Triangular Truss Research Articles

Experimental and theoretical study of the torsional mechanism of a hybrid FRP-aluminum triangular deck-truss structure

This paper investigates the torsional mechanism of a hybrid FRP-aluminum triangular deck-truss structure composed of modular structural units. A pure torsion test was conducted on a 6-m cantilever specimen to characterize the structural responses. Based on the experimental results and structural layout, a simplified analytical model is established to predict the torsional stiffness of the hybrid triangular deck-truss structure. The derivation procedures and formulae are experimentally calibrated, finding that the formulae can be conveniently used with satisfactory accuracy. It is ultimately confirmed that the torsional center of the entire triangular truss collocates with the center of the orthotropic deck. The external torsional moment is primarily resisted by the FRP lower chords and the aluminum longitudinal beams, particularly for the FRP lower chords which should be given a great consideration in the torsion design.

Experimental study of concrete-filled multiplanar circular hollow section tubular trusses

This paper presents an experimental study on concrete-filled multiplanar tubular trusses made of circular hollow section (CHS) members. A total of four types of concrete-filled multiplanar tubular trusses including Triangular truss (TT), Inverse-Triangular truss (IT), Square truss (ST) and Trapezoid truss (TZ) were tested under static loading. The failure mode, load carrying capacity, overall deflection and strain intensity of all specimens are reported. The effects of top and bottom chord members, straight and diagonal brace members and lateral bracings on the load carrying capacity, flexural rigidity and ductility of all specimens were also investigated. The typical failure modes observed from the tests include the local buckling of straight brace members, the surface plasticity and shear failure of the bottom chord members, the weld fracture around tubular joints at the bottom chord members, and the end support failure of the top chord member. The load carrying capacity, flexural rigidity and ductility of different types of multiplanar tubular trusses made of identical CHS members are quite different due to the remarkable changes of the mechanical behaviour of CHS members. On the other hand, the lateral bracings play different roles under different load levels in enhancing the load carrying capacity of different types of multiplanar tubular trusses. It is demonstrated from the comparison that the Inverse-Triangular truss (IT) has optimum flexural rigidity, ductility and efficiency in practice.

Structural performance of a hybrid FRP-aluminum modular triangular Truss system subjected to various loading conditions.

A novel hybrid FRP-aluminum truss system has been employed in a two-rut modular bridge superstructure composed of twin inverted triangular trusses. The actual flexural behavior of a one-rut truss has been previously investigated under the on-axis loading test; however, the structural performance of the one-rut truss subjected to an off-axis load is still not fully understood. In this paper, a geometrical linear finite element model is introduced and validated by the on-axis loading test; the structural performance of the one-rut truss subjected to off-axis load was numerically obtained; the dissimilarities of the structural performance between the two different loading cases are investigated in detail. The results indicated that (1) the structural behavior of the off-axis load differs from that of the on-axis load, and the off-axis load is the critical loading condition controlling the structural performance of the triangular truss; (2) under the off-axis load, the FRP trussed members and connectors bear certain out-of-plane bending moments and are subjected to a complicated stress state; and (3) the stress state of these members does not match that of the initial design, and optimization for the redesign of these members is needed, especially for the pretightened teeth connectors.

ANP Model for Evaluation of False-work Systems for Cast-in-place Cantilever Bridges

The terrain of Taiwan is characterized by large areas of mountains, while lands in urban areas have become increasingly difficult to acquire for developing infrastructures. To reduce environmental impacts and to improve traffic conditions, highway projects have adopted more and more bridges over the years and many advanced bridge construction methods have been introduced. In terms of construction of bridge superstructures, the cast-in-place cantilever method has seen wider use with many successful examples. This study investigated the false-work systems that may be selected for use in implementing the cast-in-place cantilever method in Taiwan, with the objective of developing a model for evaluating possible options. Based on a review of related researches, an evaluation framework for the false-work systems has been proposed first, which consists of six factors: system controllability, structural stability, initial cost, operating cost, segment cycle time, and closing segment construction time that are categorized into three aspects: reliability, cost, and speed. Because of the interdependencies among the factors, the model uses the analytic network process (ANP) to produce the weights of the factors and the ratings of the options in given project conditions. An illustrative example is provided, in which three false-work systems considered for a hypothetical box-girder bridge project are evaluated. The rankings of the options obtained for the example from best to worst were triangular truss, diamond truss, and suspension truss. Practitioners may use the model as a decision aid in evaluating and selecting false-work systems for the cast-in-place cantilever method for construction of bridge superstructures.

