Application of micro truss and strut and tie model for analysis and design of reinforced concrete structural elements (original) (raw)
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Strut and Tie Modelling of Reinforced Concrete Short Span Beams
Strut-and-tie modelling of reinforced concrete structures is used in the design of discontinuous or D-region structural elements which includes short span beams of clear shear span to depth ratio of less than 2. For those beams, shear is the critical mode of failure and Eurocode 2 allows for its design using strut-and-tie models (STM). However Eurocode 2 provides very little guidance in using strut-and-tie models, which covers mainly the effective concrete strength provisions for the various strut-and-tie elements. Comparing different simple strut-and-tie models to Eurocode 2 sectional model with regards to shear capacity predictions shows that the traditional sectional method gives conservative estimates. Among the various chosen strut-and-tie model methods, the model according to Eurocode 2 with concrete strength estimates based on the Modified Compression Field Theory (MCFT) yields the most accurate predictions. This paper discusses the applicability of the different design methods for shear and provides some design recommendations in designing short span beams without shear reinforcement using strut-and-tie models.
Analysis of Reinforced Concrete D-Regions Using Strut-and-Tie Model
2016
The developed Strut-and-Tie Model (STM) has no unique shape for each load case of a given structural problem as long as the selected idealized internal load-resisting truss is in equilibrium with boundary forces, and also stresses in its components "struts, ties, and nodes" are within acceptable limits. However, the optimal shapes are the well-designed with best ordinal weight number of conditional factors as the rebar amount, the load factor, and the structural concrete ductility. The current study investigates numerically based on FE method stress flow contours and micro truss techniques many alternatives with different shapes of struts and ties that transfer the flow of forces from top of the deep beam with opening to both right and left supports. Then, these alternatives with different concrete characteristics are analyzed by strut-and-tie computational tools using different code provisions for verifying its results accuracy with the numerical nonlinear finite element analysis results for studying the structure performance under applied service loads and over loading till failure. The chosen alternative produce load factor to reach capacity greater than 1, therefore the strut-and-tie method always give demand collapse load lower than the true capacity collapse load. This implies that the solution obtained from STM usually lies on the safe side with conservative sense for concrete structures subjected to service loads. That’s why the STM is emerging as an increasingly popular code-worthy methodology for the design and detailing of concrete structures D-Regions.
Strut and Tie Modeling in Reinforced Concrete Structures
Strut-and-tie modeling technique is a simple and effective method which can be used as a quick tool for analysis of discontinuous region (D-region) in reinforced and prestressed concrete structures. It serves practicing engineers to grasp load transfer characteristics in order to provide good details of reinforcement and to determine load carrying capacity of the members in very effective way. Since the method is based on lower bound theorem of plasticity, it can be assured to deliver safe designed structure. Using of strut-and-tie modeling demands clear understanding of load path and good skill in visualization of stress field. Those understandings can be improved by studying several model examples and practicing with various design problems.
The strut-and-tie models in reinforced concrete structures analysed by a numerical technique
Revista IBRACON de Estruturas e Materiais, 2013
The strut-and-tie models are appropriate to design and to detail certain types of structural elements in reinforced concrete and in regions of stress concentrations, called "D" regions. This is a good model representation of the structural behavior and mechanism. The numerical techniques presented herein are used to identify stress regions which represent the strut-and-tie elements and to quantify their respective efforts. Elastic linear plane problems are analyzed using strut-and-tie models by coupling the classical evolutionary structural optimization, ESO, and a new variant called SESO - Smoothing ESO, for finite element formulation. The SESO method is based on the procedure of gradual reduction of stiffness contribution of the inefficient elements at lower stress until it no longer has any influence. Optimal topologies of strut-and-tie models are presented in several instances with good settings comparing with other pioneer works allowing the design of reinforcement fo...
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
Truss Models for Concrete Member Design (Part II)
In the previous issue of Civil Computing, we discussed the application of strut and tie models to determine the force distribution within concrete members, in general, and deep members in particular. This, the second and last part of this article, deals with the determination of the reinforcement from the analysis of strut and tie model.
Applying Various Types of Loading on Continuous Deep Beams using Strut and Tie Modelling
Scopus, 2018
This work aims at presenting detailed procedures companied by numerical examples for designing reinforced concrete two span contin-uous 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.
Strut-and-tie modelling of short span beams
New Solutions for our Society (Abstracts Book 314 pages + CD-ROM full papers 1196 pages), 2008
In high strength concrete, (HSC) aggregate may fracture leading to relatively smooth cracks and a possible reduction in shear strength. There seems little doubt that shear strength is reduced in beams without stirrups due to aggregate fracture. The influence of aggregate fracture is less clear in beams with stirrups due to a lack of appropriate test data. This paper presents results from a series of 16 beam tests which were carried out at Imperial College London to assess the influence of aggregate fracture on the shear strength of beams with a ratio of shear span to effective depth of either 1.5 or 3.5. This paper focuses on the short span beams. A simple strut and tie model is presented for the analysis of short span beams that is consistent with the design assumptions in EC2. The model is validated with results from 214 tests and is shown to give good predictions of shear strength.
ABSTRACT: The Strut-and-Tie Model, STM, has been widely applied for the design of non-flexural and deep members in reinforced concrete structures. In this paper, strut-and-tie models for selected (shallow and deep) beams with openings, have been suggested based on the available experimental results of; crack patterns, modes of failure, and internal stresses trajectors obtained from elastic finite element analysis. The proposed STM approach is, then, applied to one group of simple shallow beams and one group of simple deep beams tested experimentally. In addition, a three-dimensional nonlinear finite element analysis using ANSYS 12.0 computer program has been employed for two selected (shallow and deep) beams which were analyzed using the STM method. Some of the important factors affecting the behavior of reinforced concrete beams (named: concrete compressive and tensile strength, span to depth ratio, shear span to depth ratio, physical and mechanical properties of horizontal, vertical web reinforcement and main steel, loading position, opening dimensions and location) are investigated throughout a parametric study with the aid of the nonlinear finite element analysis. With such analysis, results of cracking patterns, deflections, failure mode and strain and stress distributions, that cannot be determined using the strut-and-tie model, are obtained. A comparison of the finite element results with test results and STM results has been carried out.
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)