Predicting shear strength of slender beams without reinforcement using hybrid gradient boosting trees and optimization algorithms

Shear failure of slender reinforced concrete beams without stirrups has surely been a complicated occurrence that has proven challenging to adequately understand. The primary purpose of this work is to develop machine learning models capable of reliably predicting the shear strength of non-shear-reinforced slender beams (SB). A database encompassing 1118 experimental findings from the relevant literature was compiled, containing eight distinct factors. Gradient Boosting (GB) technique was developed and evaluated in combination with three different optimization algorithms, namely Particle Swarm Optimization (PSO), Random Annealing Optimization (RA), and Simulated Annealing Optimization (SA). The findings suggested that GB-SA could deliver strong prediction results and effectively generalizes the connection between the input and output variables. Shap values and two-dimensional PDP analysis were then carried out. Engineers may use the findings in this work to define beam's geometrical components and material used to achieve the desired shear strength of SB without reinforcement.     

集中荷载下无腹筋梁抗剪承载力新的设计方法

采用数理统计的方法,通过对收集到的国内外集中荷载作用的钢筋混凝土无腹筋简支梁的大量试验数据进行回归分析,对无腹筋简支梁受剪承载力的主要影响因素综合加以考虑,通过引入纵筋率及截面高度综合影响参数,提出无腹筋简支梁抗剪承载力实用计算公式,并把利用该式得到的相应计算值与试验数据进行比较。研究表明,本文所建议的计算公式与试验结果有较好的吻合度且偏于安全,基本可以应用于实际工程。     

Prediction of shear strength of steel fiber RC beams using neural networks

This paper presents the development of artificial neural network models for predicting the ultimate shear strength of steel fiber reinforced concrete (SFRC) beams. Two models are constructed using the experimental data from the literature and the results are compared with each other and with the formula proposed by Swamy et al. and Khuntia et al. It is found that the neural network model, with five input parameters, predicts the shear strength of beams more closely than the network with four input parameters. Moreover, the neural network models predict the shear strength of SFRC beams more accurately than the above-mentioned formulas. Further, the accuracy of predicted results is found not biased with concrete strength, shear span to depth ratio and the beam depth. Limited parametric studies show that the network model captures the RC beam’s underlying shear behavior very well.     

Shear strength of slender reinforced concrete beams without web reinforcement: A model using fuzzy set theory

A reliable shear strength model for slender reinforced concrete beams without web reinforcement is described based on fuzzy set theory. The fuzzy-based model was developed to consider the interaction between the shear modeling parameters and the random and non-random uncertainties in these parameters. The parameters were identified essential for modeling shear strength in slender reinforced concrete beams without web reinforcement being: the compressive strength, the effective depth and the tension reinforcement ratio. A total of 385 experimental datasets obtained from shear tests of simply supported reinforced concrete beams from the literature, are used in learning/developing and verification of the proposed model (164 for learning and 221 for verification). The shear strength predicted by the fuzzy-based model was compared to those predicted by current shear strength models suggested by design codes such as the Eurocode 2 (EC2), the American code ACI (318-05), and Canadian code (CSA A23.3-04). The fuzzy-based model yields a significant enhancement in the prediction of the shear strength while still respecting principles of mechanics governing shear failure in concrete beams.     

Behavior and capacity of RC beams strengthened in shear with NSM FRP reinforcement

A recent and promising method for shear strengthening of reinforced concrete (RC) members is the use of near-surface mounted (NSM) fiber-reinforced polymer (FRP) reinforcement. In the NSM method, the reinforcement is embedded in grooves cut onto the surface of the member to be strengthened and filled with an appropriate binding agent such as epoxy paste or cement grout. Only a few studies have been conducted to date on the use of NSM FRP reinforcement for shear strengthening of RC beams. These studies identified some critical failure modes related to debonding between the NSM reinforcement and the concrete substrate. However, more tests need to be conducted to identify all possible failure modes of strengthened beams. Moreover, virtually no test results are available on the behavior of shear-strengthened beams containing steel shear reinforcement, and on the effect of variables such as the type of epoxy used as groove filler. This paper illustrates a research program on shear strengthening of RC beams with NSM reinforcement, aimed at gaining more test results to fill the gaps in knowledge mentioned above. A number of beams were tested to analyze the influence on the structural behavior and failure mode of selected test parameters, i.e. type of NSM reinforcement (round bars and strips), spacing and inclination of the NSM reinforcement, and mechanical properties of the groove-filling epoxy. One beam strengthened in shear with externally bonded FRP laminates was also tested for comparison purposes. All beams had a limited amount of internal steel shear reinforcement to simulate a real strengthening situation. Test results are presented and discussed in the paper.     

