ANALYTICAL INVESTIGATION OF RC CURVED BEAMS

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1 Jr. of Industrial Pollution Control 33(S3)(2017) pp Research Article ANALYTICAL INVESTIGATION OF RC CURVED BEAMS MURALIDHARAN R 1*, JEYASHREE T.M 2 AND KRISHNAVENI C 2 1 M. Tech, Department of Civil Engineering, SRM University, Chennai, Tamil Nadu, India. 2 Assistant Professor, Department of Civil Engineering, SRM University, Chennai, Tamil Nadu, India. (Received 11 July, 2017; accepted 24 October, 2017) Key words: RC curved beam, Torsion, Deflection, Discretization ABSTRACT A RC curved beam is termed as a statically indeterminate structure according to the structural boundary condition and is subjected to a torsion moment. A suitable arrangement of rebarshould be used under such conditions. There are several factors that influence the ultimate torsional strength of a curved RC member, so universal theory is adopted for curved RC beam. The radius of curvature, span ratio, diameter of rebar and grade of concrete are the Parameters adopted and used here. The influence of these parameters changes the behaviour of RC curved beams. Analytical software ANSYS is used to find the optimum grade of concrete, diameter of rebar, depthof the RC curved beam. The maximum deflection of a curved RC beam is investigated analytically. The comparison of maximum deflection between conventional beam and curved beam are studied. From the present research, a three dimensional non-linear finite element models are adopted to investigate the behaviour and maximum deflection of RC curved horizontal beams. INTRODUCTION Reinforced concrete curved beams are used in many fields, for example, in the development of present day way convergences, roundabout water tanks, ring shaft conveying vaults, roundabout galleries, connect, interstate exchange and so forth. It stated that curved beams are more productive than straight beams. They are capable of exchanging loads through combined activity of twisting and stretching. There is an expanding pattern among planners to move in the opposite direction of conventional auxiliary structures, and moving towards progressively complex spatial design, using bended basic individuals. In large-scale concrete structures like highway intersections or a pre-stress concrete structure RC curved beam is adopted. The behaviour and maximum deflection of a RC curved beam is done analytically by a three dimensional Finite element modelling using Ansys. Curved beam is subjected to torsion when it is loaded transversely to its surface, in addition to bending and shear. Non homogeneous nature of materials plays a vital role in behaviour of reinforced curved beams. One of the most effective numerical methods utilized for analysing reinforced concrete members is the finite element method. Finite element analysis is done because of the complex nature of the structure. Yet studies concerning reinforced concrete curved beams are rare. Therefore, it becomes necessary to employ numerical analysis procedures, such as the finite element method, to satisfy the safety and the economy requirements. So it is important to study the behaviour of reinforced curved beams under differentcondition. Some important parameters like material properties, depth of beam, support condition, compressive strength of concrete and tensile strength of steel which plays a major role (Bharadwaj and Purushotham, 2015; Cervenka, 1985; Guodong, et al., 2015; IS 456: 2000; IS ). *Corresponding authors muralidharanraja@gmail.com

2 1388 MURALIDHARAN ET AL. ANALYTICAL STUDY Non homogeneous nature of materials plays a vital role in behaviour of reinforced curved beams. One of the most effective numerical methods utilized for analysing reinforced concrete members is the finite element method. Finite element analysis is done because of the complex nature of the structure. ANSYS Version 15 was used to stimulate the model and to find the total deflection of the beams under loading. ANSYS is ahead in development of finite element modelling and analysing for structural designing works. The framework consolidates the auxiliary investigation components of ansys with the top of the line structural designing particular abilities of Civil FEM to make an extraordinary capable apparatus for an extensive variety of uses, including power plants, bridges, tunnels, solitary structures and seaward structures. For critical projects, FEA has been found to offer significant benefits in accurately predicting structural deflections and ground movement. Civil engineers use ansys for projects as diverse as high-rise buildings, bridges, dams, stadiums, etc. Accurate results can be found for experimenting with innovative design in a virtual environment, engineers and designers can analyse safety, strength, comfort and environmental considerations (Jia-Bao, et al., 2015; Piovan and Sampaio, 2014; Subramani, et al., 2014). Modelling Curved and conventional beams are subjected to transverse loading. Two steel bars were placed as the tensile reinforcement and two steel bars as the compressive reinforcement. Also, one bar was arranged at the centre of the cross-section of beamto nullify the torsion produced in curved beams. Curved beams are horizontally placed, fixed supports are given at both ends of the beams and the beams are subjected to two point loading as shown in (Fig. 1). The above (Fig. 2) indicates the cross section of one of the models done. Similarly number of models was developed with different radius respectively to find the behaviour of the RC curved beams subjected to different boundary conditions. One of the models done in Ansys is shown in (Fig. 3). Meshing Meshing is done to all specimens in FEM using Ansys and it helps us to find the deflection or any change in the behaviour of the specimen. Solid element is used for modelling. Maximum deflection can be obtained at any point of the specimen from Fig. 1 Application of loads on RC curved beam. Fig. 2 Sectional view of RC curved beam. the software. Ultimate load and maximum deflection along the beams can be found using this FEM. Larger the number of meshing, greater the accuracy of results and also more the difficulty in solving the problem. Meshing is discretization. Discretization is the process of dividing the model into elements consisting of nodes. Meshing is used to make a structure into Finite number of elements. Meshing is done by specifying the required size of a mesh or it can also be done by giving number of the parts and then mesh is created. Automatic method of meshing may create improper mesh which causes error in solution, so meshing is controlled manually in the FEM. The methods of meshing used for beams are face sizing shown in (Fig. 4-6) and Table 1. ANALYTICAL RESULTS All conventional and RC curved beams are analysed by using ANSYS to determine the maximum deflection of conventional and RC curved beams are shown in (Fig. 7 and 8). The overall behaviour and specifications for these materials have been taken in the consideration during the built up and input data of ANSYS computer program (Tamura and Murata, 2010; Tamura, 1991; Thevendran, et al., 1999; Tsukuda, 2007). Deflections of Conventional and curved beams are tabulated below with varying parameters like grade of concrete, diameter of bars, depth of beams, radius of curvature and support conditions (Tables 2-6).

