Triangular Truss Research Articles

Theoretical and Numerical Simulation Study on the Ultimate Load Capacity of Triangular and Quadrilateral Truss Structures

Spatial truss structures (STSs), serving as the bottom support structure of a cooling tower, effectively harness the superior load-bearing capacity offered by lattice-type truss structures. STSs are composed of main bars, diagonal bars, and horizontal bars, with horizontal bars serving as vital components of the truss structure. They play a pivotal role in maintaining the overall integrity and stability of the structure. The proportional relationship between the stiffness of each bar in STSs has a profound impact on the mechanical characteristics of the overall structure. This relationship directly influences the ultimate load-bearing capacity of the structure. Therefore, conducting research on the influence patterns of this relationship is of utmost importance. This paper explores the study of triangular truss structures (TTSs) and quadrilateral truss structures (QTSs). Firstly, through theoretical analysis, considering structural elements such as the stiffness of the horizontal bars, the number of layers in the truss, and the angle between the diagonal bars and the horizontal bars, theoretical expressions for the calculation of the ultimate load capacity of TTSs and QTSs are derived. Furthermore, a parametric finite element (FE) model was established for the TTSs and QTSs. Through numerical simulations, the validity of the theoretical calculation expressions was verified. Finally, this paper discusses the influence of factors such as the stiffness of the horizontal bars, the number of layers in the truss, and the angle between the diagonal and horizontal bars on the TTSs and QTSs. It analyzes the patterns and trends of these influences. The research results indicate that the theoretical and numerical simulation results for the TTSs have an error ranging from 0.40% to 4.93%, while the relative error for the QTSs ranges from 1.59% to 4.88%. These errors are within an acceptable range for engineering calculations. As the stiffness of the horizontal bars increases, the proportionality coefficient of the truss’s ultimate load capacity shows an initial increase followed by a stable trend. It reaches an equilibrium state when the stiffness of the horizontal bars reaches a certain threshold. As the number of layers in the truss and the angle between the diagonal and horizontal bars increase, the proportionality coefficient of the load capacity gradually decreases. The research findings provide a theoretical basis for the application of TTSs and QTSs in cooling towers.

Research on Topology Optimization Design of Truss Structure

Due to continuous advances in engineering technology and architecture, the use of truss structures is expanding. The design method of ideal truss structure is the main research topic of this paper. The topology optimization method is applied to a bridge design case study. The load and total material utilization ratio of each rod of triangular truss, arch truss and Pratt truss were determined by using structural mechanics solver. By comparing the stress and material consumption of the truss structure, it shows that the truss structure has advantages in stress and can be used in the truss construction of short-distance arch bridge. Truss is the basic unit of the topology optimization method of truss structure proposed in this study. By optimizing the topological shape of the truss, the ideal design of the whole structure is realized. While maintaining structural stiffness and stability, the technology can significantly reduce the weight and cost of the structure.

Seismic Analysis of Large-span Steel Truss Structure Based on PKPM

In the construction industry, large-span steel truss structures are widely used. In order to test their seismic performance under different structures, select truss structures with better seismic performance, and use PKPM software to establish two cross-sectional triangular arch truss models with different web member arrangements, one cross-sectional trapezoidal arch truss model. Using the mode decomposition response spectrum method, simulate and analyze the displacement and stress changes of three sets of finite element calculation models under different load combinations during earthquakes. The results showed that all truss models meet seismic requirements. The change in the arrangement of the web members did not significantly improve the seismic performance of the cross-sectional triangular truss, the seismic performance of the cross-sectional trapezoidal arch truss was significantly better. The lower chord of the triangular arch truss support and the mid-span top chord are under compression, while the top chord is only compressed on one side and tensioned on the other side. The top chord of the trapezoidal arch truss is mainly under pressure.

