Design Method For Beams Research Articles

Inverse design method for tailoring the deflection of beams with functionally graded metamaterials

Abstract Functionally graded metamaterials represent a cutting-edge approach to designing structures with cellular materials. By manipulating parameters in specific regions, a customized mechanical response is achieved, optimizing material utilization. Despite various proposed methods to generate functionally graded structures, the challenge of high computational costs persists. This study introduces a novel and computationally efficient inverse design method for beams featuring segment-wise graded metamaterials. Using a semi-analytical approach based on Castigliano’s second theorem, this method significantly reduces computational demands. The approach leverages prior experimental and computational characterizations of the transverse deflection in rectangular, reentrant, and hexagonal honeycombs. Validation through finite element models and experimental tests on additively manufactured beams confirms the adequate performance of the method. The proposed framework successfully generates beams with targeted deflections, demonstrating the method’s capability for inverse design under specific loading and boundary conditions. This approach not only optimizes material utilization but also broadens the application scope of functionally graded metamaterials in structural design.

Mid-span displacement and damage degree predictions of RC beams under blast loading using machine learning-based models

Civil engineering has extensively employed RC beams in various applications. However, these beams are susceptible to damage and failure under blast loading. Assessing damage of RC beams from blasts requires real measurement data and time-intensive numerical simulation, making rapid evaluation a significant challenge. In this study, machine learning (ML) models were developed to swiftly evaluate the damage degree and predict the mid-span displacement of RC beams, comprising three models for each problem. To compensate for the lack of real experiment data, a total of 1041 data points are generated through numerical simulation using ABAQUS to create the training dataset. Additionally, for displacement prediction models, 39 collected measurement data was integrated. Initially, the ML models were established to predict the peak mid-span displacement of RC beams under explosion, with inputs including twelve RC beam structural parameters and two blast load parameters, and the output being the maximum min-span displacement of the beam. Subsequently, the ML models were developed using the same fourteen parameters as inputs, with the output being the beam’s damage degree and failure mode. These models achieved adequate performance, demonstrated by evaluation metrics such as R2, RMSE, MAE, MAPE, with values of 0.95, 5.468 mm, 3.16 mm, 17.7 %, respectively, for regression problem. For the classification problem, metrics such as accuracy, precision, recall, and f1-score were employed, with an overall value of 0.837 for the best model. The results show that the developed ML models can precisely and rapidly assess the damage degree, failure mode and predict the mid-span displacement of the RC beam under blast load, which provides a good method for the anti-explosive protection design of RC beams. The graphical user interface tool was also established for ease of use.

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.

Integrated vibration absorption and isolation design method for metamaterial beams based on bandgap wave-insulating vibration isolatior

Advanced vibration control technology is widely needed in the fields of aerospace and shipbuilding. Currently, separate vibration absorption and isolation design of most systems are separated, and existing isolation designs cannot effectively enhance the isolation of low-frequency line spectra. There is an urgent need to develop integrated vibration absorption and isolation designs and strengthen low-frequency line spectrum control. In response to this need, this paper focuses on a typical Euler beam and the investigation of the propagation characteristics of vibrations in transverse direction and longitudinal direction, the principles of integrated vibration absorption and isolation design, and the synergistic regulation of bandgaps, based on acoustic metamaterial bandgap wave-insulating vibration control configurations and analytical methods. Ultimately, without adding additional structures, the wave-insulating vibration control device is used to generate multiple modes of vibration absorption and isolation simultaneously, achieving an integrated low-frequency, broadband, and high-efficiency vibration absorption and isolation design. This method achieves broadband vibration isolation in the transverse vibration isolation path while also introducing local resonance bandgaps that significantly improve low-frequency vibration isolation. In the longitudinal (forward propagation) path, in addition to near-zero and Bragg bandgaps, multilayer isolators generate multimodal local resonant bandgaps, achieving low-frequency broadband vibration absorption and effective control in the entire frequency range. This paper elucidates the synergistic modulation of longitudinal and transverse bandgaps, showing that by superimposing these bandgaps, an impressive bandgap ratio of 87.3% below 100 Hz across the entire frequency range can be achieved. Furthermore, an entity structure is designed, and the accuracy of the analytical results is verified by using the finite element method. The findings provide feasible design ideas for realizing the integrated vibration absorption and isolation of complex structures such as beams, plates, pipelines, and frames.

