Beam Section Research Articles

Buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model

The aim of this study is to explore the buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model. The study includes the influence of turbulence integral length scale and wind yaw angle on the magnitude of buffeting force, spatial distribution of buffeting force, and buffeting displacement response. Under larger turbulence integral length scale, the buffeting force of the box beam and it’s spanwise correlation are larger, which verifies the three-dimensional effect of the buffeting force. It is worth mentioning that, unlike traditional section models, there are differences in the pressure values of the pressure strips in the aeroelastic model at the flow separation point, which may be influenced by the cables. The experimental results of different wind yaw angles show that there is little difference in the buffeting force of the box beam section under the condition of 0°∼15° wind yaw angle, indicating that the maximum buffeting response will occur in the range of 0°∼15° wind yaw angle, which is consistent with the displacement results measured by the aeroelastic model. In addition, by fixing the model with a steel wire, the static and vibration states of the model were achieved. However, due to the high stiffness of the model, it can only generate small buffeting displacement, and the self-excited force component can be almost ignored. There is no significant difference in the results between the static and vibration states.

Effect of steel fibers and the fiber-concrete adhesion stress on the nonlinear shear behavior of beams

In this article, a theoretical model in nonlinear elasticity is presented to analyze the influence of the percentage of steel fibers and the effect of the fiber-concrete bond stress on the shear force at the rupture of beams subjected to the combined effect of bending moment, normal force, and shear force. For a given beam section, it is defined by a succession of layers of concrete and longitudinal steel elements. Each layer is defined by its height hi, width bi, and position relative to one end of the section YGi. Each longitudinal steel element is also defined by its cross-sectional area and position relative to one end of the section. The steel fibers are defined by volume percentages of 0.5%, 1%, 1.5%, and 2%, taking into account the mechanical nonlinearity of the materials. This model is based on the multilayer analysis of sections and an iterative solution procedure for each layer and each section, considering a given longitudinal deformation state and shear stress. The global equilibrium of the sections is analyzed under the assumption of flat longitudinal deformations but with, in principle, an interdependence of longitudinal normal stresses and shear stresses. In this study, using the principle of virtual work, equilibrium equations for deformations and stresses, as well as partial compatibility equations between concrete deformations and mean deformations, are derived. Comparative examples between ordinary reinforced concrete beams with variable shapes and reinforcement details, and those reinforced with steel fibers, are presented to demonstrate the accuracy of the proposed model for simulating the nonlinear shear response of beams.

Research on the anti-collapse performance of steel frame structures with infilled walls in the form of reduced beam sections connections

Steel has more deformation capacity and resistance to compression buckling than concrete materials, which providing steel frames a distinct edge in preventing collapse. This study examines the anti-collapse performance and mechanism of steel frame structures with infilled walls in the form of reduced beam section connections. It also examines the effects of wall thickness, frame aspect ratio, and connection control size on performance and addresses the applicability of current code formulas in the early deformation of the structure. The study discovered that steel frame structures with infilled walls in the form of reduced beam section connections can, during the failure stage, enhance the infilled wall's contribution to the collapse bearing capacity, thereby stimulating the structure's potential performance, in contrast to those with infilled walls in the form of non-reduced beam section connections. Due to the supporting effect of the double strut that forms inside the infilled wall during the failure stage, steel frame structures with infilled walls that have non-reduced beam section connections have higher deformation capacity than corresponding pure frames; however, this effect also decreases the deformation capacity of the structure with reduced beam section. Furthermore, the infilled walls cause the structure to collapse in a same way across a range of aspect ratios, yet their contribution to the structural bearing capacity differs across these same aspect ratios. It is noteworthy that altering the local connection control size can greatly enhance the structure anti-collapse performance, even in unfavorable aspect ratio scenarios. The study also discovered that the bearing capacity of the structure studied in this paper was overestimated by the FEMA356-2000 code and the MSJC code, which were used to predict the initial bearing capacity of infilled frames. The former's overestimation reaches a maximum of 39 %, while the latter's prediction is only accurate within a limited range of aspect ratios. Furthermore, the formula by Qian and Li, which has a maximum error of 9 % in bearing capacity prediction within the standard range of aspect ratios, is better appropriate for the failure mode of the structure described in this study.