Rational structural solutions for triangular trusses

Wooden rafter structures have undoubted advantages, which determine their wide application. The object of the study is triangular rafter structures. The purpose of the research is to find the dependence of force values in the elements of the studied structure on the magnitude of its lifting boom. The calculation of a triangular truss using the Maxwell - Cremona diagram is presented. The efficiency of the proposed method was estimated on the basis of a study of the structure of a wooden truss of the “scissors” type. The following pattern has been established: the change in the coordinates of the points (abscissas) of the force diagram is inversely proportional to the change in f . It is determined the area of rational values of the lift (roof slope) at which the values of internal forces tend to a minimum. It was revealed that the values of force increments in the truss elements at each step increase from 27% to 2 times when the roof slope de-creases. Based on the graphical analysis of the obtained data the range of effective values of the roof slope at which the forces in the elements of the truss take minimum values was found. Using a graphic method of determining the forces, it is possible to check variants of the roof slope in the search for a rational solution of the “scissor” type truss structure. It follows that the proposed method contributes to the choice of the most economical structural solutions.

Study on damage failure for a new double-triangular truss core sandwich structure

In order to solve the inherent problems of low bonding strength between face and core, a new double triangular truss core sandwich structure with reinforced frame is proposed, and the face and core are melt connected by thermoplastic composite carbon fiber reinforced polyether ether ketone (CF/PEEK). The response of the new double-triangular truss core sandwich structure under three-point bending load is investigated by both theoretical and finite element methods. Firstly, the theoretical prediction equation of bending stiffness and strength of double-triangular truss core sandwich structure is established, and the failure mechanism diagram is constructed. A valid three-point bending finite element model is established by Abaqus to predict the damage pattern of the structure and obtain the results of damage initiation location, damage process, final failure modes and load-displacement curve. The effect of geometric parameters on the bending performance of the sandwich structure was investigated. The results show that the calculated theoretical deflection curves and the ones obtained by numerical simulation are in good agreement. The average error between the two is 7.94%, verifying the reasonableness of the theoretical prediction model. The effect of geometric parameters on the bending performance of the sandwich structure was investigated. The new sandwich structure has stronger bending resistance and better ultimate load capacity than traditional honeycomb and V-shaped structures. Failure modes such as panel crumpling and crushing, fracture of reinforcement frames, buckling and fracture of core rods occur in sandwich structures under bending loads.

Formulas for Calculating the Deflections of a Triangular Truss of Spatial Cover

Statement of the problem. The scheme of triangular in terms of dome type cover is proposed. The construction is statically determinate. The formulas for the dependence of the deflection on the number of panels and sizes are derived by generalizing a series of individual solutions by induction. Materials and methods. The forces in the coating rods are performed by cutting nodes in symbolic form using operators of the Maple symbolic mathematics system. The unknown systems of equilibrium equations in projections on the coordinate axis include the reactions of vertical supports located on the sides of the truss. One of the corners of the truss also has a spherical support, one is cylindrical. The Maxwell—Mohr formula is used to calculate the deflection of the vertex. The analysis of sequences of coefficients in solutions for individual trusses with different numbers of panels yields expressions for common terms included in the desired calculation formula. Results. Formulas for the dependence of the deflections of the truss on the number of panels for a vertical load evenly distributed over the nodes of the truss and a horizontal wind load applied to one of the sides of the structure are obtained. The solutions have a simple polynomial form. The curves of the dependence of the horizontal displacement of the dome top on the number of panels reveal a minimum. Asymptotics of the solutions is identified. Conclusions. A scheme of a statically determinate symmetric spatial dome is developed and its mathematical model is constructed, allowing analytical solutions with an arbitrary number of panels. The identified dependencies can be used both to evaluate the accuracy of numerical solutions and to find optimal combinations of structural dimensions in terms of rigidity.

Напряженно-деформированное состояние трехгранной фермы с неразрезными поясами пятигранного составного профиля

