Diagonal Splitting Research Articles

Prediction of Failure Modes and Minimum Characteristic Value of Transverse Reinforcement of RC Beams Based on Interpretable Machine Learning

Shear failure of reinforced concrete (RC) beams is a form of brittle failure and has always been a concern. This study adopted the interpretable machine-learning technique to predict failure modes and identify the boundary value between different failure modes to avoid diagonal splitting failure. An experimental database consisting of 295 RC beams with or without transverse reinforcements was established. Two features were constructed to reflect the design characteristics of RC beams, namely, the shear–span ratio and the characteristic value of transverse reinforcement. The characteristic value of transverse reinforcement has two forms: (i) λsv,ft=ρstpfsv/ft, from the China design code of GB 50010-2010; and (ii) λsv,fc′=ρstpfsv/fc′0.5, from the America design code of ACI 318-19 and Canada design code of CSA A23.3-14. Six machine-learning models were developed to predict failure modes, and gradient boosting decision tree and extreme gradient boosting are recommended after comparing the prediction performance. Then, shapley additive explanations (SHAP) indicates that the characteristic value of transverse reinforcement has the most significant effect on failure mode, follow by the shear–span ratio. The characteristic value of transverse reinforcement is selected as the form of boundary value. On this basis, an accumulated local effects (ALE) plot describes how this feature affects model prediction and gives the boundary value through numerical simulation, that is, the minimum characteristic value of transverse reinforcement. Compared with the three codes, the suggested value for λsv,fc′,min has higher reliability and security for avoiding diagonal splitting failure. Accordingly, the research approach in this case is feasible and effective, and can be recommended to solve similar tasks.

Strength assessment of RC deep beams and corbels

The strut-and-tie method (STM) has been widely accepted and used as a rational approach for the design of disturbed regions ('D' regions) of reinforced concrete members such as in corbels and deep beams, where traditional flexure theory does not apply. This paper evaluates the applicability of the equilibrium based STM in strength predictions of deep beams (with rectangular and circular cross-section) and corbels using the available experiments in literature. STM is found to give fairly good results for corbel and deep beams. The failure modes of these deep members are also studied, and an optimum amount of distribution reinforcement is suggested to eliminate the premature diagonal splitting failure. A comparison with existing empirical and semi empirical methods also show that STM gives more reliable results. The nonlinear finite element analysis (NLFEA) of 50 deep beams and 20 corbels could capture the complete behaviour of deep members including crack pattern, failure load and failure load accurately.

Numerical simulation of double-sided concrete corbels internally-reinforced with GFRP bars

Three-dimensional (3D) finite element (FE) models were developed in this study to simulate the nonlinear structural behavior of double-sided concrete corbels internally-reinforced with glass-fiber reinforced polymer (GFRP) bars. The accuracy of the numerical models was demonstrated by comparing their results with published experimental data of twelve specimens tested previously by the authors. Two sets of models were first developed. In one set, a perfect bond assumption was adopted between the GFRP bars and the concrete. In the other set, a bond stress-slip law was adopted at the GFRP-concrete interface. Numerical results were in good agreement with those recorded experimentally, except for the specimens with a high concrete strength and high GFRP reinforcement ratio, which failed prematurely in a diagonal splitting mode of failure. In an effort to capture such a mode of failure numerically, additional four models were developed without considering the tension-softening curve in the concrete material constitutive law. Results of the models with the bond-slip law were insignificantly lower than those with perfect bond assumption at GFRP-concrete interface. Eliminating the tension-softening curve from the concrete material constitutive law used in modeling specimens with a high concrete strength and high GFRP reinforcement ratio yielded numerical results closer to those obtained from the tests.

Behavior of Pre-stressed Concrete Deep Beams

Six simply supported deep beams were tested to show the influence of prestressing strand on the behavior of reinforced concrete deep beams. All tested beams have same gross sectional area (42000) mm2, compressive strength (30) MPa, clear span length (1000) mm, longitudinal and vertical reinforcement and the strengthened beams are strengthening by one strand with (12.7mm) diameter. Tested beams were divided into two groups according to the existence of prestressing strand, the first group consist of one deep beam without prestressing strand and it is considered as a reference, while, the second group consist of five Pre-stressed concrete deep beams divided according to the magnitude of jacking stress (fpj) ranging from (250 to 450) bar. During the test, it was found that, the load deflection curves for Pre-stressed concrete deep beams are stiffer compared with the reference beam and the percentage of stiffness was increased with the increase in the magnitude of jacking stress (fpj), and the maximum applied load increased to 8.89%, 13.68%, 18.00%, 24.77% and 33.55% with increasing the jacking stress respectively, compared with the refer beam. on the other hand, the deflection values at mid span increase with decreasing rate to 46.34%, 31.71%, 19.51%,9.75% and 2.44% with increasing the jacking stress respectively, compared with reference beam and the maximum applied load at first crack was increased to 13.64%, 15.56%, 17.4%, 20.84% and 26.93% with increasing jacking stress respectively, compared with reference beam. Finally, the failure mode for deep beam changed from flexural-shear failure to diagonal splitting failure when prestressing strand has been added.

