Truss Members Research Articles

A Novel Nonlinear Link Element for Direct Second-Order Analysis of Trusses Assembled by Weak Shear Stiffness Members

The transverse shear effect and initial imperfection have significant influence on the post-buckling performance of weak shear stiffness struts such as pultruded fiber reinforced polyester (FRP) members and lattice column. A novel nonlinear link (NNL) element was proposed to perform direct second-order analysis of trusses assembled by such members. Adopting the Engesser approach to account for shear deformability, the expressions of transverse deflection under tensile and compressive load were obtained respectively. Taking the linear tension-compression deformation and bowing effect into account, the correction coefficients of axial stiffness for FRP truss member under tension and compression were obtained. Combined with ANSYS UPFs -user programmable features, the user-defined NNL element was established. Both pultruded FRP profiles and lattice column were modeled separately by standard commercial elements and the proposed NNL element. The comparison of the obtained results verified the convenience of the NNL element in modeling and computing. Moreover, the NNL element was adopted to model and calculate two FRP plane truss structures, and the calculation result was compared with test result. It demonstrated that the NNL element can accurately predict structural stiffness change and change points during successive buckling of certain truss members, showing the promising usage of NNL element in structural design of other FRP truss structures.

Member Sizing Optimization of Large Scale Steel Space Trusses Using a Symbiotic Organisms Search Algorithm

A systematic approach of optimization is needed to achieve an optimal design of large and complex truss structures. In the last three decades, several researchers have developed and applied various metaheuristic optimization methods to the design of truss structures. This paper investigates a new metaheuristic algorithm called symbiotic organisms search (SOS) for member sizing optimization of relatively large steel trusses. The case studies include a 120-bar dome truss and a 942-bar tower truss. The structural analyses are carried out using the standard finite element method. The profiles of the truss members are circular hollow structural sections selected from a set of the American Institute of Steel Construction standard profiles. The design results using the SOS are then compared to those obtained using other metaheuristic methods, namely the particle swarm optimization, differential evolution, and teaching-learning-based optimization. The comparison shows the superior performance of the SOS in terms of the optimal solution, consistency, and convergence. Thus, the SOS is a good alternative for optimizing the design of steel truss structures in real engineering practice.

Establishing the Optimal Density of the Michell Truss Members.

Topology optimization is a dynamically developing area of industrial engineering. One of the optimization tasks is to create new part shapes, while maintaining the highest possible stiffness and reliability and minimizing weight. Thanks to computer technology and 3D printers, this path of development is becoming more and more topical. Two optimization conditions are often used in topology optimization. The first is to achieve the highest possible structure stiffness. The second is to reduce the total weight of the structure. These conditions do not have a direct effect on the number of elements in the resulting structure. This paper proposes a geometric method that modifies topological structures in terms of the number of truss elements but is not based on the optimization conditions. The method is based on natural patterns and further streamlines the optimization strategies used so far. The method’s efficiency is shown on an ideal Michell truss.

A conserving formulation of a simple shear- and torsion-free beam for multibody applications

Many engineering fields such as aerospace, robotics, and computer graphics, have applications that contain elements amenable to be modeled as slender beams with negligible shear and torsion effects. The literature contains several energy-momentum (EM) formulations for beams based on a nonlinear finite element approach but, to the best of the author’s knowledge, there are not such developments for the finite segment or lumped approach. This work proposes an energy-conserving and symmetry-preserving extension of one of these models recently proposed in the literature; this extension constitutes the main contribution of the paper. The configuration is described by a rotation-free parameterization consisting in inertial Cartesian coordinates of a collection of nodes that defines a chain of articulated truss members. The axial response is derived by from a nonlinear hyperelastic potential and the bending stiffness is represented by another potential defined on overlapped sets composed of two consecutive trusses. The fact that both effects are defined by discrete potentials has an important impact on the simplicity of the EM formulation. The resulting time-integration scheme produces an approximated solution where total mechanical discrete energy and symmetries are exactly preserved, and the numerical stability is enhanced compared to implicit standard methods. Some numerical experiments illustrate the performance of the presented formulation, including some results of well-established beam models from popular commercial software with standard integration.

