Hexagonal Openings 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.

Numerical Analysis of Corrugated Castellated Beam with and Without Openings

The construction industry is constantly seeking innovative solutions to optimize the performance and efficiency of structural elements. Castellated beams with corrugated webs have emerged as a promising option in this pursuit. Their unique geometry, including web holes, makes estimating shear load capacity different from traditional beams with solid webs. These beams are becoming increasingly popular in engineering and economics due to their advantages. The openings in the web can take various shapes, as detailed in the research paper, which compares the load versus deflection for castellated beams with rectangular and hexagonal openings, analyzed using the software ABAQUS® CAE. The trapezoidal corrugated web configuration notably augments the beam's resistance to buckling failure and furnishes superior resistance to buckling compared to a plain web beam. Predominant factors impacting the efficacy of castellated-corrugated web beams encompass the overall beam height and the size of the web opening. The study conducts a comparative analysis of the ultimate load-bearing capability of these beams about both plain and corrugated web beams. Moreover, the manuscript advances an original technological proposal entailing the integration of a trapezoidal-shaped web into a castellated beam. The load-bearing capacity of castellated beams with various web opening shapes, such as rectangles and hexagons, was contrasted with that of the I beam. Among these shapes, hexagon web opening TWHC has higher Material savings with an increase of 13 % compared to the I beam. The results detail that the corrugated web rectangular castellated beams have less weight and more strength than the corrugated web hexagon castellated beam.

Optimization of cross-sectional dimensions of castellated beams with hexagonal openings

The object of this study is a castellated beam, in which the web openings have the shape of a regular hexagon. The beam is examined to find optimal cross-sectional dimensions. The optimization task is stated as the task of finding the optimal profile numbers for top and bottom Tees of the beam and the optimal width of the web opening while ensuring the required load-carrying capacity of the beam. Minimization of the volume of the beam material was considered as an optimality criterion. The stated optimization problem was solved using the exhaustive search method. For an assortment of normal I-beams with parallel flanges, castellated beams were obtained with optimal cross-sectional dimensions depending on the steel grade, the beam span, and the magnitude of transverse uniformly distributed load. The optimization calculations proved that it was possible to increase the elastic section modulus of the beam to 35.48...50 % through the use of a castellated web. Castellated beams with optimal cross-sectional dimensions at the same load-carrying capacity are characterized by lower steel consumption (up to 23.19 %) compared to I-beams with a solid web. Analysis of the results has made it possible to devise recommendations for the optimal distribution of material in the cross-sections of such beams. The results are valid only for the assortment of normal I-beam profiles and only for the case of uniformly distributed load acting on the beam when the compressed beam flange is laterally restrained from the bending plane and the beam web has openings in the form of regular hexagons. It is under such conditions that the reported results can be implemented in practice both at the stage of selecting cross-sections of the studied class of structures, and at the development of effective assortments of castellated beams

Non-linear behavior of castellated beams consisting hexagonal and diamond openings using CFRP stiffeners

Non-linear behavior of castellated beams consisting hexagonal and diamond openings using CFRP stiffeners

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).

Comparative study on the behaviour of castellated beams provided with hexagonal, circular, and diamond-shaped web openings

Comparative study on the behaviour of castellated beams provided with hexagonal, circular, and diamond-shaped web openings

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.

Evaluation of Open-Graded Aggregates Stabilized with a Multi-Axial Geogrid Using a Large-Scale Triaxial Test Set-Up

Geogrids are commonly used in paved and unpaved roadways to stabilize base and subbase layers by laterally restraining movements of unbound aggregates under applied wheel loading, often referred to as interlocking. The geogrid-aggregate interlock is a function of the match between the geogrid aperture size and geometry and the grain size and shape characteristics of the stabilized aggregates. Open-graded coarse aggregates (OGA) are commonly used as an alternative to dense-graded materials in permeable base/subbase applications as well as in railway ballast to facilitate drainage. This paper describes an experimental study recently conducted to investigate the repeated load-deformation behavior of a geogrid-stabilized OGA material in large-scale triaxial testing. Two multi-axial geogrids with the same aperture patterns but different aperture sizes were tested. The aperture patterns include different sizes of hexagonal, trapezoidal, and triangular openings. The multi-axial geogrid with the larger apertures better matched the OGA material properties to provide a reduction in permanent deformation in the test specimen. The improved interlocking and the related local stiffness enhancement were successfully quantified using embedded shear wave transducers termed bender elements. To stabilize aggregates with relatively uniform grain sizes, for example, AASHTO No. 57 stone studied here and railroad ballast, the ratio between the aperture size and a representative particle size (i.e., D90) served as a good indicator of the effectiveness of the geogrid. The findings of this experimental study therefore provided valuable information on the governing properties and mechanisms that play a role in geogrid-aggregate interaction with multi-axial geogrids.

