Cross-sectional Stiffness Research Articles

Effect of Cross-Section Stiffness on Strength of Rectangular Steel

Concrete-filled steel tubes (CFSTs) have better application in the application of beams and columns. This application form has obvious advantages, mainly because they are not restricted by the forming process, and the filled concrete does not need long-term maintenance. However, the design and analysis of steel-concrete beam-columns is a complex task involving many factors. In the design of CFSTs, it is essential to understand the influence of these factors on the behavior of steel-concrete members. In particular, the cross-sectional shape of the member has a significant impact on its bearing capacity, stiffness, and buckling behavior. However, there is relatively little research on the influence of member slenderness on the strength of CFSTs. Therefore, this study conducted an in-depth analysis of the stability of the member, and explored in detail the influence of the member slenderness ratio on the section properties and the overall bending strength of the beam. This study provides a basis for the application of CFSTs in beam-column design and analysis. In the bending strength analysis, the member slenderness ratio has an important influence. Smaller slenderness ratios have better strength performance, but the attenuation is also relatively significant. The larger the slenderness ratio, the slower and more stable the strength change becomes. In terms of section properties, when the slender section is reached, the influence of effective section reduction will be greater, and the strength reduction may exceed the engineering allowable error range. Therefore, special attention should be paid when using slender sections.

Cross-sectional analysis of initially curved composite beams with rectangular and circular sections using an asymptotic meshless method

An analytical meshless cross-sectional dimensional reduction method is developed to perform structural analysis of initially curved composite beams. By introducing the Pascal polynomials in the Cartesian coordinates system for beams with rectangular cross-sections and in the polar coordinates system for the beams with circular cross-sections to the warping field, a three-dimensional beam problem can be split into a two-dimensional cross-sectional analysis and a one-dimensional along the reference line of the beam. The obtained cross-sectional stiffness matrix based on higher-order of the strain energy can be incorporated into a one-dimensional finite element solution for initially curved composite beams, for the purpose of strain and stress analysis. Finally, the three-dimensional strain through the thickness of the beam can be achieved by the recovery analysis. The present method takes advantage of Pascal polynomials so that the solution procedure will be more simplified and computationally more efficient compared to three-dimensional finite element (3D FE) method. The proposed method for different isotropic and anisotropic beams is examined and compared with the literature, 3D FE, and Variational Asymptotic Beam Sectional (VABS) package which is a finite element based cross-sectional analysis tool for composite beams.

Sensitivity of cross-sectional compliance to manufacturing tolerances for wind turbine blades

Abstract. Wind turbine blades are complex structures and, despite advancements in analysis techniques, differences persist between predictions of their elastic response and experimental results. This undermines confidence in the ability to reliably design and certify novel blade designs that include self-regulating features like bend–twist coupling. To address these discrepancies, this study investigates the influence of manufacturing tolerances on the compliance properties of blade cross-sections, focusing specifically on a previously disregarded feature: the trailing edge bondline. To conduct this investigation, the validated cross-sectional modelling tools BECAS and VABS are used to demonstrate that even small geometric variations can have significant influence on cross-sectional stiffness properties. The results are further examined and substantiated through the utilisation of 3D finite element models, adopting both shell and solid elements. We reaffirm that an accurate geometric representation of the cross-section is necessary to adequately capture the shear flow within it and assure accurate predictions on cross-sectional stiffness properties, providing updated guidelines for designers in industry.

Effects of using different materials at interface of trapezoidal reinforced concrete infilled frames–analytical and experimental approaches

