Hexagonal Web Research Articles

Maximum displacement prediction model for steel beams with hexagonal web openings under impact loading based on artificial neural networks

The estimation of the maximum displacement of steel beams with hexagonal web openings under impact loads is crucial for the anti-impact design of structures. The dynamic characteristics are complex, and the maximum displacement can be obtained experimentally, although the time cost, and expense of such experiments are high. In this context, a 6-5-1 artificial neural network model based on the Levenberg-Marquardt backpropagation algorithm was developed, incorporating 5-fold cross-validation techniques. Due to limited experimental data, 324 high-precision finite element models were created in bulk using Python-based ABAQUS software scripts to provide additional numerical data, and 26 specimens were designed for drop hammer tests to validate the finite element models. The artificial neural network model on the test data yielded a mean squared error of 0.0268, a mean absolute error of 0.0014, and a coefficient of determination value of 0.9806, with samples having an error of less than 10% comprising 77.16% of the total samples. Using Garson’s algorithm, the contribution of input features was estimated, and a full parameter analysis of the proposed model was conducted. The results indicate that the most significant factor is the impact mass, which accounts for 37.58%. When the impact mass increased from 530 kg to 630 kg, the maximum displacement of Q235 surged by 93.75%. The factor with the least impact is the opening spacing, accounting for 2%, with an average increase in maximum displacement of only 3.45%. Finally, ANN-based equations that can be used as design tools are established.

Effect of Horizontal Distance of Web Opening on the Ultimate Load Carrying Capacity of Castellated Steel Beams by an Analytical Approach

Objectives: The primary objective of this current research is to determine the ideal horizontal spacing for hexagonal web openings and their maximum load-bearing capacity through Finite Element Analysis (FEA). Methods: The ISMB150 was implemented as a cross-sectional profile to fabricate distinct models of castellated beams with heights of 225 mm. The height of the web openings remained constant at 150 mm for the castellated beam model. The entire analysis is being done on ANSYS 19.2. Findings: The analysis has revealed that, for castellated beams with shallower depths, an optimal horizontal spacing of 44.9 mm for the web openings yields an ultimate load-bearing capacity of 144.26 KN. The results of castellated beams are measured in terms of ultimate load-carrying capacity, span-to-deflection ratio, load density, failure location, span-to-beam depth ratio, and the ratio of horizontal distance of opening-to-opening depth. Novelty: This research contributes analytical findings for the ideal horizontal distance of hexagonal web opening through maximum load-bearing capacity. Castellated beams have gained immense popularity within the structural engineering community today due to their visually appealing design featuring a variety of web-opening shapes. The primary objective of this current research is to determine the ideal horizontal spacing for hexagonal web openings and their maximum load-bearing capacity through Finite Element Analysis (FEA). The ISMB150 was implemented as a cross-sectional profile to fabricate distinct models of castellated beams with heights of 225 mm. The height of the web openings remained constant at 150 mm for the castellated beam model. The analysis has revealed that, for castellated beams with shallower depths, an optimal horizontal spacing of 44.9 mm for the web openings yields an ultimate load-bearing capacity of 144.26 KN. The results of castellated beams are measured in terms of ultimate load-carrying capacity, span-to-deflection ratio, load density, failure location, span-to-beam depth ratio, and the ratio of horizontal distance of opening-to-opening depth. This research contributes valuable insights into optimizing the design of castellated beams for enhanced structural performance. Further exploration and validation could provide additional refinements and applications in structural engineering. Keywords: Horizontal distance of web opening, Number of openings, Ultimate load carrying capacity, Failure modes, ANSYS, Castellated beams

