Loaded Structures Research Articles

Blast Loading Prediction of Complex Structures Based on Bayesian Deep Active Learning

The prediction of blast loading for complex structures using deep learning requires extensive training data from field experiments or numerical simulations. However, the destructive nature of explosions complicates the collection of adequate field data, and traditional simulations are often time-consuming. To address these challenges, a Bayesian deep learning approach is proposed that quantifies prediction uncertainty. This method utilizes an uncertain selection strategy to actively choose high-quality samples, enhancing the simulation process and iteratively expanding the training dataset. The experimental results demonstrate that this Bayesian deep active learning method achieves a mean absolute percentage error (MAPE) of 6.1% for peak overpressure predictions. Additionally, more than 73.1% of confidence intervals include true values, with prediction times under 20 ms for single-point blasts. Notably, only 60% of the training data is required to achieve the same accuracy as conventional deep learning methods. This approach facilitates rapid and reliable predictions of blast loading for complex structures while significantly reducing training costs.

Assessment of corrosion attack morphology on reinforced concrete structures exposed to chlorides

AbstractChloride‐induced corrosion of the reinforcement steel is the main degradation mechanism for reinforced concrete, considerably affecting the load and deformation capacity of structures. Despite its importance, there is limited knowledge about the morphology of corrosion attacks and accordingly, relatively crude assumptions are generally made when considering corrosion in structural analyses. Improved understanding could reduce maintenance costs and extend the service life of structures. This study presents a systematic documentation and analysis of more than 600 corrosion attack morphologies, both from observations on actual engineering structures and from laboratory specimens (X‐ray computed tomography data from previous studies). Findings reveal that corrosion attacks—regardless of age, concrete type, or whether occurring in structures or laboratory specimens—without exception grow laterally and longitudinally along the reinforcement bar, rather than in depth. This shallow morphology deviates from the conventional description of pitting corrosion in the literature. Therefore, we propose using the term ‘corrosion attack’ instead of ‘corrosion pit’ for better differentiation. We discuss different mechanism that may lead to this growth pattern. Moreover, implications for the consideration of corrosion in structural analysis are assessed. A comprehensive database of the documented corrosion attacks is provided to enhance existing service life models, offering substantial data for probabilistic modeling of input parameters.

Neuraxial biomechanics, fluid dynamics, and myodural regulation: rethinking management of hypermobility and CNS disorders

Individuals with joint hypermobility and the Ehlers-Danlos Syndromes (EDS) are disproportionately affected by neuraxial dysfunction and Central Nervous System (CNS) disorders: such as Spontaneous Intracranial Hypotension (SIH) due to spinal cerebrospinal fluid (CSF) leaks, Upper Cervical Instability (UCI; including craniocervical or atlantoaxial instability (CCI/AAI)), Occult Tethered Cord Syndrome (TCS), Chiari Malformation (CM) and Idiopathic Intracranial Hypertension (IIH). The neuraxis comprises the parts of the nervous system (brain, nerves, spinal cord) along the craniospinal axis of the body. Neuraxial tissue includes all tissue structures that comprise, support, sheath, and connect along the neuraxis and peripheral nerves. Altered mechanical loading or vascular supply of neural structures can adversely impact neural health and conductivity, with local and remote effects on inflammation, venous congestion, and muscle control. With EDS characterized by altered structure of the connective tissues found throughout the body including the neural system, altered mechanical properties of the central nervous system (CNS) and its surrounding tissue structures are important considerations in the development and diagnostics of these CNS disorders, as well as response to therapeutic interventions. Experts have identified a need for neuraxial curriculum in medical education and hypermobility-adapted treatment approaches in pain management, neurosurgery, anesthesiology, hematology, gastrointestinal surgery, dermatology, cardiology, dentistry, gastroenterology, allergy/immunology, physical therapy, primary care, radiology and emergency medicine. This paper reviews the interactions between neuraxial biomechanics and pathology related to CNS disorders seen commonly with EDS. First, we provide a concise synthesis of the literature on neuraxial kinematics and fluid dynamics. We then discuss the interplay of these biomechanics and their involvement in clinically-relevant diagnoses and overlapping symptom presentations, modeling physiological reasoning to highlight knowledge gaps, support clinical decision-making, improve multidisciplinary management of hypermobility-associated complexity, and add weight to the call for medical education reform.