A recursive trapezoid-based algorithm designed to compute the strength- and stiffness-related geometric properties of beams with polygonal cross-sections

A new recursive trapezoid-based algorithm is proposed for calculating the strength- and stiffness-related geometric characteristics of polygonal beam sections. By taking as input the coordinate vertices of the polygon, the approach may effectively be applied to determine the cross-section area and the position of its centroid along with the axial area moments of inertia and product of inertia relative to the cross-sections’ centroidal axes. As the method combines the theory of planar moments with the well-known trapezoid numerical method, it provides a straightforward tabular procedure that can be easily implemented using any spreadsheet software. In addition, aiming to determine the principal area moments of inertia, a computation matrix formalism based on the theory of orthogonal diagonalization of symmetric matrices is put forward as an alternative to the classical method of vanishing the first derivative and solving for the principal directions. Some benchmark examples are worked out to prove the relevance and accuracy of the proposed approach for several beam sections ranging from the most common triangular and quadrilateral ones to very complex open and closed polygonal profiles. The solution presented here appears to be virtually foolproof compared to the conventional one, as it does not necessitate the decomposition of complex polygonal cross-section area into elementary surfaces of different shapes, then use the parallel axes theorem, and so forth; rather, it requires only insertion of the coordinates of the vertices of the polygon, turn by turn in the clockwise order, relative to an arbitrary cartesian coordinate system, and no further steps.

Flexural Capacity of the Normal Sections of Concrete Beams Strengthened with Corrugated Steel Plates

To explore the law of load-carrying performance enhancement of concrete beams reinforced with corrugated steel plates (CSPs), three groups of controlled bending tests were conducted on five beam specimens. The load-bearing capacity of concrete members commensurately increased with the thickness of reinforcing flat and corrugated steel plates. Additionally, for the same amount of steel, the load-bearing capacity of concrete beams improved more with CSP reinforcement than with reinforcement with flat steel plates. Accordingly, a theoretical formula for the moment of inertia of the combined section of a CSP-reinforced concrete beam was derived. Comparison verification showed that the calculation results for the beams reinforced with CSPs of different thicknesses were highly accurate. Finally, based on the damage mode of the CSP-reinforced concrete beam specimens, a formula for calculating the flexural bearing capacity of the positive cross-section of the beam with corrugated steel reinforcement was established. The calculated values agreed with the experimental values, which validated the flexural load capacity theory pertaining to positive sections and the flexural capacity model for reinforced beams.

Study of Panel Zone Behavior in Interior Beam–Column Joints with Reduced Beam Section (RBS)

Based on the post-earthquake investigation of the Beiling and Hanshen earthquakes, many welded rigid beam–column joints were found to exhibit brittle failure. The failure modes of the joint region and the overall steel frame structure under the action of the earthquake need to be studied. The seismic performance of different types of weakened beam-end interior joints was investigated. The finite element method was verified by high-strength steel beam–column joint tests conducted by our research team. Finite element modeling of weakened steel beam flanges and weakened steel beam web joints was carried out based on the validated finite element modeling method. The joints were studied and analyzed using seismic parameters such as joint stress clouds, equivalent story shear–inter-story displacement ratio curves, panel zone bending moment–shear ratio curves, ductility, stiffness, and energy dissipation. The results of this study showed that honeycomb open hole-type joints exhibit a better deformation and energy dissipation capacity compared to open circular web hole-type joints. However, their load carrying capacity is reduced, which is mainly due to the larger area of the web openings. Additionally, double reduced beam section (DRBS) joints exhibit superior seismic performance and plastic hinge outward movement characteristics compared to single reduced beam section (RBS) joints. It was also found that the deformation and energy dissipation of DRBS joints and steel beam honeycomb hole-type joints are mainly borne by the beams, with the panel zone’s participation in energy dissipation accounting for a smaller proportion of the energy.

