Eurocode EC2 Research Articles

Behavior of lap splices in reinforced concrete beams after bar yielding

AbstractStructural ductility in the case of plastic hinges forming close to a lap splice has been an open issue with the revision process of the next version of Eurocode EC2 concerning reinforced‐concrete structures. This research has provided experimental evidence by the large experimental campaign for the background for revision of the Eurocode EC2. Within this context, 38 specimens were tested in four‐point bending, with the longitudinal bars either lap‐spliced (partly or fully), or un‐spliced (for reference). The tests were carried out involving the variation of the bar diameter (12, 16, 20, and 25 mm), and the lap length (20–60 times the bar diameter). The main result is the sizeable enhancement of the structural ductility brought in by the extension of the lap length in excess of the length required by the yielding of the longitudinal bars. Based on these findings, a preliminary model is developed to describe the bond‐stress profiles in lap splices, after the yielding of the bars.

A Method to Predict the Punching Shear Strength of Flat Slabs with Shear Reinforcement Using a Strut-and-Tie Model

The use of flat slabs in constructions due to its many functional and economic advantages is wide-spread. Behavior of flat slabs in shear and flexure is a fairly complex problem. Therefore, the punching shear failure belongs to one of the most critical aspects in the design of concrete buildings.The purpose of this paper is to describe a framework of the proposed method for predicting the punching shear of flat slabs with shear reinforcement. Most of the current codes in force are mainly based on empirical formulation. The proposed method is based on a strut-and-tie model and therefore could be considered as an analytical approach. For the purpose of demonstrating the effectiveness of the proposed method, the method is compared with some of the main methods currently in use, such as Eurocode EC2, ACI 318 and Model Code 2010. The comparison consists of results of more than 90 experiments on flat slabs with shear reinforcement, gathered from publications from all around the world.

Strut-and-Tie Model for Predicting the Punching Shear of Flat Slabs with Shear Reinforcement

The purpose of this paper is to describe a framework of the proposed method for predicting the punching shear of flat slabs with shear reinforcement. The proposed method is based on a strut-and-tie model. Current methods of predicting the punching shear strength of flat slabs could be divided into these categories: models based on empirical equations, physical models, analytical methods and finite element methods. Most of the current codes in force would be best described as empirical formulations. Physical model for prediction of punching shear is described in Model Code 2010. Proposed method for flat slabs with shear reinforcement is based mainly on a strut-and-tie model and therefore could be considered as an analytical method.For the purpose of demonstrating the effectiveness of the proposed method, the method is compared with some of the main methods currently in use, such as Eurocode EC2, American code ACI 318 and Model Code 2010. The comparison consists of results of more than 98 experiments of punching shear on the flat slabs with shear reinforcement, gathered from publications from all around the world.

Concept of Ductility in Reinforced Concrete Design Explained in the Adotion of Eurocode 2 in Place of Bs 8110 in Malaysia

The design of reinforced concrete structures requires a few criteria to be fulfilled, especially in Limit States Theory adopted by many international standards in structural design. Two key criteria are ultimate limit state and serviceability limit state. Both of these limit states have one common aspect which governs the whole concept of design especially in reinforced concrete design, which is the ductility requirement. The purpose of satisfying the ductility requirement is to ensure safety of users and occupants of the designed structure. In this paper, the ductility requirement is explained in the adoption of the Eurocode EC2 in place of BS8110. In order to have a smooth transition from BS8110 to EC2, the author would also like to introduce a unified approach for the analysis and design of concrete members in flexure by utilizing a unifying parameter q (combined reinforcing index). This would allow a design engineer to analyze and to design for normally reinforced, partially prestressed, and even fully prestressed concrete and composite sections. Through this approach, it is hoped that the Malaysian practicing structural engineers can make a smooth switchover to the use of Eurocode EC2 for reinforced concrete design.

