Truss Design Research Articles

A generic optimization framework for resilient systems

ABSTRACT This paper addresses the optimal design of resilient systems, in which components can fail. The system can react to failures and its behaviour is described by general mixed integer nonlinear programs, which allows for applications to many (technical) systems. This then leads to a three-level optimization problem. The upper level designs the system minimizing a cost function, the middle level represents worst-case failures of components, i.e. interdicts the system, and the lowest level operates the remaining system. We describe new inequalities that characterize the set of resilient solutions and allow to reformulate the problem. The reformulation can then be solved using a nested branch-and-cut approach. We discuss several improvements, for instance, by taking symmetry into account and strengthening cuts. We demonstrate the effectiveness of our implementation on the optimal design of water networks, robust trusses, and gas networks, in comparison to an approach in which the failure scenarios are directly included into the model.

Modeling Knee-Brace Fastener Slippage in Post-Frame Buildings with Diaphragm-Action Design

Highlights Effects of knee braces, with and without fastener slippage, on a post-frame structure with diaphragm-action design. Modeling techniques of knee braces with fastener slippage. Effects of fastener slippage on a primary frame with knee braces. Knee brace may have an undesired (negative) effect on posts and roof trusses. Abstract. Knee braces should not be an add on after the post-frame building is designed because they do affect the behavior of the structure. It is recommended that the building designer first check the need for knee bracing when diaphragm action is included in the design. Knee braces may benefit buildings with certain geometrical configurations and loading conditions where diaphragm action alone is not enough. Modeling knee bracing within a post-frame building is complex. The complexity extends to the roof-truss design because the truss design must include the knee brace reaction forces. The building designer is responsible for reviewing truss drawings to verify that knee brace loads are applied correctly, and that correct governing load combinations are applied. In this study, a structural analog that includes knee braces, with and without slippage, was developed to model the effects of knee braces on designs of post-frame buildings with diaphragm action. In the five buildings analyzed in this study, use of knee braces produced inconsistent results. Knee braces may increase or decrease horizontal eave deflection, load demand on the diaphragm and endwalls, load demand on the foundation, and stress unity in the posts. In all buildings with knee braces, posts were subjected to additional bending stresses under gravity loads. This behavior was more pronounced in buildings with long truss spans. Knee braces should not be specified in the design documents unless their effects on the building are considered by structural analysis. Keywords: Diaphragm action, Knee braces, Modeling connection slippage, Post-frame buildings.

Head-Mounted Augmented Reality Support for Assemblers of Wooden Trusses

Wooden-house assembly is an area where still a big part of the work is done manually. In this case study, pairs of operators compose large wooden pieces together based on paper-print instructions complemented by visual guidance in the shape of laser marks projected from lasers mounted in the ceiling, based on Computer-aided design (CAD) data. Augmented Reality (AR) head-mounted displays (HMD) offer a unique platform for providing instructions and additional information superimposed in the work environment and thus can provide guidance in a cognitively ergonomic way. A particular advantage compared to other computing platforms is that the operators have free hands and can perform the manual work and follow guidance simultaneously. We present an evaluation of a prototype that dynamically transforms a CAD data file with design and measurements of wooden trusses to be manufactured, into an AR-based guidance system developed in Unity for Microsoft HoloLens 2 devices. We used an iterative participatory design process for prototyping and think-aloud protocol combined with observations for evaluation, involving professional assemblers in different stages of the process. Participants found the solution to potentially save time in their everyday work and simplify the task by offering increased visibility of the marks compared to the existing laser projection. Large-scale deployment of the system is still facing design challenges of which some are also discussed in the paper.

Hybrid multi-strategy chaos somersault foraging chimp optimization algorithm research.

