Hexagonal Openings Research Articles

Stress concentration in castellated I-beams under transverse bending

In the work on base of calculations by FEM of castellated I-beams the approximate relations for evaluation of stress level and stress concentration factor in vicinity of hexagonal fillet openings under transverse bending are derived. Calculation of simply supported castellated I-beams under action of one concentrated force applied in mid-span and two symmetrically applied forces was performed. Proposed relation for equivalent stress near openings differentiate role of each force factor V and М and allow determine level of stresses in castellated beams in wide diapason of the opening parameters under different length ratio with engineering accuracy. Obtained results were verified with experiment test on steel castellated beam with 4 m length. DOI: http://dx.doi.org/10.5755/j01.mech.22.6.13590

Capabilities of transition metals in retarding the bonding of carbon atoms to minimize dendritic graphene.

The avoidance of growing dendritic graphene on the copper substrate during the chemical vapor deposition process is greatly desired. Here we have identified a mechanism, in which (1) transition metal plates placed inside the copper pockets reduce the majority of active carbon atoms to eventually suppress the graphene growth rate, and (2) transition metals etch graphene C-C bonds along defective edges to grow into zigzag-edge ending domains with higher priorities. Via isotopic labeling of the methane method, we have observed bright-dark-alternating hexagonal-shaped rings, which are shown in Raman mapping images. Under a hydrogen atmosphere, we are capable of acquiring hexagonal openings within graphene domains by means of transition-metal-driven catalytic etching. This methodology may work as a simple and convenient way to determine graphene size and crystal orientation, and may enable the etching of graphene into smooth and ordered zigzag edge nanoribbons without compromising the quality of graphene.

Crystallographically-Oriented Macropores in Multi-Crystalline Zn

In this abstract we report on the electrochemical formation of crystallographically-oriented macropores in multicrystalline Zn sheets. The formation of macropores by electrochemical etching is well-known from silicon and other semiconductors like InP or GaAs as model systems for the growth of crystallographic pores. Besides semiconductors pores have also been formed in specific metals like Al and Ti, where the resulting pore walls turned into metal oxides. The substrate for the growth of crystallographic pores in Zn is a commercially available multicrystalline Zn sheet with a thickness of 0.1 mm and a purity of 99.95 %. The hardness degree is as-rolled. The pores are grown in a self-organized manner without any pre-structuring of the Zn substrate in pulsed-potential process in an adopted aqueous KCl electrolyte. The crystallographic nature of the pores grown is easily detectable due to the multicrystalline Zn substrate, see Fig. 1. Here, pores form pore domains typically in the dimensions of the specific grain they are growing in. Inside a pore domain the neighboring pores grow parallel to each other into the depth - see the inset of Fig.1 - under a defined angle depending on the crystal orientation of the grain. These angles can vary from perpendicular to almost parallel to the sheet surface normal. The pores exhibit a wide diameter distribution from around 100 nm up to several micrometers. This vast diameter range is a direct result of the pulsed-potential etching process causing frequent nucleations of new pores on the Zn surface. The microscale diameter pores originate from potential pulses at the beginning of the etching process. The shape of the pore openings transforms during the etching process. Young pores, i.e. late nucleated pores, typically exhibit a distorted hexagonal pore opening transforming into rhomboidal with continued etching time. This is a direct consequence of the design of the etching process itself, which is separated into a cathodic surface passivation process and an anodic dissolution process. With increasing pore length the pore wall passivation near the pore openings weakens resulting in a change in shape and a broadening of the pore openings. A renucleation of pores from the pore walls is also observed as one of the characteristic features of crystallographic pores found in III-V semiconductors. XRD measurements of the porosified and untreated Zn sample show only peaks that can be assigned to crystalline Zn in its typical hcp crystal structure. The shape of the Zn peaks indicates rather large coherently scattering areas and thus, rather big Zn grain sizes. No additional peaks or amorphous halos appeared in the diffractogram that might be associated with ZnO, etc. EDX elemental mapping performed on the pore walls of pores growing into Zn under a low angle with respect to the sheet surface normal indicates that the pore walls consist of Zn with a native oxide coverage. These Zn pore structures form a mechanical interlocking surface structure that could be employed to solve the common problem of poorly adhering paint layers on Zn plated metal surfaces. Fig.1 SEM top view on the macroporous Zn surface with multiple pore domains, inset: high magnification of single pores inside a pore domain. Figure 1