Analytical solutions for joints in an infinite Euler-Bernoulli beam on a viscoelastic foundation subjected to time-lag loads

This paper investigates the analytical method for the infinite beam with joint parts resting on a foundation under time-lag loads. The ground is simulated as a viscoelastic foundation. The existence of joint parts in beams is explained by introducing virtual forces expressed through the Dirac delta function. Integral transformation simplifies the dynamic governing equations for standard beam sections and joint parts into an algebraic equation. The convolution theorem converts the solutions into the time domain. The analytical solutions for dynamic analysis of standard beam sections and joint parts are obtained conveniently in the frequency domain. The proposed analytical method is verified by comparing it with the traditional methods and also validated by numerical examples with time-lag loads. Parametric discussions study the effects on the dynamic response of joint parts and standard beam sections, such as the amplitude and frequency of time-lag loads and coefficient of bending stiffness reduction of joint parts. The parametric analyses emphasize the dramatic effect of critical parameters on the discontinuous deformation of beams. The damage caused by critical values of some factors is emphasized. The severe effects of discontinuous deformation induced by dynamic loads in the safety of beam structures are revealed in this paper. The differences in dynamic responses between the beam and joint part must be monitored to ensure the safety of whole beam structures.

Instability of FGM rectangular hollow section (RHS) beam element under combined bending and compressive loads

Instability of FGM rectangular hollow section (RHS) beam element under combined bending and compressive loads

Structure-Structure Interaction in the Reinforced Concrete Frames-Wall

Abstract Reinforced concrete frame-wall (RC frame-Wall) structures are generally solved in a global manner by modeling the entire structure by assembling the RC frame and wall stiffness matrices into a global matrix. The bar-wall element interface is modeled at the mean line of the beam-column element, according to RPA 99, which limits the interaction to the axial and transverse components of the forces (mechanical and kinematic) thus neglecting the effects of section rotations. In order to take into account, the rotational components of the mechanical behavior of the beams (section rotation and bending moment), the interaction between the RC frame and the wall must take place at the real interface of the two substructures, i.e. at the extreme fiber of the bar elements (beams and columns). The transmission of force from the wall to the RC frame is done by transforming the tangent stresses of the wall into moment in the beam.

STRENGTH DESIGN OF REINFORCED CONCRETE SECTIONS BASED ON A NUMERICAL OPTIMIZATION METHOD

Reinforced concrete structures are widely used in construction of civil infrastructures. Classical methods are available for the analysis and design of reinforced concrete members, such as beams or columns, which are typically done by hand or using a spreadsheet program. In this study, an analysis and design approach of reinforced concrete sections is developed based on a numerical optimization method, and applied in accordance with the latest concrete design code. The basic idea of the proposed approach is to derive an optimization formulation in order to determine the minimum steel area required to support a given factored load combinations applied on a concrete section. A rigorously derived analysis and design framework of general beam sections is presented. For practical applications by civil and structural engineers, the readily-available optimization solver in Microsoft Excel spreadsheet is used. To illustrate the applicability of the approach, a numerical example with different analysis and design cases is studied. The proposed analysis and design approach using numerical optimization and spreadsheet solver works very well and is easy to implement in the Excel environment. The analysis and design results compare well with hand calculation results based on the classical method.

STRENGTH DESIGN OF REINFORCED CONCRETE SECTIONS BASED ON A NUMERICAL OPTIMIZATION METHOD

Reinforced concrete structures are widely used in construction of civil infrastructures. Classical methods are available for the analysis and design of reinforced concrete members, such as beams or columns, which are typically done by hand or using a spreadsheet program. In this study, an analysis and design approach of reinforced concrete sections is developed based on a numerical optimization method, and applied in accordance with the latest concrete design code. The basic idea of the proposed approach is to derive an optimization formulation in order to determine the minimum steel area required to support a given factored load combinations applied on a concrete section. A rigorously derived analysis and design framework of general beam sections is presented. For practical applications by civil and structural engineers, the readily-available optimization solver in Microsoft Excel spreadsheet is used. To illustrate the applicability of the approach, a numerical example with different analysis and design cases is studied. The proposed analysis and design approach using numerical optimization and spreadsheet solver works very well and is easy to implement in the Excel environment. The analysis and design results compare well with hand calculation results based on the classical method.

