Parallel Chords Research Articles

Parallel Chords: an audio-visual analytics design for parallel coordinates

AbstractOne of the commonly used visualization techniques for multivariate data is the parallel coordinates plot. It provides users with a visual overview of multivariate data and the possibility to interactively explore it. While pattern recognition is a strength of the human visual system, it is also a strength of the auditory system. Inspired by the integration of the visual and auditory perception in everyday life, we introduce an audio-visual analytics design named Parallel Chords combining both visual and auditory displays. Parallel Chords lets users explore multivariate data using both visualization and sonification through the interaction with the axes of a parallel coordinates plot. To illustrate the potential of the design, we present (1) prototypical data patterns where the sonification helps with the identification of correlations, clusters, and outliers, (2) a usage scenario showing the sonification of data from non-adjacent axes, and (3) a controlled experiment on the sensitivity thresholds of participants when distinguishing the strength of correlations. During this controlled experiment, 35 participants used three different display types, the visualization, the sonification, and the combination of these, to identify the strongest out of three correlations. The results show that all three display types enabled the participants to identify the strongest correlation — with visualization resulting in the best sensitivity. The sonification resulted in sensitivities that were independent from the type of displayed correlation, and the combination resulted in increased enjoyability during usage.

On fuzzy labeling of cycle with k-parallel P_s and C_s chords

Fuzzy Labeling is one of the emerging areas in fuzzy graph theory. In this article, fuzzy labeling of cycle with chord related graphs like cycle with parallel chord, cycle with -parallel chord, cycle with -parallel chord are investigated.

The influence of internode geometry on the bearing capacity of parallel chord wood trusses

The influence of two factors, web angle and internode spacing, on the bearing capacity of three different configurations of trusses was investigated. The constitutive model of the bearing capacity of trusses was established which are jointly controlled by web angle and internode spacing. With bearing capacity and stability as calculation indexes, the critical web angle and internode spacing values for three different configurations of trusses were obtained quantitatively, the truss structure was designed by combining web angle and internode spacing, the mid-span displacement was further calculated as a theoretical basis for finite element simulation. A bearing capacity test on truss specimens with Spruce-Pine-Fir (SPF) as the base material was conducted using the obtained results. The relationship between the load displacement of the different geometric configurations of trusses and the main failure modes was determined accordingly. Finally, the constitutive model of bearing capacity was established which is jointly controlled by web angle and internode spacing. It was found that the stability of the bearing capacity of the A-type truss (Warren type with vertical bar) increases with an increase in the web angle, but is relatively unaffected by the web angle compared to other truss types. The bearing capacity of the B-type(Warren type) truss increases as the web angle increases and is markedly affected by the web angle. The bearing capacity of the C-type(Pa type) truss decreases as the web angle increases, but this configuration is less affected by the web angle than the B-type. The influence of internode spacing on the load-carrying capacity of the truss weakens with an increase in the web angle, as well. The constitutive model, which was obtained by theoretical calculation and ABAQUS finite element simulation, is valid within the elastic deformation range but is not applicable beyond the elastic deformation range.

Bending Properties of Parallel Chord Truss with Steel-Web Members

A truss is a structure in which the members are connected and arranged such that they are primarily subjected to axial loading. A truss has the advantage that it can be used for a longer span because the structure distributes the applied force to its members well, and the load is transmitted only in the axial direction of the members. Trusses manufactured using timber have more advantages than those made of other materials. In this study, the properties of parallel chord trusses composed of timber chord and steel-web members were evaluated. We constructed truss specimens with various lengths by using upper and lower chords of 2 × 4 inch spruce-pine-fir lumber and steel-web members manufactured by S and P companies. The specimens were tested in accordance with KS F 2150. The test results showed that the load at the deflection limit and the deflection limit itself increased from L/180 to L/360 regardless of the length of the specimens. For specimens of the same length, the load at the deflection limit increased as the height of the parallel timber chord truss specimens increased from 200 to 300 mm. Successive installations of the steel-web members (SST) showed almost 2 times the load at each deflection limit compared to that of SAT specimens (alternate installation of the steel-web members). When comparing the three load–deflection limits in terms of the manufacturer of the steel-web members, the load at each deflection limit for SST specimens was higher than that for PST specimens.

Effective Lengths of Members in Parallel Chord Trusses Made from Hollow Structural Sections

Effective Lengths of Members in Parallel Chord Trusses Made from Hollow Structural Sections

住宅用流通材による斜材角度を変えた平行弦トラスの研究

The purpose of this study is to create and verify the performance of large-span parallel chord truss as a design case for medium- to large-sized timber structures. In this paper, the authors carried out the bending tests on full-size truss and validated them with elastic analysis models. The experimental results showed that the yielding of the steel used in the joints plasticized the trusses. In addition, the design criteria were satisfied by applying the uniformly distributed load to an analytical model simulating the truss.