To address the problems of slow convergence speed and low accuracy of the chimp optimization algorithm (ChOA), and to prevent falling into the local optimum, a chaos somersault foraging ChOA (CSFChOA) is proposed. First, the cat chaotic sequence is introduced to generate the initial solutions, and then opposition-based learning is used to select better solutions to form the initial population, which can ensure the diversity of the algorithm at the beginning and improve the convergence speed and optimum searching accuracy. Considering that the algorithm is likely to fall into local optimum in the final stage, by taking the optimal solution as the pivot, chimps with better adaptation at the mirror image position replace chimps from the original population using the somersault foraging strategy, which can increase the population diversity and expand the search scope. The optimization search tests were performed on 23 standard test functions and CEC2019 test functions, and the Wilcoxon rank sum test was used for statistical analysis. The CSFChOA was compared with the ChOA and other improved intelligent optimization algorithms. The experimental results show that the CSFChOA outperforms most of the other algorithms in terms of mean and standard deviation, which indicates that the CSFChOA performs well in terms of the convergence accuracy, convergence speed and robustness of global optimization in both low-dimensional and high-dimensional experiments. Finally, through the test and analysis comparison of two complex engineering design problems, the CSFChOA was shown to outperform other algorithms in terms of optimal cost. For the design of the speed reducer, the performance of the CSFChOA is 100% better than other algorithms in terms of optimal cost; and, for the design of a three-bar truss, the performance of the CSFChOA is 6.77% better than other algorithms in terms of optimal cost, which verifies the feasibility, applicability and superiority of the CSFChOA in practical engineering problems.

Design of truss adjusting mechanism for secondary mirror of large aperture telescope

Design of truss adjusting mechanism for secondary mirror of large aperture telescope

Many‑objective meta-heuristic methods for solving constrained truss optimisation problems: A comparative analysis

Many-objective truss structure problems from small to large-scale problems with low to high design variables are investigated in this study. Mass, compliance, first natural frequency, and buckling factor are assigned as objective functions. Since there are limited optimization methods that have been developed for solving many-objective truss optimization issues, it is important to assess modern algorithms performance on these issues to develop more effective techniques in the future. Therefore, this study contributes by investigating the comparative performance of eighteen well-established algorithms, in various dimensions, using four metrics for solving challenging truss problems with many objectives. The statistical analysis is performed based on the objective function best mean and standard deviation outcomes, and Friedman's rank test. MMIPDE is the best algorithm as per the overall comparison, while SHAMODE with whale optimisation approach and SHAMODE are the runners-up.•A comparative test to measure the efficiency of eighteen state-of-the-practice methods is performed.•Small to large-scale truss design challenges are proposed for the validation.•The performance is measured using four metrics and Friedman's rank test.

QL-ADIFA: Hybrid optimization using Q-learning and an adaptive logarithmic spiral-levy firefly algorithm.

Optimization problems are ubiquitous in engineering and scientific research, with a large number of such problems requiring resolution. Meta-heuristics offer a promising approach to solving optimization problems. The firefly algorithm (FA) is a swarm intelligence meta-heuristic that emulates the flickering patterns and behaviour of fireflies. Although FA has been significantly enhanced to improve its performance, it still exhibits certain deficiencies. To overcome these limitations, this study presents the Q-learning based on the adaptive logarithmic spiral-Levy flight firefly algorithm (QL-ADIFA). The Q-learning technique empowers the improved firefly algorithm to leverage the firefly's environmental awareness and memory while in flight, allowing further refinement of the enhanced firefly. Numerical experiments demonstrate that QL-ADIFA outperforms existing methods on 15 benchmark optimization functions and twelve engineering problems: cantilever arm design, pressure vessel design, three-bar truss design problem, and 9 constrained optimization problems in CEC2020.

An Efficient Approach Based on Remora Optimization Algorithm and Levy Flight for Intrusion Detection

With the recent increase in network attacks by threats, malware, and other sources, machine learning techniques have gained special attention for intrusion detection due to their ability to classify hundreds of features into normal system behavior or an attack attempt. However, feature selection is a vital preprocessing stage in machine learning approaches. This paper presents a novel feature selection-based approach, Remora Optimization Algorithm-Levy Flight (ROA-LF), to improve intrusion detection by boosting the ROA performance with LF. The developed ROA-LF is assessed using several evaluation measures on five publicly available datasets for intrusion detection: Knowledge discovery and data mining tools competition, network security laboratory knowledge discovery and data mining, intrusion detection evaluation dataset, block out traffic network, Canadian institute of cybersecurity and three engineering problems: Cantilever beam design, three-bar truss design, and pressure vessel design. A comparative analysis between developed ROA-LF, particle swarm optimization, salp swarm algorithm, snake optimizer, and the original ROA methods is also presented. The results show that the developed ROA-LF is more efficient and superior to other feature selection methods and the three tested engineering problems for intrusion detection.