Determination of shear strength of steel fiber RC beams: application of data-intelligence models

Accurate prediction of shear strength of structural engineering components can yield a magnificent information modeling and predesign process. This paper aims to determine the shear strength of steel fiber reinforced concrete beams using the application of data-intelligence models namely hybrid artificial neural network integrated with particle swarm optimization. For the considered data-intelligence models, the input matrix attribute is one of the central element in attaining accurate predictive model. Hence, various input attributes are constructed to model the shear strength “as a targeted variable”. The modeling is initiated using historical published researches steel fiber reinforced concrete beams information. Seven variables are used as input attribute combination including reinforcement ratio (\rho \mathrm{\%}), concrete compressive strength ({{\displaystyle f}}_c^{\text{'}}), fiber factor ({{\displaystyle F}}_{\mathrm{1}}), volume percentage of fiber ({{\displaystyle V}}_f), fiber length to diameter ratio ({\displaystyle {{\displaystyle l}}_f{{\displaystyle l}}_d}) effective depth (d), and shear span-to-strength ratio ({\displaystyle ad}), while the shear strength ({{\displaystyle S}}_s) is the output of the matrix. The best network structure obtained using the network having ten nodes and one hidden layer. The final results obtained indicated that the hybrid predictive model of ANN-PSO can be used efficiently in the prediction of the shear strength of fiber reinforced concrete beams. In more representable details, the hybrid model attained the values of root mean square error and correlation coefficient 0.567 and 0.82, respectively.     

Modeling of debonding failure for RC beams strengthened in shear with NSM FRP reinforcement

The shear capacity of reinforced concrete members can be successfully increased using near-surface mounted (NSM) fiber-reinforced polymer (FRP) reinforcement. Tests conducted thus far have shown that failure is often controlled by diagonal tension associated to debonding between the NSM reinforcement and the concrete substrate. In absence of steel stirrups and/or when the spacing of the NSM reinforcement is large, debonding involves separately each of the bars crossed by the critical shear crack. In order for shear strengthening of beams with NSM reinforcement to be safely designed, an analytical model able to encompass the failure mode mentioned above must be developed. This paper presents two possible approaches, a simplified and a more sophisticated one, to predict the FRP contribution to the shear capacity. In the first approach, suitable for immediate design use, an ideally plastic bond–slip behavior of the NSM reinforcement is assumed, which implies a complete redistribution of the bond stresses along the reinforcement at ultimate. The second approach, implemented numerically, accounts for detailed bond–slip modeling of the NSM reinforcement, considering different types of local bond–slip laws calibrated during previous experimental investigations. It also takes advantage of an approach developed by previous researchers to evaluate the interaction between the contributions of steel stirrups and FRP reinforcement to the shear capacity. The paper illustrates the two models and compares their predictions, with the ultimate goal to evaluate whether the first simple model can be used expecting the same safety in predictions of the second model.     

