Shell-to-Beam Numerical Homogenization of 3D Thin-Walled Perforated Beams

Determining the geometric characteristics of even complex cross-sections of steel beams is not a major challenge nowadays. The problem arises when openings of various shapes and sizes appear at more or less regular intervals along the length of the beam. Such alternations cause the beam to have different stiffnesses along its length. It has different bending and shear stiffnesses at the opening point and in the full section. In this paper, we present a very convenient and easy-to-implement method of determining the equivalent stiffness of a beam with any cross-section (open or closed) and with any system of holes along its length. The presented method uses the principles of the finite element method (FEM), but does not require any formal analysis, i.e., solving the system of equations. All that is needed is a global stiffness matrix of the representative volumetric element (RVE) of the 3D representation of a beam modeled with shell finite elements. The proposed shell-to-beam homogenization procedure is based on the strain energy equivalence, and allows for precise and quick determination of all equivalent stiffnesses of a beam (flexural and shear). The results of the numerical homogenization procedure were compared with the existing analytical solution and experimental results of various sections. It has been shown that the results obtained are comparable with the reference results.     

Strengthening of Continuous Reinforced Concrete Deep Beams with Large Openings Using CFRP Strips

To accommodate utilities in buildings, different sizes of openings are provided in the web of reinforced concrete deep beams, which cause reductions in the beam strength and stiffness. This paper aims to investigate experimentally and numerically the effectiveness of using carbon fiber reinforced polymer (CFRP) strips, as a strengthening technique, to externally strengthen reinforced concrete continuous deep beams (RCCDBs) with large openings. The experimental work included testing three RCCDBs under five-point bending. A reference specimen was prepared without openings to explore the reductions in strength and stiffness after providing large openings. Openings were created symmetrically at the center of spans of the other specimens to represent 40% of the overall beam depth. Moreover, finite elements (FE) analysis was validated using the experimental results to conduct a parametric study on RCCDBs strengthened with CFRP strips. The results confirmed reductions in the ultimate load by 21% and 7% for the un-strengthened and strengthened specimens, respectively, due to the large openings. Although the large openings caused reductions in capacities, the CFRP strips limited the deterioration by enhancing the specimen capacity by 17% relative to the un-strengthened one.     

Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.     

Impact of Adhesive Layer Thickness on the Behavior of Reinforcing Thin-Walled Sigma-Type Steel Beams with CFRP Tapes

This paper presents selected issues related to the reinforcement of steel element cold-formed with CFRP tapes. The first section of the paper is a review of source literature and a presentation of the basic information on cold-formed thin-walled steel elements and CFRP composite materials, stressing the advantages and disadvantages of using them to reinforce steel structures. Next, the authors present original research on reinforcing bent thin-walled sigma-type steel beams using adhesive CFRP tapes. Reference beams with a cross-section of Σ200 × 70 × 2 and a length of 3 m, reinforced with CFRP tape, were tested in the four-point bending scheme. Then, the paper discusses a developed numerical model that is consistent with the subject matter of the laboratory tests. The developed numerical model was prepared to represent the failure of the connection between the beam and the composite tape. This was followed by a number of numerical analyses in order to determine the optimum adhesive layer that would allow us to achieve the maximum reduction of the displacements and strains in bent thin-walled sigma-type beams. Three thicknesses of the SikaDur adhesive layer were analyzed in the study. Based on the analyzes, it was found that the increase in the thickness of the adhesive layer slightly reduced the strain and displacement in the beams, but caused a significant decrease in the load value, at which damage appeared in the glued joint.     

Evaluation and Prediction of the Bending Behavior of Circular Hollow Steel Tube Sections Using Finite Element Analysis

Circular hollow steel tube columns are widely used in high-rise buildings and bridges due to their ductility and lower weight compared to reinforced concrete. The use of this type of steel section has several advantages over using reinforced concrete members. The present study investigates the bending behavior of steel circular hollow sections when subjected to bending loads. The variations in material characteristics with regard to position along the cross-section of a steel tube member is first considered in this experimental study, providing for a more accurate definition of the material behavior in the model. A supported beam tested by two-point loads is the loading type that is used to study the bending performance of steel tubes. Ten circular hollow beam specimens were prepared and tested up to and post the failure stage with the following dimensions: thickness (2, 3, and 6 mm), diameter (76.2, 101.6, and 219 mm), and span (1000, 1500, and 2000 mm). A finite element analysis has been conducted for these ten specimens using the ANSYS program. The finite element model is compared to experimentally obtained data to verify that both local and global behaviors are correctly considered. The load-deflection results of this analysis showed a good agreement with the experimental results. A parametric study also was performed that considered two variables, which were the effect of the presence of circular rings and the change of opening location in the length direction on the specimens’ behavior. This study showed that the presence of the circular rings in the specimen led to an increase in its ultimate strength (of 53.24%) compared with the non-presence of these rings. In contrast, the presence of openings at 30, 40, and 50% from the specimen length reduced the strength capacity by 8.76, 14.23, and 17.88%, respectively.     