An Efficient Hybrid Particle Swarm and Teaching-Learning-Based Optimization for Arch-Dam Shape Design

Particle swarm optimization is a popular meta-heuristic with highly explorative features; however, in its standard form it suffers from a poor convergence rate and weak search refinement on multi-dimensional problems. The present work improves the conventional particle swarm optimizer in three ways: adding a greedy selection for better intensification; embedding an extra movement borrowed from teacher–learner-based optimization; and utilizing a neighborhood strategy by averaging over a random half of the swarm. The performance of the proposed method is subsequently evaluated on three sets of problems. The first set includes uni-modal, multi-model, separable and non-separable test functions. The proposed method is compared with a standard particle swarm optimizer and its variants as well as other meta-heuristic algorithms. Engineering benchmark problems including the optimal design of a tubular column, a coiled spring, a pressure vessel and a cantilever beam constitute the second set. The third set includes constrained sizing design of a 120-bar dome truss and the optimal shape design of the Morrow Point double-arch concrete dam as a practical case study. Numerical results reveal considerable enhancement of the standard particle swarm via the proposed method to exhibit competitive performance with the other studied meta-heuristics. In the optimal design of Morrow Point Dam, the proposed method resulted in a material consumption 21 times smaller than the best of the initial population and 26% better than a recommended practical design.

Optimal Design of Planar Trusses Using Graph Theoretical Force Method

In this paper, the purpose is to present an efficient graph method for the analysis of truss structures using the force method and compare the computational time with that of the stiffness approach. Naturally, the results of the optimization and the accuracy of calculation for both methods are identical, but the calculation time for the force method is less when the degree of static indeterminacy (DSI) is smaller than the degree of kinematic indeterminacy (DKI) of the structure. Three examples are designed, and optimization has been performed using the ECBO algorithm in MATLAB.

Optimal Design of Steel Planar Trusses Using Ant Lion Algorithm

This paper elaborates on optimized design of steel structures directed towards the sustainability of materials. The case in point is steel trusses that are extensively used structural components. Though copious research is available on use of conventional optimization methods, nature-inspired optimization algorithms have received scarce attention particularly in optimal design of planar trusses. In this paper, the development of Ant Lion algorithm for the optimal design models for steel trusses is elaborated. A comprehensive comparison with the optimized sectional weights obtained by other nature inspired optimization algorithms implemented in earlier research by the author. They include elitism based genetic algorithm (EBGA), ant colony optimization (ACO), artificial honeybee optimization (AHBO), and Particle swarm optimization (PSO) algorithm. Four steel trusses with different articulations have been considered for this purpose. It is found that the optimal weights obtained by Ant Lion algorithm are almost on par with those obtained by PSO. The other three algorithms vary marginally. However, the convergence to overall weight of trusses is different for different algorithms. ALO took 100-200 iterations for the convergence. In fact, the convergence to optimized weights are faster in case of ALO and PSO in relation to other algorithms.

Reliability-based multi-objective optimal design of spatial trusses using NSGA-II

Reliability-based multi-objective optimal design of spatial trusses using NSGA-II

Seismic behavior of steel truss and concrete composite shear wall with double X-shaped braces

