Continuous Deep Beams Research Articles

The strut-and-tie model and the finite element - good design companions

The strut-and-tie method (STM) can serve as a tool for a safe design of concrete structures or members. It aids to trace the flow of forces, appropriately lay-out the reinforcement, and safely predict the structure capacity. On the other hand, the linear elastic finite element can be utilized as an alternative in the development of the strut-and-tie models besides the load path method. In addition, the nonlinear finite element analysis assists in the optimization of the design results obtained from the STM. Hence, the two methods work well as companions in structural design. In order to demonstrate such understanding, different examples which include a deep beam with large opening and recess, continuous deep beams with and without openings, and beam ledges, have been utilized. In the STM solutions, the ACI 318-14 failure criteria have been adopted. In the nonlinear finite element analysis, material nonlinearity has been accounted for. The obtained solutions from the two methods, along with the experimental data of the selected examples of this study, revealed the reliability of the STM in obtaining a safe solution. Besides, the nonlinear finite element proved to be an efficient tool in obtaining an economic design.

Shear-Transfer Mechanisms and Strength Modeling of RC Continuous Deep Beams

Based on experimental results including the crack pattern and maximum applied strut stress, as well as on stress states obtained using a nonlinear finite-element analysis, it is identified that the typical critical shear crack of continuous deep beams is a web-shear crack, which has a large effect on shear-transfer mechanisms of deep beams. By theoretically considering the influence of the web-shear crack on the diagonal strut in a strut-and-tie model (STM) of continuous deep beams, a cracking strut-and-tie model (CSTM) has been developed. Shear-transfer mechanisms including aggregate interlock action, dowel action of longitudinal bars, and tension of web reinforcement are rationally considered. By comparing with a large database including 90 tests, the CSTM is verified to well predict the effect of main parameters including shear span-to-depth ratio, longitudinal reinforcement ratio, stirrup ratio, concrete compressive strength, and effective depth on the shear strength. Moreover, the proposed model is simplified to be used in the practical shear design, which shows a better prediction than the STM of a current standard.

Behavior of Simply Supported and Continuous Concrete Deep Beams Reinforced with GFRP Bars

Abstract Reinforced concrete deep beams are common structural elements in bridges and high-rise buildings because of their ability to support higher concentrated loads compared with slender beams. ...

Structural behaviour of SCC continuous deep beam strengthened with carbon fiber NSM and hybrid techniques

In this research, results of an experimental investigation on the shear strengthening of normal SCC continuous concrete deep beam are presented. A total of twelve continuous deep beams were cast and tested. The aim of this paper is to study the effect of carbon fiber reinforced polymers (CFRP|) through Near Surface Mounted (NSM) and hybrid techniques to improve the structural behaviour and shear resistance capacity of deep beams. Two beams were used as control with no strengthening, while the remaining ten beams were strengthened in different (with and without) steel shear reinforcement, orientation of NSM-FRP rods, hybrid techniques (combined of EBR-CFRP strip and NSM-CFRP rods). The beams were designed to fail in shear and to match with the requirements of ACI 318M-14 building code. Results showed that the hybrid technique caused an increase in the load carrying capacity for the deep beams up to 58.5 % when compared to the beams without strengthened control one.

Analysis of boundary condition effects on RC deep beams

The end support of deep beams could have different effects on behavior of the beams. In this paper, experimental results of 43 deep beams with span -to -depth ratio of less than 3, different reinforcement arrangements and boundary conditions were investigated and discussed. Results indicated that, boundary conditions have important effects on ultimate loads, modes of failure and deflections; but crack formation and their patterns are almost the same irrespective of applied boundary conditions. Furthermore, the ultimate loads of the beams with fixed ends are 1.2–6 times of simply supported and continuous deep beams, depending on amount of main bottom and top reinforcements. Furthermore, in fixed -end deep beams, modes of failure and ultimate loads mostly depend on top main reinforcement. To examine the beams theoretically, available standards and published proposed methods were used. Results indicated that, none of existing methods is suitable for fixed- end deep beams, except proposed method. However, the methods proposed by ACI 318–14 and CIRIA Guide 2 yielded very conservative results for simply supported deep beams.