The soft quark Sudakov

There has been recent interest in understanding the all loop structure of the subleading power soft and collinear limits, with the goal of achieving a systematic resummation of subleading power infrared logarithms. Most of this work has focused on subleading power corrections to soft gluon emission, whose form is strongly constrained by symmetries. In this paper we initiate a study of the all loop structure of soft fermion emission. In mathcal{N} = 1 QCD we perform an operator based factorization and resummation of the associated infrared logarithms using the formalism introduced in [1], and prove that they exponentiate into a Sudakov due to their relation to soft gluon emission. We verify this result through explicit calculation to mathcal{O}left({alpha}_s^3right) . We show that in QCD, this simple Sudakov exponentiation is violated by endpoint contributions proportional to (CA−CF)n which contribute at leading logarithmic order. Combining our mathcal{N} = 1 result and our calculation of the endpoint contributions to mathcal{O}left({alpha}_s^3right) , we conjecture a result for the soft quark Sudakov in QCD, a new all orders function first appearing at subleading power, and give evidence for its universality. Our result, which is expressed in terms of combinations of cusp anomalous dimensions in different color representations, takes an intriguingly simple form and also exhibits interesting similarities to results for large-x logarithms in the off diagonal splitting functions.

Experimental and analytical studies of reinforced concrete short beams at elevated temperatures

This paper presents an experimental and analytical programme conducted on a total of seven reinforced concrete (RC) short beams, including one test at ambient temperature and six others at elevated temperatures. This study investigates experimentally the behaviour of RC short beams when subjected to elevated temperatures under the effect of shear-span-to-effective-depth (a/d) ratio and thermal-induced axial restraint. From the literature, this type of study on short beams has not been conducted before. It is experimentally shown that, for unrestrained short beams, as a/d increases, mid-span deflections at failure also increase and failure mode changes from diagonal splitting to shear tension. Besides, the influence of axial restraint on short beams is dependent on a/d ratio. For short beams of small a/d ratios (a/d ≤ 2.00), axial restraint increases mid-span deflections and flexural cracking, whereas it restrains deflections and shortens the failure duration of short beams with a/d ratio of 2.50. Furthermore, regardless of a/d, addition of axial restraint generally shifted the failure mode to a more brittle shear mode at elevated temperatures. Secondly, a simplified analytical model based on strut-and-tie-model (STM) is proposed and verified with test data to predict the performance of RC short beams at high temperatures. This model is applicable to both axially-restrained and unrestrained short beams subjected to elevated temperatures. The proposed STM is capable of providing consistently conservative and safe predictions of temperature profile, axial restraint force, load-carrying capacity and failure duration.

Corrosion-induced shear performance degradation of reinforced concrete beams

Chloride-induced corrosion of reinforcement has been recognized as one of the most predominant causes of structural degradation. In this paper, experimental and numerical investigation was conducted to study the degraded shear performance of reinforced concrete beam. The corrosion of reinforcements, crack patterns, and structural behaviors of corroded specimens with various corrosion levels accelerated by the impressed current method were analyzed. The test results indicated that the corrosion-induced crack patterns have a close relationship with the level of reinforcement corrosion. Moreover, an obvious degradation of shear performance of corroded RC beams in terms of initial stiffness, cracking loads, ultimate bearing capacity, post-peak behavior, and energy dissipation capacity was observed, which became more pronounced as the corrosion level increased. When a severe corrosion level (ηa ≥ 12%) was encountered, the failure mode could even be changed from the shear-compression failure into a much more brittle diagonal splitting failure. In parallel, to numerically simulate the propagation of the main diagonal crack faithfully, the extended finite element method (XFEM) specified with an exponential softening traction-separation relationship was adopted. Moreover, to investigate the effect of corrosion-induced bond degradation, a user-defined element (UEL) was also developed to represent the interfacial bond response. The reasonable agreement between the numerical simulation and experimental results proved the feasibility of the proposed approach.

Experimental Study on Shear Capacity of High Strength Reinforcement Concrete Deep Beams with Small Shear Span-Depth Ratio.

