffness‐based design methods are encoded in MATLAB with the help of SAP2000 OAPI (Open Application Programming Interface) codes and genetic algorithm (GA). The computer code is designed to get most of the inputs from the building model in SAP2000, to have minimal manual inputs that define diagrid shell geometry. The code is also built so that the engineer evaluates the optimum diagrid geometry for any rectangular plan building, which is modeled in SAP2000 software. Three different buildings, which consist of 30, 60, and 90 stories, are modeled in SAP2000 without diagrid shells on facades. Based on these models, the diagrid shell geometries are analyzed for both uniform angle (UA) and varying angle (VA) geometries. A different geometry approach to VA models is proposed, consisting of symmetry and continuum for the load distribution and asymmetry, achieving minimal weight. In order to evaluate the optimum VA topology, GA, is used. Predetermined dead, live, and wind loads are applied to the models based on minimum design loads according to American Society of Civil Engineers (ASCE) 7‐10, with corresponding load factors to be able to get more realistic results. Based on the resultant module diagonal cross‐sectional areas, an algorithm is developed and encoded in order to determine minimum required pipe section sizes according to buckling design of compression members as stated in American Institute of Steel Construction (AISC) 360‐10, to give the engineer an approximate idea of what the required sections should be. Additionally, the feasibility of the optimum models is compared by complexity index parameters. The results of the analyses show that optimum VA models are more efficient than UA models concerning the diagrid shell's total weight. However, UA models are more feasible, according to complexity index values.
Inspired by the high mechanical performance of diagrid structures, the minimization of material consumption on braced tubes and the expressive potency of tensegrity modular structures, this work proposes an innovative three-dimensional system for tall buildings. A new modular structural system generated from the assembly of tetrahedral units is investigated. The paper integrates insights on the architectural implications and mechanical performance of the reticular system arranged in repetitive triangular-based modules. The impact of different geometric configurations of the structural members on the economic design is also discussed and recommendations for the optimal topology are made. Guidelines for the design and analytical formula for accessing preliminary member sizes are proposed on the basis of stiffness requirements.
Perforated steel plate shear walls (PSPSWs) are requested for passing the equipment and creating the accessing spaces. Also, the studies showed the PSPSWs enhance the ductility. In this paper, topology optimization (TO) is used to introduce a new form of the PSPSW in the moment frames based on the strain energy as the objective function. The TO is conducted using the sensitivity analysis, SIMP method and method of moving asymptotes. Four amounts of aspect ratio (0.67, 1.0, 1.5 and 2.0) and three plate thicknesses (2 mm, 4 mm and 8 mm) are defined in the TO and their effects are considered in the results. For a comprehensive study, the results of TO are compared with the three usual forms of PSPSW with circular holes and a previous optimized model. The material volume is equal for the plates with the identical aspect ratio and plate thickness. The cyclic behavior of all the models is investigated and compared in terms of strength, energy dissipation and fracture tendency. The analytic hierarchy process (AHP) is applied to score and determine the best model and form. The AHP method illustrated that the optimized models have a better performance. The results of the AHP method show that the optimized model in this study obtained 22.07% of the score from 100%, while the scores of the prior optimized model and three traditional models are 20.67%, 19.36%, 19.06% and 18.84%, respectively.
Topology optimization can be divided into continuum and discrete types, the latter being the emphasis of the present work. In the field of discrete structural topology optimization of trusses, the generation of an initial ground structure is crucial. Thus, this paper examines the generation of ground structures for generic structural domains in two and three dimensions. It compares two methods of discretization, Voronoi-based and structured quadrilateral discretizations, and proposes two simple and effective ground structure generation approaches: the macroelement and macropatch approaches. Both can be implemented with either type of discretization. This work presents several features of these approaches, including the efficient generation of initial ground structures, a reduction in matrix bandwidth for the global stiffness matrix, finer control of bar connectivity, and a reduction in the number of overlapped bars. Generic examples and practical structural engineering designs are presented. They display the features of the proposed approaches and highlight the comparison with results from either the literature, the traditional ground structure generation, or the continuum optimization method.
