This article presents an optimization-based computational method to assist in the design of reinforced concrete framed structures. The design of these structures is posed as a multi-objective ...optimization problem seeking cost minimization, strength and serviceability design objectives defined according to Eurocode 2 provisions. An entropy-based approach is used to obtain the solution of the minimax problem by minimizing a convex scalar function. Special emphasis is placed on the sensitivity analysis, which is crucial for the performance of the optimization algorithm. The discrete direct method was used to compute the sensitivities of the design objectives, the allowable values of which are dependent on the design variables. The cross-sectional dimensions of beams and columns and the longitudinal and shear reinforcement areas are the design variables. Verification examples and the optimization of a real-sized building structure are presented to illustrate the features of the developed method.
•For 20% damage, the rotation capacity reduced about 50%.•For 20% damage, the rotation capacity is still higher than the Eurocode 2 curve.•Corrosion affects the ultimate deflection much more than the ...ultimate load.•Corrosion changes the ultimate deflection of isostatic beams more than hyperstatic.•Ultimate deflection of beams with steel class C is two times higher than class A.
The corrosion of reinforced concrete structures influences not only their structural strength but also their ductility. In this scenario, the use of Special Ductility Tempcore rebars, which belong to the highest ductility class, can reduce the risk of having a brittle failure when corrosion occurs.
Therefore, this paper presents experimental and numerical studies to evaluate the rotation capacity of corroded RC beams with this type of steel. The experimental part consists of testing five beams to rupture and the numerical part uses the non-linear finite element method to correctly model the beam’s behaviour.
The results indicate that for 20% damage, the rotation capacity reduced about 50%; however, these values are still higher than the Eurocode 2 normalized curve. In this scenario, the ultimate load only reduces 12%. Nevertheless, corrosion affects the ultimate deflection of isostatic beams much more than hyperstatic beams.
Ensemble tree machine learning models have proved useful for solving poorly understood and complex problems. This paper aims to calibrate the Eurocode 2 creep model by inserting a correction ...coefficient to the model. The correction coefficient is calculated using ensemble tree (bagging and boosting) models. The results showed that the insertion of the correction coefficient obtained by both the bagging and boosting models into the Eurocode 2 model led to significantly higher prediction accuracy. These approaches may lead to a better performance prediction, thereby reducing the effect of the time-dependent deformation on concrete structures.
Several mechanical properties are key to the design of reinforced concrete members. The most important property for the ultimate design of concrete structural members is concrete compressive ...strength. Regarding the serviceability conditions of cracking and deformation, both the modulus of elasticity of concrete and its tensile strength have great importance in the response of a member. Different standards sometimes have different definitions for the same concept, and this can be a handicap for engineers who need to use several regulations. In this article, a comparison of both compressive and tensile strengths, and the modulus of elasticity from two widely used standards, ACI-318 and Eurocode 2, is presented. Data corresponding to three real concrete quality-control campaigns are studied.
•Span-to-depth ratio limits are proposed to fulfil required ductility.•Ductility limits are more restrictive than deflection limits if δ ≤ 0.9.•Current beams should have limited l/d if high amount of ...reinforcement is used.•Current slabs (δ = 0.75) present enough ductility if l/d ≤ 20.•MC2010/EC2 conditions to use plastic analysis need to be revised.
In the design of reinforced concrete structures several limit states are usually verified using simplified methods instead of using complex direct calculation. Span-to-depth ratio limits are applied for deflection control. In the same way, a redistribution factor and the relative depth of the compression zone are applied for the required ductility, but this is not enough. In fact, specific span-to-depth ratio limits, which are developed in this paper, should also complement the conditions referred to here.
A numerical study is developed to compute the deflection ductility index of a wide range of continuous beams (or one-way slabs) considering as ultimate point when the rotation capacity (given by MC2010 and EC2) is achieved. From the boundary between fragile and ductile failures, the new span-to-depth ratio limits for the required ductility are defined and compared with the existing similar limits for deflection control.
The results indicate that: (i) for normal strength concrete (up to 50 MPa), the ductility limit is more restrictive than the deflection limit when the redistribution factor δ is lower than 0.9, being always more restrictive for high strength concrete; (ii) for the current building beams, the slenderness used (10 < l/d < 20) allows ductile failures, while for typical building slabs (low reinforcement ratio, but high redistribution), the slenderness should be l/d ≤ 20; (iii) the conditions of MC2010 and EC2 to use plastic analysis without any direct check of the rotation capacity are actually incomplete and need to be revised.