Behaviour of Steel I Beams with Web Openings

This paper aims to study the behavior of steel I beams with web openings. However, web openings might lead to a noteworthy reduction in the load-carrying capacity of beams, but can also be so supportive and essential from an economic point of view. An experimental investigation and nonlinear three-dimensional finite element analysis using the ABAQUS computer program were planned and conducted on six steel I-beams having the same dimensions, different diameter ratio spacing, and opening shapes such as circular, rectangular, and hexagonal. Experimental results showed that the ultimate load of a steel beam with web openings reduced with an increase in the area of the opening. A circular opening has a stronger shape than a rectangular opening because a rectangle has fast deflection and torsion angles, so it resists an applied load less than a circular opening. Also, the beam with hexagonal openings is better than that with rectangular openings because hexagonal openings are more resistant to deflection and deformation than rectangular openings. The finite element results, which are validated against the experimental results, show good accuracy with the experiment. Besides, a parametric study is presented here to study the influence of varying the shape of openings on the value of the failure load and midspan deflection. It can be noticed that the steel beam with a circular opening, which had been tested experimentally and modeled by the Abaqus program, is the best case and gives a higher failure load as compared to the diamond, octagonal, trapezoidal, transverse, and longitudinal ellipses. Thus, providing web openings reduces the weight and increases structural efficiency. Doi: 10.28991/CEJ-2023-09-03-08 Full Text: PDF

Air entrainment and transport in a bottom outlet controlled by a cylindrical gate

This study deals with a bottom outlet that causes significant surges at both the inlet and exit. The bottom outlet comprises an intake, a vertical shaft and a tunnel underneath the rockfill dam and a submerged exit. In the intake tower, a cylinder gate controls hexagonal openings near the reservoir bottom. Operations during the dam construction show that discharges at a low reservoir water level result in upsurges of air-water mixture within the hollow gate cylinder and blowouts in the tailwater. To understand the flow behaviors, 3D CFD modeling is performed to examine air entrainment at the intake and transport down the waterway. Both low and high-water levels are simulated, and the air-water flow phenomenon is reproduced. In both cases, air pockets are generated, which undergo accumulation and breakup process. When moving downstream, they could cause severe surface fluctuations, even blowouts. Consequently, engineering solutions are required to address this issue. The aim of this study is to provide basis for risk assessment of outlet operations and potential rehabilitation measures.

Experimental study on the mechanical behaviour of castellated composite beams under a negative bending moment

In this study, mechanical tests were performed on eight castellated composite beams with hexagonal openings under a negative bending moment. The effects of concrete slab, opening rate, and transverse stiffener on the failure mode, bearing capacity, and stress distribution around the openings of the castellated composite beams were examined. The test results revealed that when the negative moment acts alone, the castellated composite beams fail owing to buckling of the compression flange. When the negative moment and shear force act together, the castellated composite beams fail because of buckling of the web post. The development curve of the stress around the opening can be used as a reference for determining the yield load of the specimen. The transverse stiffener can effectively limit the buckling of the web post of the composite beam. As the opening rate increases from 0.47 to 0.6, the bearing capacities of the castellated composite beams under the two working conditions decrease by 8.7% and 10.5%, respectively. Following the addition of the concrete slab, the bearing capacities increase by 16.8% and 7.2%, respectively. Accordingly, a calculation method for the bearing capacity of castellated composite beams considering coupling between the bending moment and shear force under a negative bending moment was proposed. The calculation results were found to be consistent with the experimental results.

Study on anti-progressive collapse performance of cellular steel frames with different web opening shapes