Impact behavior of high-strength steel beam with different web opening forms

This paper investigates the performance of high-strength steel beams with web openings (HSSBWOs) under impact by methods of tests and finite element. Based on the experimental data of 10 specimens, which were made of high-strength steel Q550D, and the effects of impact energy and web opening forms on the impact behavior of HSSBWOs are investigated emphatically. In particular, two specimens made of steel Q235D were used to study the differences in impact behavior from HSSBWOs. The test results reveal that the high-strength steel beams with circular web openings (HSSBCWOs) have better impact resistance than the high-strength steel beams with hexagonal web openings (HSSBHWOs), and the HSSBWOs have better impact resistance than the normal-strength steel beams with web openings (NSSBWOs). Moreover, HSSBWOs has excellent abilities to absorb energy, the average energy absorption rate of HSSBHWOs and HSSBCWOs is 95.78% and 93.55%, respectively. In addition, finite element models that can accurately predict the dynamic responses of HSSBWOs under impact load are established to analyze the shear force evolutions, as well as investigate the differences of impact behavior between steel beams with a variety of web openings forms. The results show that the shear force distribution ranges of HSSBCWOs are larger than that of HSSBHWOs at the time when impact force reached peak value. The HSSBWOs can sustain more impact load with the web opening shape that closer to the circle. The solid webbed steel beam (SWSB) has better impact resistance than the steel beams with web opening (SBWO).

High-strength steel beams with hexagonal web openings under impact load

A drop-weight impact testing machine was used to conduct an impact test on 15 specimens in order to examine the impact resistance of high-strength (HS) steel beams with hexagonal web openings (SBHWO). The test findings demonstrate that as steel strength increases, maximal impact force and impact platform value rise, while maximum displacement, residual displacement, beam-end rotation, reduction ratio of opening area, and energy absorption ratio decrease. The use of high-strength steel can significantly improve the impact resistance of the SBHWO. When steel Q235 was lifted to steel Q550, the average increase of impact peak and impact platform value was 17.94% and 90.80%, respectively, and the average reduction range of maximum displacement and residual displacement in the span was 45.36% and 55.30%, respectively. After steel Q550 was upgraded to steel Q690, the improvement effect of impact resistance is small. Empirical equations of the relationship between impact energy，steel strength and dynamic responses were established.

Effect of impact loading on the dynamic response of steel beams with hexagonal web opening

Owing to the limited literature on the impact performance of steel beams with hexagonal web opening (SBHWOs), this study conducted drop hammer tests and used finite element methods to investigate the dynamic response of SBHWOs subjected to impact loads. The impact force, displacements and accelerations of the beam, and the strains around a hexagonal web opening were collected during the tests. The impact process was captured by a high-speed camera. Furthermore, a finite element model was developed to analyze the post-impact internal forces of SBHWO, development and distribution of stresses in its web, the effect of impact position, and differences with solid webbed steel beam (SWSB). Results showed that the impact force, displacements, and web-post buckling of the SBHWO were significantly affected by impact energy, spacing between openings, and opening height. The average energy absorption ratio of the SBHWOs was found to be 51.56%. Additionally, the midspan acceleration decayed rapidly after impact and spread from the midspan towards the supports. The finite element analysis proved that numerical models can be used to accurately predict the dynamic responses of a SBHWO subjected to impact loads. The axial forces, shear forces, and bending moments of the SBHWO redistribute themselves during the impact, and the magnitude of the internal forces increased very rapidly before decaying gradually. The pattern through which stress developed in the SBHWO web was obtained using finite element modeling. A position close to the support approximately 1/4 of the calculated length of the SBHWO was the most unfavorable impact position. The SWSB was more resistant to impact load than the SBHWO.

Parametric study of reduced web section of beam to column welded connection with castellated beam having hexagonal openings and subjected to cyclic loading

In this paper, a finite element (FE) analysis is carried out on a beam to column welded connections with multiple hexagonal web openings. The openings are distributed along the length of the beam which is subjected to cyclic loading protocol proposed by the SAC and FEMA 350 (2000). This study focuses on the interaction of the connections from columns to the perforated beam and mobilization of stresses. Two parameters were addressed: the distance from the face of the column (S), and the web opening spacing (So) including closely spaced opening. The study revealed that the design of mostly controlled reduced web section (RWS) connections should be fundamentally based on the distance of the first opening from the face of the column. Three values of the distance (S) are presented (200 mm, 350mm, and 520 mm). A model with an ideal distance (S) of 350 mm has resulted in an ultimate rotation of 0.039649 rad, which is less than other models, in which rotations were 0.049386 rad and 0.050000 rad, respectively.