Structural Damage Identification Based on Preprocessing Samples Mixed Training of Multi-Channel and Multi-Source Dynamic Response Data

Previous studies have shown that sampling processing and identification methods for neural networks damage identification in multi-channel and multi-source structural dynamic response data exhibit diversity, and the robustness and generalization issues of the model have not been effectively solved. This paper proposes a sample preprocessing technique and mixed training method suitable for multi-channel and multi-source dynamic response data to optimize the current structural damage identification methods based on neural networks. Through multi-dimensional discrete autocorrelation processing and Fourier transform, the preprocessed datasets from multiple sensors with multi-channel can access multi-channel CNN. Furthermore, the measured datasets from the actual structures are mixed with numerical simulation datasets before being used for neural network model training to address the model calibration and the imbalanced sample size under each classification label. The results of extensive model experiments and finite element verification of specimens show that the method performs outstandingly in detecting and identifying damage to simply supported beam structures using multi-channel CNN. The neural network model trained with preprocessed samples exhibits excellent robustness. The model using the mixed training method still performs well in identifying the accuracy of damage location and degree in simply supported beam structures after changing beam section and initial excitation. The method has certain generalization ability in detecting unknown damage in simply supported beam structures.

Effect of three-dimensional space on progressive collapse resistance of reinforced concrete frames under various column removal scenarios

In this study, high fidelity finite element (FE) model was adopted to investigate the progressive collapse resistance of reinforced concrete (RC) frame structures under various column removal scenarios. The validity of the numerical model was verified by comparing with the existing experimental results. Afterwards, to facilitate the research on possible simplified boundary conditions served for further various column removal scenarios, the effect of multi-span continuous beams was firstly evaluated and the simplified methods were compared. Then, the effect of various column removal scenarios addressing the three-dimensional effect on the progressive collapse resistance of RC frame structures with and without slab was systematically evaluated. The analysis results showed that the continuous span beams increased the internal compressive force of the beam section at compressive arch action (CAA) stage, which effectively improved the CAA strength of the substructure. For simple modeling, the use of horizontal constraints at the end of the beam could replace the continuous span beams. The presence of transverse beams and slab provided additional load transfer paths for collapse resistance. The compressive membrane action (CMA) and tensile membrane action (TMA) of the slab significantly improved the progressive collapse resistance of the substructure in the small and large deformation stages, respectively. The location of the removed column significantly affected the contribution ratio of transverse beams and slab to the progressive collapse resistance of the substructure, which was quantitatively evaluated for practical design.

Non-linear behavior of functionally graded elastoplastic beam under torsion

The torsional behavior of beams graded in one and two directions under large displacements and angular deformations was analyzed using the power law and sinusoidal functions. Functionally graded material is elastoplastic, consisting of ceramic and metal. A nonlinear finite element method with isoparametric hexahedral elements was used. The finite element formulation was made using the updated Lagrangian formulation based on the virtual displacement principle. An iterative solution using Newton-Raphson and updated Newton-Raphson methods was used to solve the nonlinear equation system. The propagation of the plastic zone was calculated based on the flow theory of plasticity. Elastoplastic behavior and effective material properties were determined according to the TTO model. Numerical investigations have shown that functionally graded beams behave quite differently from homogeneous beams under torsion. Yielding of the material starts at the outer boundaries of the section of the homogeneous beams, and the plastic zone propagates symmetrically. On the other hand, yielding and propagation of plastic zones tend to shift to regions with more ceramic volume with higher effective Young modulus in functionally graded beams. Unlike homogeneous beams, the largest shear stresses can occur within the section rather than at the outer boundaries of the section. In beams graded from ceramic to metal using the power law, the section moves along the transverse direction in addition to the rotation. This transverse displacement occurs in the grading direction, and its magnitude is about 3% of the thickness at 12.5° rotation angle. Also, the shear stresses are not zero in the section's midpoint. The effects of material distribution on displacements, stresses, and plastic zone propagation were examined, and essential points were reported.