Solid Truss to Shell Numerical Homogenization of Prefabricated Composite Slabs

The need for quick and easy deflection calculations of various prefabricated slabs causes simplified procedures and numerical tools to be used more often. Modelling of full 3D finite element (FE) geometry of such plates is not only uneconomical but often requires the use of complex software and advanced numerical knowledge. Therefore, numerical homogenization is an excellent tool, which can be easily employed to simplify a model, especially when accurate modelling is not necessary. Homogenization allows for simplifying a computational model and replacing a complicated composite structure with a homogeneous plate. Here, a numerical homogenization method based on strain energy equivalence is derived. Based on the method proposed, the structure of the prefabricated concrete slabs reinforced with steel spatial trusses is homogenized to a single plate element with an effective stiffness. There is a complete equivalence between the full 3D FE model built with solid elements combined with truss structural elements and the simplified homogenized plate FE model. The method allows for the correct homogenization of any complex composite structures made of both solid and structural elements, without the need to perform advanced numerical analyses. The only requirement is a correctly formulated stiffness matrix of a representative volume element (RVE) and appropriate formulation of the transformation between kinematic constrains on the RVE boundary and generalized strains.     

Effect of Tension-Compression Asymmetry Response on the Bending of Prismatic Martensitic SMA Beams: Analytical and Experimental Study

This paper aims to analytically derive bending equations, as well as semi-analytically predict the deflection of prismatic SMA beams in the martensite phase. To this end, we are required to employ a simplified one-dimensional parametric model considering asymmetric response in tension and compression for martensitic beams. The model takes into account the different material parameters in martensite twined and detwinned phases as well as elastic modulus depending on the progress of the detwinning process. In addition, the model considers the diverse slope of loading and unloading in martensite detwinned phases favored by tension and compression. To acquire general bending equations, we first solve the pure bending problem of a prismatic SMA beam. Three different phases are assumed in the unloading procedure and the effect of neutral fiber distance from the centerline is also considered during this stage. Then according to the pure bending solution and employing semi-analytical methods, general bending equations of an SMA beam are derived. Polynomial approximation functions are utilized to obtain the beam deflection–length relationship. To validate the attained analytical expressions, several three- and four-point bending tests were conducted for rectangular and circular SMA beams. Experimental data confirm the reasonable accuracy of the analytical results. This work may be envisaged to go deep enough in investigating the response of SMA beams under an arbitrary transverse loading and stress distribution during loading and unloading, as well as findings may be applicable to a good prediction of bending behavior.     

Composite Hat Structure Design for Vehicle Safety: Potential Application to B-Pillar and Door Intrusion Beam

Regarding crashworthiness, many published works have focused on designing thin-walled structures for frontal collisions compared to side-impact collisions. This paper presents an experimental investigation and finite element modelling of a carbon-reinforced thin-walled top-hat section subjected to quasi-static and dynamic transverse bending loads at different impact speeds. The top-hat sections and their closure assembly plates were made of MTM44 prepreg carbon. The specimens were manufactured by vacuum bagging. Dynamic work was performed to validate the results obtained from the finite element analysis (FEA). The predicted results are in good agreement with the experimental results. The study also showed that the peak load and energy absorption owing to dynamic loading were higher than those under static loading. In the four-point bend analysis, the stacking sequence affected the energy absorption capabilities by 15–30%. In addition, the distance between the indenters in the four-point analysis also affected the energy absorption by 10% for the same impact condition, where a larger distance promoted higher energy absorption. The study also demonstrated that a top-hat shaped thin-walled structure is suitable for deep intrusion beams in vehicle doors for side-impact crashworthiness applications.     