Shear Strength of Reinforced Concrete Simple and Continuous Deep Beams

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Load capacity predictions of continuous concrete deep beams reinforced with GFRP bars

Nine continuous concrete deep beams reinforced with glass fibre reinforced polymer (GFRP) bars were experimentally tested to failure. Three main parameters were investigated, namely, shear span-to-overall depth ratio, web reinforcement and size effect. The experimental results confirmed the impacts of web reinforcement and size effect that were not considered by the strut-and-tie method (STM) of the only code provision, the Canadian S806-12, that addressed such elements. The experimental results were employed to evaluate the applicability of the methods suggested by the American, European and Canadian codes as well as the previous studies to predict the load capacities of continuous deep beams reinforced with GFRP bars. It was found that these methods were unable to reflect the influences of size effect and/or web reinforcement, the impact of which has been confirmed by the current experimental investigation. Therefore, a new effectiveness factor was recommended to be used with the STM. Additionally, an upper-bound analysis was developed to predict the load capacity of the tested specimens considering a reduced bond strength of GFRP bars. A good agreement between the predicted results and the experimental ones was obtained with the mean and coefficient of variation values of 1.02 and 5.9%, respectively, for the STM and 1.03 and 8.6%, respectively, for the upper-bound analysis.

Experimental tests of two-span continuous concrete deep beams reinforced with GFRP bars and strut-and-tie method evaluation

Test results of nine continuous concrete deep beams reinforced with GFRP bars and one specimen reinforced with steel rebars are reported. The investigated parameters included shear span-to-overall depth ratio (a/h), size effect and web reinforcement ratio. Two a/h ratios of 1.0 and 1.7 and three section heights of 300 mm, 600 mm and 800 mm as well as two web reinforcement ratios of 0% and 0.4% were used. The experimental results highlighted that the web reinforcement ratio improved the load capacities by about 10% and 18% for specimens having a/h ratio of 1.0 and 1.7, respectively. Additionally, a considerable reduction in shear strength occurred due to the increase of the section depth from 300 mm to 600 mm. The comparisons between the test results and those calculated using the strut-and-tie methods of the American (ACI 318-2014), European (EC2-2004) and Canadian (S806-2012) codes showed that the American code gave unsafe predictions, while the predictions of the Canadian code underestimated the load capacity of the beams tested. The European code provided the closest predictions to the test results; however, all codes presented do not consider the influence of section depth and/or web reinforcement on the shear strength, the impacts of which were confirmed experimentally.

Applying Various Types of Loading on Continuous Deep Beams Using Strut and Tie Modelling

This work aims at presenting detailed procedures companied by numerical examples for designing reinforced concrete two span continuous deep beams under various types of loading; one concentrated force, two concentrated forces and uniform load for each span. Analysis and design was conducted based on Strut and Tie modeling (STM) of ACI 318M-14 since they contain significant extents of D-regions and they show a marked truss or tied arch action. It was found that changing the loading type has a significant impact on the capacity for the same specimen that has the same dimensions, concrete and steel properties, in addition to the same amount and arrangement of steel reinforcement. In more detail, the increase in the number of concentrated forces causes an obvious increase in ultimate capacity due to the reduction in span to overall height (a/h) ratio and the increase in the value of the strut-tie angle, which causes shortening in the length of the strut. Therefore, the ultimate capacity increased by about (44-70) % when the applied load was changed from 1-concentrated force to 2-concentrated forces or to uniformly distributed load.

Shear behaviours of hybrid continuous deep beams strengthened with carbon fibre reinforced polymer

This paper investigates the shear strength characteristics of reinforced concrete continuous deep beams (RCCDB) consisting of homogenous versus hybrid concrete, and further looks at the effect of Carbon Fibre Reinforced Polymer (CFRP) on the shear strength of hybrid RCCDBs. The experimental work included testing ten specimens of RCCDB under two-point loads. The effects of high strength concrete (HSC) layer thickness and CFRP on the strength of RCCDB were thus studied. The experimental results showed that the strengthening of RCCDB by an HSC layer at the top is better than that from one at the bottom, as the increments in ultimate load strength were 17 and 34% for top strengthening and 8 and 26% for bottom strengthening for 25 and 50% thickness of total depth of beam, respectively. The optimal strengthening of RCCDB using an HSC layer at the top was at 50%. Shear strengthening using 5 cm width CFRP strips for hybrid RCCDBs increased the ultimate shear strength by 69% and 49% for strengthening with inclined and straight shapes, respectively, where such strengthening was applied near to the centre of the specimens.