Asymptotically consistent and computationally efficient modeling of short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations

This article proposes a novel computational modeling approach for short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations, and gives a detailed overview how it fits into the framework of existing fiber or beam interaction models, either considering microscale molecular or macroscale contact effects. The direct evaluation of a molecular interaction potential between two general bodies in 3D space would require to integrate molecule densities over two 3D volumes, leading to a sixfold integral to be solved numerically. By exploiting the short-range nature of the considered class of interaction potentials as well as the fundamental kinematic assumption of undeformable fiber cross-sections, as typically applied in mechanical beam theories, a recently derived, closed-form analytical solution is applied for the interaction potential between a given section of the first fiber (slave beam) and the entire second fiber (master beam), whose geometry is linearly expanded at the point with smallest distance to the given slave beam section. This novel approach based on a pre-defined section–beam interaction potential (SBIP) requires only one single integration step along the slave beam length to be performed numerically. In addition to significant gains in computational efficiency, the total beam–beam interaction potential resulting from this approach is shown to exhibit an asymptotically consistent angular and distance scaling behavior. Critically for the numerical solution scheme, a regularization of the interaction potential in the zero-separation limit as well as the finite element discretization of the interacting fibers, modeled by the geometrically exact beam theory, are presented. In addition to elementary two-fiber systems, carefully chosen to verify accuracy and asymptotic consistence of the proposed SBIP approach, a potential practical application in form of adhesive nanofiber-grafted surfaces is studied. Involving a large number of helicoidal fibers undergoing large 3D deformations, arbitrary mutual fiber orientations as well as frequent local fiber pull-off and snap-into-contact events, this example demonstrates the robustness and computational efficiency of the new approach.

Structural Optimization and Process Scheme of Large-span Gantry Crossbeam based on Response Surface

A comprehensive design method for large-span gantry beams, combining process techniques and structural optimization, is proposed to address significant deflection deformation issues caused by their own gravity and the gravity of front attachments. Selecting the beam section type, finite element static analysis is performed using ANSYS Workbench for both cast and welded gantry beams. The maximum static deformation values of the beams for both process schemes are compared to determine the process scheme for the large-span beam. Subsequently, multiple structural dimensions of the welded gantry beam are parameterized, and sensitivity analysis is conducted to determine the degree of influence of each parameter on the optimization objective. Parameters with relatively small effects on the corresponding objectives are eliminated. A response surface multi-objective genetic algorithm optimization based on Box-Behnken design experimental design method is employed to minimize deflection deformation and reduce weight. The response surface model is fitted with expressions, and variance and significance analyses are conducted to validate the model's reliability. The optimal Pareto solutions are determined based on the response surface model using a multi-objective genetic algorithm. A comparison between the beams before and after optimization shows a reduction of 0.052 in maximum static deformation of the welded beam, representing an 8.3% decrease. Additionally, the mass decreases by 1710 kg, indicating a 14.63% reduction, demonstrating significant optimization effects.

Two-photon absorption cross sections of pulsed entangled beams.

Entangled two-photon absorption (ETPA) could form the basis of nonlinear quantum spectroscopy at very low photon fluxes, since, at sufficiently low photon fluxes, ETPA scales linearly with the photon flux. When different pairs start to overlap temporally, accidental coincidences are thought to give rise to a "classical" quadratic scaling that dominates the signal at large photon fluxes and, thus, recovers a supposedly classical regime, where any quantum advantage is thought to be lost. Here, we scrutinize this assumption and demonstrate that quantum-enhanced absorption cross sections can persist even for very large photon numbers. To this end, we use a minimal model for quantum light, which can interpolate continuously between the entangled pair and a high-photon-flux limit, to analytically derive ETPA cross sections and the intensity crossover regime. We investigate the interplay between spectral and spatial degrees of freedom and how linewidth broadening of the sample impacts the experimentally achievable enhancement.