Introduction. The author considers designs of triangular trusses that can be used to design roofs of industrial and public buildings, various combined systems, and also as overpass structures of linear facilities. The design of a spatial truss as part of a patent pending development of a triangular truss cover with non-cutting closed-section chords is presented. The purpose of numerical studies is to estimate the stress-strain state (SSS) of a spanning triangular truss subjected to static nodal load and different arrangement of strut elements as well as to create a verification database for further numerical studies of non-faceted interface nodes. Materials and methods. The numerical research methodology takes into account the application of nodal static loads, modelling the placement of the enclosing structure of the pavement using purlins. The use of the unit load method is aimed at determining the response of the load-bearing system as part of a comparative evaluation and comparison with the data obtained from other research tasks. Results. In the course of numerical studies, data were obtained, characterising the deflected mode of the triangular truss model in terms of force distribution in the rods and vertical displacements of the nodes. Conclusions. Analysis of the obtained results shows that the accepted design model of a triangular truss adequately reflects its deflected mode. Practical application of the numerical research technique on the basis of application of unit nodal loads consists in the possibility of using calculation results in the form of a structured data set required in calculations by the limit states method. The results obtained can be used as a basis for verification of data obtained in further numerical studies of non-faceted node constructions within the framework of the lamellar mathematical model. The presented numerical studies are part of the complex of scientific research into the actual performance of spanning triangular trusses.

Study on Construction Molding Technology of Long-Span Space Truss Suspended Dome Structure

Typically, the upper part of the roof a gymnasium building is a radial inverted triangular truss structure, and the lower part is a cable structure. They are connected by vertical braces to form a self-balancing structural system. The whole roof is supported by a complex, spatial, prestressed structure comprising tilted Y-shaped laced columns. Such structures rely on the integrity of the form and the application of prestress to achieve the best performance; it is in an extremely unstable state during construction. In order to study the mechanical behavior of the structure in this process, finite element software was used to analyze the cumulative slip of the structure and the construction process of cable tension, and the simulation values were compared to the actual monitoring values. The stress and deformation of the structure in different construction stages were investigated, and a reasonable structural unloading scheme was put forward. The study results showed that the stiffness of the long-span space truss suspended dome structure gradually increased with the structural integrity during construction, and the vertical deformation decreased from 25.4 mm to 19.26 mm with the construction process. The location and magnitude of the structure’s maximum internal force and maximum stress varied greatly compared to the static analysis when considering the construction process effects. Hence, conducting a construction process analysis is necessary. The construction technology of symmetrical rotating cumulative slip proposed in this paper has the advantages of a short construction duration, safe and stable construction process, etc., providing technical references for similar engineering constructions.

Behavioural Study of Truss Bridge using Isogrid Members

The search for lightweight and highly efficient structural components is a continuing process. Reducing the structural weight and improving the load carrying capabilities of these structures will allow designers to append additional capabilities while reducing cost. Isogrid is a lattice of stiffened ribs forming an array of contiguous equilateral triangles. This rib pattern forms triangular trusses by maintaining isotropic property. Ribs when arranged in 60? pattern are known as Isogrid. The highly redundant nature of Isogrid stiffening concept provides high efficiency distributing loads and is less susceptible to impact damage, delamination, and crack propagation. Isogrid structure is typically found in stiffness critical components that resist buckling. The behavior and performance of Isogrid deck slab in a Bridge supported by the truss girders is studied. Isogrid is modeled, analyzed and designed using commercial Finite Element (FE) software. In the present work, a truss bridge is designed for a span of 10.305 m. The bridge is designed using three different kinds of deck configuration, rectangular section without skin, inverted T section with skin, and I section with skin. Commercial FE software is used for computing deflections and stresses. It is found that the deck profile of I section with skin is more preferable than other configurations for Truss Bridge.

The bearing capacity of arch cover structures made of thin-walled cold-formed profiles

Introduction. The article is focused on evaluating the stress-strain state of nonreinforced arch cover structures made of thin-walled cold-formed profiles and arch cover structures reinforced by arch frames made of triangular trusses and girders. The relevance of the study is backed by the need to reinforce arch covers in the event that the design area of operation of a structure is different from the actual area of operation, which is confirmed by the recent cases of collapse of these structures. To reduce the labour input into simulation, the authors suggest a 3D modelling methodology presented using the case of a hangar reinforced by orthotropic plates and rods.
 Materials and methods. A 2D analysis of an arch was performed using the parameters of the reduced cross-section and a 3D analysis of the same arch was performed using a combined cross-section of plates and rods to verify the methodology. The 2D arch and 3D models were subjected to snow loading in compliance with the regulatory document document SP 20.13330.2016 “Loads and impacts”. Parameters of reduced straight sections and stresses, arising in the 2D arch, were analyzed on the basis of identified internal forces and the regulatory document SP 260.1325800.2016 “Thin-walled steel structures made of cold-formed galvanized profiles and corrugated sheets”. A reduction in the rigidity of corrugated sections is taken into account by assessing the rigidity subjected to the effect of a single force. Finite element modeling was conducted in SCAD Office software; stresses and displacements were calculated automatically.
 Results. The 3D calculation method involving orthotropic plates and rods showed satisfactory convergence with the calculation made in the two-dimensional formulation. Maximum stresses arising in a 3D model are 2 % lower than in a 2D arch, and maximum displacements are 21 % lower thanks to a more accurate FEM analysis of the 3D behaviour of the whole hangar.
 Conclusions. The proposed modeling technique reduces the labor intensity of structural modeling and is suitable for evaluating the joint behaviour of basic and reinforced structures of any type.