Topology optimization is traditionally framed in a static and deterministic setting notwithstanding the uncertain dynamic nature of many problems. This paper presents a new data-driven simulation-based framework for the effective topology optimization of uncertain and dynamic wind-excited tall buildings. The performance of the system is described through probabilistic performance integrals that encapsulate state-of-the-art performance-based design driven by climatological, aerodynamic and fragility data sets for describing the site-specific hazard, aerodynamic response and damage susceptibility of the system. To solve the resulting probabilistic topology optimization problem, a sequential optimization strategy is developed that is based on solving a series of high quality approximate sub-problems. A suite of case studies demonstrate the effectiveness of the approach.
This paper presents a review of interesting work on optimization of highrise building structures with a focus on large-scale and real-life structures. A number of interesting projects with an eye on practicality are reviewed, a few involving practicing designers of highrise building structures. A review of literature indicates that performing a formal optimization can result in cost savings in the range of 5 to 15 % which can be especially significant in design of highrise and superhighhrise building structures. Since optimization of highrise building structures is a large-scale optimization problem the choice of the optimization approach is an important one. It should be one that is not entrapped in a local optimum solution and is stable for large-scale optimization subjected to discontinuous constraints of commonly-used design codes. The nature-based optimization approaches such as the neural dynamics model of Adeli and Park and genetic algorithms appear to be the preferred choice.
SUMMARY The procedures and formulations suggested in literature for the design of diagrid structures start from the assumption that diagonal sizing process is governed by the stiffness requirements, as usually occurs for other, less efficient, structural types, and that member strength demand is automatically satisfied by the cross section resulting from the stiffness requirements. However, thanks to the high rigidity of the diagonalized façade, strength requirements can be of paramount importance and even be the governing design criterion. In this paper, stiffness and strength design criteria for diagrid structures are examined and translated in simplified formulae for quick member sizing. The application of the two approaches for the design of a 100-storey building model, carried out for different diagrid geometrical patterns, gives the opportunity of discussing the relative influence of stiffness and strength on the design outcomes, in terms of resulting diagonal cross sections and steel weight, as well as on the structural performance. Copyright © 2013 John Wiley & Sons, Ltd.
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The main purpose of the paper is to provide an easy-to-use code for topological optimization of the least weight trusses,
written in the Mathematica programming language. The main idea of the presented approach consists in using a fixed ground
structure and the linear programming formulation of the optimization problem. The solver is based on the fast interior point
method. The strong effort is done to create the effective generator of the computational model utilizing the high regularity
of the ground structure and the high sparsity of the geometric matrix. The efficiency and reliability of the algorithm is
confirmed in several numerical tests. Due to a linear programming formulation of the optimization problem the method presented
in the paper assures finding the global optimum, hence it may be considered as the useful tool for verification of results
obtained in other ways. The appended complete Mathematica code of the program developed will be supplied by the Publisher
on SpringerLink.
KeywordsTopology optimization of trusses–Ground structure–Linear programming–Interior point method–Sparse matrix representation
This paper explores the use of manufacturing-type constraints, in particular pattern gradation and repetition, in the context
of building layout optimization. By placing constraints on the design domain in terms of number and variable size of repeating
patterns along any direction, the conceptual design for buildings is facilitated. To substantiate the potential future applications
of this work, examples within the context of high-rise building design are presented. Successful development of such ideas
can contribute to practical engineering solutions, especially during the building design process. Examples are given to illustrate
the ideas developed both in two-dimensional and three-dimensional building configurations.
KeywordsTopology optimization–Pattern gradation–High-rise buildings–Material layout–Pattern constraints
Hybrid genetic algorithms have received significant interest in recent years and are being increasingly used to solve real-world problems. A genetic algorithm is able to incorporate other techniques within its framework to produce a hybrid that reaps the best from the combination. In this paper, different forms of integration between genetic algorithms and other search and optimization techniques are reviewed. This paper also aims to examine several issues that need to be taken into consideration when designing a hybrid genetic algorithm that uses another search method as a local search tool. These issues include the different approaches for employing local search information and various mechanisms for achieving a balance between a global genetic algorithm and a local search method. Index Terms—Genetic algorithms, evolutionary computation, hybrid genetic algorithms, genetic-local hybrid algorithms, memetic algorithms, Lamarckian search, Baldwinian search.