Infilled frames are generally formed by the composite interaction between the frame and the infilled wall used for functional purposes. The composite interaction increases the in-plane lateral stiffness of the frame, which is considered an advantage. However, the interaction also alters the ductile mode of failure to the brittle mode along with the increased base shear owing to its higher stiffness compared with the bare frame. A detailed and comprehensive study of the literature revealed that many of research works have been done on rectangular and square frames, and studies on trapezoidal infilled frames are scarce. In this article, we studied different configurations of reinforced concrete frame structures known as trapezoidal frames, which have higher stiffness than rectangular frames. A trapezoidal frame is used for industrial buildings, and its behavior under a lateral load has already been established for a bare frame. However, the interaction and behavior of the infilled frame were investigated in this research. The behavior of a trapezoidal single-story frame was examined under both lateral loading and various interface materials. One of the most frequently suggested methods for infilled-frame analysis is the equivalent diagonal strut. Effective strut width design recommendations are available for rectangular and square frames but not for trapezoidal frames for macro modeling. Hence, to make the design easier, an effective diagonal width was developed for different interface materials with respect to the relative stiffness of various frame cross-sections, and further validation was conducted with a framework of ideology from biomimicry using the nature of a one-sixth scale model. The effective strut width for the trapezoidal infilled frame varied between d/8 and d/9 for the cement mortar and cork interfaces, where d is the diagonal length of the frame.

Simplified Method for Calculating the Bearing Capacity of Slender Concrete-Filled Steel Tubular Columns

Concrete-filled steel tubular (CFST) columns are one of the most effective reinforced concrete structures, and improving their calculation is a critical task. The purpose of this study was to develop a simplified method for calculating slender CFST columns, taking into account the effect of lateral compression. The idea of the method is to use the equation of a reinforced concrete column’s longitudinal bending, without taking into account the effect of lateral compression. To take into account the lateral effects, the cross-sectional stiffnesses are corrected based on the analysis of the stress–strain state in the cross-sectional plane using the finite element method. The developed method was implemented by the authors in the MATLAB environment. The approbation of the proposed method was carried out on experimental data for centrally compressed columns of a circular cross-section, as well as eccentrically compressed columns of a circular and square cross-section, presented in two papers. For the centrally compressed columns, we conducted a study on the influence of initial imperfections in the form of eccentricities and initial curvatures on the value of the ultimate load. For the eccentrically compressed columns of the circular and square cross-section, the area of their effective operation was determined.

Asymptotic analysis of Timoshenko-like orthotropic beam with elliptical cross-section

This work presents the asymptotically exact analysis of homogeneous-orthotropic prismatic beam with elliptic cross-section. Variational Asymptotic Method (VAM) has been used to systematically reduce the 3D elastic problem of beam analysis into 2D cross-sectional analysis and 1D along the length of beam analysis. This reduction simplifies beam analysis to a great extent. The 2D analysis supplies cross-sectional stiffness constants to the 1D beam problem. This analysis provides closed-form expression of cross-sectional stiffness constants, 3D displacement and strain fields in terms of 1D strain measures. Present work does not make any a priori ad-hoc assumptions about the deformation as it uses VAM and ensures asymptotic correctness of the solution. The results are obtained for Classical and Timoshenko-like beam models loaded with most general loads. These results are validated by comparing them with existing results in the literature and Finite Element Analysis (FEA) results. Current results are in close agreement with FEA results.

Rigidity of partially concreted steel beams and steelreinforced floors

The use of steel-reinforced (composite) floor structures with partially concreted steel beams and prefabricated flooring elements is an effective solution in terms of reducing the material consumption and increasing the structural rigidity. The experimental results of partially concreted composite beams and beams as part of full-size ceilings are studied and analyzed herein. It is shown that the stiffness graph of simple steel-reinforced concrete beams of any shape can be divided into 3 stages: an initial stiffness drop, normal operation, and transition to the limit state with subsequent destruction. The boundaries of these stages are identified for each beam type. The stiffness of the combined cross-section of the partially concreted beam with the rod reinforcement is calculated using well-known formulas from regulatory documents. The element rigidity without rod reinforcement is determined with the decreasing coefficient. Tests of full-size ceilings with partially concreted beams and prefabricated floors confirm the possibility of using standard formulas for the stiffness calculation. However, the width of the compressed concrete flange should be taken into account by less than 3 times than for monolithic slab. The destruction of bending composite structure is accompanied by plastic deformation in flanges of I-beam, destruction of compressed concrete and steel–concrete interaction. However, it does not lead to zeroing of its rigidity. When residual stiffness reaches the ultimate strength state, it is at least 60–70 % of its normative value. This rigidity can be used for the progressive collapse analysis of buildings.