Good Building Design and Construction Practices in Barangay Baybay, Catarman, Northern Samar

The Extension program conducted entitled “Good Building Design and Construction Practices” an adopt a Barangay program was undertaken in Barangay Baybay, Catarman, Northern Samar. It aimed to provide consultancy services on civil engineering practices. It undertakes a campaign information drive for safe building construction practices. There were 40 participants in attendance mostly composed of skilled workers. The module presented focuses on design construction, materials principles, and safety construction principles. Pre-tests and post-tests were given before and after the training program. From the administered pre-test, the lowest score was seven and the highest score was 14 out of 15 items conducted, while from the post-test examination they got a perfect score and obtained a lowest 10 points score. The result on the House Building Checklist as to the type of house building structures was derived; there was 3.66 percent on concrete houses, 43.09 percent on mixed concrete and timber house, 46.74 percent were made of steel, concrete, and timber houses, and 6.51 percent are constructed with the indigenous house. The results on indicators of house building checklist revealed that most of the structures do not have occupancy building certificates. The foundation was mostly built on sand because of its location facing the shoreline. The materials used were rivers stone and round. Most walls were covered with either concrete or hollow blocks and were tied to the column at 40 cm intervals. The roofing systems were made of more than 50 percent triangular trusses. For site drainage plan, almost 50 percent observed proper drainage plan and 65 percent of their walls are located nearer to their septic tank and 55 percent are located to floodable waterways and swampy areas. The structures are non-compliant with the building permit issuance. There were 200 structures were built within a radius of 15 meters from the seashore. The structures need to undergo repair because of the appearance of deteriorating construction materials. The results of the interview revealed that they have malpractice in the handling of construction materials and proper observation of the construction method.

Behaviour of a Space Inverted Triangular Steel Truss

Behaviour of the inverted triangular truss, which is widely used as a bridge girder, was investigated analytically and experimentally. Cold-formed square hollow cross-sections of steel grade S355J2H with dimensions 80 mm × 4 mm, 90 mm × 4 mm and 40 mm × 4 mm were selected for the top and bottom chords and bracing elements of the truss with 12.56 m span, correspondingly. Five FEM models were developed using software Dlubal RFEM. The main specific feature of the models is the difference in modelling of joint behaviour considering plastic behaviour and stiffness of truss connections. It was shown that the FE model of the truss where the members were modelled by the truss type finite elements and the joints modelled by the shell type ones allows predicting behaviour of the truss with precision of up to 3.9%. It was shown that precision of the suggested FEM model grows 4.36 to 4.62 times in comparison with the traditional FEM models where the members were modelled by the truss finite elements with the pinned and rigid joints in case of plastic joint behaviour. Precision of the suggested FEM model is identical to that of the traditional FEM models regarding the case of elastic joint behaviour.

Lightweight mechanical metamaterials designed using hierarchical truss elements

Rotating unit systems constitute one of the main classes of auxetic metamaterials. In this work, a new design procedure for lightweight auxetic systems based on this deformation mechanism is proposed through the implementation of a hierarchical triangular truss network in place of a full block of material for the rotating component of the system. Using numerical simulations in conjunction with experimental tests on 3D printed prototypes, the mechanical properties of six types of auxetic structures, which include a range of rotating polygons and chiral honeycombs, were analysed under the application of small tensile loads. The results obtained show that there is almost no difference in the Poisson’s ratios obtained from the regular, full structures and the ones made from triangular truss systems despite the latter, in some cases, being 80% lighter than the former. This indicates that these systems could be ideal candidates for implementation in applications requiring lightweight auxetic metamaterial systems such as in the aerospace industry.

