Bottle-shaped Struts Research Articles

Strength prediction of a bottle-shaped strut for evaluating the shear capacity of reinforced concrete deep beam

For the analysis and design of reinforced concrete (RC) deep beams, the strut-and-tie model is typically employed to simulate the flow of stresses. A bottle-shaped strut develops between the loading point and support, in which compressive stress spreads laterally and induces tensile strain in the transverse direction, which reduces the compressive strength of the strut significantly. Web reinforcements are provided in deep RC beams to prevent splitting of the diagonal strut due to the presence of these transverse strains. In this article, a simplified design procedure based on the strut-and-tie model (STM) is proposed for the evaluation of the shear capacity of deep beams with web reinforcement. The suggested model is based on modified compression field theory and considers the impact of shear reinforcement ratio, transverse tensile strain, post-cracking strength of concrete, and the actual dispersion of compressive stress based on strut geometry (aspect ratio) for strength prediction of bottle-shaped struts. The experimental results of RC panels and deep RC beams reported in the literature are used to validate the results of the suggested model. The findings demonstrate that the proposed STM evaluates the shear capacity of deep RC beams more precisely than capacities estimated by ACI 318-19, AASHTO LRDF, and Eurocode 2 (EC2). In addition, a comprehensive parametric study has been carried out to investigate the effect of various design parameters on the shear capacity of deep RC beams.

STRENGTH PREDICTION OF CONCRETE BOTTLE-SHAPED STRUTS

For better strength prediction using strut-and-tie models (STM), it is essential to use reliable strength parameters of the model components; e.g., struts, ties, and nodes. Among all the elements of the STM, the strength of the bottle-shaped struts is not well quantified. The purpose of this study is to develop more accurate formulas for the calculation of the effectiveness factors for 2D and 3D bottle-shaped struts that are unreinforced, reinforced with minimum reinforcement, or reinforced with sufficient transverse reinforcement. The nonlinear finite element analysis, with the aid of the software ABAQUS, has been utilized in this study, which has been verified against experimental tests. The study has been carried out for grades of concrete varying from 20 to 100 MPa, and for bearing plate to width ratio varying from 0.1 to 0.9. The obtained formulas for the effectiveness factor are functions of the concrete strength, which is not the case with the ACI 318-19 provisions. These formulas have been verified against experimental tests and have been compared with the ACI 318-19 provisions. The predictions based on these formulas are always on the safe side and are more accurate than those based on the ACI 318-19 provisions.

STRENGTH PREDICTION OF CONCRETE BOTTLE-SHAPED STRUTS

For better strength prediction using strut-and-tie models (STM), it is essential to use reliable strength parameters of the model components; e.g., struts, ties, and nodes. Among all the elements of the STM, the strength of the bottle-shaped struts is not well quantified. The purpose of this study is to develop more accurate formulas for the calculation of the effectiveness factors for 2D and 3D bottle-shaped struts that are unreinforced, reinforced with minimum reinforcement, or reinforced with sufficient transverse reinforcement. The nonlinear finite element analysis, with the aid of the software ABAQUS, has been utilized in this study, which has been verified against experimental tests. The study has been carried out for grades of concrete varying from 20 to 100 MPa, and for bearing plate to width ratio varying from 0.1 to 0.9. The obtained formulas for the effectiveness factor are functions of the concrete strength, which is not the case with the ACI 318-19 provisions. These formulas have been verified against experimental tests and have been compared with the ACI 318-19 provisions. The predictions based on these formulas are always on the safe side and are more accurate than those based on the ACI 318-19 provisions.

Strength reduction design method for reinforced concrete structures: Generalization

This work presents a generalization and enhancement of a previously developed computational strength reduction design method (SRDM) for the design of complex reinforced concrete structures. The enhanced method SRDM-3D presented in this work extends the applicability of the original method to a more general 3D state of stresses and to different possible input tension stiffening and incompatibility laws, via a new calibration procedure. It also addresses the limitations of the strut-and-tie method initially developed and often applied to 2D geometries. Application of the developed method for simple 3D configurations allowed to obtain important results regarding the shape of nodal zones, incompatibility between concrete struts and reinforcement ties and conditions for the development of bottle-shaped struts for the general 3D framework of reinforced concrete structural elements. Validation examples presented at the end of the study on reinforced concrete pile caps demonstrate the robustness of the developed method, and its ability to provide a safe lower-bound design solution to different geometry configurations and different failure mechanisms. The developed method has the advantage of using a simple constitutive law and input parameters that are standard parameters required for design of RC structures.