3 1389 Fig. 5 Loading in curved beams. Fig. 3 Ansys model of a curved beam. Fig. 6 Loading in conventional beams. Table 1. Properties used in modelling Material Density Kg/m -3 Young s Modulus (Mpa) Poison s Ratio M Concrete M M Fig. 4 Meshing. Steel Fe Fig. 7 Maximum deflection in conventional beam.

4 1390 Fig. 8 Maximum deflection in curved beam. Table 2. Maximum deflections of conventional beams Conventional models Diameter of bars Dimensions (L B H) Boundary conditions Deflection CM1 M Fixed CM2 M Fixed CM3 M Fixed CM4 M Hinged CM5 M Hinged CM6 M Hinged Table 3. Maximum deflections of curved beams with grade M20 and fixed support RC curved beam models Radius of Beam Diameter of bars Dimensions (L B H) Boundary conditions Deflection M Fixed M Fixed M Fixed M Fixed M Fixed M Fixed M Fixed M Fixed Table 4. Maximum deflections of curved beams with grade M25 and fixed support RC curved beam models Radius of Beam Diameter of bars Dimensions (L B H) Boundary conditions Deflection M Fixed M Fixed M Fixed M Fixed M Fixed M Fixed M Fixed 0.177

5 1391 Table 5. Maximum deflections of curved beams with grade M30 and fixed support RC curved beam Radius of Beam Diameter of Dimensions Boundary Deflection models bars (L B H) conditions M Fixed M Fixed M Fixed M Fixed M Fixed M Fixed Table 6. Maximum deflections of curved beams with various parameters and hinged support RC curved beam Radius of Beam Diameter of Dimensions Boundary Deflection models bars (L B H) conditions M Hinged M Hinged M Hinged M Hinged M Hinged M Hinged M Hinged M Hinged M Hinged CONCLUSIONS The conclusions that are observed from 36 analytical models by varying the grade of concrete, depth of the beam, diameter of the bars, radius of curvature and support conditions are as follows. 1. The Maximum deflections of beams get reduced by changing the support conditions and grade of concrete in both conventional and curved beams. 2. By increasing the curvature of the curved beam the max deflection is getting reduced. 3. By changing the support conditions from hinged to fixed there is a decrement of deflection by 47% in conventional beams. 4. By increasing the depth of curved beams there is a decrease of 10% in deflection for fixed support conditions. 5. By varying the grade of concrete with increase in radius of curvature subjected to hinged support conditions there is a decrease of 34% in deflection. 6. By comparing the conventional beam and curved beam there is decrease of 74% deflection in fixed support condition. 7. By comparing the conventional beam and curved beam there is increase of 33% deflection in hinged support condition. 8. Form the above analytical study the curved beam of depth 200 mm & 3000 mm radius of curvature with M30 grade is the optimum curved beam with a deflection of mm. REFERENCES Bharadwaj, D. and Purushotham, A. (2015). Numerical study on stress analysis of curved beams. International Journal of Mechanical Engineering and Technology. 6 : Cervenka, V. (1985) Constitutive model for cracked reinforced concrete. ACI Journal. 82 : Guodong, Z., Alberdi, R. and Kapil, K. (2015). Analysis of three-dimensional curved beams using isogeometric approach. Journal of Engineering structures. 1 : IS Concrete mix design. IS 456: Code of practice for plain and reinforced concrete. Jia-Bao, Y., Jat, Y.R.L., Xudong, Q. and Jun-Yan, W. (2015). Ultimate strength behaviour of curved steel concrete steel sandwich composite beams. Journal of Structural Engineering. 2 : Piovan, M.T. and Sampaio, R. (2014). Parametric and non-parametric probabilistic approaches in the mechanics of thin-walled composite curved beams. Journal of Structural Engineering. 1 : Subramani, T., Subramani, M. and Prasanth, K. (2014). Analysis of three dimensional horizontal reinforced concrete curved beam using Ansys. Journal of Structural Engineering. 4 : Tamura, T. (1991). Experimental analysis of shear strength of reinforced concrete beams subjected to axial tension. Proc. of JCI. 2 :

6 1392 Tamura, T. and Murata, H. (2010). Experimental study on the ultimate strength of R/C curved beam. Journal of Structural Engineering. Thevendran V, Sumin, C., Shanmugam, N.E. and Jat, Y.R.L. (1999). Non-linear analysis of steel concrete composite beams curved in plan. Finite Elements in Analysis and Design Tsukuda, H. (2007). Study on R/C member subjected to torsion and axial force. Fourth International Structural Engineering and Construction Conference. 1 :