Parametric analysis on hybrid design method for steel cellular beams

Parametric analysis on hybrid design method for steel cellular beams

Analysis of negative stiffness structures with B-spline curved beams

With unique mechanical properties, negative stiffness (NS) structures have presented significant advantages in energy absorption. In recent years, NS structures consisting of periodically arranged curved beams have attracted comprehensive attention. However, the curved beams of the current report mainly focus on geometrical parameters in specific configurations, and the variety of the reported geometrical configurations of the flexible beams is relatively limited. In this paper, a B-spline curved beam design method is proposed. A static analysis model of a B-spline curved beam is developed to investigate the force-displacement relations of curved beams in different configurations. The configuration for the B-spline curved beam is obtained, and the relation between the geometric parameters and the mechanical properties of the B-spline curved beam is discussed. Then the mechanical properties of NS structures with periodically arranged B-spline curved beams are analyzed by the finite element method, and the experiments verified the correctness of the simulation method. Finally, the force-displacement relation and energy-absorption properties of gradient NS structures with B-spline curved beams are discussed. The results indicate that the NS structure with B-spline curved beams has repeatability and effective energy absorption properties. The deformation form of the NS structure can be modulated by gradient NS design, and the energy absorption properties of the NS structure can be improved effectively. The research can provide a reference for the design of NS structures.

Experimental and numerical investigation on fire resistance of stainless steel core plate beams

The stainless steel core plate is an innovative lightweight structural material with broad application prospects. Experiments and finite element analyses were carried out to study the fire resistance of the stainless steel core plate beam in a three-sided fire. The load ratio and equivalent thermal resistance of the fireproof protective layer of stainless steel core plate beams were parametrically analyzed. A fire resistance design method for stainless steel core plate beams was presented. The results showed that the alternating sectional form of the core tube and mineral wool inside the beam resulted in an uneven temperature field distribution under a three-sided fire; with the premise that the weld was not damaged at high temperatures, the failure pattern of the core plate beam at high temperatures was the strength failure after the local instability of the web, which was the same as that at room temperature; the critical temperature of the lower flange decreased from approximately 870 °C to 485 °C, with an increase in the load ratio from 0.3 to 0.7; a prediction formula for the equivalent thermal resistance of fireproof protective layer required to reach a given fire resistance limit at different load ratios was established, which can be used for the design of stainless steel core plate beams for fire resistance.

Behaviour of cellular steel beams at ambient and high-temperature conditions

New developments in building construction have been observed to attain sustainable design criteria and the efficient use of raw materials, as steel is an example. This led to an increase in recent research on the optimization of geometric configurations of web-opening steel sections to meet cost-effectiveness in structural design. Improvement of the design method for perforated unrestrained steel beams to assess their behaviour under lateral torsional buckling (LTB) is still an ongoing issue for scientists and designers alike. In this article, cellular beams bound to instability were studied analytically by Eurocode and numerically by the finite element method to investigate their behaviour at ambient and elevated temperatures due to fire. The analysis encompasses the effect of the coupling and the endplates' thickness on the cellular beams' collapse strength considering the initial geometric imperfections and material nonlinearities. A parametric study including changing temperature, cross-section geometry, and web aperture configurations was done for beams subjected to uniform bending and distributed load. The analyses depicted the following failure modes: LTB and LTB+ plastification of the two T-section (P-2 T) for end moment load and yielding of top tee section's flange (B-1 T), P-2 T, web post-buckling (WPB), Vierendeel mechanism (VM) and LTB for a distributed load. Combined failure modes such as LTB + WPB, LTB + VM and LTB + VM + WPB have also been observed. Buckling curves for cellular beams were assessed by comparing FE reduction factors with those of the buckling curve recommended by Eurocode 3 for equivalent solid steel beams. A new proposed formula for the plateau length of the LTB curves was obtained, based on the mean squared error method (MSE) between the numerical results and Eurocode formulae. The comparison between the numerical and the simplified design method predicted results shows that the proposed formulae have reduced the discrepancy and improved the LTB curve to better assess the cellular beams behaviour.