Interação entre torção, flexão e cortante em vigas de concreto armado segundo NBR 6118/2014 e AASHTO LRFD 2014

abstract: Reinforced concrete beams are subjected to bending, torsion and shear simultaneously. The interaction of combined loading is complex and demands a unified model for analysis and design. Using the models from NBR 6118/2014 (variable angle truss model with parallel chords) and AASHTO LRFD Bridge Design Specifications 2014 (Modified Compression Field Theory), an algorithm was created, converting the resistance problem into a constrained optimization problem and generating an interaction surface that also displays the active constraints for each degree of interaction. Applying it to three beams previously tested, the experimental data was plotted against the surface obtained by the standards. The procedure and its optimization approach were efficient and effective in predicting the beams’ resistance. Comparison between the interaction surfaces, empirical data and existing literature showed the procedure and the standards were consistent and its application simple and practical.

Influence of mean value of the modulus of elasticity in compression parallel to the grain on the design of timber trusses

The Brazilian standard ABNT NBR 7190 (Associação Brasileira de Normas Técnicas [ABNT], 1997) recommends adopting the mean value of the modulus of elasticity to compression in the direction parallel to the grain (Ec0,m) in the calculation of displacements. The values of wood stiffness vary considerably, and they can generate displacements above the limit (L 200-1, where L is the span) established by the referred standard, which contributes to the appearance of pathologies in the structure. To evaluate the influence of the adoption of Ec0,m in the calculation of displacements, mechanical properties of wood species were obtained experimentally. With the aid of numerical models and experimental values, ten types of trusses were analyzed (Porch, Inclined Chord, Top Inclined Chord, Parallel Chord, Bowstring, Fink, Howe, K Truss, Pratt, Scissor), three spans (5, 10, and 20 m) and two species (Hymenolobium petraum Ducke e Hymenolobium sp). Initially, adopting Ec0,m for all members and performing a linear analysis, the maximum loads for the displacement L 200-1 were determined. Subsequently, experimental stiffness values were randomly assigned to each bar, and the maximum displacements were determined through nonlinear geometric analyses. Based on 1260 numerical simulations, deflections of approximately 17% (span of 5 m), 30% (span of 10 m), and 34% (span of 20 m) were observed to be higher than the result considering Ec0,m. This problem can be overcome by using non-destructive methods in the pre-classification of the structure bars, positioning the elements rationally in the regions of the highest demand.

Optimal depth selection of composite tubular-floor trusses based on cost estimation

The significance of this study initiates from the need to produce a selection guidance on the span range, span-to-depth ratio and scheme of the composite floor truss system to provide optimum performance and cost effectiveness for a particular application area. With this objective a parametric study was designed, based on three parallel chord trusses (Pratt, Howe, and Warren) using Rectangular Hollow Structural Shapes, a constant panel size of 2.5 m, four composite floor European-profiles and a range of load intensities. Hence, the span-to-depth ratios, RS/D, and dead-to-live load ratios, RDL/LL, were ranged from 3 to 27 and 0.84 to 3.22, respectively, for each truss type. The optimization was performed by using the design results of RFEM (2018) software for approximately 675 composite floor trusses with the objective of selecting optimal depth for each truss model. In addition, this paper attempts to introduce a cost function by considering the material, fabrication and painting costs and comparative figures allowing the design to be tailored with a focus on cost reduction. Accordingly, for all truss types, span-to-depth ratio of 9 to 12 with a span range of 7 to 23 m provides the most cost effective solution. Structural steel and the welding process are the two parameters that are found to have the highest impact on total cost.

Analysis of the crack development and shear transfer mechanisms of reinforced concrete beams with low amounts of shear reinforcement