The ground structure method seeks to approximate Michell optimal solutions for real-world design problems requiring truss solutions. The single solution extracted from the ground structure is typically too complex to realize directly in practice and is instead used to inform designer intuition about how the structure behaves. Additionally, a post-processing step required to filter out unnecessary truss members in the final design often leads to structures that no longer satisfy global equilibrium. Here, a maximum filter is proposed that, in addition to guaranteeing structures that satisfy global equilibrium, leads to several design perspectives for a single problem and allows for increased user control over the complexity of the final design. Rather than applying a static filter in each optimization iteration, the maximum filter employs an interval reducing method (e.g., bisection)to find the maximum allowable filter value that can be imposed in a given optimization iteration such that the design space is reduced while preserving global equilibrium and limiting local increases in the objective function. Minimization of potential energy with Tikhonov regularization is adopted to solve the singular system of equilibrium equations resulting from the filtered designs. In addition to reducing the order of the state problem, the maximum filter reduces the order of the optimization problem to increase computational efficiency. Numerical examples are presented to demonstrate the capabilities of the maximum filter, including a problem with multiple load cases, and its use as an end-filter in the traditional plastic and nested elastic approaches of the ground structure method.
Diagrid structural systems have been widely adopted for high-rise buildings in the last decades, due to their structural efficiency and architectural potentials. The paper gives a comprehensive outline of the peculiarities of diagrids, providing a complete framework of their mechanical behaviour and investigates the accuracy of the assumptions used in common practice. The study explores, firstly, the effectiveness of the stiffness-based methodology for optimal (69°) and nonoptimal (82°) diagonal inclinations, evaluating if the common approach leads to the definition of optimized cross sections in terms of reducing drifts and steel utilization. Subsequently, the paper analyses and compares diagrid models with non-uniform pattern configuration generated from topological assessments. The authors test the contribution of a hybrid structure combining diagrid and outrigger systems to appraise whether a local increase in the pattern might be advantageous and preferable to a gradual stiffening from the top of the building toward the base.
In recent years, diagrid structures have received increasing attention among both designers and researchers of tall buildings for creating one-of-a-kind signature structures. This paper presents a state-of-the-art review of diagrid structures. First, various diagrid configurations, main factors affecting their behaviors, and related design parameters and approaches are discussed. Then, diagrid applications for free-form steel and concrete structures are introduced showing the diagrid applicability for complex structures followed by recent advances in structural design of diagrid connections, diagrid nonlinear behavior, and structural control of diagrids. Recent studies about a new variation of tubular and diagrid systems, hexagrids, are discussed briefly. Finally, the diagrid potential in design of sustainable buildings is delineated.
Since its introduction, the ground structure method has been used in the derivation of closed–form analytical solutions for optimal structures, as well as providing information on the optimal load–paths. Despite its long history, the method has seen little use in three–dimensional problems or in problems with non–orthogonal domains, mainly due to computational implementation difficulties. This work presents a methodology for ground structure based topology optimization in arbitrary three–dimensional (3D) domains. The proposed approach is able to address concave domains and with the possibility of holes. In addition, an easy–to–use implementation of the proposed algorithm for the optimization of least–weight trusses is described in detail. The method is verified against three–dimensional closed–form solutions available in the literature. By means of examples, various features of the 3D ground structure approach are assessed, including the ability of the method to provide solutions with different levels of detail. The source code for a MATLAB implementation of the method, named GRAND3 — GRound structure ANalysis and Design in 3D, is available in the (electronic) Supplementary Material accompanying this publication.
This thesis encourages interdisciplinary design exploration through consideration of constructability in conceptual structural design. Six new metrics are introduced to measure variability in structural components, impose reasonable construction constraints, and encourage standardization of structural characteristics which can improve the ease, efficiency, and costs of construction. This thesis applies these original constructability metrics to truss faqade structures for an objective, quantitative comparison with structural performance metrics. The primary contribution of these new metrics is a computational method that can aid in identifying expressive, high-performing structures in the conceptual design phase, when decisions regarding global structural behavior have the greatest impact on multi-objective project goals. Key words. constructability, conceptual structural design, structural optimization, construction, buildability, structural design tools
This paper describes an integrated topology optimization framework using discrete and continuum elements for buckling and stiffness optimization of high-rise buildings. The discrete (beam/truss) elements are optimized based on their cross-sectional areas, whereas the continuum (polygonal) elements are concurrently optimized using the commonly known density method. Emphasis is placed on linearized buckling and stability as objectives. Several practical examples are given to establish benchmarks and illustrate the proposed methodology for high-rise building design. (C) 2014 American Society of Civil Engineers.