Shear Design of Strain-Hardening Fiber-Reinforced Concrete Beams

Strain-hardening fiber-reinforced concrete (SH-FRC), such as ultrahigh-performance concrete (UHPC), offers sustained tensile capacities up to high values of postcracking strains and, consequently, delivers shear resistance through different mechanisms than conventional concrete. Existing shear design methods for conventional concrete beams include empirical approximations of the tensile resistance offered by the cracked concrete that do not apply to SH-FRC materials. This article presents a design formulation that predicts the shear capacity of SH-FRC beams in support of ongoing efforts to develop UHPC structural design guidance in the United States. The proposed model leverages foundational concepts from engineering mechanics, similar to the modified compression-field theory (MCFT) for conventional reinforced and prestressed concrete, while integrating relationships that address behaviors specific to SH-FRC. The model predicts shear stress versus shear strain behavior of a cracked SH-FRC membrane element, which is then used to model the web of a beam. Verified against experimental shear test results of I-shaped prestressed and non-prestressed beams with different material properties, beam geometries, axial strains, and transverse reinforcement ratios, the proposed shear design model is demonstrated to conservatively predict the shear capacity of SH-FRC beams. As such, this work constitutes a fundamental step in developing mechanics-based SH-FRC shear design guidance.

Effect of Position of Opening in RC Beams Subjected to Flexure and Shear

Effect of Position of Opening in RC Beams Subjected to Flexure and Shear

Design method for glulam beams strengthened with flax fiber reinforced polymer sheets

The strengthening efficiency of flax fiber reinforced polymer (FFRP) reinforcement is evaluated by four-point bending tests, conducted on full-scale glulam beams strengthened with FFRP sheets. Experimental variables include different layers (three-layer or six-layer), attaching types (unidirectional or bidirectional), and attaching configurations (longitudinal, U-shaped or fully wrapped). The failure modes, load-deflection curves, strain changes, load capacities, flexural rigidity, energy absorption, and ductility of the tested specimens were recorded and discussed. Results indicate that the bending performance of a beam strengthened with three-layer longitudinal FFRP sheets outperforms that of a six-layers. The strengthening efficiency of bidirectionally attached FFRP is significantly higher than that of unidirectionally attached FFRP. Furthermore, a theoretical model for the ultimate load of test beams was developed and validated on the basis of these results, demonstrating good agreement with the experimental results. The design value of tensile strength for FFRP sheets was determined by reliability analysis. Based on the test data and recommended values for tensile strength of FFRP sheets, the reliability indexes β for the design formulas were calculated to further verify their applicability and reliability. Finally, the global modification factors for design formulas were calculated and recorded to achieve the target reliability requirement (β = 3.2 specified in the Chinese code GB50005-2017).

Intelligent beam layout design for frame structure based on graph neural networks

The layout design of the frame structure beams is a critical task in frame structure design. Traditional automatic layout methods often rely on established rules. However, the predefined rules are often incomplete, and the conflicts and priorities between different constraints are often unclear. Consequently, it is difficult for traditional automatic methods to meet the challenges of flexible layout of structures with free planar shapes. The beam–column connection of the frame structures exhibits the topological characteristics of graphs. A graph neural network is a data-driven geometric deep learning algorithm that is suitable for addressing non-Euclidean data such as graphs, thus providing a new solution for the beam layout design of frame structures. Therefore, this study proposes an intelligent plan layout design method for frame beams based on a graph neural network. A large-scale dataset of the frame structure layout was considered for the neural network training. Graph representation methods for frame structures are discussed, and a novel graph neural network model for beam layout design is proposed. The test results show that the proposed beam layout design method has high accuracy, and case studies of real-world frame structures show that the outcome of the proposed method is comparable to engineer's design.