大尺寸钢筋混凝土无腹筋梁受剪试验研究

进行集中荷载作用下7根大尺寸钢筋混凝土无腹筋简支梁的受剪试验,分析截面高度和纵筋配筋率对钢筋混凝土梁受剪承载力的影响,研究无腹筋梁斜裂缝产生和发展的过程及开裂模式。对试验梁的破坏形式、开裂荷载、受剪承载力、荷载-位移曲线、混凝土受压区应变、最大裂缝宽度和平均裂缝间距受截面有效高度的影响进行讨论。结合试验数据及国内外已有受剪试验成果的基础上对我国《混凝土结构设计规范》(GB 50010—2002)受剪承载力公式的准确性与适用性进行了探讨。     

玻璃纤维布用于加固钢筋混凝土梁抗剪性能研究

本文研究了用玻璃纤维布对钢筋混凝土染的抗剪加固，考察了不同间距、加固量及预裂对加固效果的影响，分析了纤维布对梁开裂荷载、极限荷载、刚度的影响，并提出了适用于工程实际的计算公式。     

Effects of openings on the punching shear strength of RC flat‐plate slabs without shear reinforcement

Openings in RC flat‐plate slabs are one of the critical factors that influence the punching shear strength of the slab and determine its thickness in the vicinity of the slab‐column joint. This study experimentally investigates the effects of openings on the punching shear strength of flat‐plate slabs without shear reinforcement. Tests were performed on eight flat‐plate slab specimens considering the layout and number of openings as test variables. The failure characteristics of each specimen are examined, and the effects of the test variables on the punching shear strengths of the test specimens are investigated. The measured punching shear strengths of the test specimens are compared with the predictions of several concrete design codes, including the American Concrete Institute (ACI), Comité Euro‐International du Béton and Fédération Internationale de la Précontrainte (CEB‐FIP) model and fédération internationale du béton (fib) model codes. This indicates that the reductions in punching shear strength due to the existence of openings are generally proportional to the loss of effective critical sections, and an L‐shaped opening layout around the corner of the column may further reduce the punching shear strength and may contribute to the loss of effective critical sections due to the existence of openings. Copyright © 2015 John Wiley & Sons, Ltd.     

Rehabilitation of rectangular simply supported RC beams with shear deficiencies using CFRP composites

The present study examines the shear performance and modes of failure of rectangular simply supported reinforced concrete (RC) beams designed with shear deficiencies. These members were strengthened with externally bonded carbon fiber reinforced polymer (CFRP) sheets and evaluated in the laboratory. The experimental program consisted of twelve full-scale RC beams tested to fail in shear. The variables investigated within this program included steel stirrups, and the shear span-to-effective depth ratio, as well as amount and distribution of CFRP. The experimental results indicated that the contribution of externally bonded CFRP to the shear capacity was significant. The shear capacity was also shown to be dependent upon the variables investigated. Test results were used to validate a shear design approach, which showed conservative and acceptable predictions.     

无腹筋混凝土短梁受剪承载力尺寸效应研究

《混凝土结构设计规范》(GB 50010—2010)中对于短梁受剪承载力的计算没有考虑梁高的影响,而现有研究表明无腹筋梁的抗剪承载力随梁有效高度的增加而降低。梁受剪尺寸效应的作用机制并没有统一的认识。为研究无腹筋梁的受剪尺寸效应及作用机制,设计了2组8根无腹筋梁,高度为200～1600mm,剪跨比为2.0。三点简支加载。获取了荷载 挠度曲线、纵筋应变、混凝土应变、裂缝宽度、裂缝张开 滑移位移。计算了临界斜裂缝上的应力。搜集并分析了已有的梁受剪尺寸效应试验数据。研究结果表明：无腹筋短梁抗剪承载力存在尺寸效应;骨料咬合机制对无腹筋短梁抗剪承载力贡献有限;受压区未开裂混凝土的强度具有明显的尺寸效应,进而引起了梁抗剪承载力的尺寸效应;我国规范中短梁和不配置抗剪钢筋的单向厚板的抗剪承载力计算公式基本合理,但对部分短梁和大尺寸梁的受剪承载力预测可能偏于不安全,建议在可靠度校准的基础上适当调整。     

Strengthening of RC beams in shear using GFRP inclined strips – An experimental study