Predicting the response of continuous RC deep beams under varying levels of differential settlement

This paper investigates the effect of differential support settlement on shear strength and behavior of continuous reinforced concrete (RC) deep beams. A total of twenty three-dimensional nonlinear finite element models were developed taking into account various constitutive laws for concrete material in compression (crushing) and tension (cracking), steel plasticity (i.e., yielding and strain hardening), bond-slip at the concrete and steel reinforcement interface as well as unique behavior of spring-like support elements. These models are first validated by comparing numerical predictions in terms of load-deflection response, crack propagation, reaction distribution, and failure mode against that of measured experimental data reported in literature. Once the developed models were successfully validated, a parametric study was designed and performed. This parametric study examined number of critical parameters such as ratio and spacing of the longitudinal and vertical reinforcement, compressive and tensile strength of concrete, as well as degree (stiffness) and location of support stiffness to induce varying levels of differential settlement. This study also aims at presenting a numerical approach using finite element simulation, supplemented with coherent assumptions, such that engineers, practitioners, and researchers can carry out simple, but yet effective and realistic analysis of RC structural members undergoing differential settlements due to variety of load actions.

Effectiveness factor of self-compacting concrete in compression for limit analysis of continuous deep beams

The current design codes, such as ACI 318-14, EC2 and CSA23.3-04, in addition to previous research investigations suggested different expressions for concrete effectiveness factor for use in limit state design of concrete structures. All these equations are based on different design parameters and proposed for normal concrete deep beams. This research evaluates the use of different effectiveness factor equations in the upper and lower bond analyses of continuously-supported self-compacting concrete (SCC) deep beams. Moreover, a new effectiveness factor expression is suggested to be used for upper and lower bound solutions with the aim of improving predictions of the load capacity of continuously-supported SCC deep beams. For the range of deep beams considered, the strut-and-tie method with the proposed effectiveness factor formula achieved accurate predictions, with a mean of 1.01, a standard deviation of 6.7% and a coefficient of variation of 6.8%. For the upper-bound analysis, the predictions of the proposed effectiveness factor equation were more accurate than those of the formulas suggested by previous investigations. Overall, although the proposed effectiveness factor achieved very accurate predictions, further validation for the proposed formula is needed since the only data available on continuous SCC deep beams are those collected from the current study.

Behaviour of Steel Fibre Reinforced Rubberized Continuous Deep Beams

Transfer girders and pier caps, which are in fact deep beams, are critical structural elements present in high-rise buildings and bridges respectively. During an earthquake, failure of lifeline structures like bridges and critical structural members like transfer girders will result in severe catastrophes. Ductility is the key factor that influences the resistance of any structural member against seismic action. Structural members cast using materials having higher ductility will possess higher seismic resistance. Previous research shows that concrete having rubber particles (rubcrete) possess better ductility and low density in comparison to ordinary concrete. The main hindrance to the use of rubcrete is the reduction in compressive and tensile strength of concrete due to the presence of rubber. If these undesirable properties of rubcrete can be controlled, a new cementitious composite with better ductility, seismic performance and economy can be developed. A combination of rubber particles and steel fibre has the potential to reduce the undesirable effect of rubcrete. In this paper, the effect of rubber particles and steel fibre in the behaviour of two-span continuous deep beams is studied experimentally. Based on the results, optimum proportions of steel fibre and rubber particles for getting good ductile behaviour with less reduction in collapse load is found out.