Refined strength prediction of concrete 2D bottle-shaped struts

For better strength prediction using strut-and-tie models (STM), it is essential to use reliable strength parameters of the model components; e.g., struts, ties, and nodes. Among all the elements of the STM, the strength of the bottle-shaped struts is not well quantified. The purpose of this study is to develop more accurate formulas for the calculation of the effectiveness factors for 2D bottle-shaped struts, that are unreinforced, reinforced with minimum reinforcement, and reinforced with sufficient transverse reinforcement. The nonlinear finite element analysis, with the aid of the software ABAQUS, has been utilized in this study, which has been verified against experimental tests. The study has been carried out for grades of concrete varying from 20 to 100MPa, and for bearing plate to width ratio varying from 0.1 to 0.9. The obtained formulas for the effectiveness factors of bottle-shaped struts are functions of the concrete strength, which is not the case with the ACI 318-19 provisions. These formulas have been verified against experimental tests and have been compared with the ACI 318-19 provisions. The predictions based on these formulas are more accurate than those based on the ACI 318-19 provisions. Also, the results from these formulas are always on the safe side. On the other hand, the ACI 318-19 provisions lead to unsafe results in the case of high-strength concrete and very conservative results for the case of unreinforced struts from normal-strength concrete.

Effect of Fibres on the behaviour of Bottle shaped strut

Bottle-shaped struts are the critical elements in the design of D-regions using Strut-and-Tie method. The transverse tension develops due to dispersion of compression load which further leads to splitting crack in bottle shaped strut. Due to this, the strut fails before reaching its ultimate compression capacity. Higher resistance to the transverse tension can improve the strut capacity and its efficiency in load transfer. Transverse tensile stress can be resisted by providing the steel reinforcement or through the addition of discrete fibres in the concrete. Many international codes like ACI, AASTHO, and CSA have suggested guidelines about the addition of steel fibre reinforcement in the bottle-shaped struts for resisting the transverse tension. Still, the influence of the discrete fibres on the performance of the bottle-shaped strut is not well established. The performance of the bottle-shaped strut in terms of efficiency factors, crack pattern and failure mode for different amounts of macro steel fibres and micro polypropylene fibres are studied using experimental investigation. Specimens of 600mm x 600mmx 100mm size were tested under compression. Steel fibres are added in the proportions of 0.7%, 0.9% and 1.1% volume fractions to the concrete. Effect of fibre hybridization also studied by adding micro polypropylene fibres in the proportions of 1% and 2% in addition to the steel fibres. Experimental results showed that adding discrete fibres in concrete significantly improved the resistance to the transverse tension in bottle-shaped struts and led to the increased load-carrying capacity of the specimens. A 75% improvement in the efficiency factor is observed at 0.9% volume of steel fibre addition. Addition of micro polypropylene fibres to the macro steel fibres further enhanced the load-carrying capacity of the bottle-shaped struts. Microfibres in the concrete effectively arrested the micro-cracks and delayed the occurrence of a first splitting crack in the strut region. Due to this the mode of failure changed to ductile through the formation of a greater number of small cracks with less crack width at the ultimate load. Results of this study clearly show that the addition of discrete fibres to the concrete is an effective solution to improve the performance of the bottle-shaped struts in terms of ultimate strength and serviceability.

An experimental investigation into dispersion of compressive stress in isolated bottle-shaped struts with openings

Strut and Tie Modeling (STM) can be used to simplify intricate states of stresses within reinforced concrete (RC) members with geometric or static discontinuity regions (D-regions). A bottle-shaped strut can thus form when an isolated reinforced concrete compressed member is loaded in a relatively small area of the member or in the presence of an opening. In this category of struts, the resulting compressive stresses spread in a lateral direction as they have to avoid the opening area and the strut axis. In this respect, curving compressive stress trajectories give rise to notable transverse strains in an orthogonal direction to the strut axis and subsequently longitudinal cracks will form if insufficient reinforcement is arranged; which can lead to concrete failure. Therefore, an experimental investigation was conducted in this study to examine the dispersion of compressive stresses in isolated RC struts with openings. The size of the openings were kept constant in all specimens. The major parameters were presence of opening and opening location. Consequently, In the second part of the study (Analytical investigation), on the basis of model presented by Sahoo et al. (2009) [19] and based on the geometrical characteristic of the ILC, an analytical model was proposed to predict the load-carrying capacity of a bottle-shaped strut with an opening. This new proposed model considered the effect of size and position of the opening. To conduct the experimental study, five Isolated RC struts with compressive strength of 40 MPa (5800 psi.) and then different positions of openings were tested. Axial load, axial shortening and lateral strains were measured to determine the effects of the test parameters. The obtained results were also compared with an analytical equation of isostatic line of compression (ILC) and the American Concrete Institute (ACI) 318-11 Provision. These results indicated that the presence of an opening creates a variation on the dispersion of compressive stresses and consequently produce a reduction in load-carrying capacity.