Optimum Design of Laterally Supported Castellated Beams Using Natural Forest Regeneration Algorithm

In this paper, a new meta-heuristic algorithm called natural forest regeneration is applied for finding the optimal design of castellated beams. These beams have found widespread usage in buildings because of great savings in materials and construction costs. Material economy in combination with aesthetic and architectural design has lead to sections made from standard I-beam with increased cross-sectional height and load-carrying capacity in bending. Here, two common types of web opening beams are considered as design problems: beams with hexagonal openings and beams with circular openings. Also, in this paper, castellated beams are studied with and without filled holes. The new optimization algorithm is used for obtaining the solution of the design problem. For this purpose, the minimum cost is taken as the design objective function, and three benchmark problems are selected from literature to solve by this algorithm. Numerical results show the robustness of the NFR algorithm for optimum design of these beams and prove that the proposed algorithm has good performance. The results have been compared to those reported in literature, and it is observed that using the NFR algorithm leads to the best results in most of the cases. Also, it is concluded that the use of beam with hexagonal opening leads to smaller amount of steel material in unfilled cases, but in filled cases, where the beam span is large, using of beams with circular holes can be a better choice in terms of economy.

Beyond developable

We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications.

Study and Analysis of Connecting Position on the Vibration Characteristics for Beam

This study proposes an investigation into the effect of stiffeners where local stiffness varies on the vibration characteristics of I beams. The main focus is to finding out the proper perforation for reducing the deflection that is caused by vibration characteristic of the beam. Based on the study, considering a castellated beam with hexagonal opening is taken as an example to locating the stiffeners where the local stiffness is reduced in the beam. The castellated beam with web openings and they gain its advantage due to its increased depth of section by cutting the beam into two pieces and welded it together to make hexagonal web openings. Hence, due to increase in depth of beam, variable load carrying capacity of the beam is getting increased. The increase in depth of castellated beam leads to local residual stresses in web openings and lateral torsional buckling failure when these beams are subjected to loading. There are many modes of failure like shear buckling, flexural failure, and rupture of the welded joint in a web post. In order to avoid all these failures stiffeners were introduced in the hexagonal castellated beam.

A hybrid optimization algorithm for the optimal design of laterally-supported castellated beams

In this paper a hybrid method is developed for optimum design of castellated beams by combining two meta-heuristic algorithms, namely the colliding bodies optimization (CBO) and particle swarm optimization (PSO). In this hybrid algorithm (CBO-PSO), positive features of PSO are added to the CBO. Two common types of laterally supported castellated beams are considered as design problems: beams with hexagonal openings and beams with circular openings. These beams have found widespread usage in buildings because of great savings in materials and construction costs. Here, the minimum cost is taken as the design objective function and the new hybrid method is utilized for obtaining the solution of some benchmark problems. Comparison of the results of the CBO-PSO with those of some other metaheuristics demonstrates the capability of the presented optimization algorithm. For most of the examples, the results obtained by the CBO-PSO have less cost in comparison to those of the other considered methods. It is also concluded that the beams with hexagonal openings require smaller amount of steel, hence being superior to the beams with cellular openings.

Shear buckling strengths of web-posts in a castellated steel beam with hexagonal web openings

Shear buckling behaviors of web-post in a Castellated Steel Beam (CSB) with hexagonal web openings under vertical shear were investigated using finite element method. Through treating the upper part of the web-post as a free body under horizontal shear force, whose shear buckling strength can be calculated by the thin-plate shear buckling theory, design equations for the vertical shear buckling strength of the web-post were proposed. Parameters that affected the vertical shear buckling strength of the web-post were studied, which were the opening height to web thickness ratio h0/tw, the web-post width to web thickness ratio e/tw, the web height of Tee-section above the opening to the web thickness hf/tw, the web thickness tw and the incline angle of the opening edge α. After obtaining the vertical shear buckling strength of a CSB through finite element model, the shear buckling coefficient k can be obtained through inverse analysis. Research results showed that k decreased non-linearly with the increase in e/tw and hf/tw and it increased linearly with the increase in α and h0/tw. Practical calculating method for k was proposed based on parameter analysis results. The vertical shear buckling strength of the web-post calculated using the proposed shear buckling coefficient k agreed well with that obtained from the finite element simulation. For the proposed method was based on the elastic buckling of the web-post, it overestimated the shear buckling strength when the web-post buckled in the elastic–plastic state.