Aiming to enhance the seismic performance and assembly of reinforced concrete (RC) shear walls, a novel steel truss and concrete composite (STCC) shear wall with twin X-shaped braces are proposed. Four STCC shear walls and one RC shear wall were tested under cyclic lateral and constant axial load to determine the effect of the number of channel columns and the addition of a crossbar on the seismic performance of STCC walls, as well as the difference in the seismic performance between the STCC wall and RC wall. Based on the test results, an optimal truss design is presented. Additionally, a comprehensive parametric analysis was carried out on 27 finite element models to investigate the influence of critical factors, such as the axial load ratio, the steel ratio of embedded steel columns, and the volumetric ratio of embedded braces, on the seismic performance of STCC walls. Results indicated that the ductility and the energy dissipation of the STCC shear walls were significantly improved, consequently reducing the number and extension of concrete cracks. Double channel columns could improve the bearing capacity of the STCC walls and provide sufficient support for X-shaped braces. Moreover, adding a crossbar could reduce the stiffness and bearing capacity degradation rate of the wall, but strengthening the connection between the column and the reinforcement inside the bottom foundation is recommended. The axial load ratio and the steel ratio of channel columns had more significant influence on the bearing capacity of STCC walls than the volumetric ratio of embedded braces. Finally, a calculation method is proposed, and the calculated results are in good agreement with the test findings.

A user-guided innovization-based evolutionary algorithm framework for practical multi-objective optimization problems

The knowledge of experienced users in solving real-world optimization problems can be formulated as inter-variable relationships to guide an optimization algorithm towards good solutions faster. Alternatively, such interactions can be learned algorithmically during the optimization by analysing good solutions—a process called innovization. Any common pattern extracted from good solutions can be used as a repair operator to modify candidate solutions. The key aspect is to strike a balance between the relevance of the pattern and the extent of its use in the repair operator. This article proposes a multi-objective evolutionary algorithm framework that combines problem-specific knowledge and online innovization approaches to solve two real-world large-scale multi-objective problems: a 879- and 1479-variable truss design and a 544-variable solid fuel rocket design. Four repair operators suitable for uncovering monotonic relations involving multiple decision variables are proposed. Performance variations resulting from different combinations of initial user knowledge and repair operators are also presented.

Filling the gap: a series of 3D-printed titanium truss cages for the management of large, lower limb bone defects in a developing country setting.

Large segmental long bone defects are notoriously difficult to manage. Treatment is resource-intensive due to the complexity, cost, and specialized skills required. Truss designs are known for their triangular shapes organized in web configurations. This allows for maximal mechanical strength, the least mass, and a lattice that can be filled with bone graft. Using a truss cage combined with contemporary internal fixation provides immediate stability for bone ingrowth and long-term potential union. The implant is designed using virtual 3D modelling of the patient's bone defect based on a CT scan. The truss cage can be used in a staged procedure combined with Masquelet's induced membrane technique. This study aims to review the outcomes of patient-specific, locally designed 3D titanium truss cages packed with cancellous autograft in treating segmental, long bone defects in the lower limb in a developing country setting. This retrospective series reviewed cases performed at various institutions between January 2019 and March 2022. Parameters assessed included patient demographics, size and location of the defect, time to clinical and radiological union and complications. Nine cases were included for review, with a mean age of 36years (range 19-52). Defects ranged from 60 to 205mm, and eight cases were staged procedures. Eight cases used intramedullary reamings as bone graft. Contemporary intramedullary nails were used for fixation in all cases. No peri- or post-operative complications occurred. All cases progressed to functional union. 3D-printed titanium truss cages combined with bone graft appear to be an effective treatment of large bone defects in the lower limb in a developing country setting in the short term. No complications were encountered, but longer follow-up is needed before definitive recommendations can be made. Level IV (retrospective case series).

Features of the work of large-span beam structures

Objective. This article discusses flat large-span structures, provides features of their work, as well as design examples. Formulas are given for determining the general dimensions of these structures.Method. Features of work and design, as well as calculation formulas are given. Shipping marks, types of sections and junctions of elements are given. A technique is described that allows to reduce span bending moments. Examples of rational design of beam trusses are given.Result. The given structural diagrams, as well as the analysis of their work, allow us to design long-span flat structures that are reliable, lightweight, technologically advanced in terms of manufacturing, transportation and installation. The types of sections and junctions described in the article are used in the practice of design and construction.Conclusion. The article discusses rational design solutions that allow reducing the own weight of flat large-span structures due to the optimal choice of their design and design scheme.

