Truss Members Research Articles

Yield-line mechanisms and design proposal for endplate connections in rectangular hollow section members in tension

Hollow section members are popular elements in steel constructions, especially when they are mainly loaded by normal forces, like simply supported columns or truss members. The individual hollow section members can be combined by bolted endplate connections. If the bolts are arranged at all four sides of the rectangular hollow section, the design rules for the T-stub model from the widely used Eurocode EN1993–1-8 cannot be applied due to the missing failure mechanisms (yield-line mechanisms) of the whole plate. The presented research deals with this problem. A parameter study on different endplate layouts with and without chamfers has been done using a verified numerical model. The numerical model is based on the discontinuity layout optimization (DLO) method and delivers all the relevant yield-line mechanisms of the plate and bolts. Based on these observed failure mechanisms, a simple and Eurocode conform design proposal has been worked out for endplates with and without chamfers. The obtained resistances from the design proposal and the DLO calculations are within a deviation of approximately 10%.

An Experimental Study on Energy Absorption Capability of Cast and 3D Printed Architected Cement-based Materials

Previous studies have demonstrated that Architected Cement-based Materials (ACMs), which have architected internal configurations at mm-cm scale, can have desired and/or unusual mechanical characteristics that the brittle base material does not possess. 3D Concrete Printing (3DCP) is promising technology to fabricate the complicated geometry of ACMs, but relevant research and development are still scarce. In this study, we fabricated truss-type ACMs with enhanced specific energy absorption capacity by either casting or 3D-printing. The ACM was designed by a generative design framework that integrates reinforcement learning and nonlinear structural analysis. The performances of the ACMs were evaluated by uniaxial compression tests. The cast series showed same trend in the cracking characteristics as the simulation. However, the printed ACM showed significantly lower strength and energy absorption than the simulation result. Unexpected damage localization was observed in the printed ACM, especially around the corners of the truss members where relatively large voids tend to be formed during 3D-printing. The degree and location of these defects can be partly controlled by the printing path, which was not considered in the simulation. Therefore, to realize high-performance ACMs by 3DCP, base material properties, internal geometry, and printing path should be simultaneously considered in the design process.

Experimental behavior of truss‐confined buckling‐restrained braces

AbstractBuckling‐restrained braces (BRBs) can effectively improve the stiffness, strength, and energy dissipation capacity of building structures. The key feature of the proposed truss‐confined BRB (TC‐BRB) is an additional truss confining system attached outside the central steel casing. The truss system is composed of several steel open‐web truss frames, thereby providing the required restraining rigidity and reducing the central casing section size and infilled mortar. The overall self‐weight is decreased compared with a conventional BRB, especially in cases of long‐span and large force capacity BRB applications. This research program was conducted to investigate the hysteresis behavior of the TC‐BRBs in terms of truss member response, buckling resisting ability, and cumulative deformation capacity. Six one‐third‐scale TC‐BRB specimens, each 6.3 m long and with different yield capacities, truss frame shapes and sizes, were tested using cyclically increasing loads with or without an out‐of‐plane end drift. The six specimens eventually failed either from global flexural buckling of the entire restraining system or a tensile fracture of the steel core at a very large axial strain. The experimental results demonstrated that the TC‐BRBs can be designed and fabricated to have a very stable and highly repeatable hysteretic response, meeting the American Institute of Steel Construction acceptance criteria. It provides a valuable database to support the further development of design guidelines for the engineering application of the proposed TC‐BRBs.