Effects of design parameters on behaviour in bottle-shaped struts

For this paper, an experimental investigation of the impact of the concentration ratio and the mats’ rotation angle on the behaviour and efficiency coefficient of the bottle-shaped struts was conducted. The behaviour of tested panels, including the load–transverse extension curve and strain redistribution, is presented and the quantitative effects of the concentration ratio and the mats’ rotation angle on the efficiency coefficient and the dispersion angle of compressive stresses of bottle-shaped struts are given. The related provisions of ACI 318-14 and BS EN 1992-1-1 are examined. The results indicate that as the concentration ratio increases, the efficiency coefficient and the dispersion angle decrease, and that as the mats’ rotation angle increases, the efficiency coefficient also increases. Some recommendations for ACI 318-14 and BS EN 1992-1-1 are finally presented.

Effect of confinement on the efficiency of bottle-shaped struts

Isolated strut tests were performed to study the effect of plain concrete lateral confinement on the efficiency of two-dimensional (2D) and three-dimensional (3D) bottle-shaped struts. For the 2D struts, thin plain concrete panels of varying width were tested to failure under in-plane compression. For the 3D struts, short square columns of varying cross-section were tested to failure under axial compression. The strut efficiency in short columns was found to increase with cross-section as expected, although the increase became insignificant beyond a certain limit. However, the strut efficiency in the panels increased with an increase in panel width only up to half the panel height and thereafter reduced significantly. Supported by finite-element modelling, the results revealed the hitherto unknown phenomenon that excessive confinement negatively impacts on the efficiency of wide bottle-shaped struts only in planar (plane stress) concrete members.

Experimental and analytical study on reinforced concrete deep beams

A new simple strut-and-tie model was presented in this paper to study the behaviour of reinforced concrete deep beams. This model was obtained based on bottle-shaped struts that can predict flexural, bearing and shear modes of the failure. Also, the effect of web reinforcements was considered. The proposed model was verified by laboratory test results that obtained from five deep beams with a shear span-to-depth ratio of two and some other experimental results existing in the literature. Comparison of the results of the proposed model with relations from ACI 318 and AASHTO-LRFD codes and some other relations showed that the proposed model is efficiently capable of accurately predicting the ultimate load of simply supported deep beams. Also, comparison of experimental results demonstrated that the flexural capacity of deep beams obtained from the strut-and-tie model is conservative.

Splitting force of bottle-shaped struts with different height-to-width ratios

A bottle-shaped strut is a common kind of strut in the structures, whose compression disperses, resulting in a splitting force at some distance away from the load plate. Considering characters of the geometric and physical boundary conditions which are different from previous studies, a new mathematical equation for the infinite isostatic lines of the compression (ILC) is obtained and a corresponding equation of transverse stresses distribution is derived. Then theoretical formulae to calculate the resultant splitting forces and their location in a bottle-shaped strut are proposed. Based on the principle of superposition, different compression dispersion models for the struts with different height-to-width ratios are individually formulated and simplified. A recommendation for EN1992 is presented. The transverse stresses distribution and the equations for the resultant splitting force and their locations are validated by the test and FEM results. The results show that the proposed equations have good agreements with the test and FEM result, which can provide accurate predictions for the magnitude and location of the resultant splitting force.

Whither Transverse Reinforcement in Bottle-shaped Struts?

Recommendations in many of the current design codes like the Eurocode and the AASHTO LRFD Bridge Design Code discount the effect of transverse reinforcement on strength of bottle shaped struts whereas the mechanics of the force system within a bottle-shaped strut suggests otherwise. In this investigation, the effect of amount of transverse reinforcement on strength of steeply inclined normal-strength and high-strength concrete bottle-shaped struts measured in terms of efficiency factors has been experimentally investigated for three transverse reinforcement ratios - 0.0031, 0.0046 and 0.0069, with the control bottle-shaped strut being transversely unreinforced. Efficiency factor increases of 31% and 25% in the normal-strength and the high-strength concrete bottle-shaped struts respectively were obtained when the transverse reinforcement ratio was increased from nil to 0.0031 whereas for the higher reinforcement ratios the increase in efficiency factor was relatively smaller. Service load crack widths in all the transversely reinforced struts were less than an upper bound value of 0.3 mm. The results of this investigation emphasise the role of transverse reinforcement in the strength of bottle-shaped struts and indicate that the 0.003 transverse reinforcement ratio recommended in the ACI 318-14 Building Code is the optimum amount of such reinforcement in normal-strength and high-strength concrete bottle-shaped struts.