Design of efficient steel trusses to resist progressive collapse

Nada Elkady and colleagues describe their research-based work to design a steel transfer truss resistant to progressive collapse. The project won the Institution's Research into Practice case study competition in 2022.

Designing Truss in Architecture: Method and Applications Based on Clustering Algorithms and Principal Stress Lines

Rationally and effectively balancing the design objectives of architecture and structure is challenging owing to the limitations of existing truss design methods. Inspired by visual design principles, this study proposes a non-black-box, parametric, and integrated solution based on principal stress lines (PSLs). The idea is to mine the potential data features of PSLs by the clustering algorithm. Clustering the endpoints and equipartition points of PSLs is the core operation of this method. The clustering results are then used to reflect the geometric features and distribution characteristics of PSLs. For this purpose, the framework of two clustering algorithms (DBSCAN and K-means) is adapted with additional functions for sorting, screening, and counting the sample size of specific clusters. Moreover, combined with the layout pattern of linear elements, the truss web number, size, and layout are defined based on the clustering results. In addition, to verify the feasibility of form-finding results, the method is applied to a cantilever truss and two practical projects: Taishan Bridge and the Wing Stairway. Finally, the application potential of this method is demonstrated by comparing its conventional trusses under the same load and support conditions (materials used, maximum displacement, and maximum axial stress). • The proposed truss generation concept is initiated from structural performance, and at the same time is highly compatible with the architect’s design demand for visual presentation. • Compared to the other conventional structural optimization methods based on principal stress lines, the workflow of truss form evolving methodology provided in the paper is non-black-box and achieves parametric visualization in the whole designing process. • There are multiple parameters to control truss webs’ number, size, and layout pattern, which makes diversified outcomes of form generation possible to meet the different requirements of the designers. • The tensile and compression members in trusses can be distinguished to effectively select their cross-sectional sizes, which are important in the accurate demonstration of material properties for both architects and engineers.

Minimal mass design of a new cable truss in two states

In this paper, we focus on the minimal mass design of a new cable truss structure to support concentrated vertical loads within a given span, considering both loading and unloading states. The topology and configuration of a new kind of cable truss are proposed and parameterized by several variables. The potential of the new kind of cable truss in saving mass is then explained. Structure members in symmetric positions that have the same forces are guarantee by a group matrix. The minimal mass design in loading and unloading states subject to yielding and buckling constraints is studied. Optimization of topology and configuration of the cable truss is then processed by a constrained nonlinear optimization method in terms of structure parameters. Mass of the roof and joints are added as a penalty to the total mass. The efficiency and accuracy of the proposed method are demonstrated by numerical examples.

Influence of mean value of the modulus of elasticity in compression parallel to the grain on the design of timber trusses

The Brazilian standard ABNT NBR 7190 (Associação Brasileira de Normas Técnicas [ABNT], 1997) recommends adopting the mean value of the modulus of elasticity to compression in the direction parallel to the grain (Ec0,m) in the calculation of displacements. The values of wood stiffness vary considerably, and they can generate displacements above the limit (L 200-1, where L is the span) established by the referred standard, which contributes to the appearance of pathologies in the structure. To evaluate the influence of the adoption of Ec0,m in the calculation of displacements, mechanical properties of wood species were obtained experimentally. With the aid of numerical models and experimental values, ten types of trusses were analyzed (Porch, Inclined Chord, Top Inclined Chord, Parallel Chord, Bowstring, Fink, Howe, K Truss, Pratt, Scissor), three spans (5, 10, and 20 m) and two species (Hymenolobium petraum Ducke e Hymenolobium sp). Initially, adopting Ec0,m for all members and performing a linear analysis, the maximum loads for the displacement L 200-1 were determined. Subsequently, experimental stiffness values were randomly assigned to each bar, and the maximum displacements were determined through nonlinear geometric analyses. Based on 1260 numerical simulations, deflections of approximately 17% (span of 5 m), 30% (span of 10 m), and 34% (span of 20 m) were observed to be higher than the result considering Ec0,m. This problem can be overcome by using non-destructive methods in the pre-classification of the structure bars, positioning the elements rationally in the regions of the highest demand.