Numerical modelling of the process chain for aluminium Tailored Heat-Treated Profiles

Lightweight construction in modern car design leads to an increased usage of various aluminium semi-finished products. Besides sheet material, aluminium extrusion profiles are frequently used due to their high stiffness and variety of possible cross-sections. However, similar to sheet material, aluminium profiles exhibit limited formability in comparison to mild steel materials. One possibility to increase the forming limits of precipitation hardened aluminium alloys is the so-called Tailored Heat Treatment technology. By a local short-term heat treatment, the material is softened and the material flow can be controlled to reduce stresses in critical forming zones. The purposeful definition of the heat treatment zones is mandatory to improve the forming results. Therefore, numerical methods are necessary. In this investigation, a numerical process chain is presented. It combines the thermo-mechanical simulation of a local laser heat treatment with a subsequent bending process of the heat-treated profile using the alloy EN AW-6082. The temperature distribution, mechanical properties, and finally, the bending result of the numerical model are validated by experimental tests.

Comparative Analysis of Movements of Curved Ultrasonic Instruments

The paper presents a theoretical analysis of vibrations of a curvilinear rod in the form of a loop of low rigidity formed from a quarter of a circle with a constant radius, limited by an angle π/2 < γ < π and two rectilinear rods. It is indicated that in the practice of ultrasonic technology, some types of structures are known in which elastic elements are used as resonators, waveguides, oscillation transformers and instruments for influencing the processed materials. Their use makes it possible to obtain an additional impulse of force in the working area by using the potential energy caused by the action of the elastic properties of such elements. However, insufficient attention has been paid to the theoretical justification of the use of elastic elements in ultrasonic systems. In this regard, the present work is devoted to the theoretical substantiation of the use of an elastic tool made of a thin rod having the shape of a loop. The diagram and calculation of displacements of the free end of a curved rod under the action of forces directed along the longitudinal axis are given in the paper. It is shown that elastic displacements are caused by a curved shape in the form of an arc of a circle of a curved rod. For comparison, calculation schemes of two types of curved rod with an attached rod are given. In the first case, the free ends of the rectilinear rods, directed vertically downwards, make elastic movements along two coordinates. In the second case, the ends of rectilinear rods directed at a certain angle to the vertical axis and converging at the bottom point due to the symmetry of their location, make vertical movements only along one coordinate. The considered shape of the curved rod can be successfully used as a tool for performing technological tasks in the ultrasonic method of processing holes in brittle materials, spot welding, etc. Such a scheme, in contrast to the traditional ultrasonic treatment scheme based on the use of rectilinear rods, makes it possible to increase the magnitude of the vibration amplitude of the instrument due to elastic displacements of the curved section of the rod of low rigidity. The proposed form will increase the intensity of tool vibrations and increase process productivity and processing accuracy. The resulting calculation formula shows that the amount of elastic displacements of curved rods is affected by the cross-sectional stiffness and the radius of curvature of the curved part, as well as the angle of inclination of the rectilinear rod. The theoretical calculation is supplemented by a comparative experimental study of the Chladni forms for both schemes obtained on the sheet surface using abrasive particles.

Influence of Superstructure Pouring Concrete Volume Deviation on Bridge Performance: A Case Study

Due to factors such as casting, mold making, and construction errors, the actual size of the bridge structure will inevitably deviate from the designed size and dimension, and the amount of deviation between the two volumes is generally random and the location of the deviation is not fixed. However, this phenomenon that occurs in the actual practice has not been paid enough attention within existing studies. From a theoretical point of view, the apparent size of concrete will directly affect the cross-sectional stiffness, especially for statically indeterminate structures. This effect will be further reflected in the internal force and stress distribution of the structure. In addition, the variation of the poured volume of the bridge superstructure can also influence the dead-load effect of the bridge structure. Therefore, the influence of pouring concrete volume deviation (PCVD) on the cross-sectional stiffness of large-span continuous reinforced concrete rigid-frame (CRCR) bridges was first stressed and investigated in this paper. Field data of PCVD were monitored by measuring demolished sections with tools that ensure accuracy, and a sensitivity analysis was conducted to analyze the effect of PCVD on the cross-sectional stiffness at different locations. Statistical analysis of the measured data concluded that PCVD has a significant influence on the internal-force distribution and structural stiffness of the bridge, up to 30%. Finally, a theoretical method that considers the influence of PCVD was proposed based on the field monitoring data and the statistical analysis results.