Energy Absorption Capacity of Reinforced Concrete Beam-Column Connections, with Ductility Classes Low

Once the behaviour of reinforced concrete moment resisting frame structures is investigated, it is concluded that the performance of beam column connections is not satisfactory. In order to understand the complex mechanisms and satisfactory behaviour of beam column connections, lots of investigations have been done. The most critical zone in reinforced concrete moment resisting frames would be the beam column connection. The behaviour of beam column connection once it is subjected to large forces during earthquakes has a great impact on the response of the structure. The shear failure has a brittle nature which is not a desirable structural performance during earthquakes. Two new types of shear reinforcements design are introduced in this study for the purpose of reaching a higher performance and material capacity for the connection and hence, the structure. These two shear reinforcement designs working simultaneously with other reinforcement systems and concrete have a better performance compared to that of conventional methods. The first specimen is made according to conventional method of design as control specimens in conformance with Euro code EC2 & EC8. The second specimen introduces a continued shear resistance system against discontinued conventional shear resistance system (stirrups) which is called “Single Square Spring Shear Resistance System” (SSSSRS). The third specimen possesses two continued square spring systems twisting together and making a parallel system called “Double Square Spring Shear Resistance System” (DSSSRS). A comparison was made between the performances of the improved shear reinforcement systems of beam-column connections against the control specimens. It was concluded that a lower deflection along with higher energy absorption was achieved for “Single Square Spring Shear Resistance System” (SSSSRS) and “Double Square Spring Shear Resistance System” (DSSSRS) compared to control specimens.

Anclaje de barras en zapatas de hormigón

The paper analyzes the simplified rule for footing whereby the anchorage length is developed from a distance equal to 0,5 h, measured form the end of the footing. This simplification is based on the assumption that the footings involved are stiff, but Eurocode EC-2 fails to mention that fact, while Spanish code EHE-08 prescribe the rule for flexible footing. The value of the soil contact pressure σ t notwithstanding, the shallower a footing is, the more economical. Consequently, for soils with σ t ≤ 0,2 N/ mm2 the right solution could differs from the rules laid down in the above two standards.

Comparison of Eurocode 2, Model Code 90 and ACI 318-99 with regard to shear and punching provisions for footings

Code ACI 318, Model Code 90 and Eurocode EC-2 present important differences with regard to the shear strength and punching strength, this is especially shown when the steel ratio of reinforcement is low. The above mentioned is important especially in the case of footings. The author analyses the differences either in structural design or in cost for wall footings and isolated footings, in accordance with the three mentioned Codes.

Comparison of Eurocode 2, Model Code 90 and ACI 318-99 with regard to shear and punching provisions for footings

Code ACI 318, Model Code 90 and Eurocode EC-2 present important differences with regard to the shear strength and punching strength, this is especially shown when the steel ratio of reinforcement is low. The above mentioned is important especially in the case of footings. The author analyses the differences either in structural design or in cost for wall footings and isolated footings, in accordance with the three mentioned Codes.

METHODS AND CONSTITUTIVE MODELS FOR DEFORMATIONAL ANALYSIS OF FLEXURAL REINFORCED CONCRETE MEMBERS/LENKIAMŲJŲ GELŽBETONINIŲ ELEMENTŲ DEFORMATYVUMO VERTINIMO METODAI IR FIZIKINIAI MODELIAI