Lattice modelling of substandard RC beam-column joints considering localization issues

The strain adjustment for quasi-brittle materials to minimize the mesh size effect and localization issues are investigated by the nonlinear lattice modelling approach for substandard reinforced concrete (RC) beam-column joints (BCJs). The lattice model is generated by implementing the truss analogy for the concrete and reinforcement steel members in RC BCJs. The relevant uniaxial material properties in OpenSees are assigned to the truss members. The reinforcement bond-slip relationship is modelled by zero-length springs attached to steel and concrete elements. The modelling approach is validated by comparing the simulated responses to the experimental behaviour of inadequately detailed RC test specimens. A 3-story 3-bay frame tested with a pseudo-dynamic testing procedure and two substandard RC BCJs tested under quasi-static cyclic loading, one of which contains a slab and an out-of-plane beam, are simulated. To avoid the mesh size effect and localization issues, the strain-based softening function in the uniaxial material property of concrete is adjusted by adopting the crack band approach. Analysis results of the rigid joint model assumption, which does not account for the joint deformation, are also compared with the outcomes of the lattice model. By minimizing the mesh size effect, more realistic results are obtained using the lattice modelling technique with high computational efficiency and less analysis efforts. The model accuracy in reproducing the experimental behaviour and response quantities of prime interest is at a reasonable level for the investigated test specimens.

Behavioural Study of a Bridge using Isotruss Member, Box Section and Circular Tube Sections

It is often necessary to cross a river or any other obstacle where no bridges exist or they have been collapsed due to natural disasters. In general already prefabricated bridge elements will be used. They are mostly made out of light as well transportable and detachable parts from high quality materials which could be fast to build Bridges with different span, width and load capacity. In the present paper behavior and performance of a Bridge, using three different types of truss members, namely Isotruss member, Box section and Circular tube, have been studied. Bridge is modelled and analysed using commercial Finite Element (FE) software. The Bridge is designed for a span of 10.50 m. Live load of 4 KN/m2 and wind load of 51.15 N, 70.34 N and 56.17 N applied as point load on Isotruss, Circular tube and Box section respectively are applied for designing the truss members. For serviceability condition stresses as well as deflections in members have been checked.

On Structural Design of Steel Roof Truss Geometry Used in Factory Shed

Use of steel is steadily increasing all over the world in civil engineering related fields due to its superior material properties like high strength and durability, high ductility, light weight etc. Various types of steel structures become more popular because of their high aesthetic appearance. Among these steel structures, roof trusses are widely used to cover large column free open areas like shopping malls, auditoriums, car parking lots, stadiums as well as factory sheds etc. Design of steel truss members is an important aspect to the practicing civil engineers. Hence this paper aims to study the design and analysis of different types of truss geometries used in a factory shed using commercial well-established software package STAAD Pro V8i. Various types of truss geometries like Pratt truss, Howe truss, Fink truss are considered in the present investigations with different aspect ratios. Besides these truss geometries, portal frame geometry is also taken up here to examine the best suitable geometries which are to be used as roofing units in industrial purposes. The results obtained from the present numerical experimentations are studied meticulously to extract a set of meaningful conclusions regarding the design and optimum choice of steel truss geometry which is used as roofing units in industrial sheds. The practical design guidelines along with the best choice of roof trusses are highlighted in the results and discussions section of this paper.

Weight optimization of truss structures by using genetic algorithms

Lightweight structures, especially trusses, have attracted a tremendous attention due to their extensive applications in the construction of infrastructures. Optimizing the shape and cross-sectional topology of truss members is essential since the truss systems are widely used in engineering routines. These systems form the framework of structures like bridges, steel halls for industry and trade, and towers. For the scope of this research, genetic algorithms were used for weight optimization of truss structures. This paper aims to optimize truss structures for finding optimal cross-sectional area. To optimize the cross-sectional area, all members were selected as design variables, with the structure’s weight being the objective function. The restrictions related to the change of the location of the nodes and the tension in the members were the looked-upon problems, the permissible values of which were determined under the circumstances of the problem. In addition, the resulting optimized model which masses for sizing, shape, and topology or their combinations, were compared.

