FEA of Steel Fibre Reinforced Beam Curved in Plan

Abstract

In the era of modern construction techniques and the increasing demand of aesthetic appearance of structure, beams curved in plan have found significant utilization within bridge structures, balconies, dome rounded corner buildings, water tanks etc. Concrete, the most consumable construction material has various advantages, however, one of the limitations of concrete is its low tensile strength. To compensate this limitation, fibres are added to concrete. The demand of steel fibre in construction technique is increasing as steel fibre gives high tensile strength and ductility. By adding steel fibre in reinforced concrete beam, the ultimate strength of beam can be enhanced. Finite Element Method or Finite Element Analysis is a tool used to simulate the beam in virtual environment. The objective of this study is to analyse the flexure behaviour of beam curved in plan. The curved beam with subtended angle of 450 and 600 containing fibre fraction of 0%, 0.5% and 1% by volume of concrete is used. To validate the curved beams modelled in Abaqus software, the experimental test is performed on three simply supported straight beams and same beams are analysed in Abaqus software. The straight beam contained the same fraction of 0%, 0.5% and 1% by volume of concrete.

Introduction

I. INTRODUCTION

Concrete is one of the most prominent construction materials and its consumption is increasing with time throughout the globe. One of the major characteristics of the plain concrete is low tensile strength, that is concrete is a brittle material. Thus, concrete require strengthening before it can be used extensively as construction material. Historically, this reinforcement has been done in the form of continuous reinforcing bars which could be placed in the structure at the appropriate locations to endure the imposed tensile and shear stresses. Fibres, instead of continuous, are short discontinuous, and are randomly distributed throughout the concrete to produce a new construction material, known as Fibre Reinforced Concrete (FRC). It is important to note that fibre reinforcement is not a substitute for conventional reinforcement. Fibres and steel bars have different roles to play in the modern concrete technology, and there are many applications in which both fibres and continuous reinforcing bars are used [2]. Reinforced concrete horizontally curved beams are widely used in many fields, such as in construction of modern highway intersections, raised freeways, rounded corners of buildings, circular balconies etc. A horizontally curved beam, loaded transversely to its plane, is subjected to torsion in addition to bending and shear and hence, the critical analysis of such members is very complex. Therefore, it has become necessary to employ numerical analysis procedures to satisfy safety and economic requirements. One such procedure is the Finite Element Method. [3]

II. FINITE ELEMENT ANALYSIS

Finite Element Analysis in Abaqus software includes creation of parts, assigning properties to parts, assembling of parts, application of load and boundary conditions, meshing of parts and submission of job.

A. Modelling of Beams

In Abaqus software, beam part is created using solid homogeneous material. The steel bars, stirrups and fibres are created using wire element. For concrete, Concrete Damage Plasticity model developed as in [4] is used and for steel bars, fibres and stirrups plastic properties are used. To mesh the concrete beam, C3D8 element (a 3-D solid, 8-node linear brick element) is used and the size of the mesh is 30 mm. T3D2, a 2-D linear truss element is used for steel bars, stirrups and fibres and mesh size is 30 mm, 20 mm and 5 mm respectively. Curved beam is fixed at both the ends and subjected to gradually increasing uniformly distributed load. Curved beams modelled in Abaqus is discussed in Table II.

TABLE I

MATERIAL PROPERTIES

TABLE II

DETAIL OF MODELLED BEAMS IN ABAQUS

B. Finite Element Analysis

Analysis is performed using Abaqus explicit with step time of 0.1 second. To reduce the analysis time, multiple processors are used in CPU parallelization. Load-deflection curve and deformed shape are plotted under visualization module. Total reaction force and deflection obtained from analysis are plotted on X and Y axis respectively.

III. RESULT OF ANALSYIS

Curve for the ultimate load carrying capacity and corresponding deflection is plotted for SFRC beam curved in plan with subtended angle of 450 and 600 with steel fibre fraction of 0%, 0.5% and 1% by volume.

Fig. 11 Load-Deflection Curve of CB45 Beam     Fig. 12 Load-Deflection Curve of CB60 Beam

TABLE III

FLEXURAL CAPACITY OF CURVED BEAMS FROM FEA

IV. VALIDATION OF BEAM

Experimental study is performed on straight beam and the same is validated in Abaqus. Three simply supported straight beams with fibre fraction of 0 %, 0.5 % and 1 % by volume are used in this study. The cross-section of the beam is 230 mm×150 mm×1500 mm. Ordinary Portland cement of grade 43 is used, locally available river sand passing through 4.75 mm sieve as per IS: 383 (2016) is used for fine aggregate, Crushed stones that retained on a 4.75 mm sieve is used as per IS: 383 (2016) for coarse aggregate and Thermo-Mechanically-Treated (TMT) bars of grade FE500 is used as steel reinforcement. Hooked end fibres of aspect ratio 50 and tensile strength of 1200 MPa are used to carry out the experimental procedure. The beam is tested in a Universal testing machine and the center-to-center distance between supports is kept 1200 mm. Same beam is modelled and analyzed in Abaqus software and the results between them shows good relation.