Fisher-Tippet Law Truncated Form for Loading Modeling of Machinery Structures

Introduction. Statistical data are used as a basis for assessing the reliability of engineering structures. However, incomplete data or inaccurate modeling of random variables may lead to an overestimation of reliability indicators. In practice, laws with infinitely decreasing or increasing distribution functions of an exponential family are usually used to model random variables characterizing the bearing capacity, load, and resource of engineering structures. To improve the accuracy of modeling of random variables, truncated forms of distribution laws are often used. These forms allow us to consider the random variable within a specified interval, excluding impossible values. Several studies have suggested using the Fisher-Tippett law with three parameters for modeling random variables related to the loading of engineering structures. The advantage of this law is that it limits the range of the random variable on the right side, but the left side of the distribution function decreases indefinitely, which is not ideal for load characteristics. To improve the accuracy of predicting random variables that characterize the load, it would be helpful to have a left-sided restriction using the Fisher-Tippett law. Currently, there are no descriptions of truncated forms of the distribution law in scientific literature. This article will explore the justification and development of a three-parameter truncated form of the Fisher-Tippett law and its use in calculation methods. The goal is to create a left-sided truncated version of the Fisher-Tippett distribution with three parameters to model random variables within a specific range.Materials and Methods. The article provides a detailed description of the history of the Fisher-Tippet law, including its three-parameter form, and justifies the need for obtaining its truncated form.Results. As a result of the research, a truncated form of the Fisher-Tippet three-parameter law in differential and integral forms was obtained and substantiated. The findings included graphs and calculations that demonstrated the normalization of a random variable within a given range.Discussion and Conclusion. The conclusion was drawn about the advantages and disadvantages of the truncated form of the Fisher-Tippet law. The possibility of its practical application in the schematization of random loading processes under operating conditions and testing of machine elements and structures to assess fatigue life and determine fatigue resistance characteristics was established. The direction of further research is related to the practical use of the truncated form, particularly with the need to develop a method for evaluating the parameters of the truncated distribution and verifying the consistency of the proposed model

Study on the influence of submergence depth on the hydrodynamic and wave load characteristics of semi-submersible structures induced by a solitary wave

The submergence depth directly affects the safety of semi-submersible marine structures due to that the submergence depth significantly impacts on the hydrodynamic characteristics and wave loads of structures excited by extreme wave. This paper studies the influence of submergence depth on the hydrodynamic and wave load characteristics of semi-submersible structures by establishing a numerical model of the interaction between solitary waves and semi-submersible structures based on the SPH model and Rayleigh theory. Furthermore, equations for transmission coefficient, reflection coefficient, and wave load are fitted. The calculated wave heights of solitary wave propagation test case are in good agreement with the theoretical values. The maximum relative error of the wave peak is 8.4%. The calculated wave loads of submerged horizontal plates test case has a consistent trend with the experimental data. The maximum relative error of wave load peak and valley is 54% (absolute error 0.37 N). Furthermore, the interaction between solitary waves and structures with different submergence depths is investigated by using the meshless numerical model. It is found that the reflection coefficient first increases and then decreases with increasing submergence depth, and reaching a maximum value of 0.39 at the submergence depth equal to 0.0 m. On the contrary, the transmission coefficient decreases first and then increases with the increase of submergence depth. The minimum value of transmission coefficient is 0.36 with the submergence depth of 0.3 m. As the submergence depth increased, the horizontal wave load peak of the structure gradually increases, and the maximum value of 0.13 is obtained at the submergence depth of 0.7 m. The peak of vertical wave load rapidly increases with the increase of submergence depth and then gradually decreases while the trough gradually decreases with increasing submergence depth.

Metallic Metamaterials with Auxetic Properties: Re-Entrant Structures

The present article is an exploration of metamaterial structures exhibiting auxetic properties. The study shows the effect of three geometric parameters of re-entrant auxetic cells, namely, the internal initial cell angle (θ0), the strut length ratio h/l, and the degree of opening of the unit cells expressed by the change in the Δθ angle, on the value of the Poisson’s ratio. It combines theoretical insights into physical re-entrant auxetic structures with the demonstration of structures that can be subjected to cyclic loading without being damaged. The experimental section features the results of the compression tests of a symmetrical structure made up of four re-entrant cells and tensile tests of a flat mesh structure of size 4 × 4. In the mesh structure, a modification was applied to the re-entrant cells, creating arched strut connections. It was shown that the value of the maximum load for such structures depends on the bending angle and the length of the inclined strut. The mesh structure was created using torsion springs. Its cyclic tension for different amplitudes yielded Poisson’s ratio values in the range of −1.4 to −1.7. These modifications have enabled stable, elastic, and failure-free cyclical changes of the structure’s dimensions under load.