Experimental testing of aluminum‐core buckling restrained knee braced Truss moment frames for earthquake resistance

AbstractApplication of Buckling Restrained Braces (BRBs) with Truss Moment Frames (TMFs) results in a robust seismic force‐resisting system, herein referred to as Buckling Restrained Knee Braced Truss Moment Frame (BRKB‐TMF), which utilizes the advantages of both BRBs and TMFs. Although steel is commonly used to make the core of BRBs, previous studies have demonstrated the efficacy of annealed aluminum as a preferred core material because of its high ductility and high over‐strength. However, the deformation compatibility of the truss members with the aluminum‐core BRB in BRKB‐TMFs at high drifts is not well studied in the literature. Hence, an experimental study is performed on a scaled sub‐assemblage of a BRKB‐TMF frame designed using the Performance‐Based Plastic Design method. Cyclic tests are performed on 1:3 scale models of aluminum‐core BRB and BRKB‐TMF to evaluate their performance at drifts corresponding to Maximum Considered Earthquake intensity. Also, to further compare the performance of steel and aluminum as suitable BRB core materials, cyclic tests are performed on BRBs with steel and aluminum cores designed using a consistent criterion. The experiments demonstrated the superior performance of aluminum core BRB over steel core BRB. The experimental studies on the BRKB‐TMF concluded that per the design intent, the BRB acted like a fuse for the frame by restricting all the inelastic deformations to itself and the study frame could successfully meet the target drift criteria.

Machine learning for prediction of wind effects on behavior of a historic truss bridge

This paper presents the behavior of a 102-year-old truss bridge under wind loading. To examine the wind-related responses of the historical bridge, state-of-the-art and traditional modeling methodologies are employed: a machine learning approach called random forest and three-dimensional finite element analysis. Upon training and validating these modeling methods using experimental data collected from the field, member-level forces and stresses are predicted in tandem with wind speeds inferred by Weibull distributions. The intensities of the in-situ wind are dominated by the location of sampling, and the degree of partial fixities at the supports of the truss system is found to be insignificant. Compared with quadrantal pressure distributions, uniform pressure distributions better represent the characteristics of wind-induced loadings. The magnitude of stress in the truss members is enveloped by the stress range in line with the occurrence probabilities of the characterized wind speed between 40% and 60%. The uneven wind distributions cause asymmetric displacements at the supports.

Aluminium alloy channel columns: Testing, numerical modelling and design

Aluminium alloys can be employed in a wide range of structural applications offering high strength-to-weight ratio, whilst they can easily be extruded in various shapes. Channel (C-) sections have been increasingly employed as compression members, such as wall studs and chord members of roof trusses in framed residential and commercial buildings. However, relevant studies on their compressive behaviour are quite limited and thus a greater emphasis should be placed on providing a deeper understanding. Towards this direction, this paper examines the structural performance of C-sections under axial compression. An experimental and numerical investigation was performed on 6082-T6 heat-treated aluminium alloy C-section columns. In total, 6 fix-ended stub column tests were executed to examine the cross-sectional compressive behaviour, whilst 8 pin-ended column tests were conducted to study their minor-axis flexural buckling behaviour. The obtained experimental results were utilised to validate the developed finite element models. Subsequently, extensive parametric studies were carried out to generate additional performance data over a broad range of cross-sectional aspect ratios, and cross-sectional and member slendernesses. Both the experimentally and numerically obtained ultimate strengths are utilised to assess the accuracy of Eurocode 9 design provisions, including the flexural buckling curve. On the basis of the experimental and numerical results, a new flexural buckling curve is proposed improving the design accuracy. The applicability of the Direct Strength Method on the design of aluminium alloy C-sections subjected to axial compression is also evaluated resulting in the most accurate and consistent design strength predictions.