In this paper, cellular beam-column joints with different opening shapes were taken as the object of study to investigate the resistance to progressive collapse of weakened beam-column joints through a combination of experiments and numerical simulations. Opening shapes include circular, rectangular and hexagonal. The development laws of failure mode, vertical force–deformation response, internal force development and resistance mechanism of the specimens were analyzed, and based on the validated finite element model, the effects of weakening parameters of openings with different opening shapes on the performance of the beam-column joints against progressive collapse were studied. The results demonstrate that the load carrying capacity and deformation capacity of cellular joints with different opening shapes have different degrees of improvement compared with the foundation joints, and exhibit the largest deformation in the first opening area near the column flange, where the ductile failure at the weakened section occurs in the hexagonal cellular opening, and the catenary effect can be fully developed, showing the best performance under the designed opening size, rectangular is the second and circular the worst. In addition, the failure mode and load carrying capacity of the specimens can be effectively improved by changing the opening weakening parameters. Increasing the opening diameter (parameter a) and opening edge distance (parameter c) within a reasonable range can effectively improve the vertical resistance and deformability of the specimens, and the effect of opening spacing (parameter b) on the structural load response is negligible. In the design of collapse resistance of cellular beam-column joints, it is recommended to increase the values of parameters a and c appropriately and to reduce the value of parameter b appropriately under the premise of ensuring the structural load carrying capacity, which is more conducive to the catenary action.

An appraisal of the Vierendeel mechanism capacity of cellular beams with sinusoidal openings

The aim of this research is to investigate the performance of castellated beams with sinusoidal openings against Vierendeel mechanism (VM). Material nonlinear finite element (FE) analyses were conducted in two beams subjected to four-point bending with geometries selected to exhibit the desired plastification mode. Results of simulations revealed failure mode associated with the formation of four predominant plastic hinges along with shear yielding of the web-post necked region. Differently from the usual castellated beams with hexagonal or cellular openings, the critical hinges did not form at the ‘corners’ around a single opening, but at the innermost and outermost ‘corners’ at shear span. A significant stress redistribution could also be observed during the plastification process. The observation of a unique diagonal stress pattern along the web of the analyzed beams inspired the development of a simple two-dimensional model to predict the performance. A simplified nonlinear procedure was successfully developed to assess the evolution of plastification process with loading, with good agreement with the FE model and with an experimental result reported elsewhere in literature. Finally, it is shown that the current design guidelines for castellated beams (hexagonal and cellular) are not readily applicable to beams with sinusoidal openings for assessment of VM capacity.

Prediction of the castellated beams deflections

Introduction. Existence of openings in webs of beams reduce their shear rigidity and increase deflections compare with beams of the same dimensions with solid web. Investigation of the castellated beam’s deflections is important, because one of main demands to beams of engineering structures is guarantee of necessary rigidity, i.е. restriction of ratio deflection to length. In the work it was studied deflections of castellated beams with diamond shape, hexagonal, sinusoidal and circular openings, widely used in structural industry.
 
 Materials and methods. Effect of openings on transverse deflections of the castellated steel beams was studied analytically with theory of composite bars, with the finite element method and experimentally on four meters’ double consoled beams under loading with concentrated forces applied at consoles.
 
 Results. Universal analytical relation was obtained which allow reliably evaluate deflections of simply supported beams with various shape of openings under different kind of loading. Analysis of results of calculation of beams by FEM using program complex ANSYS demonstrates satisfactory correspondence to experimental data and to analytical relations.
 
 Conclusions. Obtained with the theory of composite bars analytical dependences for deflections of simply supported beams are applicable for beams with various type of perforation and different kind of loading.

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.

EFFECT OF STIFFENER VARIATION ON THE FLEXURAL CAPACITYOF CASTELLATED BEAM HEXAGONAL OPENING

One of the innovations that could be done is to change the WF steel profile into a castellated beam with hexagonal openings. This research examines the effect of adding stiffener variations on castellated beams with hexagonal openings on flexural capacity. The steel profile used is a WF 150x75x5x7 steel profile with BJ 37 which is made into a castellated beam with hexagonal openings with an opening angle of 45° and a profile cut width of 50 mm with a beam length of 2000 mm with variations of stiffeners are plate 35x6, reinforcement Ø-16, and elbows. 25.25.4 with variations in distance of 200 mm and 400 mm. The analysis in this study uses manual analysis and numerical testing using the software. From the results obtained from the analysis, the flexural capacity, deformation, stress, and failure patterns that occur with each model will be compared. Based on the research results, it was found that the capacity of all models using stiffeners was greater than that of castellated steel beams without stiffeners. The reinforcement with a distance of 200 mm is the largest stiffener that can withstand the load with an increase of 6.25%.