Although a sufficient quantity of shear reinforcement can improve the shear resistance of reinforced concrete beams, the shear failure of beams with a low amount of shear reinforcement is normally characterized by the formation of a single shear crack. In this case, it is not possible to make the basic assumptions inherent in the parallel chord truss analysis or the compression-field approaches, namely, that distributed shears cracks form a pattern of quasi-parallel shear cracks. As an extension of an approach to describing the critical shear crack formation within the critical shear band, this paper presents an analysis of crack development and shear transfer mechanisms in beams with a low amount of shear reinforcement. The starting point for the analysis was the shear cracking state, which was described in the previous stage of the development for beams without shear reinforcement. The shear crack development and shear resisting mechanisms were analyzed using a group of appropriate equilibrium conditions, geometric conditions and constitutive relationships. The proposed method was validated by comparing the predicted shear resistance with the test results for rectangular, simply supported beams subjected to point loads included in the ACI-DAfStb databases. Furthermore, the validated analysis was used to investigate the relative contributions of different shear resisting mechanisms during the shear crack development. Through regression analyses of the concrete contribution and the ultimate crack length, a simplified model for the shear resistance of rectangular beams with a low mount of shear reinforcement was obtained. Predictions using both the analytical and simplified models are in good agreement with the test results, providing suitable tools for the transition from beams without reinforcement to those with high quantities of shear reinforcement.

3-Vertex Friendly Index Set of Graphs

Graph labeling is an assignment of integers to the vertices or the edges, or both, subject to certain conditions. In literature we find several labelings such as graceful, harmonious, binary, friendly, cordial, ternary and many more. A friendly labeling is a binary mapping such that where and represents number of vertices labeled by 1 and 0 respectively. For each edge assign the label , then the function f is cordial labeling of G if and , where and are the number of edges labeled 1 and 0 respectively. A friendly index set of a graph is { runs over all f riendly labeling f of G} and it is denoted by FI(G). A mapping is called ternary vertex labeling and represents the vertex label for . In this article, we extend the concept of ternary vertex labeling to 3-vertex friendly labeling and define 3-vertex friendly index set of graphs. The set runs over all 3 ? vertex f riendly labeling f f or all is referred as 3-vertex friendly index set. In order to achieve , number of vertices are partitioned into such that for all with and la- bel the edge by where . In this paper, we study the 3-vertex friendly index sets of some standard graphs such as complete graph Kn, path Pn, wheel graph Wn, complete bipartite graph Km,n and cycle with parallel chords PCn.

On odd harmonious labelling of even cycles with parallel chords and dragons with parallel chords

Labelling in graph theory is an active area of research due to its wide range of applications. A graph labelling is an assignment of integers to the vertices (or) edges (or) both subject to certain conditions. This paper deals with one such labelling called odd harmonious labelling. A graph G = (V, E) with |V (G)| = p and |E (G)| = q is said to be odd harmonious if there exist an injection f : V (G) → {0, 1, 2, …, 2q – 1} such that the induced function f* : E (G) → {1, 3, 5, …, 2q – 1} defined by f*(uv) = f(u) + f(v) is bijective. In this paper we prove that every even cycle Cn (n ≥ 6) with parallel P3 chords is odd harmonious. We also prove that the disjoint union of two copies of even cycle Cn with parallel P3 chords and the joint sum of two copies of even cycle Cn with parallel P3 chords is odd harmonious. Moreover we show that the chain of even cycles Cn (n ≥ 6) with parallel P3 chords, joining two copies of even cycles Cn by a path and also dragons with parallel chords obtained from every odd cycle Cn (n ≥ 7) after removing two edges from the cycle Cn, dragons with parallel P4 chords obtained from every odd cycle Cn (n ≥ 9) after removing two edges from the cycle Cn are odd harmonious.

On odd harmonious labelling of even cycles with parallel chords and dragons with parallel chords

On odd harmonious labelling of even cycles with parallel chords and dragons with parallel chords

Built-up CFS column with lacings and battens

The built-up columns are generally used in industrial buildings, either as posts for cladding when their buckling length is very long, or as columns supporting a crane girder. The built-up columns are composed usually of two parallel chords interconnected by lacings or battens. In the paper the special type of built-up column will be analysed from Llentab Company. It consists from four parallel chords with cold-formed C cross-sections which are interconnected by lacing in one plane and by battens in four perpendicular planes. Such types of columns are especially convenient for the relatively high light steel halls. Analysis of the behaviour of such column will be performed: a) on the model with smeared equivalent bending and shear stiffness’s using analytical solution, b) on the discrete model using FEM and commercial program ANSYS. The theory of the second order taking into account the initial imperfections and the shear deformations will be employed.