This study aimed to investigate the shear capacity performance for eight deep beams with HTRB600 reinforced high strength concrete under concentrated load to enable a better understanding of the effects of shear span–depth ratio, longitudinal reinforcement ratio, vertical stirrup ratio and in order to improve design procedures. The dimension of eight test specimens is 1600 mm × 200 mm × 600 mm. The effective span to height ratio l0/h is 2.0, the shear span–depth ratio λ is 0.3, 0.6 and 0.9, respectively. In addition, the longitudinal reinforcement ratio ρs is set to 0.67%, 1.05%, 1.27%, and the vertical stirrup ratio is taken to be 0%, 0.25%, 0.33%, 0.5%. Through measuring the strain of steel bar, the strain of concrete and the deflection of mid-span, the characteristics of the full process of shear capacity, the failure mode and the load deflection deformation curve were examined. The test results showed that the failure mode of deep beams with small shear span–depth ratio is diagonal compression failure, which is influenced by the layout and quantity of web reinforcement. The diagonal compression failure could be classified into two forms: crushing-strut and diagonal splitting. With decreasing of shear span–depth ratio and increasing longitudinal reinforcement ratio, the shear capacity of deep beams increases obviously, while the influence of vertical web reinforcement ratio on shear capacity is negligible. Finally, the shear capacity of eight deep beams based on GB 50010-2010 is calculated and compared with the calculation results of ACI 318-14, EN 1992-1-1:2004 and CSA A23.3-04, which are based on strut-and-tie model. The obtained results in this paper show a very good agreement with GB50010-2010 and ACI 318-14, while the results of EN 1992-1-1:2004 and CSA A23.3-04 are approved to be conservative.

Quantum Dynamics in a Fluctuating Environment

We theoretically investigate the dynamics of a quantum system which is coupled to a fluctuating environment based on the framework of Kubo-Anderson spectral diffusion. By employing the projection operator technique, we derive two types of dynamical equations, namely, time-convolution and time-convolutionless quantum master equations, respectively. We derive the exact quantum master equations of a qubit system with both diagonal splitting and tunneling coupling when the environmental noise is subject to a random telegraph process and a Ornstein-Uhlenbeck process, respectively. For the pure decoherence case with no tunneling coupling, the expressions of the decoherence factor we obtained are consistent with the well-known existing ones. The results are significant to quantum information processing and helpful for further understanding the quantum dynamics of open quantum systems.

A diagonal splitting method for solving semidiscretized parabolic partial differential equations

AbstractIn this work, a diagonal splitting idea is presented for solving linear systems of ordinary differential equations. The resulting methods are specially efficient for solving systems which have arisen from semidiscretization of parabolic partial differential equations (PDEs). Unconditional stability of methods for heat equation and advection–diffusion equation is shown in maximum norm. Generalization of the methods in higher dimensions is discussed. Some illustrative examples are presented to show efficiency of the new methods.

Comparison of Different FE Modeling for In-Plane Shear Strengthening of Brittle Masonry with FRCM

Few design oriented models on strengthening of unreinforced masonry (URM) panels under in-plane actions with composite systems are currently available (among them, the pioneers researches [1, 2] and the guidelines [3, 4] for FRPs). Usually, the in-plane shear capacity of a strengthened panel is evaluated as the sum of two terms: the contribution of URM masonry and that of the composite strengthening system (usually only the fibers are considered, also in the case of inorganic matrix, as illustrated in [5, 6, 7], neglecting the shear contribution of the matrix). Mostly, the models proposed to compute the strength increment of the URM can be seen as extensions of provisions for steel-reinforced masonry, where the reinforcement is modeled by the truss analogy [8] and an effective ultimate strain is introduced to account for premature failure of fibers in shear applications. However, the development of the ideal truss in a masonry wall is strongly conditioned by a proper anchorage of fibers and availability of a fiber grid, which is not always ensured. Several failure modes can be expected for strengthened masonry, like diagonal splitting cracking, sliding of a portion over the other, so that the contribution of the composite can be engaged in different ways. The aim of this study is to compare different modeling strategies in the numerical field accounting for matrix as a continuum or as a stiffening of individual fibers, and to provide novel FEM analyses revealing the different role of fiber orientations and matrix properties.

Effectiveness factor of the strut-and-tie model for reinforced concrete deep beams strengthened with CFRP sheet

In the current study, a new strut effectiveness factor based on Strut-and-Tie Model (STM) was proposed to assess the ultimate shear strength of carbon fiber reinforced polymer (CFRP) strengthened concrete deep beam. Derivation of new effectiveness factor of concrete struts is based on the failure principles of Mohr–Coulomb. Two types of concrete failure mode, namely diagonal splitting and concrete crushing are proposed and investigated. Experimental results obtained from the literature results were evaluated using the proposed effectiveness factor and compared with other existing models. The proposed effectiveness factor is validated by utilizing the experimental results which shows good accuracy for predicting the shear strength of CFRP-strengthened concrete deep beams.