EXPERIENCE OF CREATING PRELIMINARY SELF-STRESSED IN COMPRESSED STEEL-REINFORCED CONCRETE ELEMENTS

Problem statement. Compressed steel-reinforced concrete structures work effectively as individual racks or columns of buildings and structures for various functional purposes, and as compressed elements of spatial steel-reinforced concrete structures (for example, compressed truss members). Usually, such structures consist of a steel shell filled with concrete. The creation of the concrete core preliminary compressive stresses allows increasing the overall bearing capacity and reducing the deformability of the specified compressed elements. Purpose of the article is to analyze the existing practical methods of creating preliminary compressive stresses in the concrete core of compressed steel-reinforced concrete structures and to distinguish from them methods of the concrete core self-stressed without the use of special mechanical and force measures. Conclusion. Based on the analysis of existing scientific publications in the indicated direction, it was found that pre-stressed in the concrete core of compressed steel-reinforced concrete elements can be created due to the preliminary compression of the concrete core with jacks in outer steel pipe-shell (in a through shell), cutting outer steel shell with deformation seams into separate sections, installation of a pre- stressed double shell, etc. Preliminary self-stressed in the concrete core are created due to the following measures: use for concrete solution preparation stressed cement or a concrete mixture compaction by centrifugation during the combined structures manufacture. The specified methods of creating preliminary stresses can also be used when strengthening existing steel structures by concreting or inclusion in the steel shell joint operation reinforced concrete columns reinforcement.

Towards the optimal design of support structures for laser powder bed fusion-based metal additive manufacturing via thermal equivalent static loads

In laser powder bed fusion (LPBF)-based metal additive manufacturing, support structures play a crucial role in ensuring part-printability. However, support structures often consume significant amount of material, print-time and post-processing time. Furthermore, the optimal design of these support structures is challenging due to the transient nature of the LPBF process. Consequently, support structures are often sub-optimal, and are designed based on experience. Here, we propose the concept of an aggregate equivalent static load (ESL) for the design of support structures. Starting with a simple transient simulation of the layer-wise LPBF build process, we extract the ESL at the end of each time step. An aggregate ESL is then computed for minimizing the thermal compliance of support structures, subjected to a volume constraint. The ESL concept is demonstrated here using truss-type support structures; however, it is equally applicable for other types of supports. Truss-type supports are generated using a novel greedy algorithm, and then the aggregate ESL strategy is applied to optimize the size of truss members. Numerical experiments are conducted to ascertain the self-consistency of the proposed method. The optimized cross-section areas of truss members are then converted to manufacturable designs, and sample parts are fabricated for validation.

Integral sliding of a 800 T steel roof truss for a cultural and art center building

Lifting of large heavy steel truss is challenging. Collaborative Reporting for Safer Structures UK (CROSS-UK) recently reported the failure of a 40 m long steel truss during lifting operation (Report ID: 1035). The incident was caused by the lack of checking stability and strength of the truss during the large lifting operation. Stress states during construction differ from those in the permanent condition, which should keep track at all stages of construction. This paper presents the integral sliding of a steel roof truss of a culture and art center building. The roof truss has a self-weight of 830 ton and its span is 36 m long. Before starting the integral sliding process, the finite element software Midas Gen was used to simulate the sliding construction process. Based on the site situation and cost consideration, the whole roof truss was divided into three parts and slid into design position in three steps in plan. This plan also was confirmed by the finite element method. The vibrating-wire surface strain gauges were installed on the truss members to measure the stress state of the first part steel members. The measured and numerical simulation results were consistent and showed that the stress state had no relationship with the pushing speeds when using the hydraulics synchronous pushing technology. Therefore, the highest pushing speed was implemented to install parts 2 and 3 of the roof truss. This study shows that using proper numerical simulation method to analyze the stress states of structures during the sliding construction process can offer reasonable decision support for the construction process. The methodology presented in this case study is recommended for construction of large heavy steel truss.

A single step optimization method for topology, size and shape of trusses using hybrid differential evolution and symbiotic organisms search

In this article, a single step optimization approach for topology, size and shape of trusses subjected to multiple static and free vibration constraints is developed. For that aim, a topology pseudo-area variable based on a penalty parameter is discretely assigned by either 10−3 or 1 which represents the absence or attendance of a truss member. This helps to not only dodge the singularity of global stiffness matrix as resolving the equilibrium equation system, but also preserve the intact finite element model structure without unnecessarily and repeatedly done time-consuming performances in finite element analyses. The members’ cross-sectional area serves as discrete/continuous size variables, whilst nodes’ spatial coordinates are considered as continuous shape ones. The structural weight is minimized with multiple restrictions on kinematic stability, stress, displacement, natural frequency and Euler buckling loading. A hybrid differential evolution and symbiotic organisms search is employed as an optimizer and refined to tackle both continuous and discrete variables. Eight well-known examples for simultaneous topology, size and shape optimization of 2D and 3D trusses imposed by multiple static and free vibration constraints are tested to verify the reliability and the robustness of the suggested paradigm. The current method can result in competitive high-quality solutions against other state-of-the-art algorithms in most of the examined examples. In addition, the current approach can be also extended to apply for simultaneous topology, size and shape optimization of large-scale trusses in practice.