Test and Numerical Model of Curved Steel–Concrete Composite Box Beams under Positive Moments

Compared with straight steel–concrete composite beams, curved composite beams exhibit more complicated mechanical behaviors under combined bending and torsion coupling. There are much fewer experimental studies on curved composite beams than those of straight composite beams. This study aimed to investigate the combined bending and torsion behavior of curved composite beams. This paper presents static loading tests of the full elastoplastic process of three curved composite box beams with various central angles and shear connection degrees. The test results showed that the specimens exhibited notable bending and torsion coupling force characteristics under static loading. The curvature and interface shear connection degree significantly affected the force behavior of the curved composite box beams. The specimens with weak shear connection degrees showed obvious interfacial longitudinal slip and transverse slip. Constraint distortion and torsion behavior caused the strain of the inner side of the structure to be higher than the strain of the outer side. The strain of the steel beam webs was approximately linear. In addition, fine finite element models of three curved composite box beams were established. The correctness and applicability of the finite element models were verified by comparing the test results and numerical calculation results for the load–displacement curve, load–rotational angle curve, load–interface slip curve, and cross-sectional strain distribution. Finite element modeling can be used as a reliable numerical tool for the large-scale parameter analysis of the elastic–plastic mechanical behavior of curved composite box beams.     

Effect of Shear and Pure Bending Spans on the Behaviour of Steel Beams with Corrugated Webs

The shear span-to-effective depth ratio is known to modulate the shear behaviour of steel beams with corrugated webs (SBCWs). However, present design standards for SBCWs do not adequately address this issue. The impact of shear span-to-effective depth ratio and pure bending spans on the failure mechanism of SBCWs was investigated in this study. Under four-point bending, three beams with shear-span-to-effective-depth-ratios ranging from 1.65 to 2.5 were examined to investigate the relationship between shear and bending spans and failure mechanisms. ANSYS software was used to create finite element models for the tested SBCWs using the finite element technique. In addition, the experimental findings are compared to two codes, specifically DASt-Rishtlinie015 and EN 1993-1-5. Moreover, an analytical section comprised of the creation of a three-dimensional (3D) finite element model (FEM) was implemented. Finally, a parametric study using the verified FE model was conducted to assess the impact of shear and pure bending spans on the overall behaviour of SBCWs. As a result, the shear span and horizontal fold length of CWSBs are key components for determining the strength and failure modes of beams. Furthermore, the load capabilities and stiffness of CWSBs were more greatly affected by increasing the shear span than by increasing the pure bending one.     

Shear Performance of Reinforced Concrete Beams with Small Circular Openings Strengthened Using Rectangular and Octagonal-Shaped Reinforcement

An experimental case study was carried out to investigate the shear performance of reinforced concrete beams with small circular openings under a cyclic anti-symmetric bending moment. The openings were strengthened by using a newly developed reinforcement continuously bent into rectangular and octagonal shapes, which was convenient for installation and effective for crack control. The presence of web opening reinforcement, the reinforcing method, and the web opening spacing were employed as main variables in the design of five specimens. The cyclic performance of all specimens was evaluated in terms of failure mode, crack pattern, strength and stiffness degradation, and strain distribution. Experimental results were discussed to assess the suitability of the proposed web opening reinforcement in RC web opening beams. It was confirmed that the proposed web opening reinforcement exhibited outstanding crack control and served as a shear resistance component in place of the concrete cross-section lost due to web openings. Finally, the shear strength of all specimens, obtained from the cyclic loading tests, were compared with those obtained from the equation proposed by Mansur (1998) and the Architectural Institute of Japan standard 2010.     

A Method to Calculate the Support Length of Beams Resting on Masonry Walls

Rehabilitation, strengthening, and retrofitting of existing masonry buildings represent an important challenge for the construction engineering field. Often, slab strengthening/retrofitting is performed by replacing existing timber and steel beams or by adding new beams to improve the slab load-carrying capacity. The computation of the stresses at the beam–masonry interface (i.e., the contact pressure) is crucial to properly design the beam support length, preventing local failure of masonry and beam. This paper presents a simple analytical procedure to compute the contact pressure at the beam–masonry interface. The analytical procedure is validated by comparison between analytical and corresponding numerical results obtained by finite element modeling. Different types of beam (solid and laminated timber beams and steel beams) were considered, as well as different support conditions (simply resting on the wall considering different support lengths or fully embedded). The results obtained show that the method proposed is simple and reliable, which makes it suitable for professional practice.     