The paper reviews both analytical and finite element methods for deformational analysis of flexural reinforced concrete members subjected to short-term loading. In a state-of-the-art summary of various proposed stress-strain relationships for concrete and reinforcement, a special emphasis is made on critical survey of modelling post-cracking behaviour of tensile concrete in smeared crack approach. Empirical code methods of different countries (American Code (ACI Committee 318 [7]), the Eurocode EC2 [8], and the Russian (old Soviet) Code (SNiP 2.03.01-84 [5]) for deflection calculation of flexural reinforced concrete members are briefly described in section 2. Although these methods are based on different analytical approaches, all of them proved to be accurate tools for deflection assessment of members with high and average reinforcement ratios. It should be noted that these methods have quite a different level of complexity since the Russian Code method employs a great number of parameters and expressions whereas the ACI and EC2 methods are simple and include only basic parameters. Approaches of numerical simulation and constitutive relationships are discussed in Chapter 3. All numerical simulation research can be classified into two large groups according to two different approaches for crack modelling (subsection 3.1): 1) Discrete cracking model. In this approach, cracks are traced individually as they progressively alter the topology of the structure. 2) Smeared cracking model. The cracked concrete is assumed to remain a continuum, ie the cracks are smeared out in the continuous fashion. After cracking, the concrete becomes orthotropic with one of the material axes being oriented along the direction of cracking. Constitutive relationships for steel and plain concrete are presented in subsection 3.2. A special emphasis is made on critical survey of modelling post-cracking behaviour of tensile concrete in smeared crack approach. It has been concluded that although empirical design codes of different countries ensure safe design, they do not reveal the actual stress-strain state of cracked structures and often lack physical interpretation. Numerical methods which were rapidly progressing within last three decades are based on universal principles and can include all possible effects such as material nonlinearities, concrete cracking, creep and shrinkage, reinforcement slip, etc. However, the progress is mostly related to the development of mathematical apparatus, but not material models or, in other words, the development was rather qualitative than quantitative. Constitutive relationships often are too simplified and do not reflect complex multi-factor nature of the material. Existing constitutive relationships for concrete in tension do not assure higher statistical accuracy of deflection estimates for flexural reinforced concrete members in comparison to those obtained by empirical code methods. The author has developed integral constitutive model for deformational analysis of flexural reinforced concrete members [36]. The integral constitutive model consists of traditional constitutive relationships for reinforcement and compressive concrete and the integral constitutive relationship for cracked tensile concrete which accumulates cracking, tension stiffening, reinforcement slippage and shrinkage effects. This constitutive model can be applied not only in a finite element analysis, but also in a simple iterative technique based on classical principles of strength of materials extended to layered approach.

METHODS AND CONSTITUTIVE MODELS FOR DEFORMATIONAL ANALYSIS OF FLEXURAL REINFORCED CONCRETE MEMBERS

Summary The paper reviews both analytical and finite element methods for deformational analysis of flexural reinforced concrete members subjected to short-term loading. In a state-of-the-art summary of various proposed stress-strain relationships for concrete and reinforcement, a special emphasis is made on critical survey of modelling post-cracking behaviour of tensile concrete in smeared crack approach. Empirical code methods of different countries (American Code (ACI Committee 318 [7]), the Eurocode EC2 [8], and the Russian (old Soviet) Code (SNiP 2.03.01-84 [5]) for deflection calculation of flexural reinforced concrete members are briefly described in section 2. Although these methods are based on different analytical approaches, all of them proved to be accurate tools for deflection assessment of members with high and average reinforcement ratios. It should be noted that these methods have quite a different level of complexity since the Russian Code method employs a great number of parameters and expressions whereas the ACI and EC2 methods are simple and include only basic parameters. Approaches of numerical simulation and constitutive relationships are discussed in Chapter 3. All numerical simulation research can be classified into two large groups according to two different approaches for crack modelling (subsection 3.1): 1) Discrete cracking model. In this approach, cracks are traced individually as they progressively alter the topology of the structure. 2) Smeared cracking model. The cracked concrete is assumed to remain a continuum, ie the cracks are smeared out in the continuous fashion. After cracking, the concrete becomes orthotropic with one of the material axes being oriented along the direction of cracking. Constitutive relationships for steel and plain concrete are presented in subsection 3.2. A special emphasis is made on critical survey of modelling post-cracking behaviour of tensile concrete in smeared crack approach. It has been concluded that although empirical design codes of different countries ensure safe design, they do not reveal the actual stress-strain state of cracked structures and often lack physical interpretation. Numerical methods which were rapidly progressing within last three decades are based on universal principles and can include all possible effects such as material nonlinearities, concrete cracking, creep and shrinkage, reinforcement slip, etc. However, the progress is mostly related to the development of mathematical apparatus, but not material models or, in other words, the development was rather qualitative than quantitative. Constitutive relationships often are too simplified and do not reflect complex multi-factor nature of the material. Existing constitutive relationships for concrete in tension do not assure higher statistical accuracy of deflection estimates for flexural reinforced concrete members in comparison to those obtained by empirical code methods. The author has developed integral constitutive model for deformational analysis of flexural reinforced concrete members [36]. The integral constitutive model consists of traditional constitutive relationships for reinforcement and compressive concrete and the integral constitutive relationship for cracked tensile concrete which accumulates cracking, tension stiffening, reinforcement slippage and shrinkage effects. This constitutive model can be applied not only in a finite element analysis, but also in a simple iterative technique based on classical principles of strength of materials extended to layered approach.