Numerical analysis of the ground-mounted solar PV panel array mounting systems subjected to basic wind for optimum design

Comprehensive numerical modeling and investigations have been carried out to analyze the effect of wind loads on various solar array mounting frame structures using ANSYS 18 Workbench (Mechanical). Extensive damages of solar arrays and mounting frames have been reported the world over due to high winds. In this study, six array mounting frame types have been considered, subjected to the basic wind of 55 m/s specified for coastal regions of India. India has six basic wind speed zones ranging from 33 m/s to 55 m/s. Many utility-scale solar farms installed in this region are susceptible to high winds. Solar arrays considered of dimension 6 m × 4 m consisting of 12 photo-voltaic (PV) panels each of size 1 m × 2 m, with panel tilt angle varying from 10° to 50°. Wind load subjected to the PV panels in the solar array considered as normal pressure force over the top and bottom surfaces to simulate forward and backward wind direction. Three different materials with their respective mechanical properties, i.e., structural steel channel for mounting truss members, aluminum casing to encapsulate PV panels, and plexiglass sheet for PV panels, were considered and simulated. Wind pressure forces have been determined, using respective net wind pressure coefficients, induced by respective wind speed and tilt angle. Maximum deformation and maximum stresses were determined by modeling and simulation in ANSYS Workbench and compared the results with various array mounting system arrangements for each case of panel tilt angle subjected to both forward and backward wind incidence.

Static and dynamic behaviour of a hybrid PFRP-aluminium space truss girder: Experimental and numerical study

A novel hybrid pultruded fiber reinforced polymer (FRP)-aluminum space truss system was proposed, aiming to be used as pedestrian bridge or platform in marine areas. A large-scale space truss girder substructure was assembled, and the full-scale static and dynamic tests were separately conducted. The girder’s static behaviour was analysed using three-point bending test, and the girder shows satisfactory bending stiffness contributed by the structural form of space truss. To reveal the girder’s dynamic properties, the output-only modal identification method was used. Some unfavorable dynamic properties such as low natural frequency and the torsion mode as the first order mode shape were observed, which is mainly caused by the unique material properties and structural form. Thereafter, a strategy of adding diagonal bracing at the bottom chord plane to improve dynamic performance was proposed. To accurately predicting the static and dynamic properties, the fine line elements (FLE) model simulating all components’ stiffness of the truss member were built. The simple-link-system (SLS) model was used for comparison. Based on FLE model, parametric analysis was conducted to reveal influences of key parameters. Finally, an efficient design strategy was proposed for this novel hybrid system with combined use of SLS and FLE model.

Crosswind aerodynamic characteristics of a stationary interior railway carriage through a long-span truss-girder bridge

This paper investigates the aerodynamics of a stationary model of an interior railway carriage inside a long-span truss-girder bridge in a wind tunnel. Effects of principle parameters of the truss bridge-girder configuration on the aerodynamics were examined, including bridge wind angle of attack (α), truss bridge-girder solidity ratio (Φ, projected area to envelope area ratio), and aspect ratio (B/D, truss bridge-girder width to height ratio). By varying α, the tested pressure distribution of the carriage model was analyzed in terms of the underlying flow physics of the carriage-bridge interaction. Consequently, the schematic flow patterns were inferred and subsequently utilized to expound the variations in the mean and fluctuating aerodynamic force coefficients. The results indicate that qualitatively the aerodynamic interaction of the truss bridge-girder on the carriage model is characterized by the shielding effect caused by upstream truss members, the suppression of underbody vortex-shedding due to the girder lower deck, and the quasi-Reynolds number effect on the upstream carriage shoulder. Compared to the results of the carriage model without the truss bridge-girder, the shielding effect reduces the mean drag force, whereas the suppression of underbody vortex shedding decreases the mean rolling moment and all the fluctuating forces. The quasi-Reynolds number effect surfaces as α varies given that the inflow Reynolds number is held constant, thus altering the aerodynamic forces abruptly. For the variation of the other two truss bridge-girder configuration parameters (Φ and B/D), qualitatively similar carriage-bridge interaction on the carriage aerodynamics was observed, although with some quantitative differences. The imperfect spanwise correlation of sectional aerodynamics was also observed as mostly owing to the shielding effect formed by the diagonal truss members. In addition, the influence of carriage-bridge interaction on the bridge aerodynamics was also examined and briefly discussed.