The Lotte Super Tower is a unique form that transforms from a square, 70-meter square footprint to a 40-meter circle at 555 meters above ground. The shape of the building has been wind engineered to reduce wind forces and accelerations. A dual system comprised of an exterior steel diagrid and an interior reinforced concrete core is being employed for lateral resistance to wind and seismic effects. Each of the components of the structural system have been optimized to provide material efficiency and geometrically rationalized to increase constructability.
The Karamba plug-in developed by Clemens Preisinger in collaboration with Bollinger + Grohmann Engineers has been developed to predict the behaviour of structures under external loads. Intended to be used by architects rather than being solely confined to an engineering setting, it enables a seamless flow of data between structural and geometric models. Preisinger here describes the program's evolution and application.
In this paper the authors define a framework for assessing the “local” structural issues in the design of diagrid tall buildings, and present a methodology for establishing the need for a specific secondary bracing system (SBS) as a function of the diagrid geometry. Further, design criteria for secondary bracing systems are worked out and applied to some 90 story building models, characterized by perimeter diagrid structures with different module height and diagonal cross sections. The outcomes of the proposed simplified procedures, both for assessing SBS necessity and for the consequent SBS member design, have been compared to the structural response of the diagrid building models, obtained without and with SBS, demonstrating both the accuracy of the proposed formulations and the primary importance of the discussed local questions. In fact, all analyzed diagrid models exhibited problems concerning stability of interior columns (i.e. multi-storey buckling modes) and/or local flexibility (excessive interstory drift); the above local problems are completely solved after the introduction of a SBS at the central core location, and, against a modest increase of structural weight (about 3%), any flexural engagements in the diagrid member is eliminated.
Topology optimization methods were originally developed in a deterministic setting notwithstanding the inherently uncertain environment in which the final structural systems must exist. Indeed, most design applications are affected by uncertainties in material properties, model idealization etc. as well as loads that are inherently aleatory in nature. In addition, the responses of the systems of interest to this study are generally affected by a significant amount of dynamic amplification therefore complicating the governing equations. While the performance-based assessment and optimization of fixed-topology structures set in the aforementioned environment has been the focus of a number of studies, the possibility of performing topology optimization within this setting has yet to be fully investigated.
This paper presents a performance-based topology optimization framework developed for wind-sensitive tall buildings that rigorously accounts for the time-variant stochastic nature of the aerodynamic loads while considering additional time-invariant uncertainties describing the state/knowledge of the system parameters defining the mechanical properties of the structure. The framework is based on decoupling the performance-based assessment from the topology optimization problem through the definition of a number of approximate sub-problems. The successive resolution of these results in a final design that is not only optimum but also satisfies the user-defined performance targets.
The originality of form is one of the new trends that can be identified in the current design of tall buildings. In this design trend, the so‐called diagrid structures, which represent the latest mutation of tubular structures, play a major role due to their inherent esthetic quality, structural efficiency and geometrical versatility. In this paper, an overview on application of such typology to high‐rise buildings is carried out; in particular, in the first part of the paper, the peculiarities of diagrid systems are described: starting from the analysis of the internal forces arising in the single diagrid module due to vertical and horizontal loads, the resisting mechanism of diagrid buildings under gravity and wind loads is described, and recent researches and studies dealing with the effect of geometry on the structural behavior are discussed. In the second part of the paper, a comparative analysis of the structural performance of some recent diagrid tall buildings, characterized by different number of stories and different geometries, namely the Swiss Re building in London, the Hearst Headquarters in New York and the West Tower in Guangzhou, is carried out, and some general design remarks are derived. Copyright © 2012 John Wiley & Sons, Ltd.