Load configuration, geometry and web reinforcement effects on failure modes of sandwich deep beams

In this article, an experimental investigation is carried out to understand the behaviour of sandwich deep beams. The shear strength, load transfer mechanism, integral action and failure modes are reported. Primary variables of this study include distribution of web reinforcement, beam geometry and type of loading. Twelve full-scale beams were tested with simply supported end conditions classifying them into two groups. Each series consists of six beams with rectangular and I-shaped cross-sectional geometry. Two types of loading, i.e. concentrated and uniformly distributed loads, were adopted to understand the influence of distribution of horizontal reinforcement along the depth of beam in the web. Using both types of cross-sections, two beams were tested under uniformly distributed loads, and all the remaining beams were subjected to concentrated load with two different shear span-to-depth ratios (a/d). Observations of the study with respect to strength and serviceability include initial cracking load, ultimate load, crack width, transverse deflection and out-of-plane deformations. The test results indicated that confined or unconfined I-beams in the web failed due to punching shear under concentrated or distributed loads. The modes of failure of rectangular beams with web confinement were diagonal splitting and shear-compression, whereas the unconfined beams failed in flexure. Shear strength expression for conventional deep beams is refined for sandwich beams, and the predicted shear strength agrees well with the experimental results.

Strut effectiveness factor for reinforced concrete deep beams under dynamic loading conditions

In a current study, a new strut effectiveness factor based on Strut-and-Tie Model (STM) is proposed to assess the ultimate shear strength of reinforced concrete (RC) deep beam subjected to dynamic loads. The derivation of the new effectiveness factor of concrete struts is based on Mohr–Coulomb criterion failure. Two types of concrete failure, diagonal splitting and concrete crushing failure modes, are proposed and examined. The modification of the proposed model is simulated in a MATLABSIMULINK environment. The proposed model exhibits efficiency in assessing dynamic shear resistance for deep beams. Moreover, a parametric study is then conducted to examine the effect of flexural reinforcement ratio, transverse reinforcement and shear-span to depth ratio on shear behavior of RC deep beams with consideration of the changes in strain rate. The proposed effectiveness factor is validated by utilizing the experimental results obtained from the literature and shows good accuracy for prediction the shear strength of reinforced concrete deep beams under different loading conditions.

Results and Discussions on Transaction Splitting Technique for Mining Differential Private Frequent Itemsets

researchers are now working on designing of data mining algorithms which also provides differential privacy. Especially so, in mining of frequent itemsets. Individual privacy may get affected by revealing frequent itemsets. Therefore, a frequent itemset mining algorithm with differential privacy is important which will follow two phase process of preprocessing and mining. This paper discusses diagonal splitting of transactions in splitting mechanism. As proposed mechanism, diagonally splits each transaction then size of transaction reduces, resulting in complexity and processing time reduction. By splitting the transaction diagonally, it divides the transaction in two subparts. This paper demonstrated the performance of diagonal algorithm through experiments on real datasets. Result has been taken on various threshold values and calculated f-score measure for output frequent itemsets. Time taken for frequent itemset mining also studied. An experimental comparison with existing algorithms shows that diagonal splitting algorithm achieves better F-score measure and is about an order of magnitude faster for various top k frequent item mining.

Combined Loading Behavior of Basalt FRP–Reinforced Precast Concrete Insulated Partially-Composite Walls

AbstractThe axial and flexure combined loading performance of a slender partially-composite concrete insulated wall design constructed using basalt fiber-reinforced polymer (BFRP) shear connectors and longitudinal BFRP reinforcement is investigated. The load-bearing wall panel sections, 600 mm wide and 2,700 mm long, were first subjected to axial loads ranging from 0 to 900 kN applied to the structural wythe only. The panels were then loaded to failure in four-point bending to develop the axial load-bending moment interaction diagram of the partially-composite system, which was compared to theoretical fully-composite and noncomposite curves. As axial load increased, failure under transverse loading changed from shear-compression of the structural wythe to diagonal splitting of insulation foam and rupture of BFRP connectors, then to crushing of the structural wythe. Composite action by the strength criterion reduced from 47 to 3% as axial load increased from 150 to 900 kN; while that by the stiffness crite...

