Use of Strut-and-Tie Models to Calculate the Strength of Deep Beams with Openings

Strut-and-tie modeling is a method applicable to almost every design situation in reinforced concrete. This is a behavioral theory proposed as a alternative to past design strategies utilizing empirical formulas and parameters. Since the original presentation of this method in the 60' s numerous experimental studies have been conducted, yet the topic of deep beams with large web openings has not been widely covered. Design codes and guidelines also do not commonly cover this topic. However empirical design equations have been proposed based on previous research in the field. An empirical method is presented and the relation to the beam geometry and behavior is discussed. A discussion of the strut-and-tie method is also given including the limited previous research and application of the method. These two methods are compared using previous experimental results of deep beams with openings. The comparison includes analysis of predicted loads and ultimate loads as well as predicted behavior using the strut-and-tie method for beams with and without web reinforcement. For beams with reinforcement a model was constructed to compare a realistic reinforcement detail. This generates a fairly accurate assessment of strength and behavior with the experimental results. In beams without reinforcement a model is presented using ties only where available. This general model was then adapted to three of the experimental beam geometries. This model gives consistent prediction of the ultimate load and beam behavior in each beam. The results presented reinforce the strut-and-tie method as a safe approach in structurally diverse situations where empirical methods may have a limited range of application

Strengthening of Concrete Deep Beams with Extreme Discontinuities Using Near-Surface mounted Composites

Installation of a web opening that fully interrupts the natural load path in concrete deep beams produces regions of extreme discontinuities and reduces the shear strength. This research examined the effectiveness of using near-surface-mounted carbon fiber-reinforced polymer (NSM-CFRP) reinforcement to restore the shear strength of deep beams with extreme discontinuities. The strut-and-tie model (STM) procedures were utilized to develop three different strengthening solutions around the discontinuity regions. A total of eight deep beam specimens (150 x 500 x2700 mm) with a shear span-to-depth ratio of a/h = 0.8 were constructed and tested. One beam was solid. Seven beams had a square opening in the middle of the shear span with an opening height ratio of ho/h = 0.2. Six beams were strengthened with NSM-CFRP around the discontinuity regions. Three-dimensional finite element (FE) models were developed to simulate the nonlinear behavior of the tested specimens. Experimental results were compared to predictions of the FE models and the STM design solutions to examine their accuracy and validity. Installation of the web opening resulted in a 40% reduction in the shear strength. The NSM-CFRP strengthening solutions fully restored the original shear strength, except in two cases where only 93% and 94% of the capacity were restored. The laboratory test results were used to determine the optimal NSM-CFRP strengthening solution. The STM based on provisions of the American Concrete Institute provided realistic and consistent predictions for the nominal strength of the tested specimens with an average predicted-to-measured strength ratio of 1.01±0.09. In contrast, the STM predictions based on provisions of the Canadian Standards Association tended to be conservative with an average predicted-to-measured strength ratio of 0.71±0.29. Predictions of the FE models were sensitive to the mesh size and the concrete constitutive law adopted in the analysis. The inclusion of a bond-slip model between the CFRP and concrete resulted in up to a 5% reduction in the predicted strength. The use of a small mesh size of 15 mm and a “user” concrete constitutive law rather than a “default” law yielded more accurate predictions that were insignificantly different from those obtained from the test

Web buckling study of the behaviour and strength of perforated steel beams with different novel web opening shapes

This paper presents an experimental and analytical study on the behaviour of perforated steel beams with closely spaced web openings. Seven specimens including two typical cellular beams (i.e. circular web openings) and five perforated beams with novel web opening shapes were tested to investigate the failure mode and load strength of the web-post between two adjacent web openings. Fourteen numerical test specimens were developed and analysed by the finite element method and the results were compared with the full scale experiments. The effect of web opening spacing/web opening depth of web-posts was studied to investigate the effective ‘strut’ action of the web-post buckling. The effect of the web opening depth/web thickness was also studied to investigate the stability (slenderness) of the web-post subjected to vertical shear load. Two hundred and twenty-fine elastic-plastic finite element analyses were then employed in a comprehensive parametric study to propose an empirical formula which predicts the ultimate vertical shear load strength of web-posts formed from the particular web opening shapes. Perforated beams with standard circular, hexagonal and elongated web openings are mostly used nowadays. Various non-standard web opening shapes are introduced through this paper. These new pioneering web opening shapes improve the structural performance of the perforated beams when examined under the web-post buckling failure mode. In addition, the manufacturing procedure of these non-standard web openings show great advantage in comparison with the manufacturing way of the more popular perforated beams with circular web openings (i.e. cellular beams)