Multi-parameter optimization of lightweight composite triangular truss structure based on response surface methodology

A multi-parameter optimization approach for a lightweight FRP composite triangular truss under nonlinear structural response constraints is presented in this paper. The composite truss exhibited bilinear behavior under three-point bending which was observed by both experimental and numerical investigation. Sensitivity analysis was conducted to evaluate the effects of geometric parameters on the flexural performance of the composite truss. A response surface, developed from a finite element analysis, was employed to replicate the outputs of nonlinear structural responses with respect to four key geometric parameters. Gradient-based and Genetic Algorithm optimization processes were selected and implemented from the MATLAB Optimization Toolbox. Final adjustments to the optimal design, obtained using MATLAB, were made according to the results of sensitivity analysis. The results show that significant improvement in terms of weight saving were achieved by adopting the proposed optimization design procedure.

Analysis of Two Cross Arm of Reactive Powder Concrete Pole Design with Structure Materials in Civil Engineering

SAP2000 structural analysis software is used to designed two of 500kV partially prestressed reactive powder concrete pole cross arm; moreover, poles of the two cross arm program have been compared. The results show that the triangular truss cross arm has good mechanical properties, improving the main mate’rial of the stress state, the pole reduced height 10m, by the analysis of the structure shows, this cross arm has higher reliability under the operating conditions, which can be used in 500kV transmission line; from economic and technical performance, the pole cost of this program is greatly reduced, while speeding up the construction progress and improving the comprehensive benefits of the poles in the transmission line.

Composite Truss Bridges: new trends, design and research

AbstractDevelopments and new trends in composite truss bridges are reviewed, and recent designs are presented for road and railway bridges. The structural scheme may range from a continuous truss girder to a cable‐stayed bridge with a double deck for both road and rail traffic.Composite decks with 3D tubular triangular trusses for road bridges are discussed; design issues are outlined and some results for the elastoplastic redistribution of internal forces at ULS, based on recent numerical and experimental research studies, are presented.Recent designs of skew semi‐through composite trusses, for High Speed Railway, are reported in what concerns the dynamic behaviour under traffic loading and the stability of the compressed chord. The Base Case Design of a cable‐stayed bridge, 540 m long main span, with a double composite truss deck, for the new railroad crossing of the Tagus River in Lisbon, is discussed.

Equivalent Elastic Constants of Truss Core Sandwich Plates

A plate structure of a triangular truss core sandwiched by two panels is treated as an equivalent homogeneous laminated plate by obtaining equivalent anisotropic elastic constants. The equivalent elastic constants are obtained by considering generalized Hook’s law of a three dimensional elastic body with no a priori assumption and the equilibrium of a segment deformed by bending moments. To verify the accuracy of the equivalent elastic constants, a linear static analysis of sandwiched aluminum plates subjected to lateral pressure is carried out. The results of the finite element analysis applied to the equivalent laminated plates are compared with those of a NASTRAN analysis of the original structural layouts. The results are also compared with a closed-form solution, which simplifies the sandwiched plate as a homogeneous orthotropic thick plate continuum (Lok and Cheng, 2000, “Elastic Stiffness Properties and Behavior of Truss-Core Sandwich Panel,” J. Struct. Eng., 126(5), pp. 552–559). As the maximum deflections of three analyses agreed closely, one has assurance that the method of the homogeneous plate with equivalent elastic constants is valid and useful.

A Shape‐Morphing Ceramic Composite for Variable Geometry Scramjet Inlets

The development of ceramic composites with three‐dimensional fiber reinforcement architectures formed by textile methods has led to the potential for active shape‐morphing surfaces that can operate in high temperature and variable pressure environments. This technology is of particular interest for hypersonic applications, where SCRAM jet engines require variable inlet geometry to achieve efficient flight over realistic flight profiles and variable flight conditions. The experiments reported here show that significant shape morphing can be achieved and good control of the shape sustained even in the presence of large temperature and pressure gradients. Experiments were carried out using a subscale morphing hypersonic inlet with rectangular cross‐section in a Mach 8 wind tunnel facility with a total temperature of 800 K. The upper surface of the inlet consisted of a C–SiC composite plate (0.7 mm thick, 37.5 cm long, and 11 cm wide) connected to five actuators through a triangular truss support structure. The lower surface was a flat plate instrumented with an array of pressure taps along the flow centerline. As the shape varied, the surface contour was reliably controlled for high efficiency, low loss compression. A factor of six inlet area ratio variation was achieved and good agreement with model predictions was observed.

