ICCAE-10-2014 International Conference on Civil and Architecture Engineering (original) (raw)
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Behavior of reinforced concrete deep beams with openings strengthened with steel fibers
The International Conference on Civil and Architecture Engineering, 2014
Strut-and-Tie models are effective in designing reinforced concrete structures with discontinuity regions where linear stress distribution is not valid. Deep beams are typically short girders with a large point load or multiple point loads. These point loads, in conjunction with the depth and length of the members, contribute to a member with primarily discontinuity regions. ACI 318-08 Building Code Requirements for Structural Concrete provides a method for designing deep beams using either Strut-and-Tie models (STM) or Deep Beam Method (DBM). Large openings in reinforced concrete (RC) deep beams generally interrupt the load transfer by concrete struts and cause a sharp decrease in strength and serviceability. The reinforcement detailing of these deep beams based on strut-and-tie models (STMs) can be complex and, very often, these models may not predict the failure mechanism of deep beams due to localized damages. The main objective of this paper is to study Steel Fiber Reinforced Concrete (SFRC), offered as an alternative material, to the cumbersome and iterative steps involved in strut-and-tie (STM) methodology. Additionally, a similar reinforced concrete (RC) specimen was tested under the same controlled condition designed with classical strut-and-tie model design methodology reinforced using conventional steel bars. In this investigation, three types of steel fibers, and three percentage of steel fibers, and two aspect ratios were aiming to show the effect of these parameters on the behavior of concrete deep beams. Material testing was conducted on the materials used in the large scale specimens to ensure that the actual material mechanical properties were known for the analysis. Computer Aided Strut and Tie (CAST) software was used to quantify the experimental data obtained from the controlled conditions testing. The eight beams were compared and contrasted throughout the study to show the effect of fiber on the behavior of deep beams. This study provides information on the viability of using steel fiber reinforced concrete in complex D-regions in structural elements.
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. Link to Full-Text Articles : http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0130734&representation=PDF
This study investigates the applicability and reliability of the strut-and-tie modelling that is recommended by the ACI 318 Building Code (2002) for designing continuous deep beams with openings. Presented herein are experimental results of two full-scale continuous reinforced concrete deep beams with openings subjected to concentrated loads. Each specimen was designed using the ACI 318 provisions for strut-and-tie models. Both specimens were found to be able to carry loads greater than the factored design load. The failure mechanism of each specimen corresponds well with the designed strut-and-tie models. The experimental results thus illustrate the reliability and conservative nature of strut-and-tie modelling for designing continuous deep beams with openings.
Analysis of Fibre Reinforced Concrete Deep Beams Using the Strut and Tie Model
The present study aimed at evaluating the adequacy of the strut and tie model which was proposed by the ACI Code (318-11), AASHTO, FIB recommendations and an Equation proposed by Narayanan and Darwish for predicting the shear strength of fibre reinforced concrete deep beams. The four methods were applied to 68 fibre reinforced concrete deep beams whose geometrical, materials and experimental results were previously published. The collected test results cover a wide range of the variables that affect the shear strength of fibre reinforced concrete deep beams, like the shear span to effective depth ratio which varied from 0.29 to 1.91, concrete compressive strength from 18.2 to 54.9 MPa and steel fibres volume percentage from 0.25 to 1.25. Ten of the beams were loaded with one concentrated load at the midspan section and the others were loaded with two points loads. The ACI Code (318-11), AASHTO LRFD, FIB recommendations underestimated the shear strength of the investigated fibre reinforced concrete deep beams. Since these recommendations are for conventional reinforced concrete deep beams, the effect of steel fibres has to be incorporated in the materials properties affecting the shear strength of fibre reinforced concrete deep beams. On the other hand the equation proposed by Narayanan and Darwish overestimated the shear strength of the investigated fibre reinforced concrete deep beams. A realistic prediction method is therefore required so that it can be used as a design guide.
Use of Steel Fiber Reinforced Concrete for Enhanced Performance of Deep Beams with Large Openings
Reinforced concrete deep beams are used as primary load distribution elements in various civil engineering structures. Large openings often interrupt the load transfer by concrete struts in these beams and cause a sharp decrease in strength and serviceability. Although the strength evaluation and reinforcement details around the openings are essential considerations, the ACI Building Code does not provide explicit guidance for designing these elements with openings. Strut-and-tie models are commonly used for strength evaluation and design of deep beams with openings. However, reinforcement detailing based on these models can be very complex and the failure of deep beams may be due to localized damages that could not be predicted by the strut-and-tie models. In this study, an experimental investigation was conducted on two concrete deep beam specimens with large single opening, namely, reinforced concrete (RC) and steel fiber reinforced concrete (SFRC), to evaluate their performance ...