Unstable Delamination Growth in Stiffened Composite Panels Under Cyclic Loading Conditions.

Aeronautical structures can be damaged by objects during operation and maintenance. Indeed, foreign object impacts (FOIs) affect the overall performance of composite structural components. Delamination is the most critical damage mechanism as it is undetectable and develops silently. This phenomenon can be worsened by cyclic loading, as residual strength and stiffness can decrease rapidly, potentially leading to collapse. Unstable delamination growth is critical because it can occur without an increase in the applied load, threatening the integrity of the structure. Predicting this behaviour under fatigue loading is challenging for standard non-linear finite element methods (FEMs), which often face convergence problems when simulating the dynamic nature of delamination growth. This paper presents an efficient alternative methodology for analysing the propagation of delamination under cyclic loading in composite structures, with non-linear static analyses. This new methodology has been shown to be able to correctly account for the decrease in load carrying capacity during growth by performing ad hoc iterations with alternating force and displacement-controlled FEM simulations. To achieve this objective, the Paris law approach has been implemented in the ANSYS FEM code together with an enhanced virtual crack closure technique (VCCT)-based method. The model correctly predicted delamination growth in stiffened aeronautical panels with artificial delaminations subjected to cyclic compression loading.

Are cleft sentence structures more difficult to process?

This study compares the processing of cleft structures against that of monoclausal sentences using event-related potential (ERP). We aim to understand how syntactic complexity is processed by comparing the neural response to cleft and single-clause sentences with identical verb phrases, controlling for verb bias frequency effects. Sixty participants were tested, and we presented 100 cleft and 100 monoclausal sentences, balanced for active and passive verb usage. We examined the P600 component, an ERP associated with syntactic complexity, to assess the processing of cleft structures. Results showed that cleft structures incur a greater processing load, as indicated by a larger P600, compared to monoclausal sentences. The P600 response indicates that processing cleft sentences requires additional syntactic operations, consistent with behavioral studies showing that clinical populations have difficulty comprehending complex sentences.

Eco-Friendly Brick Produced from Bagasse Ash and Lime, Jaggery: A Study of Waste Reuse

The building construction industry in India, which is one of the fastest-growing in the world, heavily relies on limited natural resources, especially burned clay bricks, which raise greenhouse gas emissions. This study investigates the viability of using the laterite soil-based bagasse bricks as an affordable and environmentally friendly substitute. This brick's greater compressive strength, decreased water absorption, and improved insulating qualities are the result of combining sugarcane bagasse—a byproduct of sugar production—with the laterite soil, lime, and jaggery. These bricks' low weight limits the dead load in tall structures, which lowers the price of building with reinforced cement concrete (RCC). Employing bagasse also lessens the effects of stubble burning, an ancient custom in India that seriously pollutes the air. The goal of the study is to encourage the use of laterite soil-bagasse bricks as an environmentally friendly building material by highlighting their many uses in construction. This research aims to encourage environmentally friendly practices in the building sector by promoting the use of sustainable materials by architects, designers, and builders. Key Words: Sustainable construction, laterite soil, bagasse bricks, greenhouse gas emissions, compressive strength, insulation, stubble burning, eco-friendly materials, RCC construction.