Experimental Analysis of Cold-Formed Steel C-Sections with the Notch Subjected to Axial Compression

Studies on the use of cold-formed steel (CFS) C-section, which is a civil engineering material, in building and civil engineering work are still on-going. The advantages of the CFS C-section are becoming so interesting that it is often being used as a roof truss system, storage rack, and wall framing. In order to have a roof truss system with a strong, safe, and stable condition, a study on truss member was carried out using the cut-curving process. Before the CFS C-section was curved, the process started by cutting the section in a proper way. A parametric study was conducted to determine the suitability of the cut pattern which recognised as a notch in the section and find out whether or not the notch depth would affect the ultimate load of the CFS C-section column. The study of CFS C-section was separated into two parts; firstly, to investigate the mechanical behaviour of the column in different notch depths and secondly, to investigate the behaviour in different column height with fixed notch depth. The notch width of 3 mm and notch spacing of 100 mm for both parts were fixed. Total specimen for both parts were 15 specimens. The results of the study showed that the reduction of the ultimate load was about 56–65% of the variation of notch depth section when compared with the normal section. Therefore, the ultimate load of the section with the notch decreased when the notch depth increased. In addition, the study illustrated that the reduction of the ultimate load was 64–82% of the variation of column height between 100 mm to 500 mm. Finally, the average percentage of the column height was 72% which can use in the modification of CFS C-section without notch to CFS C-section with notch calculation.

Safety evaluation of truss structures using nested discrete Bayesian networks

Truss structures have been widely adopted for civil structures such as long-span buildings and bridges. An actual truss system is usually statically indeterminate having numerous members and high redundancy. It is practically difficult to evaluate the truss safety through traditional reliability-based approaches in view of complex failure modes and uncertainties. Moreover, monitoring data are generally insufficient in reality due to limited sensors under cost consideration. Therefore, a nested discrete Bayesian network has been developed for safety evaluation of truss structures. A concept of member risk coefficient is first proposed based on the mechanical relationship between load effects and member resistance. According to the coefficients of all members, member risk sequences are found as the basis for establishing the topology of a member-level Bayesian network. Each network node represents a truss member and a nodal variable having three states: elasticity, plasticity, and failure. Two relevant member nodes are connected by a directed edge whose causality strength is expressed by a conditional probability table. Meanwhile, a system-level network topology is established to reflect the effects of member states on the truss system. The system is assigned with a node having two states: safety and failure. The directed edge of each member node directly points to the system node. Then, the two networks are combined to form a nested network topology. By this means, direct topology learning is avoided in order to find rational and concise topologies satisfying the mechanical characteristics of civil structures. After that, the conditional probability tables for the nested network are obtained through parameter learning on complete numerical observation data. The data acquirement procedure takes into account uncertainties by defining the randomness of cross-sectional areas and external loads. With the conditional probability tables, the nested network is ready for use. When new evidence from limited monitored members is input into the nested network, the state probabilities of the other members, as well as the system, are simultaneously updated using exact inference algorithms. The inference ability using insufficient information well accords with the demand of engineering practice. Finally, the proposed method has been successfully verified against both numerical and experimental truss structures. It was found that the network estimations could be further confirmed with more evidence.

Analytical equations for the connectivity matrices and node positions of minimal and extended tensegrity plates

Tensegrity structures are three-dimensional networks of truss members loaded in tension or compression. The location of the end points of the truss members, denoted as the nodes, and the associated node-member connectivity matrices are the fundamental descriptors in the modeling and design of tensegrity structures. This paper presents systematic analytical formulas for such node locations and connectivity matrices for tensegrity plates of two different topologies. The formulas apply to plates of any thickness, diameter, and complexity. As application examples, dynamic simulations demonstrating a strategy for morphing the planar plates toward domes are studied. The presented formulas allow for efficient computations and can be employed in the numerical analysis and design of shape-controllable antennas and mirrors, architectural constructions, and other applications based on tensegrity plate and dome-like structures.

In-situ retrofit strategy for transmission tower structure members using light-weight steel casings

A practical technique to increase the robustness of existing light truss electric power transmission towers by restraining the buckling of their critical members is presented in this paper. Such buckling-critical members are enclosed by a tight-fitting rectangular casing comprised of two identical light gauge steel C- or U-shapes connected using screws. The steel casing was designed to postpone a decrease in the compression load-carrying capacity of the tower truss member by restraining its lateral-torsional and weak-axis buckling. Five full-scale restrained specimens and one unrestrained base-line specimen were manufactured and tested. One of the restrained specimens was loaded cyclically, while the other ones were tested under monotonic compression. Numerical models of the specimens were built by ABAQUS, and the simulation results were found to match the test observations. A parametric study was conducted using the validated numerical model to investigate the effect of the restraining casing thickness on the behavior of the restrained member. It was revealed that a steep drop in the compression capacity of the restrained member could not be substantially postponed when the thickness of the restraining casing was less than half of that of the restrained member legs. Conversely, the compression capacity of the restrained member could approach its yield strength in case that the thickness of restraining casing was set to be larger than 85% of that of the restrained member legs. The outcome of both experimental and numerical investigations demonstrates the feasibility of the proposed buckling restrainers for use in practice to enhance the mechanical robustness of light truss electric power transmission towers.