Experimental study on seismic behaviour of the outrigger truss-core wall spatial joints with peripheral CFST columns

To understand the feasibility and seismic behaviour of the outrigger truss-core wall joints with peripheral concrete-filled steel tubular (CFST) columns, this paper presented an experimental study on outrigger truss-concrete shear wall joints under quasi-static cyclic loading. Two joint specimens with various details, namely, the length of the shear wall, were tested and intensively compared. The failure mode, load versus displacement hysteretic curve, strain distribution, failure mechanism and the key indexes reflecting the seismic behaviours, i.e., strength degradation, stiffness degradation, ductility and energy dissipation capacity of joints were analysed, respectively. The results show that the failure process of joints can be divided into three stages, namely, stress stages of shear wall and outrigger truss, outrigger truss and concealed column system, and failure stage of truss system, and the energy consumption of joints mainly occurs in the second stage. The failure of the two joints are located at the connection of outrigger truss and concealed column in shear wall. The length of wall has limited influence on the peak bearing capacity of joints, and the concentrated load of chord and web members of outrigger truss is transferred to shear wall through concealed column connection. The reasonable transition of stiffness of the connection between the shear wall and the outrigger truss should be adopted in the joint design, and the increase of the distance from the concealed column to the edge of the shear wall is beneficial to improve the mechanical performance and ductility of joints. The average ductility factor of two tested joints under the positive and negative loading is 1.67. The average value of the equivalent viscous damping coefficient of tested joints is 0.23, which is 130% higher than that of reinforced concrete joints of 0.1. These indicate that the tested joint exhibits a superior seismic performance and energy dissipation capacity.

Prediction of the local buckling strength and load‐displacement behaviour of SHS and RHS members using Deep Neural Networks (DNN) – Introduction to the Deep Neural Network Direct Stiffness Method (DNN‐DSM)

AbstractThe traditional separation of analysis and verification during the structural design of steel structures is a known source of conservatism and inaccuracy, as the true deformation/rotation capacity of sections and the redistribution of internal forces in systems remains only vaguely known in many cases. This particularly affects structures made of high‐strength steel, since often sections would need to be classified as slender, thus disallowing the possibility to account for plasticity and stress redistribution. Shell‐element FEM‐models with material nonlinearities and imperfections would be suitable to overcome this separation and increase the accuracy and economy of designs, yet are computationally intensive and impractical for design of whole structures. In this paper, a novel approach for carrying out a computationally economical beam‐element analysis that accounts for the nonlinear load‐displacement behaviour of sections of various local slenderness is presented: the ”DNN‐DSM“, which makes use of machine learning techniques (deep neural networks – DNN) to predict the nonlinear stiffness matrix terms in a beam‐element formulation for implementation in the Direct Stiffness Method. Based on trained DNN models from an extensive pool of nonlinear (GMNIA) shell element results. The motivation, general features, and first implementations of this method in the sense of a ”proof‐of‐concept“, for the case of hollow‐section truss members, are presented in the paper, as well as an outlook on the method's on‐going, full implementation.