Though there have been a number of studies on shear strengthening of RC beams using externally bonded fiber reinforced polymer sheets, the behaviour of FRP strengthened beams in shear is not fully understood. This is partly due to various reinforcement configurations of sheets that can be used for shear strengthening and partly due to different failure modes a strengthened beam undergoes at ultimate state. Furthermore, the experimental data bank for shear strengthening of concrete beams using FRP remains relatively sparse due to which the design algorithms for computing the shear contribution of FRP are not yet clear. The objective of this study is to clarify the role of glass fiber reinforced polymer inclined strips epoxy bonded to the beam web for shear strengthening of reinforced concrete beams. Included in the study are effectiveness in terms of width and spacing of inclined GFRP strips, spacing of internal steel stirrups, and longitudinal steel rebar section on shear capacity of the RC beam. The study also aims to understand the shear contribution of concrete, shear strength due to steel bars and steel stirrups and the additional shear capacity due to glass fiber reinforced polymer strips in a RC beam. And also to study the failure modes, shear strengthening effect on ultimate force and load deflection behaviour of RC beams bonded externally with GFRP inclined strips on the shear region of the beam.     

密实截面组合梁的竖向抗剪强度Ⅰ:受正弯矩作用的组合梁

挖掘混凝土翼板的抗剪潜力,充分利用钢-混凝土组合梁的组合抗剪作用,有利于进一步提高组合梁的经济效益.采用通用有限元程序ABAQUS 6.5,对密实截面组合梁正弯矩区的弯剪强度问题进行研究.分析结果表明,提出的有限元分析方法,特别是钢-混凝土的界面模型,可以准确预测组合梁的弯剪强度,同时对组合梁的变形刚度也可以较准确地模拟.在此基础上,利用有限元方法,对混凝土翼板截面尺寸、剪力连接程度、剪跨比等参数进行计算分析,回归得到考虑剪力连接程度影响的组合梁竖向抗剪强度计算公式.研究发现,在正弯矩区段,组合梁抗剪强度相对于钢梁腹板抗剪名义值的提高,不仅来源于混凝土翼板的抗剪作用,组合作用的贡献也很显著;采用建议的抗剪强度公式,可以不考虑简支组合梁弯矩与剪力的相互影响.     

Flexural strengthening of RC beams using distributed prestressed high strength steel wire rope: theoretical analysis

Various strengthening techniques for structural elements using different materials have been investigated. Recently, a new, reliable and cost-effective strengthening technique with distributed prestressed high strength steel wire rope (P-SWR technique) was proposed. This paper mainly focuses on theoretical analysis of the flexural behaviour of reinforced concrete (RC) beams strengthened with the P-SWR strengthening technique. First, mechanical properties of steel wire rope such as ultimate strength, ultimate tensile strain and relaxation were tested. Second, an evaluation method, including the prediction of cracking load and flexural capacity of RC beams strengthened with P-SWR, was proposed. Third, prestressed level of P-SWR, ratio of reinforcement, and bond strength of P-SWR and concrete responsible for short-term cross-sectional stiffness were studied and associated calculation equations are suggested. Finally, according to parametric studies, an entire evaluation system, including a modified Rao & Dilger code calculation method and hypothetical tension method, as well as a simplified method for predicting the maximum crack width, is proposed. All of these analytical procedures are based on experimental studies. A great similarity between the experimental and analytic results suggests that the proposed methods are highly accurate.     

Estimating uniaxial compressive strength of rocks using genetic expression programming

The aim of this paper is to estimate the uniaxial compressive strength(UCS) of rocks with different characteristics by using genetic expression programming(GEP).For this purpose,five different types of rocks including basalt and ignimbrite(black,yellow,gray,brown) were prepared.Values of unit weight,water absorption by weight,effective porosity and UCS of rocks were determined experimentally.By using these experimental data,five different GEP models were developed for estimating the values of UCS for different rock types.Good agreement between experimental data and predicted results is obtained.     