This paper presents an overview of a proposed tall building design platform that has the aim of determining the optimal external shape and structural system for tall buildings subject to aerodynamic loads. The platform is intended to bridge the gap between the traditionally manual conceptual design stage and the more automated detailed design stage in an attempt to define a new generation of innovative tall buildings. Shape optimization will be used to sculpt the optimal external profile of the building, topology optimization will be utilized to determine the optimal configuration of the structural system, and reliability-based optimization algorithms will be used in the detailed design stages. This paper presents the results of several preliminary studies concerning the topology optimization stage of the platform, performed on simplified building structures, to highlight the concept and benefits of this approach.
Optimization of large structures consisting of thousands of members subjected to the highly nonlinear constraints of the actual commonly used design codes, such as the American Institute of Steel Construction (AISC), Allowable Stress Design (ASD), or Load and Resistance Factor Design (LRFD) specifications (AISC 1989, 1994), requires high-performance computing resources. We have previously developed parallel optimization algorithms on shared memory multiprocessors where a few powerful processors are connected to a single shared memory. In contrast, in a distributed memory machine, a relatively large number of microprocessors are connected to their own locally distributed memories without globally shared memory. In this article, we present distributed nonlinear neural dynamics algorithms for discrete optimization of large steel structures. The algorithms are implemented on a recently introduced distributed memory machine, the GRAY T3D, and applied to the minimum weight design of three large space steel structures ranging in size from 1,310 to 8,904 members. The stability, convergence, and efficiency of the algorithms are demonstrated through examples. For an 8,904-member structure, a high parallel processing efficiency of 94% is achieved using a 32-processor configuration.
Only a small fraction of the hundreds of papers published on optimization of steel structures deal with cost optimization; the great majority deal only with minimization of the weight of the structure. Those few that are concerned with cost optimization deal with small two-dimensional or academic examples. In this article, the writers present a fuzzy discrete multicriteria cost optimization model for design of space steel structures subjected to the actual constraints of commonly-used design codes such as the AISC ASD code by considering three design criteria: (1) minimum material cost; (2) minimum weight; and (3) minimum number of different section types. The computational model starts with a continuous-variable minimum weight solution with a preemptive constraint violation strategy as the lower bound followed by a fuzzy discrete multicriteria optimization. It is concluded that solving the structural design problem as a cost optimization problem can result in substantial cost savings compared with the traditional minimum weight solution, especially for large moment-resisting structures. In a 36-story moment-resisting space frame with bracings, the cost savings is in the range of 15.6-28.8%.
From the Publisher:The emergence of modern solid modeling systems and geometry-based applications such as automatic mesh generation techniques has led the design community to focus their efforts on exploiting these relatively new technologies for the optimal design of structures. In addition, the use of formal optimization methods in multidisciplinary systems has emerged as a major area of research interest, primarily due to an increased awareness of the potential gains from the use of these methods in realistic design problems. Much of the literature on the key technologies of geometry modeling, optimization and CAD applications is narrowed on a particular technology and does not take a broader perspective of the entire design process. This book represents the first attempt to expose the CAD community to the various islands of technology that constitute the design process. The purpose of this book is to provide the design community with a comprehensive approach to structural design which includes geometry representation for structural domains, automated techniques for finite element modeling, coupling self-adaptive techniques with finite element models, optimization, design sensitivity analysis, and integration of optimization techniques with geometry models for a fully automated structural design system. This book also addresses other real world design situations related to approximation concepts for computational efficiency and multicriterion and multidisciplinary structural design optimization. In selecting the chapters in this book, the aim has been to present the state-of-the-art in various key technologies required for the automation of multidisciplinary design. The organization of the chapters is in-line with the actual design methodology which extends from computer representation of the domain to the multicriterion, multidisciplinary design through automatic mesh generation, coupled self-adaptive analysis, and shape optimization. This book is intended to be used as a ref
The use of diagrid structural systems for tall building design has continued to increase. Characteristics and stiffness-based preliminary design methodology of diagrid structures are discussed. The design methodology is applied to a set of diagrid structures, 40, 50, 60, 70, and 80 stories tall. The diagrid structure of each storey height is designed with diagonals placed at various uniform angles as well as gradually changing angles along the building height in order to determine the optimal uniform angle for each structure with a different height and to investigate the structural potential of diagrids with changing angles. Based on these design studies, design guidelines are provided for the optimal configuration of the diagrid structure grid geometry within a certain height range.