Experimental and numerical investigations of S960 hot-rolled ultra-high strength steel seamless circular hollow section beam–columns

The rapid development of manufacturing techniques and material science enables advanced hot-rolled ultra-high strength steel (UHSS) with material grades up to S960 to be available recently. The structural performance of S960 hot-rolled UHSS seamless circular hollow section (CHS) beam–columns manufactured through the advanced fabrication approach was experimentally and numerically investigated and reported in this paper. In physical testing, totally ten beam–column specimens were tested, with the complementary material testing and initial global geometric imperfection measurements through the innovative digital image correlation (DIC) method performed. FE modeling was then carried out; FE models of S960 hot-rolled UHSS seamless CHS beam–columns were established and then validated the test observations in terms of the failure loads and the load–mid-height lateral displacement curves. Parametric studies were thereafter performed, with cross-section dimensions, member lengths and loading combinations varying within a certain range, resulting in the additional 300 data to be acquired. Finally, the applicability of existing design methods, as prescribed in the European code, the Australian standard and the American specification, to S960 hot-rolled UHSS seamless CHS beam–columns was evaluated. It can be concluded from the evaluation results that all the three design codes provide accurate and consistent failure load predictions for S960 hot-rolled UHSS seamless CHS beam–columns.

Numerical method for predicting first crack load on hollow-cored beams subjected to point load at Midspan

Predicting the initial crack load in concrete is important to detect early warning of a problem. In this study, a model for predicting the first crack load on a hollow-cored rectangular beam point loaded at mid-span was developed by combining a numerical method and an experimental approach. The modulus of rupture was introduced into the governing moment-curvature relationship. Experimentally, flexural testing with point loads at mid-span was performed on fifteen (15) beams made up of three (3) beam types at 1 kN intervals for a span of 750mm using the Universal Testing machine. The beams were simply supported by roller points. The dimensions of the beams were kept constant and later varied while investigating the following hollow diameters: 0, 30, 60, 75, and 105mm. Numerically, the beams were designed as a beam element point loaded at mid-span with a span of 700mm centers, and the support conditions were defined as pinned support. Governing equations relating failure load with the modulus of rupture, stiffness matrix, shape functions, and moment of inertia were developed. The equation for predicting the first crack load, incorporating the modulus of rupture, was derived. The moment of inertia was calculated by discretizing the hollow-cored beam section using an isoparametric geometric transformation. The experimental results were used to validate the numerical model. 90.55% agreement between experimental and numerical results was observed. The overall average percentage difference between the two methods recorded is 9.45%. This shows that at about 91% confidence level, both approaches are the same and can be applied with confidence in the prediction of the first crack load on hollow- cored reinforced concrete beams.

Application of Installations with Uniform-Strength Beams as Working Deformation Standards

A method for obtaining homogeneous deformation along the length of the measuring section of a uniform-strength beam and the possibility of its application as part of a working deformation standard are considered. The results of the analysis of the bending model and the design of a uniform-strength beam are presented. In the focus of attention are the parameters included in the measurement equation and related to methodological factors, as well as influencing the result of relative deformation measurements. The subjects of research are the presence of contact friction forces, heterogeneity of material properties, the special nature of the load application (bending, torsion, the presence of residual stresses in the body, geometrical parameters of the calibration beam, orientation of primary transducers on the beam, application of bending load, measurement of deflection and displacement of the neutral layer). The advantages and disadvantages of using a uniform-strength beam for determining the characteristics of primary strain transducers during testing, calibration, and verification were established. The deviation of signals of primary transducers located outside the axial cross-section when oriented along the beam axis and along the force lines converging at the point of load application was experimentally revealed. The error due to the orientation of the primary transducers on the beam depending on the angle between the lateral faces can range from 0.15 to 0.23 %. The study adds to the theoretical knowledge base on the possibility of using a cantilever uniform-strength beam as a load-bearing element in calibration installations. The conclusions may be useful for testing, calibrating, and verifying primary strain transducers.