Full static resistance of castellated steel beams with hexagonal web openings for blast response predictions

To avoid structural collapses by explosions and terrorist attacks, castellated steel beams (CSBs) could become an alternative to parent steel beams (PSBs) in structures due to high energy absorption capabilities, which offered through a combination of high strength and ductile response. The static resistance function, obtained by either experiments or FE modeling, is considered an important item of data in calculating the dynamic response of a system using Single Degree of Freedom models. This research estimated and promoted the static resistance of CSBs to enhance their ductility and dissipate blast energy through large deformation kinematics. Quasi-static experiments on CSBs were performed to investigate the effect of end connections and different strengthening techniques (closed holes and vertical stiffeners) on the static resistance of CSBs. Load-deflection and strain data were recorded for each specimen up to failure. Moreover, a Finite Element (FE) model was developed and verified against tests. Good matching through all phases of resistance was obtained between the FE and test results. An extensive parametric study was carried out to predict the full static resistance of CSBs under the effect of cross-section geometries. Different ranges of spans were investigated to determine the minimum effective span-to-depth ratio. By providing vertical stiffeners as well as bolted head plate connections, CSBs obtained a larger capability of deformation through the tension membrane stage to resist blast loads under simultaneous high tension and shear forces.

Surfaces that are covered by two pencils of circles

We list up to Möbius equivalence all possible degrees and embedding dimensions of real surfaces that are covered by at least two pencils of circles, together with the number of such pencils. In addition, we classify incidences between the contained circles, complex lines and isolated singularities. Such geometric characteristics are encoded in the Néron–Severi lattices of such surfaces and is of potential interest to geometric modelers and architects. As an application we confirm Blum’s conjecture in higher dimensional space and we address the Blaschke–Bol problem by classifying surfaces that are covered by hexagonal webs of circles. In particular, we find new examples of such webs that cannot be embedded in 3-dimensional space.

Investigation of the stress-strain state of beams with different types of web perforation

This article is devoted to evaluating the effectiveness of I-beams with different web perforations: hexagonal, round, oval and elliptical. The technology of manufacturing of castellated beams is described. For the purpose of verification the analytical calculation of the beam with hexagonal web perforation and for comparison the calculation by the finite element method is given. To correctly assess the stress-strain state, the mesh of finite elements in the area of openings was concentrated. The results of maximum normal stresses and strains obtained by different methods were compared with each other and the efficiency of using the finite element method to determine the stress-strain state of castellated beams was proved. In the castellated beams there is a complex stress-strain state, which was confirmed in this work for the most characteristic shapes of openings. Beams with hexagonal, round, oval (horizontal and vertical), elliptical and elliptical (rotated by 45°) openings are considered in the article, their geometric parameters and characteristics as well as advantages and disadvantages are described. Beams with round openings are currently the most widely used. In addition, the parameters that affect the efficiency of castellated beams with oval (horizontal and vertical) and elliptical rotated by 45° openings were identified. In this work, it was found that the shape of the openings significantly affects the stress-strain state of the castellated beams, especially for hexagonal openings, which are mainly used so far. The stress distribution in the first opening for each of the considered types of perforations and the nature of the change of σmax in other openings is shown. The stress-strain state of castellated beams was studied using the finite element method. The results of this study are of practical value because they can be used when arranging the sections and openings of castellated beams.