Lavr Dmitrievich Proskuryakov at the Imperial Moscow Engineering School (IMES)

It is difficult to overestimate the importance of works, teaching methods and bridge structures for the domestic and world bridge building, designed according to the projects of the outstanding engineer Lavr Dmitrievich Proskuryakov. He was the first to use graph – analytical methods for calculating bridges; developed simple statically determinable triangular truss grid systems, more convenient to manufacture and install; developed a methodology for teaching compromising materials on the basis of three principles: visibility, accessibility, quick wit and much more. L.D. Proskuryakov worked for more than 15 years at IMIU, MIIIPS, MIIT, leaving a rich engineering legacy in the form of: a mechanical laboratory with unique facilities that have been operating to date; a real project of the Moscow Andreevsky bridge in two folios; bridge designs across the Oka – at Murom, Kashira; through the Volkhov, Cheremshanka, etc. Studying the engineering heritage of L.D. Proskuryakov will help him better understand and use this knowledge for work at present.

Raspored ukrućenja, ukrućenje čvorova i veza s krajnjim osloncima čeličnih cevastih lučnih mostova

Three characteristics of steel tubular arch bridges are being discussed. The brace members, connecting the main chord tube to an upper concrete or composite deck can be arranged either as triangular truss members, or as rigid node vertical or slightly sloping frame members. As can be expected, the former arrangement results in lower bending of the arch chord and lower compression near its centre. However, the number of brace tubes for triangular arrangement is twice as much as for the frame system. In addition, the nodes of the truss system necessarily join at least 4 tubes and are of the K-type. The latter are more complicated to design and to fabricate than T-nodes, used in the frame arrangement. Fatigue resistance of welded tubular nodes is rather low. Should the chord diameter be sufficiently large, internal diaphragm stiffeners can be provided, thus increasing considerably the fatigue resistance. Both numerical and experimental research demonstrates that an optimal location of the diaphragms can be found. However, this optimum location does not necessarily correspond to the minimum of stress concentrations. Most springs of steel tubular arch bridges are rigidly connected to a concrete abutment. Generally prestressing bars are used to achieve this. Unfortunate experience has shown that this connection may still be too flexible to prevent axial rotation due to torsion. The alternative of using various connectors has been implemented in few bridges. The torsion resistance of such a connection has been assessed in 3 scaled tests. The results have given more insight into the mechanism of torsion connection and results in experimental values of the torsion stiffness. The preliminary conclusion of this research indicates that stud connectors show larger stiffness than strips, which is a rather unexpected outcome.

An Equivalent Truss Model for In-Plane Nonlinear Analysis of Unreinforced Masonry Walls

According to the importance of seismic evaluation of existing unreinforced masonry (URM) buildings, researchers have been interested in numerical modelling of these types of structures and their components. On the other hand, in seismic performance evaluation and retrofitting codes which are mostly based on Performance Based Seismic Design (PBSD), different analysis methods such as linear and nonlinear, static and dynamic analyses are employed. Therefore, simple equivalent frame models with lower computational cost are very useful for modelling and analysis of unreinforced masonry buildings. In this article, a simple equivalent truss model is proposed for modelling and analysis of an unreinforced masonry wall with sliding shear failure as the governing in-plane failure mode. The model is developed according to an analogy between the internal forces in a triangular truss and the Mohr-Coulomb failure criteria. Then, the proposed model is generalized for modelling and push over analysis of combinations of walls. Finally, the modelling procedure is applied for push over analysis of an unreinforced masonry wall consists of some piers and the push over curve of the wall is determined and discussed.