Downlink beamforming design for mobile users in massive MIMO system

With numerous antennas, the massive multiple-input multiple-output (MIMO) system can precisely point to the user equipments (UEs) with narrow beams. Mobile UEs, however, may suffer from the narrow beam nature of the massive MIMO system, since UEs may move out of the beam coverage. Frequent CSI feedback and beam adjustment help to track mobile UEs. However, a significant amount of transmission and computation overhead is incurred. In this paper, we consider a mobility adaption problem in massive MIMO systems with infrequent CSI feedback. We propose a beam design method to use one beam to serve multiple transmissions, thus reducing the overhead of frequency beam adjustment. An optimization problem is formulated that maximizes the overall system sum rate during one beam adjustment, i.e., during the entire time interval between CSI feedback. We assume that each transmission antenna has a peak power constraint, as the power amplifier in each branch limits the transmit power. A fractional programming based algorithm is proposed to solve the problem. To further reduce the computation overhead, a sub-optimal solution is obtained. Simulation results show that the proposed algorithms achieve satisfactory performance with little transmission and computation overhead compared to existing algorithms.

Intelligent design method for beam and slab of shear wall structure based on deep learning

Beam and slab design is a critical component of shear wall structure design. Currently, conventional manual design is time-consuming, and defining objective functions and design variables of an optimization design is challenging. In contrast, deep learning methods can learn high-dimensional image features and generate new designs, providing new solutions for efficient and intelligent structural design. Therefore, based on deep neural networks, this study proposes an intelligent layout design method for beams of reinforced concrete shear-wall structures using the input of fused building space and element attributes. This method learned the implicit laws of existing designs and realized the inferential generation of new layout schemes. Subsequently, based on mathematical statistics, methods to determine the type and size of coupling and frame beams are proposed. A typical case study shows that the structural performance of the beam and slab designed by this method was comparable to that of competent engineers. The maximum inter-story drift ratio of the result designed by the proposed method differs from that designed by engineers by no more than 5 × 10−5. The differences in the maximum vertical typical-floor-slab displacement, the concrete consumption, and the steel consumption between the design result of the proposed method and the engineer's design result are 0.8%, 2.88%, and 6.20%, respectively. Moreover, the design efficiency was significantly improved by more than 30 times.

Tests and design method on overall buckling behaviours of welded I-section two-span continuous beams for Q460 high strength steel

To investigate the overall buckling behaviours of welded I-section two-span continuous beams for Q460 high strength steel and assess the reliability of the overall buckling design method for such beams stipulated in the Standard for design of high strength steel structures (JGJ/T483-2020) of China, a total of six two-span continuous beams were tested under concentrated loads, and the overall buckling modes and capacities were obtained. The finite element model (FEM) considering initial geometric imperfections and residual stresses was established and validated through comparing with the test results, and extensive parametric analyses were carried out through the validated FEM. Based on the formula of the elastic critical moment for simply supported beam given in Standard for design of steel structures (GB50017-2017) and the finite element analysis (FEA) results, the formula of the elastic critical moment for two-span continuous beam was proposed. The above proposed formula was substituted into the buckling factor formula in JGJ/T483-2020 to obtain the overall buckling design curves of two-span continuous beams for Q460 high strength steel. Furthermore, the obtained design curves were compared with the test and FEA results, which indicates that the design method in JGJ/T483-2020 is suitable for the overall buckling design of two-span continuous beam for Q460 high strength steel with non-dimensional slenderness value less than 1.5, and the design method in JGJ/T483-2020 is relatively conservative for the overall buckling design of two-span continuous beam for Q460 high strength steel with non-dimensional slenderness value greater than 1.5.

Behaviour and detailing of coupling beams with high-strength materials

High-strength steel (HSS) has the potential to reduce reinforcement congestion and construction difficulties for coupling beams. This paper aims to investigate coupling beams using HSS diagonal bars and HSS transverse reinforcement. Four coupling beam specimens with a clear span-to-depth ratio of 2.0 were built with varying concrete materials and confinement details and tested under quasi-static reversed-cyclic shear loading. Despite using the maximum transverse reinforcement spacing that is allowed in ACI 318–19, all coupling beam specimens exhibited satisfactory seismic performance in terms of adequate deformation capacity and stable hysteretic response. Favorable performance, characterized by a greater damage control ability, larger shear strength, and deformation capacity, was achieved in specimens using high-strength concrete, especially fiber-reinforced high-strength concrete. The coupling beam specimen with confinement provided for the entire beam cross section outperformed the specimen with confinement provided for the individual diagonals. The state-of-practice design methods for coupling beams are evaluated with experimental results.