Multiparameter seismic behavior of castellated beam-to-column connections based on stress migration

This paper presents a study on the castellated beam-to-column connections with four regular hexagonal web openings and one solid web beam-to-column connection that considering the opening rate and whether there is a combination of floor slabs (composite action) while subjected to the cyclic loading. Furthermore, the initial geometric imperfection was carefully incorporated in the FE model and the models have been validated against published experimental results. There is a slightly different about 5% between FE and test results including ultimate bearing capacity and other hysteresis behaviors. Investigation of 38 FE models subjected to cyclic loading focuses in the variation regularity of the failure mode, plastic development, stress migration, and seismic behaviors under the coupling effect of various factors, including the composite action of the floor slab, opening rate, the distance from the first opening to the face of the column, depth-to-thickness ratio of the web, and opening spacing. It is found that the composite action can improve the stress distribution around the first opening and raise the bearing capacity and ductility of the connections to a certain extent. Further, when the opening rate is either smaller than 0.5 or higher than 0.7, the plastic hinge of the connections with the floor slab occurs at the beam-to-column connection weld, which is completely different from the failure mode that without composite action. When the distance from the first opening to the face of the column is equal to or greater than 1.375 times the depth of beam, the plastic hinge formed in the beam-to-column weld while the composite action is taken into account; when disregarding the composite action causes the plastic hinge emerged in the beam section. Also, the ultimate bearing capacity of the castellated beam-to-column connections with closely spaced web openings significantly decreases; however, widely spaced web openings make stress concentration around the first opening and hinder the migration of stress to other openings, which has an adverse effect on the ultimate bearing capacity and ductility of the connections. The depth-to-thickness ratio of the web is also an important factor affecting the damage mode either web buckling or beam plastic hinge.

Finite Element Analysis on Shear Strength of a Castellated Beam with Hexagonal Web Opening

A beam (flexural member) with several regular openings with different shapes is called a castellated beam. The castellated beams are well accepted in the industry, multi-story buildings, and power plants due to their increased depth of the section along with the web results in increased strength and stiffness. Though numerous simulation and experimental analyses have been made on the castellated beam, with intermediate transverse stiffener, bearing stiffener and torsion stiffener are used to increase a load-bearing capacity of the beam, but the study on the understanding of diagonal stiffener in the opening is very meager. The objective of the research is to investigate the linear behavior – ISMB150 and IC225 castellated beam of hexagonal openings with and without diagonal stiffeners and the effect of fillet radius at the corner of the openings is studied. Using finite element analysis software,Hyper works, with OptiStruct as a solver, under simply supported beam construction with four-point loading conditions was analyzed by developing an efficient 3D model for the analysis. Due to the openings in the section, the sharp corner of the opening is subjected to Vierendeel failure by the formation of plastic hinges at the corners, which makes critical hence by providing diagonal stiffener in the direction of diagonal tension and diagonal compression for the smooth flow of shear forces. The results show an improvement in load-bearing capacity of 1.51 times in the castellated beam than the parent section ISMB150. The stiffener provided further enhances the same to 1.45 times compared to the ISMB150 section. The linear results show lesser stress concentrations at the web opening corners, thus reducing the prominence of failure at the corners.

Behaviour of hybrid steel beams with closely spaced web openings

In this paper, the behaviour of hybrid steel beams having openings in the web has been analytically studied. Hybrid beams are often used when the design requirement is not satisfied by hot rolled sections or homogeneous built-up sections. Typically, the steel grade in flange is higher than the web. The presence of openings in the web tends to result in different modes of failure such as web-post buckling and vierendeel mechanism. This paper attempts to analyse a hybrid steel beam with hexagonal web openings. The modes of failure of such beams are compared to their homogeneous counterparts along with the load carrying capacity for each. Center-to-center spacing of openings is varied as well as the effect of change in depth of openings is observed in this study. A general observation is made for modes of failure which are found to be very similar for homogeneous and hybrid beams. An optimum ratio of spacing and width of opening is determined to be 1.5 for beams having a depth of opening lower than 60% the beam depth. For opening depths larger than 60%, load carrying capacity is drastically reduced. For spacing ratio below 1.5, web-post buckling is pronounced and the beam does not reach its plastic capacity.