STRUT-AND-TIE MODELING OF R.C. CONTINUOUS DEEP BEAMS
A strut-and-tie model (STM) is proposed for the shear carrying capacity of continuous RC deep beams. First, the mathematical formulation is given to fully describe the geometry, derivation of internal forces, evaluation of compressive and tensile stresses, and consideration of concrete tension softening. Second, validation studies for the modified STM are made for number of tested beams from the literature. Finally, a comparative study is presented between the results of proposed STM with the models of ECP code and the ACI code. The strut-and-tie method can be used for the design of Disturbed regions (D-regions) of structures where the basic assumption of flexure theory, namely plane sections remaining plane before and after bending, does not hold true. Such regions occur near statical discontinuities arising from concentrated forces or reactions and near geometric discontinuities, such as abrupt changes in cross section. The strut-and-tie method of design is based on the assumption that the D-regions in concrete structures can be analyzed and designed using hypothetical pin-jointed trusses consisting of struts and ties interconnected at nodes. Since continuous deep beams contain significant extents of D-regions and they exhibit a marked truss or tied arch action, the strut-and-tie method offers a rational basis for the analysis and design of such beams. The current paper presents the formulation and results for a proposed STM for continuous deep beams as given in [1]. 2. Strut-and-Tie Model (STM) of Continuous Deep Beams The proposed model is an extension to STM; proposed earlier for continuous deep beams [2]. A STM for two-span continuous deep beams with a top point load at each mid-span is given in Fig. (1). It can be idealized as a statically indeterminate truss as shown in Fig. (2). The deep beam under consideration can be assumed to be made up of a primary negative moment truss and a primary positive moment truss as presented in Fig. (2). The location and orientation of the struts and ties are defined by the position of the nodes. The horizontal position of the nodes can be assumed to lie on the line of action of the respective applied loads and the support reactions. For vertical position of nodes, in order to exploit the full load carrying capacity of the beam, it is imperative that nodes A, B and A' lie as close as possible to the bottom face of the beam. Similarly, the nodes C and C' assumed to lie as close as possible to the top face of the beam with providing sufficient concrete cover to the tie reinforcement. The inclined angle of the diagonal strut θ s can be obtained by: tanθ s = (h – l c /2 – l d /2) / a = (h – c 1 – c 2) / (l e / 2) (1) Where l e is the effective span measured between centre-to-centre of supports, h is the beam total depth, a is the shear span measured from centre lines between the load and support bearing plates , l c and l d are the respective depths of bottom and top nodal zones as shown in Fig. (3) and were taken as: l c = 2 c 2 (2) l d = 2 c 1 (3)
Development of Strut-and-Tie Models in Deep Beams with Web Openings
Advances in Structural Engineering, 2007
The strut-and-tie models of a total of fourteen (14) concrete deep beams with varying size and location of web openings are developed herein using a topology optimisation approach. By systematically eliminating inefficient materials from an over-designed discretized domain, the load transfer mechanism in deep beams is progressively characterised by the residual part of the structure. Both von Mises stress and displacement sensitivity number are used as deletion criteria with the aim of maximising the material efficiency and overall stiffness of the structural beam. The performance indices in terms of von Mises stress and nodal displacement are evaluated to monitor the optimisation process and to determine the optimal topology which is transformed to the strut-and-tie model. The relationship between the strut-and-tie models and the ultimate load-carrying capacity of the beams are discussed in some detail. A series of comparisons offer insight into the varying characteristics of the s...
Assessment of Strut-and-Tie Methods to Estimate Ultimate Strength of RC Deep Beams
Reinforced concrete (RC) deep beams are structural members characterized by relatively small shear span to depth (a/d) ratios. Sectional analysis as well as design procedures are not valid for these members due to the complex interaction of flexure and shear. The strut-and-tie method (STM) has been widely accepted and used as a rational approach for the design of such disturbed regions (D regions) of reinforced concrete members, where traditional flexure theory cannot be used. The flow of stress is idealized as a truss consisting of compressive struts (concrete) and tension ties (reinforcing steel) transmitting the loads to the supports. Usually, STM considers only equilibrium. Hence, there is no unique solution for a given system, as one can find more than a single truss geometry admissible for a given force field. Therefore, the model which gives the maximum capacity can be considered as the most appropriate one. This paper attempts to predict the ultimate strength of deep beams failing in diagonal compression as well as tension, from the experimental database available in literature based on STM. A modified approach has been used, considering the crushing and splitting failures of the diagonal strut separately. Crushing failure of the diagonal strut has been predicted using a plastic Strut-and-tie model with varying compression zone depth. A localized STM has been considered to predict the splitting failure of the diagonal strut. Index Terms-Crushing, Deep beams, Disturbed, Splitting, Strut and tie I. INTRODUCTION einforced concrete deep beams find wide applications as transfer members in high rise buildings. These are characterized with shear span to depth ratios less than 2, making the behaviour shear dominated. According to St. Venant's principle, also supported by an elastic stress analysis, the localized effect of a concentrated load or geometric discontinuity will attenuate about one member depth away from the discontinuity. These regions, known as 'D' regions ('D' stands for discontinuity/disturbed) are assumed to extend one member depth from the loading point or geometric discontinuity. Therefore, the entire region of a deep beam can be considered to be disturbed. Schlaich (1987) developed the Strut-and-tie method (STM) to primarily design 'D' (discontinuity or disturbed) regions, where the strain distribution is nonlinear. STM is a
A Strut and Tie Model for Steel Fiber Reinforced Concrete Deep Beams
INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING AND BUSINESS SCIENCES (IJAEBS), 2023
A modified Strut-and-Tie model (MSTM) was developed for fibrous deep beams to include the contribution of steel fibers in the internal resistance for compression and tension. The proposed (MSTM) calculates the ultimate loads for several experimental results. The ratio between experimental results and MSTM predictions (Pu(EXP) /Pu(MSTM)) for 79 specimens is 1.20%. The results of the Strut-and-Tie for the American Code (Pu(ACI)) and Egyptian Code (Pu(ECCS)) are more conservative. The inclusion of steel fibers increases the shear capacity of deep beams by 13% and 19% respectively in compassion with ACI Code and the Egyptian Code. The ratio for (Pu(EXP) /Pu(ACI)) and (PuEXP /Pu(ECCS)) are 1.36 and 1.43, respectively. The predictions of (MSTM) are consistent, accurate, and have a great degree of validation for (HSSFRC) deep beams with different geometrical properties, concrete compressive strength, fibers, main and web steel ratios.