The assessment of Italian trusses: survey methodology and typical pathologies

ABSTRACTThe triangular truss is the most typical structural frame of Italian historic roofs. Mostly, but not exclusively, used to transfer vertical loads to walls, it has been developed during centuries into different geometrical compositions by using also different wood species and materials.The aim of this article is to describe the most typical features of the Italitan trusses and the survey procedures by using practical examples taken from hundreds of inspected structures. The complete assessment of a roof structure is an interdisciplinary activity, while this article is intended to present the point of view of the wood technologist, only partially considering the structural aspects.The survey is performed on the basis of a step-by-step procedure, with increasing levels of analysis: starting from a general analysis of the structure as a whole to the analysis of the single members and connections, gaining so far more and more detailed information, which can explain the results of the previous level of analysis. The most common pathologies occurring on timber trusses and structures are also described.Finally, before general conclusions, a quick case study, based on a roof structure from the beginning of 19th century, is shown, presenting the principal results obtained.

Finite Element Analysis of Deformation and Stress Situation of Triangular Truss Under Different Loads

In this paper, the two methods for solving finite element problem, theoretical calculation method and ANSYS simulation analysis method, were used to study deformation and stress situation of each node of triangular truss under different distribution loads. The results of theoretical calculation were compared with those of ANSYS simulation, which showed that the counter-acting forces of each node were exactly the same. For the calculation results of the equivalent stiffness constants of each unit could not be accurate, values of each node deformation calculated by theoretical calculation could be error, but the maximum error rate was no more than 3.6%. By the comparison results, conclusion could be made that the results of ANSYS simulation are more intuitive and image, the values are more accurate and reliable, comparing with those of theoretical calculation, the influence of accuracy of equivalent stiffness constant is much more smaller.

Evaluation of the torsional mechanism by analytical solution for a hybrid fiber-reinforced polymer–aluminum triangular deck truss beam

The hybrid fiber-reinforced polymer–aluminum triangular deck truss beam composed of modular structural units has the advantages of lightweight, high-bearing capacity, and faster installation. Although the analysis-oriented studies have been carried out by laboratory tests, numerical simulations, and theoretical analyses, the design-oriented study convenient for the application of the novel structure subjected to pure torsion is still lacking. Based on previous researches, some reasonable assumptions are presented to obtain a simplified analytical model. Analytical solutions of the torsional angle and torsional stiffness for the hybrid triangular deck truss beam subjected to pure torsion are derived. The derivation procedures and formulae are experimentally and numerically calibrated, finding that the formulae can be used to design with a satisfactory accuracy. The accuracy of the torsional stiffness predicted reaches to more than 90%. It is concluded that for the new hybrid triangular deck truss beam, the applied torsional moment is primarily resisted by the bending of its bilateral vierendeel trusses and the torsion of the fiber-reinforced polymer lower chords, which contribute approximately 37% and 62% for the total torsional stiffness, respectively.

Assessing regional sustainable development through an integration of nonlinear principal component analysis and Gram Schmidt orthogonalization

The regional sustainable development level (SDL), sustainability of regional development (SRD) and system coordination (SC) make up the triangular truss of regional sustainable development assessment, but it is debated how should traditional practice best weight and calculate the whole sustainable development system level. The Bohai Rim, covering three provinces and two municipalities in China, lies in a region that is sensitive to profound conflict between socioeconomic development and environment pollution in the process of sustainable development. Considering the defects of traditional models and the multidimensionality of regional sustainability issues, we proposed an integrated model of nonlinear principal component analysis and Gram Schmidt orthogonalization and presented a novel regional sustainable development assessment method and framework from three perspectives for the society–economy–environment system of the Bohai Rim region. The results show that: (a) the integration of nonlinear principal component analysis and Gram Schmidt orthogonalization can well remedy the defects of traditional methods and provide a more objective conceptual framework; (b) the sustainability of regional development and system coordination models graphically demonstrate the essence and connotation of a dynamic sustainable development system; (c) the empirical study demonstrated that the Bohai Rim region has experienced a distinct development period in which the SRD experienced a steady decline and the SDL and SC generally increased; (d) the coordination ability can be improved by a decline in the environmental sustainability, which reveals the importance of environment subsystem optimization; and (e) the weight distribution of variables demonstrates that the most significant factors affecting sustainable development are the indicators from the dimensions of people's standard of living, economic structure and environmental pollution. This study enriches the sustainable development assessment theory and methodology, and lays the foundation for further sustainable development research in the Bohai Rim region.