Analysis of rotational end restraint for cross beams of railway through truss bridges

Cross-beams of modern through truss bridges are connected to truss chord at its nodes and between them. It results in variable rotational end restraint for cross-beams, thus variable bending moment distribution. This feature is captured in three-dimensional modelling of through truss bridge structure. However, for preliminary design or rapid assessment of service load effects such technique of analysis may not be available. So an analytical method of assessment of rotational end restraint for cross-beam of through truss bridges was worked out. Two cases – nodal cross-beam and inter-nodal cross-beam – were analyzed. Flexural and torsional stiffness of truss members, flexural stiffness of deck members and axial stiffness of wind bracing members in the vicinity of the analyzed cross-beam were taken into account. The provision for reduced stiffness of the X-type wind bracing was made. Finally, general formula for assessment of rotational end restraint was given. Rotational end restraints for cross-beams of three railway through truss bridges were assessed basing on the analytical method and the finite element method (three-dimensional beam-element modelling). Results of both methods show good agreement. The analytical method is able to reflect effects of some structural irregularities. On the basis of the obtained results the general values of rotational end restraint for nodal and inter-nodal cross-beams of railway through truss bridges were suggested.

On the investigation of providing space truss roofs with ductility until failure under monotonically increasing vertical loads

The aim of this paper is to investigate the nonlinear behavior of space truss roofs subject to different load accumulation forms considering the effect of initial imperfection and slenderness ratio of the truss members. For this, a typical space truss roof using MERO-connection type with flat double-layer was selected as a sample. 3D model of the roof was developed and analyzed by using OpenSEES. Nonlinear behavior of each typical bar of the space truss roof, which, was mainly composed of particular sub-elements such as a tubular element, bolts, sleeves and spheres was represented by a single truss bar. Axial load-displacement relationship of each single truss bar was obtained from nonlinear analysis performed under reversal cyclic loading. Besides, three different types of load distribution that simulates accumulation of rainwater or drifted snow were taken into account as an external load acting on upper layer of the roof system. Analyses results showed that load carrying capacity of the space truss roofs was susceptible to the form of accumulation and reduces abnormally when the accumulation, in particular, occurred locally. Furthermore, failure mode of the system designed with optimal solution was dominated by buckled truss bars and brittle failure occurred. Also initial imperfection had a negative effect on the members in compression.

Full-Scale Testing and Design of Special Truss Moment Frames for High-Seismic Areas

AbstractThe US design code provisions for steel special truss moment frames (STMFs) were formulated based on research work carried out in the 1990s with double-angle sections as truss members. To p...

Gravity compensation system of mesh antennas for in-orbit prediction of deployment dynamics

Large deployable mesh antennas are central components of high gain satellites that are used for gathering electromagnetic signals. Deploying such antennas in-orbit is a delicate and precise process, and any failure in their unfolding can result in satellite malfunction. Thus, on-ground experiments have been used to attempt to predict the in-orbit deployment performance of mesh antennas. However, Earth's gravitational field presents a great obstacle in achieving this goal, and how best to design a gravity compensation system for the flexible webs of mesh antennas remains unclear despite various proposed gravity compensation techniques. In this paper, we attempt to address this problem via flexible multibody simulations. The results first reveal that, if the webs are not offloaded at all, the weight of the webs causes the driving forces of the motors and the bending moments of the truss members obtained during on-ground tests to deviate from those experienced by the antenna in-orbit. To counteract this problem, two different gravity suspension systems for the webs of mesh antennas were designed and evaluated. In particular, the different numbers and positions of the suspension nodes were investigated. The results show that no matter which of the two proposed designs is adopted, the number and location of suspension nodes should be carefully selected to achieve well-behaved compensation performance. Furthermore, the proposed modeling and analysis methods can also be applied to other flexible mechanical systems requiring gravity compensation.