Some Observations Regarding Stochasticity of Dynamic Response of 2D Disordered Brittle Lattices

It had been long recognized that the tensile strength of brittle materials increases with increase of the loading rate. In the present article, a statistical approach to rupture of a disordered 2D triangular truss lattice consisting of fragile nonlinear springs is attempted in hope to elucidate some generic effects of structural and geometrical disorder on the tensile strength and the (stress-peak and post-peak) damage energy rates. The simulation results reveal increase of the mean and decrease of the standard deviation of the macroscopic tensile strength with increase of the structural and geometrical order till the ‘theoretical strength’ saturation. At the same time, the increase in lattice disorder results in increase of the mean and standard deviation of the stress-peak damage energy rate, followed by the decrease of the same in the softening regime.

EXPERIMENTAL STUDY ON THE ROOF-STRUCTURE OF “HORYUJI-KONDO”

The oldest wooden temple in the world “Horyuji-Kondo” consists of a framework of interlocking members; cloud-shaped bracket sets, diagonal tail rafters, horizontal brackets and wooden dowels which construct triangular trusses together. The axial force effect has not been cleared yet, but the tension of tail rafters should be supported by horizontal pre-tensioned arms like a whole space-frame. We try to analize the structural system of the ancient temple 1300 years ago by the experiments of 1/2 scaled models.

Well-posedness and exponential stability of a thermoelastic Joint–Leg–Beam system with Robin boundary conditions

An important class of proposed large space structures features a triangular truss backbone. In this paper we study thermomechanical behavior of a truss component; namely, a triangular frame consisting of two thin-walled circular beams connected through a joint. Transverse and axial mechanical motions of the beams are coupled though a mechanical joint. The nature of the external solar load suggests a decomposition of the temperature fields in the beams leading to two heat equations for each beam. One of these fields models the circumferential average temperature and is coupled to axial motions of the beam, while the second field accounts for a temperature gradient across the beam and is coupled to beam bending. The resulting system of partial and ordinary differential equations formally describes the coupled thermomechanical behavior of the joint–beam system. The main work is in developing an appropriate state-space form and then using semigroup theory to establish well-posedness and exponential stability.

Truss Beam with Tendon Diagonals: Mechanics and Designs

A straightforward means to reduce the mass of some truss beams is to replace rigid diagonals with prestressed tendons. Pretension, however, aggravates the deployment challenge, loads the remaining struts, as well as affects the design in more subtle ways. The present paper helps navigating this trade-off by reviewing the mechanics of and some design considerations for a regular triangular truss beam with three lacing options: one redundant and two statically determinate combinations of tendon diagonals with diagonal pretensioning. Considered are member vibration, the interaction of mission loads with parasitic forces (redundant design), truss face accuracy and longeron compression eccentricity effects (determinate designs), as well as stiffness issues. A scrutiny of shear effects reveals that some shear compliance formulas regularly used for truss beam Timoshenko continuum modeling are incorrect.

Cubiertas de madera de las iglesias fernandinas de Córdoba

After Cordoba´s reconquest by king Saint Ferdinand in 1236, Cordoba town was urbanized into fourteen districts, or parishes. Social, administrative and religious center of these districts was situated in fourteen churchs. These buildings are named ferdinand churchs’, because they were constructed by king Saint Ferdinand. A similar architectural pattern was followed in construction of these churchs. This pattern is characterized by reiteration of fixed arquitectural elements, like roof structure made of timber, in central and lateral church-bodies. Roof timber structure used in lateral church-bodies was tilted frame, while triangular truss with butress and anchor was used in central church-body. Some of these churchs have been destroyed or greatly transformed. However, in survivor ferdinand churchs’ is posible to study the roof timber structure, a singular cover system that was originated by union of medieval constructive and mussulman ornamental technics. The aim of this article is to describe the roof timber structure of cordovan ferdinand churchs’ as well as to research into their origin.

Optimal Design of a Novel High Authority SMA Actuator

Statically determinate structures with truss elements have simple mechanisms, light weight, and high rigidity. Based on the flexural truss structure, a high authority actuator comprising a triangular truss core, a facesheet, and actuation elements is proposed. It is clamped at one end and free at the other. The actuation element comprises a one-way shape memory alloy ( SMA ) wire and a helical spring. The elements are activated by heating, and recovered by the force supplied from the compressed spring and/or the external force once the SMA wire is cooled. A design that integrates this basic unit into a high authority flexural system has been analyzed. The actuation force and strain of SMA actuation elements are obtained by solving a coupled problem that combines a thermomechanical constitutive model of SMAs, heat conduction equation, and the spring response. An optimization procedure has been devised and used to determine the preferred designs by determining the minimum weight. The design is subjected to multiple linear/nonlinear constraints: (i) the specified minimum authority (product of end displacement and dead weight to be lifted); (ii) the upper limit for the power consumption; (iii) no structural failures such as face/core yielding and face/core buckling; and (iv) the requirements for the optimal design of the compression spring.