Experimental Analysis of Steel Circular Hollow Section under Bending Loads: Comprehensive Study of Mechanical Performance

The present study aimed at evaluating the mechanical performance under bending loads of circular hollow sections of steel. Different bending tests have been carried out by applying two-point loads, to determine and examine the effects of the diameter, the thickness of the section, and the span of the beam on the performance of the steel tube. The effects of square opening and variation in the number of openings on the performance of these sections have also been examined. Ten samples of hollow circular beams of varying thickness (2 mm, 3 mm, and 6 mm), varying diameter (76.2 mm, 101.6 mm, and 219 mm), and varying span (1000 mm, 1500 mm, and 2000 mm) were fabricated and tested for pre-failure and post-failure stages. The dimensions of the reference specimen considered were 3 mm in thickness, 101.6 mm in diameter, and 1500 mm in span. The results have shown that on increasing the section thickness by 200%, ductility and bearing strength were enhanced by 58.04% and 81.75%, respectively. Meanwhile, decreasing the section thickness by 67%, ductility and bearing strength were reduced by 64.86% and 38.87%, respectively. Moreover, on increasing the specimen diameter and on decreasing span, a significant increase in bearing strength and stiffness was observed; however, ductility was reduced. Meanwhile, on increasing the span of the specimen, all the parameters observed, i.e., bearing strength, stiffness, and ductility, decreased. On observing the ultimate strength of each specimen with square opening, the ultimate strength was reduced by 17.88%, 19.71%, and 14.23% for one, two-, and three-square openings, respectively. Moreover, the ductility was significantly reduced by 72.40%, 67.71%, and 60.88% for one, two-, and three-square openings/apertures, respectively, and led to the sudden failure of these specimens. The local buckling failure dominated for specimens having a D/t ratio more than 50 and showed very negligible levels of ovalization of the cross-section. Local buckling failure was observed to be prevented after providing the circular rings in the specimen, since bearing strength increased compared with the specimen without rings.     

The Influence of CFRP Sheets on the Load-Bearing Capacity of the Glued Laminated Timber Beams under Bending Test

Composite materials are increasingly used to strengthen existing structures or new load-bearing elements, also made of timber. In this paper, the effect of the number of layers of Carbon Fiber Reinforced Polymer (CFRP) on the load-bearing capacity and stiffness of Glued Laminated Timber beams was determined. Experimental research was performed on 32 elements—a series of eight unreinforced beams, and three series of eight reinforced beams: with one, three and five layers of laminate each. The beams with a cross-section of 38 mm × 80 mm and a length of 750 mm were subjected to the four-point bending test according to standard procedure. For each series, destructive force, deflection, mode of failure, and equivalent stiffness were determined. In addition, for the selected samples, X-ray computed tomography was performed before and after their destruction to define the quality of the interface between wood and composite. The results of the conducted tests and analyses showed that there was no clear relationship between the number of reinforcement layers and the load-bearing capacity of the beams and their stiffness. Unreinforced beams failed due to tension, while reinforced CFRP beams failed due to shear. Despite this, a higher energy of failure of composite-reinforced elements was demonstrated in relation to the reference beams.     

Bending Behaviour of Prestressed T-Shaped Concrete Beams Reinforced with FRP—Experimental and Analytical Investigations

Materials such as high performance (HPC) or ultra-high performance concrete (UHPC), and fibre-reinforced polymer (FRP) reinforcement can be used to improve the resource efficiency in concrete construction by, for example, enabling the production of thin-walled structures. When building filigree concrete beams two essential factors must be considered: the low stiffness of the structure and the bond between the materials. By prestressing the structural stiffness is improved while an adequate concrete cover ensures sufficient bond strength. Based on this the bending behaviour of prestressed T-shaped beams reinforced with FRP, focussing on determining the influence of four parameters on the bearing capacity, bond behaviour and failure mode, is investigated in this paper. Comprehensive experimental investigations prove the potential of the approach and show that a reduction of the web thickness down to 40 mm, a lower concrete quality, and the use of glass FRP instead of carbon FRP allow a more resource-efficient structure while the applied prestressing leads to a higher utilisation of the high performance materials.     

The Effect of Steel Beam Elastic Restraint on the Critical Moment of Lateral Torsional Buckling

This paper reports the results of the next stage of the authors’ investigations into the effect of the elastic action of support nodes on the lateral torsional buckling of steel beams with a bisymmetric I-section. The analysis took into account beam elastic restraint against warping and against rotation in the bending plane. Such beams are found in building frames or frame structures. Taking into account the support conditions mentioned above allows for more effective design of such elements, compared with the boundary conditions of fork support, commonly adopted by designers. The entire range of variation in node rigidity was considered in the study, namely from complete freedom of warping to complete restraint, and from complete freedom of rotation relative to the stronger axis of the cross section (free support) to complete blockage (full fixity). The beams were conservatively assumed to be freely supported against lateral rotation, i.e., rotation in the lateral torsional buckling plane. Calculations were performed for various values of the indexes of fixity against warping and against rotation in the beam bending plane. In the study, formulas for the critical moment of bilaterally fixed beams were developed. Also, approximate formulas were devised for elastic restraint in the support nodes. The formulas concerned the most frequent loading variants applied to single-span beams. The critical moments determined in the study were compared, with values obtained using LTBeamN software (FEM). Good compliance of results was observed. The derived formulas are useful for the engineering design of this type of structures. The designs are based on a more accurate calculation model, which, at the same time offers simplicity of calculation.     