Topology optimization of truss support systems for a point- supported glass curtain wall based on truss-like continua

Steel truss structures for point-supported glass curtain walls with a web member configuration are presented using topology optimization based on truss-like continua. The initial structure comprises chords and partial web members. The initial design domain, surrounded by the members of the initial structure, is filled with a truss-like continuum, which is used to simulate the distributive web members of a steel truss. The structure members, together with the truss-like continuum, are analysed and calculated under horizontal point forces. The densities and orientations of the truss-like members at every node are taken as design variables and optimized. The members in the truss-like continuum are optimized using the fully stressed criterion. The topology optimization problem of minimum compliance with volume constraints is solved. Thus, an optimal web member configuration that suitably reinforces the lateral stiffness of the structure is obtained.

Phononic band gaps by inertial amplification mechanisms in periodic composite sandwich beam with lattice truss cores

In order to acquire multiple and wider stop bands in periodic sandwich lattice, this work applies the inertial amplification mechanisms to the composite sandwich beam with pyramidal truss cores and presents a theoretical study on the wave propagation characteristics of the proposed sandwich lattice. An analytical model based on the plane wave expansion method and the Galerkin method is developed to investigate the dispersion relation of transverse waves propagating through the sandwich beam, whose validity is verified by the numerical simulations of spatial decaying performance predicted by the finite element method. Numerical results of complex band structures show that the proposed sandwich beam can obtain multiple stop bands and possess much wider bandwidth. Employing the developed model, the effects of varying attached substructure, the layout of truss members and the material damping on the attenuation performance are discussed to show the flexibility and to obtain thorough understanding of the system.

A deep learning-based procedure for estimation of ultimate load carrying of steel trusses using advanced analysis

In the present study, Deep Learning (DL) algorithm or Deep Neural Networks (DNN), one of the most powerful techniques in Machine Learning (ML), is employed for estimation of ultimate load factor of nonlinear inelastic steel truss. Datasets consisting of training and test data are created based on advanced analysis. In datasets, input data are the member cross-sections of the truss members and output data is the ultimate load factor of the whole structure. An example of a planar 39-bar steel truss is studied to demonstrate the efficiency and accuracy of the DL method. Five optimizers such as Adadelta, Adam, Nadam, RMSprop and SGD and five activation functions such as ELU, LeakyReLU, Sigmoid, Softplus, and Tanh are considered. Based on analysis results, it is proven that DL algorithm shows very high accuracy in the regression of the ultimate load factor of the planar 39-bar nonlinear inelastic steel truss. The number of layers can be selected with a small value such as 1, 2 or 3 layers and the number of neurons in each layer can be chosen in the range [Ni, 3Ni] with Ni is the number of input variables of the model. The activation functions ELU and LeakyReLU have better convergence speed of the training process compared to Sigmoid, Softplus and Tanh. The optimizer Adam works well with all activation functions considered and produces better MSE values regarding both training and test data.
 Keywords:
 deep learning; artificial neural networks; nonlinear inelastic analysis; steel truss; machine learning.

Effect of Joint Stiffness on Deformation of a Novel Hybrid FRP–Aluminum Space Truss System

To achieve light weight, high load-carrying capacity, and corrosion resistance, a novel hybrid FRP-aluminum space truss system is proposed in detail. An advanced pretightened teeth connection (PTTC) and its combined joint–aluminum bolt–ball connecting system (ABCS) were designed to interconnect pultruded FRP elements. In view of the significant effect of the ABCS on structural deformation, the axial stiffness properties of the ABCS were first investigated through experimental tests and numerical simulations. Then, in establishing a structural calculation model for the hybrid space truss, a new combined-line-elements solution was proposed to simulate the complex axial stiffness variation in the ABCS, to which the traditional Timoshenko beam element cannot be applied. Beam elements with different cross sections were adopted to simulate the FRP truss member and the PTTC. The structural calculation model was verified with a previously published case. The design of a hangar structure using this hybrid space truss system is discussed here. The preliminary design was made using the traditional simple-link-system model, and a comparative calculation was made with the new combined-line-elements model. The results indicated that the structural design of this unique hybrid system under a flexural moment is stiffness-driven rather than strength-driven owing to the low elastic modulus of the materials. The conventional simple-link-system model ignores actual differences in component stiffness and thus is dangerous for structural design. Based on the discussion, a design strategy for the hybrid space truss system is proposed.

Long-Term Monitoring of Temperature Effect on Horizontal Rotation Angle at Beam Ends of a Railway Steel Truss Bridge

AbstractIn steel truss bridges, some truss members are exposed to solar radiation, while others are shaded by steel decks, which may result in large temperature gradients between truss members and ...