Modelación numérica de vigas continuas de gran peralto de hormigón armado

This paper presents a study of the behavior of reinforced concrete continuous deep beams by numerical simulation, where results of the numerical analysis are calibrated and validated from existing experimental results in the international literature. In the modeling, a bilinear model is considered with Von Mises failure criteria for reinforcing steel and Concrete Damage Plasticity for concrete, where a good correspondence was achieved between the numerical results to estimate the load capacity and the displacement between the reference numerical and experimental results. The adequate calibration of the physical-mechanical diagram of the experiment allows numerically studying the influence of different geometric factors and reinforcement configurations. The numerical study evidences the influence of the main and vertical reinforcements in the load capacity of these structures, where the most significant contribution of the vertical reinforcement is found in beams with higher shear spaneffective depth ratio (a/d). Diagrams of continuous deep beams with circular web openings are analyzed, showing favorable positions for the location of these openings and their direct influence on the load capacity reduction for beam diagrams with concentrated and distributed load.

Experimental investigation on continuous reinforced SCC deep beams and Comparisons with Code provisions and models

The test results on eight two-span deep beams made of self-compacting concrete (SCC) are presented and discussed in this paper. The main parameters investigated were the shear span-to-depth ratio, and the amount and configuration of steel reinforcement. All beams failed due to a major diagonal crack formed between the applied mid-span load and the intermediate support separating the beam into two blocks: the first one rotated around the end support leaving the other block resting on the other two supports. Both concrete compressive strength and web reinforcement had a major effect in controlling the shear capacity of the beams tested. For the shear span-to-depth ratio considered, the vertical web reinforcement had more influence on the shear capacity of the specimens than the horizontal web reinforcement. The shear provisions of the ACI 318M-11 are unconservative for most of the beams tested. Comparisons of test results with the strut-and-tie model (STM) suggested by ACI 318M-11, EC2 and CSA23.4-04 showed that the predictions are reasonable for continuous deep beams made with low and medium compressive strength. Although the equation suggested by ACI 318M-11 is very simple, its prediction is more accurate than the STM suggested by different design codes.

Strut-tie model for two-span continuous RC deep beams

In this study, a simple indeterminate strut-tie model which reflects complicated characteristics of the ultimate structural behavior of continuous reinforced concrete deep beams was proposed. In addition, the load distribution ratio, defined as the fraction of applied load transferred by a vertical tie of truss load transfer mechanism, was proposed to help structural designers perform the analysis and design of continuous reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie was introduced to ensure the ductile shear failure of reinforced concrete deep beams, and the primary design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete were reflected upon. To verify the appropriateness of the present study, the ultimate strength of 58 continuous reinforced concrete deep beams tested to shear failure was evaluated by the ACI 318M-11\'s strut-tie model approach associated with the presented indeterminate strut-tie model and load distribution ratio. The ultimate strength of the continuous deep beams was also estimated by the experimental shear equations, conventional design codes that were based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the proposed strut-tie model and load distribution ratio was examined through the comparison of the strength analysis results classified according to the primary design variables. The present study associated with the indeterminate strut-tie model and load distribution ratio evaluated the ultimate strength of the continuous deep beams fairly well compared with those by other approaches. In addition, the present approach reflected the effects of the primary design variables on the ultimate strength of the continuous deep beams consistently and reasonably. The present study may provide an opportunity to help structural designers conduct the rational and practical strut-tie model design of continuous deep beams.

Nonlinear Behavior of Reinforced Concrete Continuous Deep Beam

This paper presents numerical investigation of nine continuous reinforced concrete deep beams were experimentally tested and collected from literature. The collected specimens cover several parameters which usually influenced on strength and behavior of continuous deep beams as shear span to depth ratio, the reinforcement ratio, the effective depth, and the concrete compressive strength. All beams had the same longitudinal top and bottom reinforcement and no web reinforcement to assess the effect of changing the beam depth on the shear strength of such beams. A three-dimensional finite element model using (ANSYS 12) program is used. It was found that the general behaviors through the linear and nonlinear ranges up to failure of the finite elements model show good agreement with observations and data from the experimental beam tests. Keywords—Continuous deep beams; Finite element; Ansys.

