New modifying truss model and numerical simulation of steel fiber reinforced concrete under pure torsion
Introduction
The fiber reinforced concrete technology has developed over 30 years, which has been used in some important cases of engineering applications, such as tunnels, highways and subway segments. It has been proven to be an applicable alternative for the conventional steel reinforcement in construction practices. For example, in Holland and Belgium [1,2], there were the elevated floors constructed by fiber reinforced concrete, which were tested to have higher performance on strength, deflection and ultimate strength than conventional RC members. The most efforts having done are the mechanical behavior in concrete which formed to be the constitutive laws in the main principles of FRC theory. Previous experiments have been focused on the flexibility, prismatic testing under tension, shear capacity and dynamic mechanical behavior [[3], [4], [5]]. Due to demands of structural design of steel fiber reinforced concrete arising, FRC has many potentials on future application. We intended to investigate torsional behavior of FRC, our purpose of this campaign was to find the best estimations of mechanical principles of FRC. Torsion is a common kind of mechanics existing in many structures, and torsional behaviors have always been found to be the combination of flexibility and shear, or the combination of bending and tension [6,7]. Since torsion is an important factor that affects structural safety, it is necessary to find a more suitable model to describe members subjected to torsion, in order to make accurate structural design possible, when fibers are applied in practice. Due to limitations of fiber reinforced concrete theories, none of standard codes on design process of fiber reinforced concrete has been published. Fiber committee has published the guidelines on the FRC structure design process, in order to enhance the probability on using FRC for structure [6]. But in many experiments, existing model fails to accurately predict torsional behavior of SFRC. Thus, we desired to improve accuracy and to modify existing model. Furthermore, in this paper we prepare to compare results of the fiber reinforced concrete subjected to the pure torsion to find out the most suitable methods of evaluating the torsional mechanics and finite element simulation. This new model of steel fiber reinforced concrete members subjected to pure torsion has featured the most suitable model on predicting service limited state and ultimate limited state when members are under pure torsion condition.
Section snippets
Pre-cracking behavior
The basis of members subjected to torsion is shear flow theory, an assumption that the cross section is enclosed by shear flows when member is subjected to torsion. The Fig. 1 and Fig. 2 are shown as follows:where φ is the angles between two sections, φ′is rate of twist; a, b are longer and shorter dimensions of cross section, respectively. G, It is torsion module and inertial product; γ is poison's ratio. Once the tension strength exceeded (τx = fcm), the shear
Post-cracking behavior
In the post-cracking stage, the concrete is considered to be the significant contributors when it is subjected to the loads. Elastic theory is often used for predicting the cracking strength which means the maximum strength in Serviceability Limit State (SLS). Likewise, the ultimate limit state of fiber reinforced concrete (ULS) is the maximum strength in post-cracking response, in which the stress after post-cracking stage reaches the maximum tensile stress. In this paper, SLS1, SLS2 are
Saint Venant theory and bending truss model by Hsu
where, x and y are the outer dimensions of the cross section; At is the cross-section area of stirrup, A1 is the cross section of longitudinal steel bars. fty is the yield of stirrups, f1y is the yield strength of longitudinal bars, fc’ is the compressive strength of concrete, S is the space of the stirrups. ×1 and Y1 are the shorter and longer length of arms of the stirrups, respectively.
Since the fiber in concrete can
Conclusions
This paper presents results of ANSYS simulation and the modifying model of fiber reinforced concrete under torsion. There are some limitations in this model we believe, those are this proposed model calculating the ultimate strength of beam under pure torsion, but not predicting the toughness of beams. ANSYS used SOLID 65 as material unit for simulating FRC beams under torsion, in which elastic theory acts as pre-cracking torque-twist response and compression field theory acts as post-cracking
Acknowledgement
I am grateful to Chinese Scholarship Council, CSC that financially supports my fees in Universitat Politecnica De Catalunya, UPC in Barcelona, Spain. I am also thankful for my supervisor Prof. Francesc Lopez Almansa. His guidance in the research do me a lot of favor during my PH.D study.
Conflicts of interests
The authors of this paper declare that none of interests exist in the paper.
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