On the role of dowel action in shear transfer of CFRP textile-reinforced concrete slabs

Carbon-fiber-reinforced polymer (CFRP) grids or textiles for concrete have high application potential in thin planar members such as bridge deck slabs or façade plates. With the high tensile strength of CFRP, shear failure governs design in wider regions, which calls for optimized shear models incorporating all relevant load-transfer mechanisms. The contribution of dowel action to shear resistance is often neglected in shear models derived specifically for FRP reinforcement. As reasons, the low transverse modulus of the anisotropic material and the small cross-sectional areas per reinforcement element and thus small cross-sectional stiffness are mentioned. Yet fundamental research on this mechanism for CFRP grids is amiss. This paper presents a new test setup for characterizing the dowel action of CFRP grids that are pre-strained, similar as in real applications where the reinforcement in the shear crack is stressed in flexural tension. The influence of (pre-) crack width, pre-strain and concrete cover is discussed. By comparison to results from flexural shear-tests it can be shown that, depending on the effective depth, the contribution to shear resistance can be significant. Furthermore, the important role of dowel cracking in the shear-compression failure mechanism could be analyzed using the results of the new dowel test.

Adaptive mesh refinement for finite element analysis of elastic buckling disturbance of circularly curved beams due to multiple micro-cracks damage

PurposeThis study aimed to overcome the challenging issues involved in providing high-precision eigensolutions. The accurate prediction of the buckling load bearing capacity under different crack damage locations, sizes and numbers, and analysing the influence mechanism of crack damage on buckling instability have become the needs of theoretical research and engineering practice. Accordingly, a finite element method was developed and applied to solve the elastic buckling load and buckling mode of curved beams with crack damage. However, the accuracy of the solution depends on the quality of mesh, and the solution inevitably introduces errors due to mesh. Therefore, the adaptive mesh refinement method can effectively optimise the mesh distribution and obtain high-precision solutions.Design/methodology/approachFor the elastic buckling of circular curved beams with cracks, the section damage defect analogy scheme of a circular arc curved beam crack was established to simulate the crack size (depth), position and number. The h-version finite element mesh adaptive analysis method of the variable section Euler–Bernoulli beam was introduced to solve the elastic buckling problem of circular arc curved beams with crack damage. The optimised mesh and high-precision buckling load and buckling mode solutions satisfying the preset error tolerance were obtained.FindingsThe results of testing typical examples show that (1) the established section damage defect analogy scheme of circular arc curved beam crack can effectively realise the simulation of crack size (depth), position and number. The solution strictly satisfies the preset error tolerance; (2) the non-uniform mesh refinement in the algorithm can be adapted to solve the arbitrary order frequencies and modes of cracked cylindrical shells under the conditions of different ring wave numbers, crack positions and crack depths; and (3) the change in the buckling mode caused by crack damage is applicable to the study of elastic buckling under various curved beam angles and crack damage distribution conditions.Originality/valueThis study can provide a novel strategy for the adaptive mesh refinement for finite element analysis of elastic buckling of circular arc curved beams with crack damage. The adaptive mesh refinement method established in this study is fundamentally different from the conventional finite element method which employs the user experience to densify the meshes near the crack. It can automatically and flexibly generate a set of optimised local meshes by iteratively dividing the fine mesh near the crack, which can ensure the high accuracy of the buckling loads and modes. The micro-crack in curved beams is also characterised by weakening the cross-sectional stiffness to realise the characterisation of locations, depths and distributions of multiple crack damage, which can effectively analyse the disturbance behaviour of different forms of micro-cracks on the dynamic behaviour of beams.