Three-Parameter Kinematic Theory for Shear Behavior of Continuous Deep Beams

Three-Parameter Kinematic Theory for Shear Behavior of Continuous Deep Beams

Failure mechanism and shear strength of steel–concrete–steel sandwich deep beams

In steel–concrete–steel (SCS11SCS: steel–concrete–steel.) sandwich deep structural members the shear performance becomes rather critical. This paper describes an experimental study on the shear behavior of SCS continuous deep beams. Three beams with different shear spans were tested under anti-symmetric concentrate loads, and the failure pattern is found to be different from reinforced concrete members. Tests show that the shear capacity depends strongly on the steel plates and the shear connectors, and the membrane action of the outer steel plates provides the beams with excellent strength and ductile performance. On the basis of the experimental observations (both the continuous beam tests in this paper and the simple beam tests conducted earlier), a plastic limit analytical model is developed to explain the force transfer mechanism and predict the shear strength of both simple and continuous members. Considering equilibrium and boundary conditions, the lower bound approach shows satisfactory predictions for the shear performance of SCS deep beams.

Environmental Studies and Researches Institute, University of Sadat City, Egypt

Reinforced concrete deep beams may exist in many structural applications such as offshore structures,transfer girders, pile caps, tall buildings and water tanks. The depth of deep beams is much greaterthan normal in relation to their span. Since the beam is short in this case, shear deformations are moreimportant and special design methods should be applied in this case rather than normal beam theory.Continuous deep beams are defined in the Egyptian Code of Practice (2012) [2]as those beams whoseheight to effective span ratio greater than 0.4. Deep beams are members with special features. In suchbeams, plane sections do not remain plane after bending, with significant warping of the crosssectionsbecause of high shear stresses. The resulting strain distribution is no longer linear andflexural stresses are not linearly distributed even in the elastic range. Recently, high strengthconcrete, defined by the American Concrete Institute ACI318-08[3], as concrete with cylindercompressive strength greater than 60Mpa, is being widely used in the construction industry.However, limited research efforts were directed towards the study of the behavior and shear strengthof reinforced high strength concrete continuous deep beams. Furthermore, sometimes web openingshave to be provided in deep beams for the purpose of access or for providing services. The presenceof such openings may affect the shear strength of deep beams. However, limited investigations weredirected towards the study of continuous deep beams with openings. Also, strengthening simplysupported deep beams using carbon fiber reinforced polymers (CFRP) was investigated by manyresearchers. However, limited research papers were directed towards CFRP strengthening ofcontinuous deep beams. Experimental tests have been carried out on rectangular reinforced concretecontinuous deep beams with a/d=1.17, under static loading up to failure. The study takes intoconsideration the following parameters: Percentage of web reinforcement (ρh), Positions ofopenings and number of openings. Also, strengthening of openings in continuous deep beams usingglass fiber reinforced polymer (GFRP) was studied in this research. Test results indicated that thepresence of web openings within exterior or interior shear spans had great effect on the beamcapacity and its behavior. Existence of web openings within exterior or interior shear spans caused ahigh reduction in the shear capacity of the beams by about 35%. Therefore and whenever should be kept clear of the natural load path joining the loading and reaction points (solid) free from openings.Also, the strengthening of openings contains the cracks and increase the crack and ultimate load.Finally we will compare the test results with the theoretical values for beam A1 which were evaluatedusing strut and tie analysis according to Egyptian code (2012). The strut–and tie method can be used forthe design of Disturbed regions (D- regions) of structures where the basic assumption of flexure theorynamely plane sections remaining discontinuities arising from concentrated forces or reactions and neargeometric discontinuities such as abrupt changes in cross section etc. The strut – and- tie method ofdesign is based on the assumption that the D-regions in concrete structures can be analyzed and designusing hypothetical pin-jointed trusses consisting of struts and ties interconnected at nodes. The usualdesign practice for continuous deep beams has been to employ empirical equations which are invariablybased on simple span deep beams testes. Given the unique behavior pattern of continuous deep beams,this practice is unreliable. Since continuous deep beams contain significant extents of D-regions and theyexhibit a marked truss or tied arch actions, the strut- and – tie method offers a rational basis for theanalysis and design of such beams. The mechanics and behavior of continuous deep beams are brieflydiscussed from which a strut–and–tie model for such a beam is developed.