Improvements on design and analysis of deep beams based on the strut-and-tie method

La adaptación del método de las bielas y tirantes para el análisis de estructuras tridimensionales es un problema complejo. Los recientes análisis realizados por muchos investigadores desde una perspectiva parcial hacen que muchas veces se pierda la visión global del problema. El trabajo trata de hacer un análisis crítico de las últimas adaptaciones publicados tratando de despejar un camino válido para futuras investigaciones.The adaptation o the strut-and-tie method for the 3D structures is a complex problem. Lastest published findings from many researchers have pointed an specific side of the problem, sometimes loosing an overall perspective. This work is a critical analysis of all these advances, trying to give a guidance to the next point to improve the knowledge of the method.Vancoillie, T. (2018). Improvements on design and analysis of deep beams based on the strut-and-tie method. http://hdl.handle.net/10251/106242TFG

Specification of Deep Beams Affect the Shear Strength Capacity

Reinforced Concrete Deep beams researches have attracted attentions of professionals and academics due to the wider use of this type of structures in construction projects; because of characteristics in transferring significant amount of load.  Ultimate strength of deep beams has been a great challenge because of the complexity to Evaluation for this structural member. However, code provisions for capacity of beam equations are conservative.  Essentially influencing parameters are Loading and Supporting Conditions, horizontal and vertical web reinforcement, shear span-to-depth ratio,   load and support bearing plates, distribution of the reinforcement along depth of the deep beam‘s web, tension  reinforcement and compressive strength.  Least influencing parameters are bottom cover, side cover, width of the beam, distribution of vertical stirrups in the web, and aggregate size, presence the web openings. The effect of above factors on the shear capacity and behavior of RC deep beams have been reviewed. Keywords: Deep beams, D-region, Loading condition, Shear strength, Reinforcement distribution, Failure mode

Study the behavior of prestressed concrete deep beams using FEM simulations

The objective of this master‘s thesis is to study and analyze the behavior of prestressed concrete deep beams and how prestressing changes the strut and tie model. The method used for analyzing the behavior is finite element modeling in ATENA. The strut and tie models are developed by analyzing the principal tensile and compressive stresses for the different models at yield. The models are analyzed without prestressed reinforcement, with 25 MPa prestressed reinforcement and 100 MPa prestressed reinforcement. In order to analyze how different load patterns affect the principal stresses, this paper analyzes three different load patterns. In total, two different models are analyzed, each containing three different load patterns. The models are analyzed without prestressed reinforcement, with 25 MPa and 100 MPa prestressing. The prestressed reinforcement is placed straight and curved. One of the models is also analyzed with two openings with three different placements of the openings. The results show a decrease in the distance between the bottom of the deep beam and the tie when adding prestressed reinforcement. A proposed equation to calculate the distance from the bottom of the deep beam to the tie is included in this thesis. The equation takes both the height of the deep beam and the amount of prestressing into account. The equation is based on the results gathered in this thesis

NUMERICAL SIMULATION OF CONCRETE BEAMS WITH DISCONTINUITY REGIONS REINFORCED WITH NONMETALLIC REINFORCING BARS

Nonmetallic Glass Fiber-Reinforced Polymer (GFRP) reinforcing bars are considered a viable alternative to the conventional steel reinforcement because of their high strength-to-weight ratio and noncorrosive nature. This research aimed to investigate the nonlinear structural behavior of GFRP-reinforced concrete beams with discontinuity regions (D-regions) through numerical analysis. Three-dimensional (3D) numerical models were developed to simulate the nonlinear structural behavior of GFRP-reinforced deep beams with and without web openings. The models adopted realistic constitutive laws that accounted for the nonlinear behavior of the materials used. Predictions of the numerical models were validated against published experimental data. A parametric study was conducted to examine the effect of key variables on the structural behavior of GFRP-reinforced deep beams with and without web openings. The interaction between the concrete compressive strength (fc’), shear span-to-depth ratio (a/h), size and location of the web opening was elucidated. Simplified analytical formulas capable of predicting the shear capacity of GFRP-reinforced beams with D-regions were introduced based on an inverse analysis of results of the numerical simulation models. Predictions of the proposed analytical formulas were in good agreement with the results of the simulation models