STUDI PERILAKU BALOK KASTELA BENTANG PENDEK DENGAN VARIASI DIMENSI LUBANG HEKSAGONAL MENGGUNAKAN METODE ELEMEN HINGGA

Modification technology of castellated beams of Wide Flange beam (I WF) are now varied, starting from addition high beam variation so that moment of inertia larger than origin beam, until the hole dimension variation for the aesthetic and mechanical-electrical installations. In the castellated beams design should be noted weakening effect shear forces and buckling due to the hole modified. This study was to determine the behavior of castellated beam with hexagonal holes dimensional variations using the finite element method. The method in this research is to create a numerical model of the castellated beam 225x75x7x5 mm span of 1 meter with a hexagonal hole openings using the finite element method are verified first by the results of an experimental model. Geometry, material properties and loading both models are the same. After the numerical model results closer to experimental model results, then made 9 other castellated beam numerical models with variations in the dimensions of the hexagonal holes. The results showed that the higher and the wider hole so the larger tensile stress and compressive stress. Deflection is proportional to tensile stress and compressive stress. The smaller the ratio of the hole and holes number so the smaller the shear stress.

EXPERIMENTAL ANALYSIS TO COMPARE THE DEFLECTION OF STEEL BEAM WITH AND WITHOUT WEB OPENINGS

As a result of decreasing the cost of steel structures and increasing the stiffness of steel members, several new methods have been adopted. Castellated beams are one of the solutions .Castellated beams refer to a metal beam in which the web portion is firstly divided by a zigzag cut along its lengthwise direction and then welding together its two halves. During welding, the two halves are joined together in such a way that holes are formed in the web portion. This increases the depth of the section and thereby its strength. Castellation means holes. Openings are provided in web portion for the allowance of passage of services through the beam. As the provisions are provided through the web portions, it will help to reduce the effective floor depth. For roofs supported by cambered beams, aesthetic beauty may be considered as an advantage. As castellated beams are same as that of a solid beam, its erection is not a difficult task. In this paper, experimental analysis was conducted to compare the deflection of steel beam without web opening and castellated beam having hexagonal and circular opening. ISMB 150 was selected as the parent section and was used for the fabrication of castellated beams with hexagonal openings and circular openings (cellular beam). Experimental analysis was performed and from that the better shape was determined. Experimental analysis showed that castellated beams having hexagonal openings have more load carrying capacity and lesser deflection as compared to solid beam and beam with circular openings.

Pterygodermatites(Paucipectines)andyraicolan. sp. (Spirurida: Rictulariidae), an Intestinal Nematode of Neotropical Molossidae Bats from Brazil

A new nematode species, Pterygodermatites (Paucipectines) andyraicola n. sp., is described from the small intestine of 4 neotropical species of Molossidae bats captured in Sao Paulo State, Brazil. The newly recognized species is characterized by the presence of a subterminal hexagonal oral opening with 24 triangular and prominent denticles of the same shape and size and a buccal capsule with 3 oesophageal teeth with jagged edges. The male has a robust body covered with 40 to 43 pairs of subventral cuticular spines, a coiled tail with thin caudal alae, 10 pairs of papillae, and a single, precloacal, semicircular cuticular fan on the ventral surface. The first pair of precloacal papillae are composed of 2 short pedunculated papillae, a feature that seems to be unique to P. (P.) andyraicola when compared to other species of the subgenus Pterygodermatites (Paucipectines). Equal spicules and the cone-shaped gubernaculum poorly sclerotized. The female has a robust body, thinner in the anterior portion, covered by 2 rows of 67 to 80 cuticular spines, of which the first 41 to 43 pairs are anterior to the vulvar opening and symmetrically arranged, which is in contrast to the asymmetrical disposition of the postvulvar spines. This is the 15th species in the genus described from mammals in the Neotropical ecozone and the third parasitizing bats in this biogeographic region.