Effect of Fillet Radii on Moment Carrying Capacity of Sinusoidal Web Opening Castellated Steel Beams in Comparison with Hexagonal Web Openings

In recent times, the use of castellated beams with various web openings for structures like high-rise building and industrial structure has turned out to be extensive. It offers an increase in depth of section without any extra weight, high strength-to-weight ratio, lower maintenance and painting cost. The most important advantage of the castellated beam is its higher bending stiffness, simplicity of service facility and beautiful appearance. The aim of this research paper is to offer a new web opening shape as a sinusoidal opening to avoid failure of the castellated beam due to shear stress concentration at the corner of the opening and also to study the maximum moment carrying capacity and deflection of castellated beams. In this research, 15 beams were fabricated. Four models of castellated beams were considered for experimentation. This research is focussed on hexagonal and sinusoidal openings of a castellated beam subjected to flexural loading. The variables were considered are fillet radii for sinusoidal openings with one-fourth, one-sixth and one-eighth of hexagonal opening. All the beams were analysed by the finite element method using ANSYS software, and the results were compared with experimental outcomes. The experimental results for maximum moment carrying capacity and deflection show good agreement with the corresponding value observed in ANSYS software. The experimental results show that castellated beam with fillet radius one-fourth of opening has 20.78% more moment carrying capacity and 11.51% less deflection compared to hexagonal opening. The outcomes consider relevant for practical applications.

Prediction of Ultimate Load Carrying Capacity of Castellated Beams by Experimental and Analytical Investigation

The aim of this research paper is to offer a new angle of web opening for hexagonal castellated beams to avoid failure due to shear stress concentration at the corner of the web opening and to investigate the ultimate load carrying capacity and deflection of hexagonal and rectangular castellated beams. This research is focused on hexagonal and rectangle openings of a castellated beam. This research includes testing of 18 castellated steel beams out of 21 numbers of steel beams and 3 solid beams to investigate ultimate load carrying capacity and deflection. The variables were considered are the angle of opening for hexagonal shape with 30°, 45° and 60°, and the equivalent length of opening for a rectangular shape. All the castellated beams were analysed by using ANSYS software and the results were compared with experimental outcomes. The experimental and ANSYS results for ultimate load carrying capacity and deflection shows good agreement. Experimental results showed that the castellated beam with 30° hexagonal web opening having 28.63% more load carrying capacity and 83.52% less deflection compared to the solid beam.

Experimental and Finite Element Method of Castellated Steel Beam with and without Hexagonal web opening

Castellated beams are made from the conventional I section by the process named as Castellation Process. As of late, broad examination on these castellated steel beams has been directed, including various shapes in web openings. The primary objective of these examination works was to assess and dissect its ideal opening sizes and shapes arrangement. For the most part castellated beam are given hexagonal, round and square formed openings. The finite element investigation is most favored technique for comprehension the flexural strength of castellated beams. In this examination, experimental and numerical displaying approach is utilized for deciding spacing between openings on hexagonal castellated beam. ANSYS software was utilized for the investigation. Opening edge 60o with various opening dispersing 0.15d and 0.25d have beam utilized. Investigation was selected steel beam with and without web openings of ISMB 150 and solid ISMB200 section. Results demonstrated that the castellated bar with hexagonal opening indicated more load carrying capacity and less significant deflection contrasted with solid beam.

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.

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.

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.

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.

Darboux cyclides and webs from circles

Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ⩽4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Möbius geometry, we provide computational tools for the identification of circle families on a given cyclide and for the direct design of those. In particular, we show that certain triples of circle families may be arranged as so-called hexagonal webs, and we provide a complete classification of all possible hexagonal webs of circles on Darboux cyclides.