Fatigue Performance of Overhead Truss Sign Structure Coupler Connections

Nearly all aluminum overhead truss sign structures (OHTSSs) in Kansas constructed before 2015 use an identical type of hot-riveted coupling assembly to provide connections between vertical poles and horizontal truss members. Although many of the connections have been in service for 30 to 40 years, no research has been conducted to determine their fatigue performance. This paper presents a study aimed at characterizing the fatigue performance of the coupler connections. The study includes a series of finite-element (FE) analyses and 24 experimental fatigue tests. The FE analyses were used to determine design-level fatigue demands on the coupler connections and to provide information for designing the experimental setups used in this test program. Four sign structures with three connection properties and six loading modes were modeled. The experimental tests were conducted to characterize the fatigue performance of the connection. Tests were conducted for three loading modes with respect to the load on the rivet connecting the two interior half-couplers: (1) tension, (2) vertical shear, and (3) horizontal shear. Results indicated that when loaded below 10 Ksi (68.9 MPa), the connection can be classified as a Category E′ based on stress in the rivet. The FE analyses and test results indicated that fatigue failures are unlikely to occur in the coupler connections used in OHTSSs. In addition, two used coupler assemblies from OHTSSs taken out of service were also tested and the failure surfaces were examined under a microscope. No reliable evidence of preexisting cracks was found.

Practice-Accessible Methodology for Nonlinear Refined Analysis of Gusset Plate Connections for Steel Truss Bridges

A new approach is proposed for estimating structural capacity of gusset plate connections of steel truss bridges. The approach involves nonlinear refined analysis of a truss model, consisting of a single truss made of shell elements for two gusset plates at a subject connection and frame elements for truss members. Connectors (bolts or rivets) are excluded from the proposed model in order to simplify the model, with the knowledge that their associated failure modes can be addressed by simplified design calculations. Only yielding and buckling failure modes of gusset plates are considered. The new approach is calibrated by comparison with laboratory test data from NCHRP Project 12-84. The primary intent of this paper’s approach is to reduce the complexity of the refined analysis developed under this National Cooperation Highway Research Program project and make it more user-friendly to load rating engineers seeking accurate estimation of gusset plate capacity. Further, an imperfection sensitivity curve characterizing reduction in capacity as a function of lateral imperfection (gusset plate out-of-flatness) in gusset plate geometry is introduced as an added tool for the load rating engineer, providing more confidence in capacity estimation. Based on a limited case study, the proposed refined analysis provides an estimate of gusset plate capacity that is approximately equal to capacity calculated by the truncated Whitmore method of the AASHTO Manual for Bridge Evaluation (2018). In other words, the proposed approach validates the truncated Whitmore method as compared to the more conservative partial shear method of the AASHTO Manual.

Improving brace member seismic performance with amplified-deformation lever-armed dampers

This study focused on the development and validation of a novel brace design that incorporated a hinged truss member and a set of lever-armed damper (LAD), namely LAD-Brace, for structural performance enhancement. The lever-armed damper was designed with adequate rotation mechanism to generate amplified-deformation and uniform yield zones in the tapered energy dissipation plate for efficient energy dissipation. A series of cyclic loads and constant peak amplitude tests were conducted on LAD-Braces with various geometries in the energy dissipation plates. Analytical expressions for yield strength estimation were derived and effectively validated by the test results. Cyclic load test results showed that adequate strength, effective equivalent viscous damping and significant energy dissipation were simultaneously achieved which justified the design applicability for earthquake-resistant purposes. Investigation through constant peak amplitude tests revealed that LAD-Braces, when designed with adequate geometries, possessed further seismic resilience after experiencing major earthquake excitation, thus validated the proposed design effectiveness and robustness.

Bio-Inspired Algorithms for Optimal Design of Trusses

Trusses are one of the major civil engineering structural articulations that are studied for optimized design. However, application of bio-inspired algorithms for the design of planar trusses is found to be scanty. In this paper, four bio-inspired algorithms namely, Elitism based genetic algorithm (EBGA), Ant colony optimization (ACO), Artificial honey bee optimization (AHBO), and Particle swarm optimization (PSO) algorithms have been implemented for the optimization of size of the members of planar trusses. For this purpose, 4-planar trusses have been considered. The results show that the said algorithms vary marginally as far as the optimized weights are concerned. However, the differences are seen in terms of number of iterations required for convergence and standard deviation of weights. In this context, PSO and EBGA, converged quickly for all the four examples considered. Both the algorithms also showed lower values of standard deviation with respect to the optimized overall weight of the trusses.