ИССЛЕДОВАНИЯ СБОРНЫХ ЖЕЛЕЗОБЕТОННЫХ НЕСУЩИХ СИСТЕМ С ПЛОСКИМ ПЕРЕКРЫТИЕМ

The paper gives a brief review of existing load-bearing frame systems with a flat bottom edge of the slab, performed using prefabricated reinforced concrete products. The basic provisions and results of field testing of floor elements of the prefabricated reinforced concrete load-bearing frame, which is not widely spread in the Russian Federation, according to patent No. 132814 «Prefabricated Reinforced Concrete Frame» are also described. Research on the existing load-bearing systems with flat bottom edge of the slab was carried out by studying the patent documentation available in the All-Russian Patent and Technical Library; information posted by the authors in open sources, scientific articles by the authors of the load-bearing systems. In-situ tests of the slab elements of the framework according to the patent No. 132814 «Prefabricated reinforced concrete framework» were performed by means of empirical experiment with loading of prefabricated elements according to the considered system of prefabricated-monolithic reinforced concrete construction. During the tests, the vertical displacements of the elements, the appearance and width of their crack opening were measured, and the destructive load was recorded. The safety factor according to GOST 8829-2018 for the tested slab elements was calculated based on the recorded destructive load. The values of destructive load of the slab structures obtained in the test results confirm the reliability of the adopted solutions, which substantiates the expediency of their further development. The safety coefficients of transoms and floor slabs obtained according to GOST 8829-2018 satisfy the strength requirements for building structures.

A fast search method of buckling load for telescopic boom structure

The telescopic boom structures are extensively utilized in engineering applications involving large mobile cranes, aerial work platforms of significant height, and similar mechanical devices. These are predominantly fabricated using solid-webbed box types, latticed truss designs, or a combination thereof. Under load, they exhibit pronounced geometric nonlinear effects, with the relationship between load and displacement demonstrating marked nonlinear characteristics. This paper focuses on the geometric nonlinear modeling of slender multi flexible beam structures. The overall structural system is divided into several substructures, and the concept of multi flexible system modeling is borrowed to establish a follow-up connected body foundation on each substructure. By decomposing the node displacement and rotation in the substructure, the large displacement and large rotation of the node are decomposed into rigid body motion of the connected base and small displacement and small rotation relative to the connected base, effectively representing the large displacement and large rotation of the substructure as rigid body motion of the connected base. A modeling method for the geometric nonlinear analysis of slender and flexible multibody beam structures is proposed. By decomposing the nodal displacement and rotation within the substructures, the large displacement and rotation of the nodes are broken down into the rigid body motion of the body-fixed coordinate and small displacement and rotation relative to the body-fixed coordinate. This approach establishes the application conditions for calculating the structure’s virtual power of deformation using traditional beam elements with linear strain. A method for solving the instability load of slender and flexible multibody structures is proposed. This method integrates the characteristics of the system’s nonlinear equilibrium equations with respect to load, by deriving the system equations with respect to a load increment control parameter. This paper converts nonlinear equilibrium equations into first-order ordinary differential equation (ODE). The method proposed in this paper provides a more efficient solution for the buckling load of the telescopic boom. It can be used to systematically and quickly calculate the structure of the telescopic boom.

An analytical solution to “pillowing effect” for composite fuselages

Abstract “Pillowing effect”, introduced by inner cabin air pressure on stringer-frame stiffened fuselage cylinder, is a critical loading case for civil aircraft fuselage. The “pillowing effect” causes out-of-plane bending and shear to fuselage panels, which is a rather huge load for such membrane structures. The fuselage’s longitudinal load and bending load interact nonlinearly with each other in a so called “beam-column” formation, invalidating the superposition principle for linear elasticity. An analytical solution to the axisymmetric “beam-column” model is given in this study to account for the “pillowing effect” of orthotropic composite fuselages. This formula can be employed to perform stress checks against “pillowing effect” during fuselage design.

Experimental study on aerodynamic performance of turbine blade squealer tip with different trailing edge designs under high-speed relative casing motion

Over-tip leakage (OTL) flow leads to great aerodynamic performance reduction in high-pressure turbine, reasonable blade tip design can effectively control the loss caused by OTL flow. The relative casing motion is one of the key boundary conditions that can significantly influence OTL flow. In this study, aerodynamical tests were conducted for a high-pressure squealer tip with different trailing edge designs of full cavity squealer tip, pressure-side cutback and suction-side cutback at both stationary and rotating conditions. Loss distribution and blade near tip loading of different trailing edge structures at high-speed rotating condition are firstly reported and evaluated. The result indicates that pressure-side cutback design significantly increases the aerodynamic loss compared with full cavity tip, while suction-side cutback design has close overall loss to full cavity tip. This conclusion was consistent with numerical simulation based on Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) analysis, which reveals that pressure-side cutback design causes the cavity vortex leaks earlier compared with full cavity tip, a small vortex formed at cut region forms and results in higher total pressure loss. The effect of relative motion between blade tip and shroud reinforces this trend. The total pressure loss difference can reach 42 % compared with 8 % in stationary condition, which indicates that relative casing motion needs to be take into consideration when ranking different tip sealing designs.