NUMERICAL ANALYSIS OF GEOMETRIC AND MATERIAL NONLINEARITY OF BEAMS IN THE PLANE

The paper presents a simultaneous numerical analysis of the geometric and material nonlinearity of the beams. It describes a process of determining the bearing capacity of a stratified cross-section of a beam made of homogeneous and isotropic material in linear and nonlinear domains of material behaviour. Material nonlinearity is analysed by the variation of the cross-sectional stiffness of the beam on bending EI in the stiffness matrix of the system obtained according to the first-order theory. Geometric nonlinearity is introduced into the calculation using the geometric stiffness matrix of the system. Numerical examples present an application of the procedure for solving problems of nonlinear structure analysis. The calculation results obtained in accordance with the procedure described in the paper are compared with the results of the SCIA software package.

Modern Design Methods on Optimised Novel Aluminium Profiles

Within the framework of optimisation of structural elements, in the last years, significant activity has been demonstrated towards developing new sectional designs beyond standardised forms aiming to combine aesthetic innovation, material efficiency, and weight over stiffness, together with structural reliability and manufacture cost savings. Moreover, in terms of sustainability performance, as material-weight reduction leads to less carbon emissions from production to installation processes, the pursuit of suitable materials that can correspond to this challenge becomes imperative. In this context, aluminium is lightweight and corrosion resistant, but due to its low elastic modulus, an increased cross-sectional stiffness is required. In this paper, 16 previously optimised aluminium cross-section profiles are presented and analysed using the finite element analysis software ABAQUS. The obtained ultimate compression resistances were compared with the predictions made in accordance with Eurocode 9, the direct strength method (DSM), and the continuous strength method (CSM). The percentage of difference of these design methods with respect to FE results is depicted. The outcomes point out the vagueness in accuracy of the prediction methods, particularly in reference to stocky or slender cross-sections.

Analysis on the crimping quality of overhead transmission line conductors considering equivalent cross-sectional stiffness

Approximately 58% of wire failures are caused by slippage and fracture of electrical connectors, and the crimping quality analysis of connectors is based on equivalent cross-sectional stiffness. First, a JL/GLA 400/35 steel cord aluminum strand and NY-400/35 strain clamp are selected to fabricate 26 groups of specimens with different pipe penetration depths, opposite edge distances, inner diameters of the aluminum tube, and die widths. Then, through crimping tests on the aluminum tube and conductor and the steel core and steel anchor, five main crimping failures, namely, the slip at the outlet of the clamp, the slip at the outlet of the clamp with some broken aluminum strands, fracture of the aluminum tube in the non-pressure area, wire fracture at the outlet of the clamp, and separation of steel anchors, are observed. Finally, a failure analysis method for conductor crimping is proposed based on equivalent cross-sectional stiffness. Through the analysis of grip force and crimping quality, four failure modes and simplified curves of the load–displacement curve are obtained, and the failure principle of the conductor crimping is further elaborated. The results show that the stress release caused by the steel core and steel anchor of the crimping wire and the crimping aluminum tube and wire is the main reason for the slippage and fracture of the transmission line conductors and that it is also the key to improve the installation quality of the transmission line.

Study on mechanical properties of wind turbine blades with bend-twist coupling effect

Bend-twist coupling (BTC), a method of passive load alleviation for turbine blade, has a significant influence on blade mechanical properties. The coupling behavior between bending and twisting motions stems from the material anisotropy in blade laminate or from the unique blade geometry such as sweep, deflection, and pre-bending. The material-based approach is employed in this research to determine influence regularity of BTC design on blade mechanical properties. To begin with, the blade property analysis tool PreComp that integrates a shear flow method with the classical laminate theory is adopted to compute the cross-sectional stiffnesses of the blades with different degree of BTC effect. Next, the bend-twist coupling coefficients for the BTC blades with different fiber orientation are calculated. Finally, the remaining mechanical properties including static performance, modal characteristics and buckling limits for different BTC blades are determined by the finite element method and the influence of changes in the degree of BTC effect on all these mechanical properties is further evaluated. The results show that the BTC effect markedly influences the different mechanical properties of the blade in different patterns. The 20° BTC blade has the highest BTC coefficient and the edgewise BTC coefficient at 100 m is 2.5 times higher than the flapwise BTC coefficient, while the maximum value of the torsional modal frequency of 3.8429 Hz and the greatest critical buckling load of 4328.1 kN corresponds to the 10° BTC blade and the 15° BTC blade respectively.