The new span-to-depth ratio limits proposed in this paper, which satisfy both ductility and deflection requirements, depend on the redistribution factor, characteristic compressive strength of concrete and total mechanical reinforcement ratio.
The punching shear design procedures according to current codes (e.g., Eurocode 2 or Model Code 2010) are similar. However, the predicted punching shear capacities may differ significantly depending ...on the background (e.g., semi‐empirical or physical) of the design provisions and the considered influences. For the evaluation and improvement of the existing provisions for flat slabs without and with high amounts of shear reinforcement, a large number of punching test series on reinforced concrete flat slabs is available in the literature. Nevertheless, the evaluation of the code equations for the design of the shear reinforcement (failure inside the shear‐reinforced zone) is still not possible since only few punching tests on flat slabs with low and medium amounts of shear reinforcement have been conducted.
To investigate the punching shear behavior of flat slabs with a varying amount of shear reinforcement, three systematic test series without and with stirrups as shear reinforcement were conducted. The experimental program included three reference tests without and eight tests with low and medium amounts of shear reinforcement. In the tests, the amount of shear reinforcement was varied by changing the stirrup diameter only. Further investigated influences were the shear span‐depth ratio and the effective depth. The results of the test series are discussed and compared to the predictions according to Eurocode 2, Model Code 2010 and the draft of the second generation of Eurocode 2.
This work is devoted to the study of fresh and hardened properties of concrete containing recycled gravel. Four formulations were studied, the concrete of reference and three concretes containing ...recycled gravel with 30, 65 and 100 % replacement ratios. All materials were formulated on the basis of S4 class of flowability and a target C35 class of compressive strength according to the standard EN 206-1. The paper first presents the mix design method which was based on the optimization of cementitious paste and granular skeleton, then discusses experimental results. The results show that the elastic modulus and the tensile strength decrease while the peak strain in compression increases. Correlation with the water porosity is also established. The validity of analytical expressions proposed by Eurocode 2 is also discussed. The obtained results, together with results from the literature, show that these relationships do not predict adequately the mechanical properties as well as the stress–strain curve of tested materials. New expressions were established to predict the elastic modulus and the peak strain from the compressive strength of natural concrete. It was found that the proposed relationship
E
–
f
c
is applicable for any type of concrete while the effect of substitution has to be introduced into the stress–strain (
ε
c1
–
f
c
) relationship for recycled aggregate concrete. For the full stress–strain curve, the model of Carreira and Chu seems more adequate.
•Punching behaviour of RC column footings rested on the ground is studied.•A new analytical model for the punching shear capacity assessment is proposed.•Experimental tests on footing punching ...failure are conducted in in situ conditions.•The proposed model is evaluated by comparison with the existing design codes.•The proposed model has a significantly better agreement with the experimental results.
The assessment of the punching shear capacity of column footings in the current design codes is proposed mainly on the basis of experiments performed on slabs. Experimental investigations considering reinforced concrete foundations were rather rare and they were mostly performed in laboratory conditions, whereby the soil was simulated in various ways, most often with springs, hydraulic jacks, and line supports, whereas only a small part of experimentally investigated foundations was tested on the ground. Precisely for that reason, this study is aimed to determining the punching shear capacity of column footings in more realistic terms regarding the footing resting. For this purpose, the given problem is considered from two aspects – analytical and experimental. Firstly, a novel analytical approach to assessment of the punching shear capacity of column footings without shear reinforcement has been proposed, referring to the theory of reinforced concrete, by taking into consideration all relevant factors related to concrete, tensile reinforcement, as well as subsoil reactive pressures, both for the case of concentrically loaded footings and for the case of eccentrically loaded footings. Furthermore, an experimental investigation of footing punching has been conducted in in situ conditions, wherein the foundations were laid on a subgrade cohesionless soil with the predesigned and controlled properties. Lastly, the results obtained on the basis of the proposed analytical procedure and conducted experimental tests, both the own ones and of other authors, have been compared with the results according to the European (Eurocode 2), American (ACI 318-19), and fib Model Code 2010 standards. The research results have revealed that the proposed analytical approach, which comprehensively considers the relevant parameters, gives values of the punching shear capacity of reinforced concrete column footings that are closer to the experimentally obtained values when compared to the values obtained according to the considered design regulations.
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