A Spring Model for Pullout Behavior of Curved, Flexible Structures Embedded in Soil

ABSTRACTThe shape and flexibility of embedded structures, such as tree roots, piles, and anchors, have important impacts on the pullout behavior. However, the rate and manner of mobilization of soil resistances along such structures has not been rigorously explored across a wide range of shapes and structural properties. A spring model for computing compatible displacements of the structure and soil for curved, flexible structures is defined, validated against commonly used methods for computing pile pullout behavior, and then parametrically explored to demonstrate how resistances are mobilized along the length of such structures. The present model allows description of combined axial and transverse loading of these nonlinear structures. The simulation results for the case of normally consolidated clay show that the curvature of a structure causes the distribution of bearing resistance to extend further along the structure than for linear cases. The requirement of equilibrium of the structure produces a coupling between the mobilized bearing and tensile resistance in terms of rate of development and magnitude. Thus, the choices of structure shape impact the magnitude and distribution of mobilized resistance of embedded flexible structures. Implications for anchorage of tree root structures and principles of bioinspired design of anchorage systems are discussed.

Adaptive-Quadratic-Neural-Network-Based Multifidelity Modeling Approach for Buckling of Stiffened Panels

This paper presents a method for predicting the buckling load of stiffened panels using multifidelity modeling based on quadratic neural networks (QNNs) with adaptive activation functions. The effectiveness of the proposed approach is demonstrated through a series of simulations on a range of stiffened panel configurations, and the results are compared to those obtained from traditional multifidelity and high-fidelity models in terms of accuracy and computational efficiency. Numerical experiments demonstrate that the model can accurately and efficiently predict the buckling load of stiffened panels while significantly reducing the computational cost of evaluating the surrogate model. In particular, the proposed adaptive quadratic neural networks (AQNNs) model achieves convergence approximately three times faster and four times less trainable parameters compared to traditional artificial neural networks while maintaining the same validation loss. This approach can significantly improve the design and optimization of aerospace structures by easily and quickly exploring various design configurations and finding stable and efficient configurations. This study highlights the potential of a new multifidelity modeling framework for predicting the buckling load and collapse load of aerospace structures by enhancing convergence speed and prediction accuracy while reducing the computational complexity of neural networks.

Effect of PGV/PGA ratio on seismic-induced vibrations of structures equipped with parallel tuned mass dampers considering SSI

Tuned mass damper is one of the effective methods used to reduce dynamic loads in structures under the influence of environmental loads such as earthquakes, wind, and traffic loads. In the current TMD design, the fixed base approach is mostly considered when determining the dynamic properties of the structure. However, in cases where the structure-soil interaction (SSI) is important, the frequency values of the structure are significantly different from those obtained for the fixed foundation approach. This situation negatively affects the performance of TMD operating in a narrow frequency range. Therefore, using a control system consisting of multiple TMDs connected in parallel (MTMD) instead of a single TMD may be a promising solution for the control of structural vibrations. In this study, a parameter design and efficiency assessment of MTMD for reducing the seismic responses of the structure considering SSI is studied. The particle swarm optimization (PSO) algorithm is adopted to obtain the optimum parameters (i.e., damping ratio, frequency ratio, and frequency bandwidth) of the MTMD. The effects of different support conditions, number of TMD units, and peak ground velocity (PGV) / peak ground acceleration (PGA) ratio on the performance of MTMD are also evaluated comprehensively. The dynamic responses of the structure are obtained under 42 near -fault ground motions from the time history analysis. The results reveal that ground motions with low PGV/PGA ratio can significantly increase the responses of the structure for both with and without SSI cases. Moreover, it has been observed that optimized TMDs placed parallel to the top floor of the structure are effective in reducing the seismic responses of a ten-story building considering SSI.