While the weight of a steel structure is a major component of the total cost, the minimization of the cost should be the final objective for optimum use of available resources. The total cost of a steel structure includes (a) the material cost of structural members such as beams, columns, and bracings, (b) the fabrication cost including the material costs of connection elements, bolts, and electrodes and the labor cost, (c) the cost of transporting the fabricated pieces to the construction field, and (d) the erection cost including the material costs of connection elements, bolts, and electrodes and the labor cost. In this article, a chronological review of the journal articles on cost optimization of steel structures is presented. Articles on deterministic, reliability-based, and fuzzy logic-based optimization of steel structures are reviewed. Research on cost optimization can encourage the use of the optimization approach in structural steel design practice by providing a more realistic way of modeling structural steel design and resulting in additional savings compared with the weight optimization problem.
This paper presents preliminary design guidelines specifically for diagrid tube structures composed of straight diagonals with gradually changing angles. A graphic approach to configurating a diagrid of this type is introduced, with two basic geometric variables involved, i.e. the bottom and top diagonal angles. In terms of both stiffness and strength design criteria, a methodology for calculating diagonal member sizes is developed and applied to a set of diagrid tube structures with height-to-width aspect ratios ranging from 3.6 to 9. The diagrid tube structures are designed with various combinations of bottom and top angles in order to investigate the effects of bottom and top angles on the material usage. Based on the results, the optimal values of bottom and top angles are suggested, then, the optimal geometries for diagrid tube structures with different aspect ratios are determined. This paper attempts to help the designer arrange the structurally efficient diagrid layout conveniently and perform approximate calculations of the diagonal member sizes. Copyright © 2010 John Wiley & Sons, Ltd.
Sustainable structural engineering strategies for tall buildings are presented with an emphasis on stiffness-based material-saving design methodologies. The design methodologies are applied to the systems with diagonals such as braced tubes and more recently developed diagrid structures. Guidelines for determination of bending and shear deformations for optimal design, which uses the least amount of structural material to meet the stiffness requirements, are presented. The impact of different geometric configurations of the structural members on the material-saving economic design is also discussed, and recommendations for optimal geometries are made. The design strategies discussed here will contribute to constructing built environments using the minimum amount of resources. Copyright © 2008 John Wiley & Sons, Ltd.
This article addresses the life-cycle cost optimization of steel structures. The main factors influencing the life-cycle cost of a structure are delineated and their effects on various cost functions are discussed. A four-criteria optimization model is presented for the life-cycle cost optimization of steel structures. These criteria are (i) select discrete commercially available sections with the lowest cost, (ii) select commercially available sections with the lightest weight, (iii) select the minimum number of different types of commercially available sections, and (iv) select commercially available sections with the minimum total perimeter length. The last criterion models a representative type of cost incurred over the life of the structure, that is, preventative maintenance in the form of periodic painting of an exposed steel structure to avoid corrosion. The life-cycle cost optimization model is based on fuzzy logic with the goal of formalizing the life-cycle design process but with some input from the design engineer through introduction of weighting coefficients reflecting the relative importance of various criteria. The model is applied to a large steel structure with over 3300 members. Copyright © 2002 John Wiley & Sons, Ltd.
Diagrid structural systems are emerging as structurally efficient as well as architecturally significant assemblies for tall buildings. This paper presents a simple methodology for determining preliminary member sizes. The methodology is applied to a set of building heights ranging from 20 to 60 stories, and parameters for the optimal values of the grid geometry are generated for representative design loadings. These values are shown to be useful for architects and engineers as guidelines for preliminary design. Associated architectural and constructability issues of diagrid structures are also discussed here. Copyright © 2007 John Wiley & Sons, Ltd.
This article presents an innovative research project (sponsored by the National Science Foundation, the American Iron and Steel Institute, and the American Institute of Steel Construction) where computationally elegant algorithms based on the integration of a novel connectionist computing model, mathematical optimization, and a massively parallel computer architecture are used to automate the complex process of engineering design. Copyright © 1996, American Association for Artificial Intelligence. All rights reserved.
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