Derivation of the equation of isostatic line of compression and splitting force in a bottle-shaped strut

The reported data deal with the derivation of the equation of isostatic line of compression (ILC) and splitting force in a bottle-shaped strut with different height-to-width ratios. The final data show that the splitting force in a bottle-shaped strut is not only related to the height-to-width ratio (h/b), but also related to the load area ratio.

Behavior predictions of deep beams with short straight bar anchorages using strut-and-tie models and nonlinear analysis

Abstract This paper investigates the laboratory test results of 12 deep beams available in the literature, where the longitudinal reinforcement was anchored into the support using short straight bar anchorages. Four different specimen groups with three different shear span-to-depth ratios (a/d) were selected and most of the deep beams failed by strut crushing after yielding of the main longitudinal reinforcement. In order to investigate the behavior of the selected deep beams, an enhanced strut-and-tie model assuming geometrical adaptability (possibility of update in the dimensions of the struts and ties as the main tie starts to yield) is proposed. The analytical results obtained using this approach may be considered as much as accurate than some conducted complex nonlinear analysis considering smeared fixed cracking model and bond-slip behavior. However, an improvement on the effective strength factor of bottle-shaped struts by means of an iterative strut-and-tie model is needed, once the effective strength factor prescribed by NBR6118 (2014) has shown to be over conservative for all ranges of span-to-depth ratio (a/d) investigated. Finally, the obtained results indicated that short bar anchorages did not seem to influence significantly the shear strength of the deep beams investigated, especially the strength of bottled-shaped struts when appropriate crack control reinforcement is present.

Refinement of Strut-and-Tie Model for Reinforced Concrete Deep Beams.

Deep beams are commonly used in tall buildings, offshore structures, and foundations. According to many codes and standards, strut-and-tie model (STM) is recommended as a rational approach for deep beam analyses. This research focuses on the STM recommended by ACI 318-11 and AASHTO LRFD and uses experimental results to modify the strut effectiveness factor in STM for reinforced concrete (RC) deep beams. This study aims to refine STM through the strut effectiveness factor and increase result accuracy. Six RC deep beams with different shear span to effective-depth ratios (a/d) of 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00 were experimentally tested under a four-point bending set-up. The ultimate shear strength of deep beams obtained from non-linear finite element modeling and STM recommended by ACI 318-11 as well as AASHTO LRFD (2012) were compared with the experimental results. An empirical equation was proposed to modify the principal tensile strain value in the bottle-shaped strut of deep beams. The equation of the strut effectiveness factor from AASHTTO LRFD was then modified through the aforementioned empirical equation. An investigation on the failure mode and crack propagation in RC deep beams subjected to load was also conducted.

Efficiency factors of recycled concrete bottle-shaped struts

Reported test results of reinforced concrete beams made with coarse recycled concrete aggregate have been re-analysed using strut-and-tie models and the efficiency factors of the recycled concrete aggregate concrete bottle-shaped struts compared with those made of natural coarse aggregate. The objective was to ascertain whether strut-and-tie model provisions for efficiency factors of bottle-shaped struts in current design codes and the recent literature, originally meant for natural coarse aggregate concrete, can be conservatively applied to recycled concrete aggregate concrete, or not. The results of the re-analysis indicate that the efficiency factors of the natural coarse aggregate as well as the recycled concrete aggregate concrete bottle-shaped struts were comparable and conservative when benchmarked against the predictions of CSA A23.3-04 and an efficiency factor model proposed by the authors. However, both ACI 318-08 and Eurocode 2 gave unsafe efficiency factor predictions for the recycled concrete aggregate as well as the natural coarse aggregate concrete bottle-shaped struts under investigation. This is attributed to the insensitivity of these two codes to strut inclination with adjoining tie(s) and does not per se indicate any inherent inferiority as far as recycled concrete aggregate concrete is concerned. This investigation indicates that recycled concrete aggregate concrete bottle-shaped struts can be designed using the efficiency factors recommended for natural coarse aggregate concrete bottle-shaped struts in CSA A23.3-04.

