Software Module Development for the Parametric Generation of Truss Structure Geometry in a Two-Dimensional Setting

This research investigated the reliability of a newly designed steel roof truss system of an industrial building to be constructed in one of the major cities in Nigeria. The probabilistic analysis technique was done with the aid of CalREL, a general-purpose structural reliability analysis software program. The longest span truss element (consisting of 73 members), is the most critical in the system, was selected and first analysed using SAP2000 Advanced 12.0.0 finite element analysis (FEA) software program in order to obtain the forces in the steel truss members; this forms part of the inputs required in CalREL. Four load variations (referred to as load ratios in the study) were tested on the selected truss. The strengths of the truss members and other properties were determined as specified in BS 5950-1: 2000. Limit state equations were derived for the calculation of the probability of failure of the individual members of the truss system. A reliability index as a measure of structural performance and related to the probability of failure was developed for all the elements of the truss. The results showed that compression members displayed a noticeable violation of the ultimate limit state requirement, while tension members showed a negligible violation. Sensitivity factors that reflect the relative importance of the individual variables in the design of roof trusses were also presented. The estimated reliability indices also revealed structural members that require immediate redesign; though they appear satisfactory in the level of deterministic design. A probabilistic approach for the reappraisal of new and existing civil structures is well supported by the findings of this investigation.

With the rapid development of social construction, various structural types and demands are increasing, and truss structure is thus born. People not only pursue safety and stability, but also pay more and more attention to economic efficiency and endeavour to reduce material usage. Therefore, the optimisation of truss design has become an important trend. In this paper, with the help of structural mechanics solver, a truss design is carried out for a real engineering condition and a simple design optimisation is made. The project is analysed and researched according to the three steps of design-calculation-optimisation. With the help of the axial force and bending moment of each member output from the structural mechanics solver, the material dosage is calculated, and the design scheme is constantly improved, from which a brief optimisation method is sought to find a practical and feasible method. The design scheme is divided into the under-bearing type and the combined type, and the optimisation of the two is carried out, and the optimal design scheme is further proposed, and finally a comprehensive comparison is made. It is found through example calculations that material usage can be reduced by reducing spans, using short bars and adopting parallel truss design while ensuring the safety and stability of truss bridges. Especially when designing multi-span truss bridges, the overall material usage is reduced by increasing the use of short members, although the overall number of members will be increased.

In external radiotherapy, the use of missing tissue compensation has been proposed for the improvement of dose distributions resulting from radiation beams entering through oblique or irregular surfaces of the patient. The well-known inconveniences related to conventional compensators justify the investigation of alternative techniques such as the use of dynamic multileaf collimators. The combination of a number of software and hardware modules was necessary for the implementation of dynamic collimation for missing tissue compensation. First, a software module that calculates, with a ray-tracing technique, the missing-tissue deficit from computed tomography scans and generates a desired 2D intensity modulation pattern has been developed. Then a second software module that converts the 2D intensity map to a leaf motion plan for practical delivery with dynamic collimators has been implemented. Finally, the existing primary-scatter separation dose model of the authors' TPS had to be extended to account for the intensity modulation generated by the dynamic MLC. As an example of the 'virtual' compensator technique, the MLC sequence that would compensate an arbitrary patient irregular surface has been calculated. Then, film was used to measure the dose on a plane perpendicular to the beam axis at the specified depth of compensation. A comparison between measured and calculated dose distributions shows that an acceptable accuracy in dose calculations can be achieved. Finally a comparison between uncompensated and dynamically compensated fields demonstrates that the 'virtual' compensator was able to flatten the off-axis dose across a plane perpendicular to the beam axis at the depth of compensation.

Manufacturing errors in the length of members or joint diameters of large truss reflector backup structures may result in unacceptable large distortion errors or member forces. However, it may be possible to accurately measure these length or diameter errors. The present work suggests that a member and joint placement strategy may be used to reduce distortion errors and internal member forces. A member and joint exchange algorithm is used to demonstrate the potential of this approach on several 102-member and 660-member truss reflector structures. It is shown that it is possible to simultaneously reduce the rms of the surface error and the rms of member forces by two orders of magnitude by member and joint exchanges.