Experimental and numerical study on the axial compression performance of the prestressed sleeved members

The progressive collapse of large-span spatial structures can be triggered by the buckling of compression members. To further improve the stable load capacity of compression members, this study proposes a prestressed sleeved member by combining a prestressed stayed column system with a sleeved member. The experimental results show that the prestressed sleeved members possess a high load capacity, large secondary stiffness and moderate recovery performance, with the buckling modes of the members including first-order and second-order buckling. A nonlinear finite element (FE) model for the prestressed sleeved members is developed based on the experimental model. In addition, a series of parametric analyses are conducted to investigate the effects of the initial imperfection amplitude ratio, inner tube length to slenderness ratio, strand cross-sectional area ratio, inner and outer tube cross-sectional stiffness ratio and central support plate equivalent height ratio on the axial compression performance of the specimens. Furthermore, a simplified calculation model of the prestressed sleeved members is proposed for the case of second-order buckling, and theoretical calculation formulas are presented for three key points of the axial force–displacement curves of specimens. In contrast to the theoretical and FE results, the maximum errors of axial displacement and axial force do not exceed 15%. In addition, the steel strand tension, the contact force, and the lateral deflection of the middle section of the inner half-tube are highly consistent, which verifies the proposed relevant assumptions and theoretical calculation formulae.

Flexural strengthening of reinforced concrete T-beams using a composite of prestressed steel wire ropes embedded in polyurethane cement (PSWR-PUC): Theoretical analysis

A composite of prestressed steel wire ropes embedded in polyurethane cement (PSWR-PUC) is a new and efficient strengthening method. This paper mainly studies theoretical analysis of reinforced concrete (RC) T-beams strengthened with PSWR-PUC. First, the mechanical properties of the polyurethane cement (PUC) such as ultimate flexural strength and ultimate compressive strength were studied experimentally. Second, the calculation methods of cracking load and maximum bearing capacity were proposed. Third, degree of prestress, ratio of reinforcement and thickness of PUC responsible for the short-term cross-sectional stiffness were analyzed. Finally, calculation equations for predicting average crack spacing and maximum crack width were suggested. The results from using the proposed methods agree well with the experimental ones. Theoretical analysis and proposed calculation equations are feasible.

Simple consideration of second-order effects in the calculation of RC column fire resistance

The article presents a simple method of calculating the fire resistance of reinforced concrete columns with second-order effects taken into consideration. To involve the effects, the calculations include an increase in the eccentricity of the initial longitudinal force that is determined according to the Nominal stiffness method (EN 1992-1-1) and Euler's formula. It is assumed that the stiffness of the column cross-section in fire conditions decreases in proportion to a decrease in the moment of inertia of the concrete cross-section with dimensions reduced in accordance with the assumptions of the 500°C Isotherm method (EN 1992-1-2). The load-bearing capacity of the column cross-section, under the longitudinal force acting on the eccentricity enlarged according to the proposed procedure, is calculated with the 500°C Isotherm method.The calculation results are compared with the available in the literature test results of RC columns of 30 × 30 and 20 × 20 cm cross-section which failed when heated, under the simultaneous action of compressive force. It is found that the calculation results were well consistent with the test results of columns with a cross-section of 30 × 30 cm while the results of the calculated load-bearing capacity of columns with a cross-section of 20 × 20 cm were underestimated.

DETERMINATION OF BENDING OF A BEAM FROM A NONLINEAR DEFORMABLE MATERIAL BY RITZ-TIMOSHENKO METHODS AND FINITE DIFFERENCES TAKING INTO ACCOUNT DEGRADATION FUNCTIONS OF CROSS SECTION RIGIDITY

The article solves the problem of determining the deflections of a beam made of a nonlinearly deformable material - a polyester composite held in water using the numerical methods of Ritz-Timoshenko and finite differences. The influence of the aggressive environment on the material of the structure was taken into account by introducing the degradation function of the stiffness of the element cross-sections into the calculation algorithms of the above methods. The problem of determining the time and conditions for the onset of the limiting state of the structure in the second group in accordance with the current norms and rules has been solved.