Flexural Response and Failure Analysis of Solid and Hollow Core Concrete Beams with Additional Opening at Different Locations

It is essential to make openings in structural concrete elements to accommodate mechanical and electrical needs. To study the effect of these openings on the performance of reinforced concrete (RC) elements, a numerical investigation was performed and validated using previous experimental work. The effect of the position and dimension of the opening and the beam length on the response of the beams, loads capacities, and failure modes was studied. The simulated RC beams showed different responses, loads capacities, and failure modes depending on the position and dimension of the opening. The transversal near support opening (TNSH) and longitudinal holes (LH) showed lower effects on the load capacities of the beams than the transversal near center opening (TNCH). The supreme reduction percentages of the load capacity (µ_u%) for beams with TNCH and TNSH were 37.21% and 30.34%, respectively (opening size = 150 × 150 mm²). In addition, the maximum µ_u% for beam with LH was 17.82% (opening size = 25% of the beam size). The TNSH with a width of less than 18.18% of the beam shear span (550 mm) had trivial effects on the beam’s load capacities (the maximum µ_u% = 1.26%). Although the beams with combined LH and TNCH or LH and TNSH showed different failure modes, they experienced nearly the same load reductions. Moreover, the length of the beam (solid or hollow) had a great effect on its failure mode and load capacity. Finally, equations were proposed and validated to calculate the yield load and post-cracking deflection for the concrete beams with a longitudinal opening.     

Analytical and Numerical Approaches for the Design of Concrete Structural Elements with Internal BFRP Reinforcement

Although basalt fiber-reinforced polymers (BFRPs) have been known for a few decades, new trends such as sustainability and environmental care have provoked intensified research on its structural applications. In construction, BFRPs, as internal reinforcement, have to compete with traditional steel reinforcement products. Because of their high resistance to aggressive environments, BFRPs have emerged as an attractive solution for the infrastructure in coastal zones. In this article, we discuss some aspects of BFRP applications such as flexural reinforcement of concrete beams. The mechanical performances of a BFRP-reinforced beam are illustrated by using a widely accepted model based on the classical beam theory. The elasticity modulus of the BFRP reinforcement is lower than that of structural steel. Therefore, to meet serviceability requirements (e.g., in terms of limitation on the mid-span deflection of a beam), BFRP could be pre-tensioned. The positive effect of pre-tensioning is outlined by finite element analysis. An original numerical procedure involves a constitutive relation for concrete based on damage mechanics. Experimental results previously reported in the literature provide the background for the numerical model procedures. The numerical procedure predicts the mechanical response of the concrete beam with BFRP reinforcement subjected to four-point bending in terms of load-deflection relationship and dominant failure mode.     

Debonding of Thin Bonded Rubberised Fibre-Reinforced Cement-Based Repairs under Monotonic Loading: Experimental and Numerical Investigation

In this study, the durability of cement-based repairs was observed, especially at the interface of debonding initiation and propagation between the substrate–overlay of thin-bonded cement-based material, using monotonic tests experimentally and numerically. Overlay or repair material (OM) is a cement-based mortar with the addition of metallic fibres (30 kg/m³) and rubber particles (30% as a replacement for sand), while the substrate is a plain mortar without any addition, known as control. Direct tension tests were conducted on OM in order to obtain the relationship between residual stress-crack openings (σ-w law). Similarly, tensile tests were conducted on the substrate–overlay interface to draw the relationship between residual stress and opening of the substrate–overlay interface. Three-point monotonic bending tests were performed on the composite beam of the substrate–overlay in order to observe the structural response of the repaired beam. The digital image correlation (DIC) method was utilized to examine the debonding propagation along the interface. Based on the different parameters obtained through the above-mentioned experiments, a three-point bending monotonic test was modelled through finite elements using a software package developed in France called CAST3M. Structural behaviour of repaired beams observed by experimental results and that analysed by numerical simulation are in coherence. It is concluded from the results that the hybrid use of fibres and rubber particles in repaired material provides a synergetic effect by improving its strain capacity, restricting crack openings by the transfer of stress from the crack. This enhances the durability of repair by controlling propagation of the interface debonding.