Strut deformation in CFRP-strengthened reinforced concrete deep beams.

Strut-and-tie model (STM) method evolved as one of the most useful designs for shear critical structures and discontinuity regions (D-regions). It provides widespread applications in the design of deep beams as recommended by many codes. The estimation of bottle-shaped strut dimensions, as a main constituent of STM, is essential in design calculations. The application of carbon fibre reinforced polymer (CFRP) as lightweight material with high tensile strength for strengthening D-regions is currently on the increase. However, the CFRP-strengthening of deep beam complicates the dimensions estimation of bottle-shaped strut. Therefore, this research aimed to investigate the effect of CFRP-strengthening on the deformation of RC strut in the design of deep beams. Two groups of specimens comprising six unstrengthened and six CFRP-strengthened RC deep beams with the shear span to the effective depth ratios (a/d) of 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00 were constructed in this research. These beams were tested under four-point bending configuration. The deformation of struts was experimentally evaluated using the values of strain along and perpendicular to the strut centreline. The evaluation was made by the comparisons between unstrengthened and CFRP-strengthened struts regarding the widening and shortening. The key variables were a/d ratio and applied load level.

Efficiency factors of recycled aggregate concrete bottle-shaped struts

Efficiency factors of steeply inclined unreinforced recycled aggregate concrete bottle-shaped struts have been experimentally found and compared with their natural coarse aggregate (NCA) concrete counterparts and the predictions of ACI 318–08, AASHTO bridge design specifications and Eurocode 2. The experiments involved testing of scaled deep beam specimens configured so as to develop bottle-shaped struts under applied loading. The replacement level of the coarse recycled concrete aggregate (RCA) in the saturated surface-dry moisture condition was the only parameter under investigation. Service load crack widths in the NCA and the RCA concrete bottle-shaped struts were smaller than the permissible value, their failure modes were similar, their measured efficiency factors were comparable and the coarse aggregate replacement level had an insignificant effect on the measured efficiency factors. The efficiency factor models in the ACI 318–08 and Eurocode 2, which are insensitive to strut inclination, gave overly conservative predictions, whereas relatively accurate predictions were obtained from the AASHTO bridge design specifications and an efficiency model given in the literature, both of which account for the effect of inclination on efficiency factors of bottle-shaped struts.

Efficiency factors of recycled concrete aggregate concrete bottle-shaped struts

A comparison with code-based predictions of efficiency factors of bottle-shaped struts computed using strut-and-tie models from shear test results of coarse recycled concrete aggregate concrete beams reported in the literature is presented. The objective of the comparison was to ascertain whether strut efficiency factors in current design codes originally meant for natural coarse aggregate concrete can be conservatively applied to concrete made with coarse recycled concrete aggregate or not. In addition to the codal provisions, a strut efficiency factor model developed from first principles was also used in the comparative study. The results of the comparison indicate that the AASHTO LRFD code provisions and the proposed efficiency factor model gave conservative predictions for the coarse recycled concrete aggregate concrete bottle-shaped struts although the ACI 318-08 predictions were unconservative. The most accurate predictions were obtained from the Eurocode 2 model, although with an erratic degree of conservatism. The lack of conservatism vis-à-vis the ACI code recommended strut efficiency factors does not per se indicate inferior strength of coarse recycled concrete aggregate concrete but may be attributed to the insensitivity of the ACI code efficiency factors to strut inclination with adjoining tie(s).

An appraisal of design provisions for bottle-shaped struts

Ever since their inception, strut-and-tie modelling (STM) provisions in most of the current design codes have remained virtually unchanged, in spite of significant research-driven advances in the recent past. An appraisal of the ACI 318 STM provisions related to bottle-shaped struts has been carried out in the context of research findings reported in the literature. This appraisal has been used to propose a simple and robust analytical model for the efficiency factor which is used to estimate the strength of bottle-shaped struts. The proposed strut efficiency factor model, besides taking into account the strength of concrete, also considers the effect of inclination of the strut with an adjoining tie. For struts with inclination angles less than a certain threshold value that depends on the concrete strength, the efficiency factors recommended by current design codes are shown to be unconservative when compared with the predictions of the proposed model and other similar models in the literature. An alternative to the ACI minimum reinforcement formulation for bottle-shaped struts, which takes into account material strength characteristics, is discussed and the corrected form of the minimum reinforcement formulation has been used to identify a conflict in the deep beam web reinforcement provisions of ACI 318-08.