EVALUATION OF CONCRETE LINEAR CREEP IN DETERMINATION OF STRESS STATE AND STEEL PRESTRESS LOSSES IN CONCRETE MEMBERS/BETONO TIESINIO VALKŠNUMO ĮVERTINIMAS, NUSTATANT GELŽBETONINIŲ ELEMENTŲ ĮTEMPIMŲ BŪVĮ IR ARMATŪROS IŠANKSTINIO ĮTEMPIMO NUOSTOLIUS

Determination of stress-strain state imposed by concrete linear creep and specification of steel prestress losses in linear prestressed concrete member is discussed in this article. Particularities of regulations of the Code acting in Lithuania [1] and of Eurocode [2] are analysed and a modified method for calculation of steel prestress losses due to concrete linear creep in prestressed concrete linear members suitable for assessment of Code regulations is presented. Also, the method is used for analysis of results of long-term tests of reinforced concrete members. In Lithuania, a code based on investigations of prestressed concrete members is used for calculation of steel prestress losses due to concrete creep. Therefore calculation of losses is associated with stress-strain state of the member in time t in empirical way only and time dependent stress-strain state is adjusted by additional coefficients to take into consideration concrete creep. Analogous calculations of steel prestress losses by Eurocode are presented in a more general form and are based on creep theory. It is clear that in the first [1] and the second [2] cases the same change in stress-state is evaluated by different parameters. Therefore it is important to create a general method based on concrete creep characteristics. General case of eccentrically reinforced prestressed concrete linear member under the action of prestressing forces changing with time in relation to prestress losses due to concrete creep is analysed (Fig 1). Stress-strain time dependent state of such member with the changing concrete stress σ b (t) and σ′ b (t) is determined using well-known equations of equilibrium (1–4) and integral differential equations (7–8) for evaluation of concrete creep deformations [4–8]. These equations are solved by numerical method (9–10) dividing time period considered in intervals. In reference [9] a more particular solution method evaluating variation of interval magnitude in relation to accuracy of solution is presented. In such a way it is possible to assess reduction of concrete stress (13–14) at time moment t when loss of steel prestress due to concrete creep takes place (33–34). There are many experiments performed for investigating concrete creep and determinating time dependent stress-strain state of reinforced concrete members. Various methods are applied for analysis of these data. Assumptions of these methods influence the conclusions of the analysis. In this article there is presented a general method giving opportunity to assess creep of concrete members by the same characteristics, when specific creep (51) or coefficient of creep (52) is determined by tests on eccentrically prestressed linear members (the case of axially prestressed members is presented in [9]). Pure specific creep C* (t,t 0) values determined according to the method proposed in this article and results of experimental investigations [12] of prestress in steel of eccentrically prestressed concrete members and also according to data of analysis [11] of the Code [1] are presented in Fig 2. Using the same creep characteristics method of the Code EC-2 and proposed in this article losses of prestress in steel due to concrete creep were calculated according to EC-2 and the method proposed. Values of these losses and their ratio are presented in Fig 3 and 4. In Fig 5, losses of prestress in steel due to creep predicted after 70 years were calculated in accordance with data of the Code SNiP [1] analysis [11] and regulations of the Code EC-2 [2]. Relationships (62) including (63), (64) formulas are modified EC-2 method for regulation of steel prestress loss due to concrete creep calculation for doubly reinforced members are proposed in the article. Results of analysis of regulations of Eurocode EC-2 and the Code SNiP indicate that design according to Code [2] method for steel prestress loss due concrete creep calculation in all cases gives increased values of stiffness and crack resistance characteristics of the structure, but larger amount of steel is to be used in comparison with the design according to SNiP [1].