Mathematical formulation of an analytic approach to the stress field in a flattened Brazilian disc

Although more than fifteen years have passed since the flattened Brazilian disc test was introduced, analytic studies on the respective stress field are scarce, mainly due to difficulties related to the shape of its boundary. In this context, an alternative mathematical formulation, providing a full-field solution for the distribution of stresses in the flattened Brazilian disc, is here proposed, based on the configuration of an intact circular disc, under a large number of equal point forces, arranged at equal distances along two symmetric parallel chords of the disc. Considering each point force as the resultant of stresses acting on an eliminated hole, a great number of such forces implies the introduction of a large number of small holes, dividing the uniform disc into three distinct parts; the one between the two chords is to stand as the flattened disc under uniform compression. This particular problem for the uniform disc is here solved with the aid of Muskhelishvili’s complex potential technique, providing a closed-form, full-field solution for the stresses on the as above “truncated” disc, and thus, in a first approximation, on the flattened Brazilian disc. The analysis, apart from highlighting the advantage of the flattened against the classical intact Brazilian disc (regarding the reduction of stress concentration along the disc-loading platen contact region), revealed, also, that the pressure on the flat edges of the flattened disc should be non-uniform in order to better approximate the experimental reality. In this direction, a numerical model was developed, indicating the proper non-uniform distribution of pressure that should be applied along the flat edges of the flattened Brazilian disc, in order for these edges to remain plane after deformation, in accordance to the laboratory implementation of the experiment.

Cycle With Parallel Chords Are Odd Even Graceful

If C_n is a cycle of length n, then the graph cycle with parallel chords is obtained from C_n by adding an “edge “is the graph obtained by attaching a pendant edge at each vertex of the cycle” C_(n.) In this paper we prove that the graphs n-for n≡0,3(mod 4). the graph P_(a,b) obtained by identifying the end points of a internally disjoint paths each of length b, are odd even graceful for odd values of a and b.

Modular frame trusses of buildings

The paper describes space-planning and structural concept in source-efficient buildings that provides multiple functions of the rooms and large-span space.The main load-bearing structures of two adjacent storeys are metal trusses with parallel chords between which (between top and bottom chords) intermediate storeys are designed and the space between trusses is occupied by the free plan storeys. Bottom and top chords of the truss resist together with floor structure forming two-storey steel-reinforced concrete unit. To calculate value of deformation capacity for nodal connection a numerical experiment focused on modelling a part of building from solid finite elements has been performed. The results of performed analysis are the average values of stiffness of nodal interface of solid floor slab on corrugated deck and truss chords for finite elements KE 55 of typical layout (of flat finite elements). The obtained average values of stiffness were introduced into structural design of flat finite elements. Taking into account flexibility of floor slab that supported by middle trusses for the given structural concept leads to decreased span bending moments and increased support bending moments by 25% compared with hinge support of floor.

Experimental and numerical analyses on nonlinear behaviour of wooden parallel chord trusses composed of self-tapping screws

Five different wooden parallel chord trusses were made of Canadian spruce 2 by 4 lumbers. Chord–web nodal points were composed of self-tapping-screws (STS) whose numbers per nodal point and allocations in nodal point were considered as the main experimental parameters which were varied from 2rows-2lines till 2rows-4lines. Load–slip relationships at nodal point were evaluated using the joint specimens made of similar materials. These parallel chord trusses were modeled using a finite element method (FEM) program by taking not only nonlinearity of nodal point joints but also material nonlinearity of chord members using fiber model into consideration. Strength properties of the chord members were deduced via specific gravity of chord member based on the regression equations given by a literature. Static monotonic central point loading tests were conducted on five specimens to investigate nonlinear behaviors of wooden parallel chord trusses. Comparisons between observed results by experiments and computed ones by FEM calculations showed a tendency that material nonlinearity gave less effect on the total nonlinear behaviour of the specimens when joint performance was inferior, on the other hand, as the joint performance increased material nonlinearity gave dominant effect on the total nonlinear behaviour of the specimens.

Geometric optimization of steel trusses with parallel chords

Geometric optimization of steel trusses with parallel chords

Technical Feasibility Study for the Use of Alternative Timber in Latticework for Roofing with Spans between 16 and 26 Meters

Wood, a renewable source material, has been part of the progress of mankind, being widely used in construction for centuries. However, with the passage of time, new construction techniques were being applied, new materials have been rising and, in the meantime, wood was being left out, being labelled as a material with huge incidence of pathologies. That due to its empirical use without any technical knowledge regarding its physical and mechanical properties, which still happens nowadays, being used mainly for temporary purposes. In order to show the technical viability of the use of this material as a structural element, the elaboration of projects with the following characteristics was proposed: buildings with truss structures (parallel chord) type Howe (10° inclination - steel tile); 16, 18, 20, 22, 24 and 26 meters span; side openings types of the building – 1:1, 2:1, 6:1 and open; preservative treatment. Thus, it was determined the ratio of the volume of wood (m³) and the built area (m²) for timbers classes C-20 and C-30, following the NBR 7190:1997 guidelines. With the results, it is possible to assure the real possibility of using wood species C-20 and C-30 as structural material.