철근콘크리트 깊은 보의 파괴거동과 전단강도 산정식

깊은 보의 파괴거동은 전단경간과 유효깊이의 비(a/d)에 따라 크게 변한다. a/d≤1.0의 깊은 보는 복부의 쪼갬현상과 하중점과 재하점 부근에서의 콘크리트의 연화현상을 동반하는 파괴모드가 지배적인 파괴모드가 되는 것과 복부에 배치된 전단철근은 보의 파괴모드를 변화시키는 역할을 하고, 이러한 목적으로 복부철근을 배근할 때에는 반드시 연직 및 수평철근을 동시에 사용하거나 또는 사인장균열에 직각을 이루도록 철근을 배치하여야 한다. 한편, 1.0＜a/d≤2.5의 깊은 보의 경우, 전단파괴시 주인장철근이 항복상태에 도달하지 않도록 충분히 배치되어져 있다면 복부에 배치된 수평철근으로 인한 전단강도 증가는 거의 기대하기 어렵다. 하지만 연직전단철근은 1.0＜a/d≤2.5의 깊은 보가 일찍 타이드아치기구로 전이되는 현상을 방지함으로서 전단강도를 증대시키는 역할을 한다. 본 연구에서는 깊은 보에 대한 기존의 실험연구로부터 얻어진 파괴거동과 그것에 영향을 미치는 주요 인자들에 대해 정성적으로 분석하고, 소성이론을 적용하여 파괴강도를 구하는데 기초가 되는 역학모델을 정의하였다. 또한 정의된 역학모델을 근거로 소성이론의 상계정리(upper bound theorem)를 적용하여 a/d가 1이하의 깊은 보에 대한 전단강도식을 이론적으로 유도하였다. 이 연구에서 제안된 전단강도 산정식은 a/d≤1.0의 깊은 보의 전단강도를 정확하게 예측하였다.

UPT rectangular and flanged shear walls of high-strength CASIEL-TLM masonry: Experimental and numerical push-over analysis

The mechanical behaviour of unbonded post-tensioned (UPT) shear walls of high-strength CAlcium SIlicate ELement masonry with Thin-Layer Mortar (CASIEL-TLM masonry) was investigated experimentally and numerically. Eight walls were tested with the following key variables: unit type, prestress level and cross-sectional shape (rectangular or T-shaped with interlocking of web and flange). An extensive measurement scheme was adopted that allowed derivation of average curvatures and strains in the bottom region of the wall in addition to wall displacements. Since UPT masonry is characterised by the absence of local compatibility between masonry and the UPT tendons, a numerical model for quasi-static, monotonic push-over analysis was developed that provides an iterative solution for the global interaction between masonry and UPT tendons. A common masonry stress–strain diagram was adopted in the numerical model. A peculiarity of CASIEL-TLM masonry is the kicker course, which reduces the stiffness of the bottom region of the shear wall. This layer was modelled with no-tension, linear-elastic behaviour and a reduced stiffness. Nevertheless, the model underestimates the experimental deformations of the rectangular shear walls, while the strength is in reasonable agreement. The walls with T-shaped cross-section failed prematurely by shear of the web-flange interface, resulting in diagonal splitting cracks in the interlocking units. This paper deals with the experimental results of UPT CASIEL-TLM masonry shear walls with rectangular and T-shaped cross-section and with the numerical modelling of the overturning behaviour of UPT shear walls with rectangular cross-section.

Determination of concrete fracture parameters based on peak-load method with diagonal split-tension cubes

Using the boundary element method, unnotched and notched split tension-cubes were analyzed by applying compressive forces in the diagonal planes. The maximum tensile stress of the unnotched diagonal cubes and the linear elastic fracture mechanics formulas of the notched diagonal cubes, KI, CMOD and COD profile, were determined for different load-distributed widths. Subsequently, to investigate the extent to which the diagonal split-cube tests could simulate the fracture behavior of concrete, four series of tests were performed. Finally, the advantages of diagonal splitting cubes are discussed in comparison to other splitting specimens.

Direct Strut-and-Tie Model for Ultimate Shear Strength of Reinforced Concrete Structural Walls

A direct strut-and-tie model to calculate the ultimate shear strength of structural walls based on an interactive mechanical model (C.Y.Tang et al.) is presented. Two common failure modes, namely, diagonal splitting and concrete crushing, are examined in this paper. Ultimate shear strengths of structural walls are governed by both the transverse tensile stresses perpendicular to the diagonal strut, and the compressive stresses in the diagonal strut. Such proposed model is verified aganist three experimental case studies of structural walls. Generally, predictions by the proposed model are not only accurate and consistent in each case study, but also conservative.