Stress analysis of I-beam with web opening via finite element analysis and experimental study

PurposeThe purpose of this work is to perform the finite element analysis (FEA) for the numerical discretization of sections with different arrangements of Web openings to investigate the torsion behavior. Typical hexagonal and circular Web opening sections are extensively used in steel construction due to economic development in building design. However, the use of sections with different arrangements of Web opening had improved the performance of the section with Web opening in terms of structural behavior which leads to economic design compared to typical I-beam.Design/methodology/approachThe accuracy of FE results allows extensive numerical analysis of stress concentration magnitude for sections with Web openings, concentrating on the sizes and positions of the Web opening. Five shapes and three sizes of Web opening are used in this work. The shapes involved are c-hexagon, hexagon, octagon, circular and square, whereas the sizes of the Web opening involved are 0.67 D, 0.75 D and 0.80 D where D is the height of the Web. Two types of models for 200 × 100 × 8×6 mm steel section involved which is Model 1, where the section with 50 mm edge and 150 mm center-to-center distance and Model 2, where the section with 100 mm edge and 200 mm center-to-center distance.FindingsIt was found that these configurations affect the section with various shapes of Web openings sizes (0.67 D, 0.75 D, and 0.80 D). This also includes the spacing distances, with 50 mm edge and 150 mm center-to-center distance and also a section with 100 mm edge and 200 mm center-to-center distance. Through the FEA results of Model 1 and Model 2, it is found that 50% reduction in horizontal member length in hexagon Web opening, from 50 mm to 20 mm, caused increment about 30%–53% stress concentration in Web for c-hexagon. However, for a stress analysis of c-hexagon, geometry resulted in a lower stress concentration in the Web than other Web opening.Originality/valueAdditionally, the work emphasized the efficiency of Web opening shapes by using an appropriate Web opening radius in section with c-hexagon, hexagon, octagon, square and circular shapes. The final results show the contribution of appropriate Web opening radius to increase the section torsional capacity. It is observed that the torsional capacity at certain loading condition and its angle of twist is analysed.

Effect of Web Post Width on Strength Capacity of Steel Beams with Web Openings: Experimental and Analytical Investigation

Day by day, technology has been changing progressively because of the remarkable hastening of research and development activities. Perforated beams are one such example of advancement in construction technology. Steel beams with web openings are those that have regularly spaced web openings along the length of the beam. The web openings are created in various ways such as wire cutting and welding. Castellated and cellular beams differ in the creation of web openings. Studies addressing the effect of web post width of steel beams with web openings on the strength capacity of beams are rare. Therefore, the objective of the present work was to examine the influence of web post width on the strength capacity of beams with web openings. First, experimental tests were carried out on three full-scale specimens of a steel beam with oval-shaped web openings, cellular beam, and solid web beam. The same beam was modeled using finite-element software ANSYS and the behavior was compared in terms of load–displacement curve and failure modes. Later, a detailed parametric study was carried out to study the behavior of beams with web openings having variation in web post width using nonlinear finite-element analysis. The simply supported steel beams with web openings subjected to midspan concentrated load with varying web post width and shape of openings were modeled and analyzed. From the analysis results, it was found that the shape of web openings and the web post width play an important role in the strength capacity of the perforated beams. The maximum strength reduction capacity was found to be 51.78% for hexagonal openings of depth 150 mm and having a web post width of 50 mm. The minimum strength reduction capacity was found to be 8.93% for hexagonal openings of depth 100 mm having a web post width of 500 mm. Web post width plays a significant role in the ultimate strength capacity of beams. Web post buckling is a predominant failure mode in steel beams with web openings and it can be prevented by maintaining sufficient web post width.

Determining the Optimum Geometric Shape for Web Opening of Wide Flange Beams using Response Surface Methodology

In the field of civil engineering, the priority of a structural engineer is the safeness and stability of each structural element present in the structure. However, there were some concerns with regards to easy access and flexibility of the utilities such as electrical and mechanical systems. In response to these concerns, web opening was introduced to wide flanges to give way for the utilities, provided that the strength and durability of the structure will not be compensated. This study aims to obtain the optimum geometric shape of web opening for wide flange beams with regards to its performance for bending stress. The web opening on the wide flanges was designed first based on the parameters of the web opening. Then, the effects of circular, square, hexagonal and elliptical web openings were analyzed using Finite Element Analysis (FEA). Three varying support conditions in each opening case were used and analyzed using nonlinear static and nonlinear dynamic analysis in the finite element modeling software called Abaqus. During the FEA, deflection control method was used to obtain the value of force and stress upon reaching the deflection control value. Values of maximum stress and maximum force for each case were then obtained from the analysis, were used as factors for the Response Surface Methodology (RSM), which will define which shapes performed the best under specific conditions. Results obtained from RSM showed that considering value of the stress and deflection from nonlinear static and nonlinear dynamic analysis, elliptical web opening produced the largest force and smallest stress. Thus, elliptical web opening, considering bending stress, performed better compared to the other web openings.