የቦሎቄ (Phaseolus vulgaris L.)የምህንድስና ባህሪያት ለመውቂያ ማሽን ዲዛይን በአካላዊ እናፍራክሽናል መለኪያዎች አንፃር

When designing appropriate machinery systems, equipment, and infrastructures for interacting with, cultivating, gathering, and agriculture-related processing, it is required to have an understanding of the engineering characteristics of agricultural products. This unpredictability makes it difficult to design or develop machines that can efficiently and effectively manage a wide range of product characteristics. Experimental analysis was used to accomplish the study's objective, which was to investigate the implications of variation on the physical characteristics and frictional parameters of common beans (Phaseolus vulgaris L.) concerning the design of the threshing machine. One hundred bean seeds from each variety were randomly selected and their three primary dimensions were measured with a digital vernier caliper (least count 0.01 mm) and a micro-screw gauge in order to determine the dimensional parameters. The remaining parameters (elongation at the width, thickness, and vertical orientation, geometrical mean diameter, arithmetic mean diameter, square mean diameter, equivalent mean diameter, roundness, sphericity, flakiness ratio, aspect ratio, cross-sectional area, projected area, transverse surface area, and the seed volume) were calculated using mathematical models. Gravimetric characteristics true density and seed volumes were calculated using the toluene displacement method. The data were subjected to analysis of variance (ANOVA), and the Duncan multiple range test was used to separate the means. Significance was accepted at 95% confidence interval (p< 0.05).The results data are required for predicting loads in agricultural storage structures, and to establish useful sources for the development of machinery for handling, cleaning, storing, transporting and drying, among other things.

Effect of three-dimensionality of turbulence on the along-wind loads of square cross-sectional structures

The existing theories for along-wind loads on slender structures, based on the “strip assumption” overlook the three-dimensionality of turbulence. However, numerous experimental phenomena contradicting the “strip assumption” highlight the need to consider the effects of three-dimensional turbulence (3D effect). This study develops an analysis model that considers the three-dimensionality of turbulence and derives a function containing the section-shape-dependent characteristic parameters to represent the 3D effect. A method for identifying the parameters through a wind tunnel test is proposed to solve this function. The parameters for the square cross section are then identified in two different turbulence fields, revealing that the identification parameters of both cases are nearly identical. This similarity indicates that the parameters are independent of the turbulence validating the proposed theories. Finally, the 3D effect on square cross-sectional structures with different aspect ratios under various turbulence integral scales is analyzed. The results showed that as the ratio of the turbulence integral scale to the windward width of the structures increases, the 3D effect reduces, but the rate of reduction slows down. In addition, increasing the aspect ratios of structures further mitigates the 3D effect, enhancing the accuracy of the “strip assumption.” These results can be a reference for evaluating the accuracy of the “strip assumption” theory for square cross-sectional high-rise buildings in atmospheric boundary layer turbulence. The proposed method can be applied to investigate the 3D effect on along-wind loads of slender structures with various cross-sectional shapes.

Parametric Study on Slab Construction Loads in Multistory-shored RC Structures Including Non-typical Stories with Different Slab Thicknesses

Parametric Study on Slab Construction Loads in Multistory-shored RC Structures Including Non-typical Stories with Different Slab Thicknesses

Bracing systems for three-ribbed arch bridges against out-of-plane buckling

This paper is concerned with the design of bracing systems for three-ribbed parabolic arch bridges against out-of-plane buckling. Typical bracing systems for the three-ribbed arch bridges include K-bracing system and X-bracing system as well as transverse bracing system. The buckling criterion of the braced funicular three-ribbed arch bridge is derived from an exact matrix stiffness method (MSM) with a 14 × 14 s-order element stiffness matrix of three-dimensional beam-column elements that allows for torsional and warping deformations. The lateral torsional buckling load and mode are given by the lowest eigenvalue and eigenvector associated with the assembled structural stability stiffness matrix. A comparison study between different bracing system configurations suggests that the three-ribbed arches with the integral K- or X-bracing system (a K/X-bracing across the three arch ribs) have lower lateral torsional buckling loads than their arch counterparts with the independent K- or X-bracing system (the adjacent arch ribs are connected by K/X-bracing respectively), because the latter ones could provide more restraint on the middle arch rib to avoid early lateral torsional instability. Further, a bracing utilization efficiency index (defined as the normalized buckling capacity over material usage for bracing system) is proposed to quantify the effect of bracing systems in improving the lateral torsional buckling capacity of arch bridges. Highly efficient bracing systems that maximize the lateral torsional buckling load of three-ribbed arch structures with the lowest bracing material usage are then recommended.