Lightweight structures comprise of actual pieces or segments that give the crucial ability to function while weighing less than other possibilities as well. The aerospace industry invented this particular branch of expertise, which is sometimes referred to as lightweight engineering or lightweight construction. This paper focuses on how lightweight structures are developed and applied in the field of structural engineering which is essential to achieving the high standards and breakthroughs of modern science. Comparison is made depending on different types of lightweight materials such as titanium alloys, shape memory alloys, magnesium, aluminum alloys, and wood composites, benefits, and applications of each type of material are discussed. Recent technologies and innovations in the field of lightweight design are performed including deployable and morphing structures, 3D printing, embedded sensors and actuators, and advanced joining technologies. Moreover, research is also being done on these structure types of evolution, uses, and significance, as well as their design techniques and innovations. Truss, tensegrity, pantographic, cable, origami, and sandwich structures are identified by explaining their properties and working mechanisms. The usage of several lightweight structures in the fields of aerospace, robotics, civil engineering, architecture, automotive, and biomedicine is examined in this paper. Additionally, the comparison is made between the application of tensegrity, truss, pantographic, and sandwich structures in aircraft applications in detail, while the importance of shape morphing and deploying of pantographic and origami structures is explained in the field of aerospace and robotics. In addition, different types of bridge structures and architecture are mentioned according to applications of suspension cables, stayed cables truss structures, and tensegrity techniques. Furthermore, the paper covers the improvement of computational and numerical techniques in the analysis and design of lightweight structures including the force method, dynamic relaxation method, and finite element method (FEM), trends in optimization techniques and their applications are included mentioned sequential quadratic programming (SQP) and interior point optimization, with applications on different types of lightweight structures. Also, perspectives and future directions of lightweight design through sustainability and smart construction are taken into account, importance of lightweight design in the form of environment and innovation is clearly supported.

Truss structures are widely employed in the industrialized world. They appear as bridges, towers, roof supports, building exoskeletons or high technology light space structures. This paper investigates the simultaneous size, geometry and topology optimization of real life large truss structures using Genetic Algorithms (GAs) as optimizer and Finite Element Method as analyzer. In general the large truss structures are constructed from the duplication of some basic modules called bays. Thus, the final optimum design may be reached by optimizing the characteristics of the basic bays instead of optimizing the whole structure. Both single and multi-objective functions based on the mass of the structure and the maximum nodal displacement, have been considered as the cost functions. In order to have realistic optimal designs, the cross-sectional areas have been extracted from the standard profiles according to AISC codes and practical conditions are imposed to the bays. The design optimization problem is also constrained by the maximum stress, maximum slenderness ratio and the maximum and minimum cross-sectional area of the truss members. To accommodate all these constraints, two different penalty functions are proposed. The first penalty function considers the normalization of violated constraints with respect to the allowable stress or slenderness ratio. The second penalty function is a constant function, which is used to penalize the violations of the slenderness ratio. Two illustrative examples of realistic planar and space truss structures have been optimized to demonstrate the effectiveness of the proposed methodology.

Ultra-efficient wound composite truss structures

For plane truss structure, starting from the analysis of ideal truss model, the influence of tangential deformation and angular deformation on the secondary internal force of the truss is fully considered through Python program. It is obtained through analysis that: in the ideal truss model, the Pδ second-order effect causes the member to produce tangential deformation and angular deformation, resulting in secondary internal forces. Numerical analysis shows that due to the influence of secondary internal force, the axial force error of ideal truss model can reach 19.731% and the secondary shear force is almost all the members of the truss, and the secondary moment only appears at the support. The research results have important reference value for the engineering design and high-precision internal force analysis of truss structures.

The fundamental theorem of linear algebra establishes a duality between the statics of a pin-jointed truss structure and its kinematics. Graphic statics visualizes the forces in a truss as a reciprocal diagram that is dual to the truss geometry. In this article, we combine these two dualities to provide insights not available from a graphical or algebraic approach alone. We begin by observing that the force diagram of a statically indeterminate truss, although itself typically a kinematically loose structure, must support a self-stress state of its own. Such an “extra” self-stress state is described by the fundamental theorem of linear algebra. We show that the self-stress states of a truss are in a one-to-one correspondence with linkage-mechanism displacements of its reciprocal, and the relative centers of rotation of these mechanism displacements correspond to centers of perspective of a projection of a plane-faced three-dimensional polyhedral mesh. We prove that this polyhedral mesh is exactly the continuum Airy stress function, restricted to describe equilibrium of a truss structure. We use the Airy function to prove James Clerk Maxwell’s conjecture that a two-dimensional truss structure of arbitrary topology has a self-stress state if and only if its geometry is given by the projection of a three-dimensional plane-faced polyhedron. Although a very limited number of engineers have been aware of the relationship between trusses and a polyhedral Airy function, the authors believe that this is the first truly rigorous elucidation. We summarize the properties of this “dual duality,” which has the Airy function at its core, and conclude by showing applications to design of tensegrities, planar panelization of architectural surfaces, and optimization of trusses.

Small-scale physical models have been used to determine the most efficient form of pure compression and tensile structures since the 17th century – and to predict structural behaviour of some full-size structures since the mid-19th century. This paper traces the development of model testing in the design of building structures from its origins in the design of bridges and ship hulls in the 19th century, to the design of gravity and arch dams in the early 20th century, through the early days of designing concrete shell roofs in the 1920s and 1930s, to its most sophisticated use in the 1960s and (in conjunction with computer modelling) the 1970s. The great strength of model testing was, and is, to deal with new types of structures without design codes and even without precedent.