The comparative analysis of optimal designed web expanded beams via improved harmony search method

This study aims at comparing the optimum design of two common types open web expanded beams: with hexagonal openings, also called castellated beams and beams with circular openings referred to as cellular beams. The minimum weights of both beams are taken as the objective functions while the design constraints are respectively implemented from The Steel Construction Institute Publication Numbers 5 and 100. The design methods adopted in these publications are consistent with BS5950 parts. The formulation of the design problem considering the limitations of the above mentioned turns out to be a discrete programming problem. Improved harmony search algorithm is suggested to compare the optimum design of mentioned web-expanded beams to analysis the performance of both beams. The design algorithms based on the technique select the optimum Universal Beam sections, dimensional properties of hexagonal and circular holes and total number of openings along the beam as design variables.

Optimum design of laterally-supported castellated beams using CBO algorithm

In this study, two common types of laterally supported castellated beams are considered as design problems: beams with hexagonal openings and beams with circular openings. The main goal of manufacturing these beams is to increase the moment of inertia and section modulus, which results in greater strength and rigidity. These types of open-web beams have found widespread use, primarily in buildings, because of great savings in materials and construction costs. Hence, the minimum cost is taken as the design objective function and the Colliding Bodies Optimization (CBO) method is utilized for obtaining the solution of the design problem. The design methods used in this study are consistent with BS5950 Part 1 and Part 3, and Euro Code 3. A number of design examples are considered to optimize by CBO algorithm. Comparison of the optimal solution of the CBO algorithm with those of the Enhanced Charged System Search (ECSS) method demonstrate the capability of CBO in solving the present type of design problem. It is also observed that optimization results obtained by the CBO algorithm for three design examples have less cost in comparison to the results of the ECSS algorithm. From the results obtained in this paper, it can be concluded that the use of beam with hexagonal opening requires smaller amount of steel material and it is superior to the cellular beam from the cost point of view.

Vertical shear buckling capacity of web-posts in castellated steel beams with fillet corner hexagonal web openings

The shear buckling behavior of the web-post in a castellated steel beam with fillet corner hexagonal web openings is studied using the finite element method. The buckling modes and buckling capacity of the web-post in the castellated beam with fillet corner hexagonal web openings are compared with those having circular and elongated circular openings. The web-post in a castellated steel beam with the proposed opening shape can achieve as good structural performance as that with circular openings. The effects of the opening distance, the opening height, and the web thickness on the buckling behavior of the web-post are investigated. The Strut Model is modified for predicating the shear buckling capacity of the web-post in the castellated steel beam with fillet corner openings. The equivalent rectangular opening is also modified to calculate the Vierendeel failure capacity of the castellated steel beam with the fillet corner hexagonal openings at the perforated sections. The load bearing capacity of the castellated steel beam with the proposed opening shape is the minimum value among the web-post buckling capacity, the Vierendeel failure capacity at the perforated section, and the shear rupture capacity of the horizontal weld.

Investigation on Vierendeel mechanism failure of castellated steel beams with fillet corner web openings

Vierendeel failure of castellated steel beams (CSBs) with fillet corner web openings is investigated by the Finite Element Method. Compared to beams with circular openings, CSBs with the proposed fillet corner web openings need only one cut along the web centerline. Therefore the fabrication cost can be reduced. Effects of opening dimensions and opening shapes on the Vierendeel failure of web-perforated members are investigated in this paper. Numerical results indicate that CSBs with the proposed fillet corner web openings enjoy a higher load bearing capacity than those with traditional rectangular or hexagonal openings on condition that they have the same opening height. The M–V interaction method for predicting the load bearing capacity of CSBs with fillet corner web openings is proposed. Predictions obtained from the proposed M–V interaction equation agree well with numerical results.