TABLE IV

DETAILS OF BEAMS MODELLED IN ABAQUS AND CASTED FOR EXPERIMENT

TABLE ?

ULTIMATE LOAD CARRYING CAPACITY FROM FEA AND EXPERIMENT

It is observed that the load deflection curve obtained from Finite Element Analysis is slightly different as compared to experimental study. This may be due to the microcracks in concrete which may occur because of shrinkage or due to handling of beam. On the other hand, in case of Abaqus software, the finite element models do not consider the microcracks as the beam is assumed to be solid homogenous material. Another reason could be that in Abaqus modelling there is perfect bond between the bars, fibre and concrete, as bars and fibres are perfectly embedded in concrete, however this assumption would not be true for experimental study [1].

Conclusion

From the Finite Element Analysis of Steel fibre reinforced beams in the research work, following conclusions can be drawn. 1) On adding steel fibres in the beam, flexural capacity for beam with subtended angle of 450 is increased by 42.24 kN and 104.72 kN on increasing the fibre from 0 % to 0.5 % and 1 %. 2) On adding steel fibres in the beam, flexural capacity for beam with subtended angle of 600 is increased by 53.09 kN and 75.82 kN on increasing the fibre from 0 % to 0.5 % and 1 %. 3) Curved beam with subtended angle 450 has higher ultimate load carrying capacity as compared to the beam with subtended angle of 600. 4) Results from experimental study and results from FEA in Abaqus software shows good correlation.

References

[1] Mehmet Özcan, Alemdar Bayraktar, Abdurrahman Sahin, Tefaruk Haktanir and Temel Türker, “Experimental and Finite Element Analysis on the steel fibre-reinforced concrete (SFRC) beams ultimate behavior”, Constr. Build. Mater., Vol.23, pp. 1064-1077,2009. [2] Shivanand Jalade, B. K. Kolhapure, “Comparative Study on Behavior of Medium and High Strength Concrete Beam With and Without Fiber under Flexure”, Int. J. Eng. Res. and Tech. Vol.2, pp.28-32,2013. [3] T. Subramani, M. Subramani, K. Prasath, “Analysis of Three Dimensional Horizontal Reinforced Concrete Curved Beam Using Ansys”, Int. J. Eng. Res. App. Vol. 4, pp. 156-161, 2014. [4] Milad Hafezolghorani, Farzad Hejazi, Ramin Vaghei, Mohd S. B. Jaafar, “Simplified Damage Plasticity Model for Concrete”, Struct. Eng. Int. pp. 68-78, 2017. [5] Jigna Jagdeish and L. Lekshmi, “Non Linear Finite Element Analysis of Beams”, Int. J. Appl. Eng. Vol. 14, pp. 108-115, 2019. [6] Goshu Kenea, “Analytical Study of Geometric Parameter Effect on the Behavior of Horizontally Curved Reinforced Concrete Deep Beam”, J. Eng. Pp. 1-14, 2022. [7] M. A. Yassir, T. Ahmet and A. S. Nadeem, “Improving the structural behavior of shear-deficient RC deep beams using steel fibers: Experimental, numerical and probabilistic approach”, J. Build. Eng., Vol. 46, pp. 1-20, 2022. [8] Marwan A. Saman, Mehmet A. Çankaya, “Plasticity Based Nonlinear Finite Element Analysis of Steel Fiber Reinforced Concrete Beams” Int. Sci. Cong. pp. 82-88, 2023. [9] IS 456:2000 “Indian Standard Code of practice for Plain and Reinforced Concrete”, Bureau of Indian Standards, New Delhi India. [10] IS 383:2016 “Coarse and Fine Aggregate for Concrete-Specification”, Bureau of Indian Standards, New Delhi India. [11] IS 10262:2019 “Concrete Mix Proportioning -Guidelines”, Bureau of Indian Standards, New Delhi India

Copyright

Copyright © 2024 Mohammed S. Sakka, Ranveer S. Shekhawat, Trilok Gupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.