The General Method for the fire design of I-section web-tapered beams

The present investigation describes a numerical and parametric study on the validation of the General Method (GM) for the fire design of web-tapered steel beams using GMNIA.The GM covers the safety check of structural elements with complex support conditions and/or of non-prismatic members, as the non-uniform geometry prevents the use of the standard verification clauses. However, the fire part of the Eurocode 3 (EN 1993-1-2) provides no further indication regarding its applicability at elevated temperatures, apart from adapting the methodology to fire using the reduction factors for steel material properties, which is identified as a gap in the current version of the norm.However, previous investigation by the authors have shown overly conservative results for the adapted General Method and a calibration of the EN 1993-1-2 buckling curve has previously been proposed, although the parametric study was not representative enough for full validation.With that in mind, supported by an extensive numerical framework of over 25000 laterally restrained and unrestrained tapered beams at elevated temperatures, a precise and accurate calibration of the General Method is developed in the scope of this work.

Numerical study on fire resistance of rectangular section stainless steel-concrete composite beam

To investigate the fire resistance of stainless steel-concrete composite beams (referred to as stainless steel composite beam), numerical simulations of rectangular section stainless steel composite beams under fire were carried out. The influences of load ratio, thickness of concrete slab, width of concrete slab, reinforcement ratio of concrete slab, height of stainless steel beam, width of stainless steel beam and span of composite beam on the fire resistance of rectangular section stainless steel composite beams were analyzed. Due to the large coefficient of thermal expansion of stainless steel material, the expansion of stainless steel beam will produce an additional bending moment in the stainless steel composite beam under fire, which has a great influence on the fire resistance of stainless steel composite beams. Finally, a simplified calculation method of temperature field distribution of rectangular section stainless steel composite beam was proposed. To adjust and enlarge the maximum bending moment at the mid-span of stainless steel composite beam, the coefficient of temperature additional bending moment was introduced into the calculation formula of critical temperature of stainless steel composite beams, which effectively improves the accuracy of the fire-resistant design method for stainless steel composite beams.

Shaped beams: unlocking new geometry for efficient structures

Society is building at an unprecedented rate: to house over 200,000 people moving to cities each day building stock will need to double by 2060. Importantly, the embodied carbon of construction due to material extraction, manufacturing, transportation, and demolition accounts for 11% of global carbon emissions, and this number is only expected to rise. With no end to construction in sight, it is essential that we develop better building practices. The research presented in this paper begins with the critical issue of embodied energy in horizontal structural systems. In high-rise buildings, between 60 and 80% of the mass and embodied energy of the structure can be found in the floors, suggesting a compelling starting point for materially efficient design. A reduction in a floor system’s mass can lead to a similar reduction in the mass of vertical (columns, walls) and lateral systems. This paper focuses on the design of horizontal spanning elements, such as floor beams and slabs, and has two parts. The first part evaluates and compares historic methods of shaped beam design and classical methods of structural optimization. The second part presents a new flexible method of beam shape optimization. These design methods for structural efficiency allow us to build far more with far less, reducing the environmental and economic costs of construction while meeting the demands of a growing population.

A new design method of the equivalent stress–strain relationship for hybrid (FRP bar and steel bar) reinforced concrete beams

Hybrid reinforced concrete (hybrid-RC) beams consisting of fiber-reinforced polymer (FRP) bars and steel bars can provide high strength, serviceability, and durability. However, based on a review of the literature, the design methods for hybrid-RC beams fail to effectively predict the flexural failure mode of these structures. Therefore, an equivalent constitutive relationship is proposed, which considers the FRP bar and steel bar as a new material with a bilinear constitutive relationship. Two balanced reinforcement ratios were introduced in the design method, which can accurately predict the failure mode of both the hybrid-RC structure and FRP strengthened RC structure. The feasibility of the proposed method was then confirmed by experimental testing.