Lateral behavior of steel frames with discretely connected precast concrete infill panels

As an alternative to the conventional structures for tall buildings, a hybrid lateral load resisting structure has been designed at Eindhoven University of Technology. It consists of discretely connected precast concrete panels with window openings in steel frames, and is a new application in infilled frames. Besides the structural advantages of hybrid construction, this structure offers an alternative construction method, improving the constructability of tall buildings. This will result in more economical and high quality buildings. The infilled frame is a type of structure that has proven to be effective and efficient in bracing low-rise and medium-rise buildings to resist in-plane lateral loads. It acts by composite action between the infill and its surrounding frame. Structural interaction between the two components produces a composite structure with a complicated behavior due to the fact that the frame and the infill mutually affect each other. Since the early fifties extensive research has been done into the composite behavior of infilled frames with masonry and cast-in-place concrete infills without openings. However, the application of discretely connected concrete panels with openings as bracing elements in steel frame structures has not been performed yet and represents a new area of research in infilled frames. The main objective of this investigation is to develop practical universally applicable design models for infilled steel frames with discretely connected precast concrete panels, allowing for an accurate prediction of the strength, stiffness and deformation capacity of this type of structure. In order to develop these design models, the structure has been subjected to experimental, numerical and analytical investigation. First, full-scale tests on single-storey, single-bay infilled frame structures were carried out. Objectives of this experimental study were to observe the general behavior of the infilled frame in terms of stiffness, strength and failure modes. In addition, experiments were performed on components of the discrete panel-to-frame connection. Subsequently, finite element models were developed and validated by simulating the experiments. For this purpose, finite element analyses taking non-linear material and structural behavior into account were performed. It has been shown that the finite element model developed for the overall infilled frame behavior can be used to predict the lateral load versus deflection relationship and the ultimate lateral load with good accuracy. Accordingly, the validated finite element model has been used to carry out a parameter study to investigate various configurations of the infilled frame. Four parameters have been studied with respect to their influence on the structural response. These parameters are the frame member dimensions, the rotational stiffness of the frame joints, the infilled frame aspect ratio and the panel opening geometry. From the simulated load-deformation curves, structural characteristics have been derived. These have served as a verification for the developed analytical models for the prediction of the lateral stiffness, the ultimate lateral load and deformation capacity of the structure under consideration. The analytical models are based on the concept of the equivalent diagonal strut, considering the structure as an equivalent braced frame system with a compression diagonal replacing the infill. Finally, a practical method for designing steel frames with discretely connected precast concrete infill panels has been proposed. The aim of this method is to get a good prediction of the internal forces and the lateral deflection in the preliminary phase of the design, without the use of advanced computer simulations. The design method provides a useful guideline that a design engineer can follow, in order to design building structures consisting of steel frames with discretely connected precast concrete infill panels, resulting in a ductile structure, possessing both adequate strength and stiffness

Design methods for reinforced concrete deep beams

Cílem této diplomové práce je analýza výpočetních modelů pro sténové nosníky. Ve stručnosti jsou představeny přístupy řešení stěnových nosníků dle Českých technických norem (ČSN EN 1992-1-1) a Amerického institutu pro beton (ACI 318-14) a doporučení uvedená v odborné literatuře. Jednotlivé výpočetní modely jsou popsány a porovnány. Z výsledků je patrné, že některé metody jsou nepřesné a proto jsou pro řešení stěnových nosníků nevhodné. Návrh vybraného stěnového nosníku je proveden výpočetním modelem, který byl při porovnání vyhodnocen jako nejvhodnější.The aim of this diploma thesis is to investigate design methods of deep beams. In brief, approaches of Czech technical standard (ČSN EN 1992-1-1) and American Concrete Institute (ACI 318-14) as well as recommendations from technical literature are presented herein. All design methods are introduced in detail and then compared. The results show that some methods are inaccurate and therefore unsuitable for the design of deep beams. The design method which was evaluated as the best one is then applied to design a selected deep beam