Truss selection design is an important link in both theoretical research and practical engineering problems. The topic of this study is truss selection based on optimization design. Firstly, this paper analyzes the mechanical properties. Then, the material ratios of the three different truss structures are studied by changing the axial force data of the three members using the structural mechanics solver. Finally, through comprehensive analysis and system optimization consideration, the conclusion is drawn that the parallel truss has better performance than the triangular truss and the parabolic-like truss. Through the comparison of three common truss structures and the comprehensive consideration of force analysis, the different advantages and disadvantages of the three trusses are obtained, which provides reference for the selection design of trusses. This paper aims to provide an effective reference for the optimization design of trusses, and also provides inspiration for other professionals to study more types of trusses in the future.

The introduction of steel into Brazilian civil construction in the late 19th and early 20th centuries marked a turning point, with domestic production gaining prominence following the establishment of the National Steel Company (Companhia Siderúrgica Nacional) in 1946. Steel’s high strength and ductility have made it indispensable for large-scale projects, offering execution efficiency and recyclability. However, its high production costs and energy consumption raise environmental concerns, as the steel industry contributes significantly to global CO2 emissions. Within this context, this study investigates the influence of the end vertical member length on steel consumption and the sizing of steel sections in roof trusses. Using the Finite Element Method (FEM) through a computational tool developed in Python, 21 simulations were performed, varying the vertical member length from 0 to 100 cm in a Howe truss with a 24-meter span and a 10% slope in the top chord. The results indicated a 52% reduction in steel mass between the extreme values, highlighting the importance of geometric adjustments to optimize material consumption. Increasing the vertical member length redistributed internal forces, enabling the use of lighter sections. These findings underscore the relevance of optimization in structural design to promote sustainable solutions, reducing resource consumption and the environmental impact of steel constructions.

Earthquakes are known to produce one of the most destructive forces on earth. It has been seen that during past earthquakes many of the building were collapsed. Therefore, realistic method for analysis and design are required. Performance Based Design is the modern approach for earthquake resistant design. It is an attempt to predict the performance of buildings under expected seismic event. It involves the calculation of load and total Seismic weight of building from that the base shear is calculated in different zone. The study is carried out with the help of both manual calculations and ETABS software for a three story building in the campus. Analysis of structure is used to verify the fitness of the structure for use. To perform accurate analysis information such as structural loads, geometry, support condition and material properties should be determined. ETABS is the acronym of extended 3D analysis of building system is software developed by Computers and Structures, Inc. (CSI). ETABS is an engineering software product that can be used to analyze and design multi-story buildings using grid-like geometry, various methods of analysis and solution techniques, considering various load combinations. ETABS can also handle the largest and most complex building models, including a wide range of nonlinear behaviors, making it the tool of choice for structural engineers in the building industry. ETABS can be effectively used in the analysis and design of building structures which might consists of structural members like beams, columns, slabs, shear walls and the like. To perform accurate analysis information such as structural loads, geometry, support condition and material properties should be determined. The results of such an analysis typically include support reactions, stresses and displacements. Advanced structural analysis may examine dynamic response, stability and nonlinear behavior. KEYWORDS: Extended three analysis dimensional system, analysis and comparison, beams, building geometry, material properties

A new method for solving an isotropic, linear, elastic solid structure is presented. Based on the simple knowledge of the mechanics of materials, the model considers a new element called the “Ke” element. This element is a truss, and the solid structure is considered to consist of many such “Ke” elements. Thus the solid structure becomes a truss structure, and the internal forces and displacements of the solid structure can be found by calculating this truss structure. The physical sense of this new method is clear, and it is very simple and wonderful. The paper not only provides a new method for solving a solid structure, but also reveals the mechanical mechanism of a solid body.

One type of structures that implements steel angles as its members is truss system of telecommunication tower. For this structure, reinforcements on tower legs are also needed when antennas and microwaves installation placed on the peak of tower increases in quantity. One type of reinforcement methods commonly used is by increasing areas section capacity, where tower leg consisted of single angle section will be reinforced to be double angle sections. Regarding this case, this research discussed behavior two types of double angle steel section 2L 30.30.3 that were designed identically in area section but vary in length: 103 cm and 83 cm. At the first step, compression member together with tension member was formed to be a truss system, where compression and tension member were met at the joint plate. Schematic loading was implemented by giving tension loading on the joint plate, and this loading was terminated when each specimen reached its failure. Research findings showed that implementing shorter double angle (83 cm) sections, increased compression strength of steel angle section up to 13 %. Significant deformation occurring only on the flange for both of specimens indicated that implementing double angle is effective to prevent lateral-torsional buckling.