The Stringer System — A Truss Model of Membrane Shells for Analysis and Design of Boundary Conditions

This paper deals with the problem: What sort of boundary conditions are to be prescribed on the edge of a shell that is to be in a statically determinate membrane state? Triangulated single layer trusses have been suggested as a model for membrane shells by (Calladine 1983) and have been investigated by (Szabo and Tarnai 1992). However, these efforts have not solved the problem completely. The paper presents a triangular single layer truss system – the stringer system – which differs from the above mentioned models in two ways: the systematic topology makes it relatively simple to control whether or not the system is statically and geometrically/kinematically determinate, the geometry corresponds to the curvature of the considered surface and ensures that the system can be applied as a valid static and geometric model for the membrane shell. In most cases, the stringer system regarded as a static model of membrane shells leads to the same results as the theory of partial differential equations, as investigated by (Tarnai 1980a, 1981, 1983). However, some new boundary conditions for shells with positive and zero Gaussian curvature have been found and the types of supports and the connection between statical and geometrical determinacy have been further generalised. The paper is based on parts of the Ph.D. Thesis by (Almegaard 2003).

Optimization of Ring Trusses for Antenna Structures Using Line Geometry

Two types of trusses were optimized using the simple, yet powerful, mathematical technique of employing line geometry as defined by the mathematicians Plucker and Grassmann. The key benefit to this design methodology is simplicity. Multiple-node designs were analyzed, with particular focus placed on the triangular truss. The methodology is based on a geometric stability criterion called the quality index. This approach allowed for a simple equation to be created that identifies the optimal geometry based on the exterior angles and the number of sides. Trusses with single and double connecting points are considered using the quality index. An example of a double connection truss is the triangular truss. In this case, each node (either on the top or the base) has two structural elements connecting to the other nodes. It is shown that there are optimal design criteria for the upper, lower, and separation dimensions. These optimal geometric designs yield conical trusses. Further consideration of the 3-3 truss produced a closed-form solution. This equation holds significant potential for truss designs, providing a clear comparison between single and double connections.

The Antrenas Tubular Arch Bridge, France

For the Antrenas interchange, the architects originally proposed a concrete arch bridge, with no intermediate supports at this relatively open and visible location. When the project was presented to SETRA, the French National Highway and Road Department, an alternative arch solution was proposed by the consulting engineer. The alternative was based on a previous, unrealized design for an arch made of concrete-filled steel pipes with a prestressed concrete deck slab; the slab being connected to the arch by a triangular spatial steel truss. One of the goals of the design was to eliminate vertical supports between abutments and arch. A polygonal arch was selected since the thrust in a circular arch is only marginally balanced by the weight of the tube. Even when filled with concrete, its self-weight would have only balanced one-tenth of the radial force generated by the arch thrust.

Extending the fatigue life of multi-layer metal joints: Finnev, J.M. and Evans, R.L. Fatigue Fract. Eng. Mater. Struct. (1995) 18 (11), 1231–1247

This paper presents an experimental study on concrete-filled multiplanar tubular trusses made of circular hollow section (CHS) members. A total of four types of concrete-filled multiplanar tubular trusses including Triangular truss (TT), Inverse-Triangular truss (IT), Square truss (ST) and Trapezoid truss (TZ) were tested under static loading. The failure mode, load carrying capacity, overall deflection and strain intensity of all specimens are reported. The effects of top and bottom chord members, straight and diagonal brace members and lateral bracings on the load carrying capacity, flexural rigidity and ductility of all specimens were also investigated. The typical failure modes observed from the tests include the local buckling of straight brace members, the surface plasticity and shear failure of the bottom chord members, the weld fracture around tubular joints at the bottom chord members, and the end support failure of the top chord member. The load carrying capacity, flexural rigidity and ductility of different types of multiplanar tubular trusses made of identical CHS members are quite different due to the remarkable changes of the mechanical behaviour of CHS members. On the other hand, the lateral bracings play different roles under different load levels in enhancing the load carrying capacity of different types of multiplanar tubular trusses. It is demonstrated from the comparison that the Inverse-Triangular truss (IT) has optimum flexural rigidity, ductility and efficiency in practice.

The dynamic behavior of a three-member plane truss with and without cracks

The response of a three-member plane truss with and without cracks to impact vibration is being experimentally investigated. The impact location is varied and the results are being analyzed. It is expected that the presence of a crack would affect the response pattern. The crack will be introduced in that member which has the maximum probability of being cracked in a truss under externally loaded conditions. The crack will then be modeled and the vibration response predicted using finite element analysis. The results obtained from this analysis will then be compared with the experimental results. The purpose of this work is to understand the response pattern for a triangular truss which could be considered as the building block for more complicated trusses found in bridges and other structures. [Work supported by NSF Grant No. MSS-9024224.]