High strength circular concrete-filled steel tubular slender beam-columns, Part I: Numerical analysis

High strength circular concrete-filled steel tubular (CFST) slender beam-columns are frequently used in high-rise composite buildings because they possess higher strength and stiffness than normal strength ones. Most nonlinear inelastic methods of analysis for circular CFST slender beam-columns have not considered the effects of high strength materials and concrete confinement that significantly increases the strength and ductility of the concrete core. As a result, these methods produce computational solutions that deviate considerably from experimental results. This paper presents a new numerical model for predicting the nonlinear inelastic behavior of high strength circular CFST slender beam-columns under axial load and bending. The numerical model developed not only accounts for confinement effects on the concrete core and circular steel tubes but also incorporates initial geometric imperfections of beam-columns. Axial load-moment-curvature relationships obtained from the fiber element analysis of column cross-sections are utilized to determine the equilibrium states in the inelastic stability analysis of slender beam-columns. Computational algorithms are developed for determining the axial load-deflection and axial load-moment interaction curves for slender beam-columns. The numerical model is implemented in a computer program, which is shown to be an efficient and accurate simulation tool that can be used to investigate the fundamental behavior of high strength circular CFST slender beam-columns. The verification and applications of the numerical model are given in a companion paper.     

High strength thin-walled rectangular concrete-filled steel tubular slender beam-columns,Part I: Modeling

High strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns under eccentric loading may undergo local and overall buckling. The modeling of the interaction between local and overall buckling is highly complicated. There is relatively little numerical study on the interaction buckling of high strength thin-walled rectangular CFST slender beam-columns. This paper presents a new numerical model for simulating the nonlinear inelastic behavior of uniaxially loaded high strength thin-walled rectangular CFST slender beam-columns with local buckling effects. The cross-section strengths of CFST beam-columns are modeled using the fiber element method. The progressive local and post-local buckling of thin steel tube walls under stress gradients is simulated by gradually redistributing normal stresses within the steel tube walls. New efficient Müller's method algorithms are developed to iterate the neutral axis depth in the cross-sectional analysis and to adjust the curvature at the columns ends in the axial load–moment interaction strength analysis of a slender beam-column to satisfy equilibrium conditions. Analysis procedures for determining the load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns incorporating progressive local bucking and initial geometric imperfections are presented. The new numerical model developed is shown to be efficient for predicting axial load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns. The verification of the numerical model and parametric studies is given in a companion paper.     

Uncertainty of concrete strength in shear and flexural behavior of beams using lattice modeling

This paper numerically studied the effect of uncertainty and random distribution of concrete strength in beams failing in shear and flexure using lattice modeling, which is suitable for statistical analysis. The independent variables of this study included the level of strength reduction and the number of members with reduced strength. Three levels of material deficiency (i.e., 10%, 20%, 30%) were randomly introduced to 5%, 10%, 15%, and 20% of members. To provide a database and reliable results, 1000 analyses were carried out (a total of 24000 analyses) using the MATLAB software for each combination. Comparative studies were conducted for both shear- and flexure-deficit beams under four-point loading and results were compared using finite element software where relevant. Capability of lattice modeling was highlighted as an efficient tool to account for uncertainty in statistical studies. Results showed that the number of deficient members had a more significant effect on beam capacity compared to the level of strength deficiency. The scatter of random load-capacities was higher in flexure (range: 0.680–0.990) than that of shear (range: 0.795–0.996). Finally, nonlinear regression relationships were established with coefficient of correlation values (R²) above 0.90, which captured the overall load–deflection response and level of load reduction.     

Two-dimensional FE model for evaluation of composite beams, I: Formulation and validation

This paper develops a two-dimensional finite element model for composite beams, based on the use of the commercial package ANSYS. Different degrees of continuity can be taken into account, permitting the investigation of systems ranging from simply-supported to fully-continuous. Beams with either full or partial shear connection can be considered, as well as different slab typologies. The model represents the behaviour of all components of the composite arrangement, based on the best available current understanding, including the reinforcing bars (considering the tension-stiffening effect), the load-slip characteristic of the shear connectors, and the key components of the beam to column connection. In addition, material nonlinearity for all components is taken into account. The model has been fully verified by extensive comparisons against experimental and numerical results and it has been demonstrated that it is suitable for comprehensive parametric studies of the behaviour of composite beams. A sensitivity study focusing on both the required and the available rotation capacities and their importance for moment redistribution in semi-continuous composite beams is presented in the companion paper.