Studies on In-Plane Stability Behavior of Arches with Web Openings

As a new type structural member, the steel arch with web openings combines the features of both arches and members with web openings and its applications has been found. Studies on in-plane stability behavior of two-hinged arches with web hexagonal openings are made using Eigen buckling model of the finite element software ANSYS. The buckling load and buckling mode are obtained and the in-plane buckling mode is antisymmetrical. It is shown that buckling load decreases gradually as the circumcircle radius of openings increases and it increases as the gap between openings increases through analysis of buckling load with different parameters such as r/h, g/h, f/l. It can be found that the structural efficiency is the highest when the radius of openings is 0.3h with the aid of optimized function.

Numerical modelling of castellated beams with hexagonal openings

In this paper, a numerical model is developed to predict the behaviour of castellated beams with hexagonal. The numerical model takes into account both material and geometric non-linearity. To initiate buckling, an initial small out-of-plane geometric imperfection, obtained from an eigenvalues buckling analysis, was imposed to the model. Calibration with experimental data obtained from previous work shows that the model is able to predict, with relatively good accuracy, the ultimate load. A parametric study is then followed to determine the effect of web thickness, yielding stress and opening height on the ultimate load of the beams. Based on the parametric studies results, the accuracy of the cross-section classification for castellated beams proposed in the Annex N of Eurocode 3 is assessed.

Optimisation of novel elliptically-based web opening shapes of perforated steel beams

A new study was carried out and presented herein, on the optimisation of novel elliptically-based web opening shapes which enhance the structural behaviour of the perforated beams as well as lead to economic design in terms of both manufacture and usage. The finite element (FE) model used in the study was validated against experimental work conducted by the authors and the results of the comprehensive study are presented in this research paper. For ease of comparison, the yield patterns and deflected shapes of the perforated beams are presented at three characteristic load level points. Finally, shear-moment interaction FEM curves are presented for six different web opening shapes to allow for easy use of the empirical design formulas that have previously been proposed by the authors in a complementary research paper. An overall study of many standard and non-standard web opening shapes, it was shown that perforated beams with vertical and inclined classic elliptical web openings (3:4 width to depth ratio) behave more effectively compared to perforated beams with conventional circular and hexagonal web openings, mainly in terms of stress distribution and local deflection. Therefore, perforated steel beams with large novel elliptically-based web openings with short critical opening length at the top and bottom tee-section as well as straight-line edges are presented for first time and examined in the current research programme.

Anisotropic Hydrogen Etching of Chemical Vapor Deposited Graphene

We report a simple, clean, and highly anisotropic hydrogen etching method for chemical vapor deposited (CVD) graphene catalyzed by the copper substrate. By exposing CVD graphene on copper foil to hydrogen flow around 800 °C, we observed that the initially continuous graphene can be etched to have many hexagonal openings. In addition, we found that the etching is temperature dependent. Compared to other temperatures (700, 900, and 1000 °C), etching of graphene at 800 °C is most efficient and anisotropic. Of the angles of graphene edges after etching, 80% are 120°, indicating the etching is highly anisotropic. No increase of the D band along the etched edges indicates that the crystallographic orientation of etching is in the zigzag direction. Furthermore, we observed that copper played an important role in catalyzing the etching reaction, as no etching was observed for graphene transferred to Si/SiO(2) under similar conditions. This highly anisotropic hydrogen etching technology may work as a simple and convenient way to determine graphene crystal orientation and grain size and may enable the etching of graphene into nanoribbons for electronic applications.

Nonlinear FE analysis of the ultimate behavior of steel castellated beams

A numerical model is developed to predict the behavior of castellated beams with hexagonal and octagonal openings up to failure. The numerical model takes into account both material and geometric nonlinearities. To initiate buckling, an initial small out-of-plane geometric imperfection, obtained from an eigenvalues buckling analysis, was imposed to the model. Results of experimental data obtained from previous works have shown that the model is able to predict, with good accuracy, the ultimate load and to some extent the mode of failure. A parametric study is then realized to assess the cross-section classification given in the Annex N and to compare between the ultimate load behavior of castellated beams with hexagonal and octagonal openings when subjected to flexure and shear force. The numerical results have been compared with those obtained with the design method presented in ENV1993-1-1 Annex N.