Analysis of Flexural Behaviour of Singly and Doubly Reinforced High Strength Concrete Beams Using Ansys

Transcription

1 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 23 rd June Analysis of Flexural Behaviour of Singly and Doubly Reinforced High Strength Concrete Beams Using Ansys H.R. Manjunath, K.R. Kavya, Kalyani Rao, M.R. Prakash and R. Prabhakara Abstract--- The nature of fracture in high strength concrete (HSC) is brittle and therefore, the investigation on flexural behavior of HSC members is important. This paper describes the nonlinear finite element modelling and analysis of singly and doubly reinforced HSC beams for flexural behaviour. Nonlinear behavior of RC beams is complex due to involvement of various parameters. The finite element method is an analytical tool which is able to model RCC and calculate the non-linear behaviour of the structural members. Many attempts have been made by the past researchers to predict the behavior using ANSYS. The finite element adapted by ANSYS nonlinear software was used for the present work. The concrete was modelled with 8-noded SOLID-65 element that can translate either in the x-, y-, or z-axis directions and longitudinal and transverse steels were modelled as discrete elements using 3D-LINK8 bar element available in the ANSYS element library. Concrete and reinforcing steel are represented by separate material models which are combined together to describe the behaviour of the reinforced concrete material. A total of nine beams were modelled and analysed by varying the l/d ratios and percentage of reinforcement of HSC beams. The beams were simply supported and tested under two point loading. Analyses were carried out by calculating the cracking load, deflection, ductility and ultimate moment by various codes such as IS, ACI. The comparisons between analytical, experimental and calculated results using IS and ACI are observed with the objective to establish the validity of the proposed models and identify the significance of various effects on the response of HSC members. Keywords: Hexavalent Chromium, High Carbon Iron Filings (HCIF), Mass Transfer Limitations, Permeable Reactive Barriers (PRBs) R I. INTRODUCTION EINFORCED cement concrete has become one of the most important structural building materials and is widely H.R. Manjunath, Associate Professor, Department of Civil Engineering, R V College of Engineering, Bangalore, India. K.R. Kavya, PG Student, Department of Civil Engineering, MSRIT, Bangalore, India. Kalyani Rao, PG Student, Department of Civil Engineering, MSRIT, Bangalore, India. M.R. Prakash, Associate Professor, Acharya Institute of Technology, Bangalore, India. R. Prabhakara, Professor & HOD, Department of Civil Engineering, MSRIT, Bangalore, India. r.prabhakara@gmail.com used in many types of engineering structures. The primary difference between HSC and NSC relates to the compressive strength that refers to the maximum resistance of a concrete sample to applied load. In the 1970 s, any concrete mixtures that showed 60 MPa or more compressive strength at 28-days were designed as HSC. Later, MPa concrete mixtures were commercially developed and used in the construction of high-rise buildings. The compressive strengths approaching 138 MPa have been used in cast-in-place buildings [1]. It has been observed from the literature that HSC up to 200 MPa can be produced using locally available materials. The economy, efficiency, strength, durability and stiffness of reinforced concrete make it an attractive material for a wide range of structural applications. Doubly reinforced sections are generally adopted when the dimensions of the beam have been predetermined from other considerations and the design moment exceeds the moment of resistance of a singly reinforced section. For some design and analysis problems, a linear analysis may not be sufficient when consider the requirement of satisfying a serviceability limit states such as calculating deflections. A large number of investigations have been carried out in the past on flexural behavior of HSC beams, but still there remain some vital design issue. One such issue is the serviceability requirement of deflection. Beams tested by several investigators consistently demonstrated significantly larger deflections at service load than what would be predicted by codal provisions. In order to assess the margin of safety of RCC structures against failure, an accurate estimation of the ultimate load is essential and the prediction of the load-deformation behavior of the structure throughout the range of elastic and inelastic response is desirable. Another important design issue is the ductility or the ability of a RC member to deform at or near the ultimate load without significant strength loss. Because concrete becomes increasingly more brittle as its compressive strength is increased, guaranteeing adequate ductility represents one of the primary design concerns when HSC is involved [2]. II. LITERATURE REVIEW Antonio F. Barbosa and Gabriel O. Ribeiro (1998)[3] carried out the analysis of reinforced concrete structures using ANSYS nonlinear concrete model. Reinforced concrete model consists of a material model to predict the failure of brittle materials. A simply supported reinforced concrete beam subjected to uniformly distributed loading had been analyzed considering only longitudinal reinforcement. Two kinds of meshing namely discrete and smeared modelling was

2 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 23 rd June considered. Each mesh had been analysed four times according to four different material models. It was observed that load deflection curves showed very close results at early stage of load history analysis for all kinds of models. The linear elastic models quickly reached the failure in compression zone and could not converge to a solution. As the steel was assumed to behave linearly, failure of these models occurred as soon as compressed concrete reached the failure surface. For elasto-plastic models with work hardening in compression have provided a longer load history. By keeping the crushing option active, the failure of the model was still premature and when crushing option was disabled complete load deflection diagram was obtained. Saifullah, M.A. Hossain, S.M.K.Uddin, M.R.A.Khan and M.A.Amin (2011) [4] performed the nonlinear analysis of RC Beam for different reinforcement patterns by finite element analysis. Six 3D beams without and with different patterns of shear reinforcement was built using ANSYS. The static non linear analysis was done to find out ultimate capacity, formation of first crack and its distance from support, initiation of diagonal crack and its distance from support. Load deflection response was also closely observed and compared with the result from theoretical calculation. It was observed that the initiation of diagonal tension crack occurs at larger loads and for the beam without shear reinforcement diagonal tension crack initiates at larger distance from support with compared to others. Theoretical calculation and ANSYS analysis gave almost same results for steel stressing at first crack. Farked Kais Ibrahim (2010) [5] carried out the research work on nonlinear finite element investigation on the behavior of lightweight reinforced concrete beams. Four different grades of concrete and the influence of using different longitudinal reinforcement ratios and different shear spandepth (a/d) ratio on the load-deflection curve was investigated. It was found that with increase in concrete compressive strength and increase in longitudinal reinforcement ratio, ultimate load capacity, cracking load and post-cracking stiffness was increased. But increase in shear span depth (a/d) ratio was found to decrease ultimate load capacity and post-cracking stiffness. L. Dahmani, A. Khennane, and S. Kaci (2010) [6] has been carried out the research work on crack identification in reinforced concrete beams using ANSYS software. The goal of this study was to know the different phases of the FE model behaviour from initial cracking, yielding of steel until failure of the concrete beam and to know the applicability of ANSYS software for analyzing and predicting of crack patterns in the reinforced concrete beam. After the analysis the analytical results were compared with the hand calculations and it was found that the load applied to cause initial cracking and at failure of the reinforced concrete beam well correlates with hand calculations. Ihsan A. S. Al-Shaarbaf, Nabil A-M. J. Al-Bayati, Dhar I. A. Al-Kaisy (2007) [7] carried out the nonlinear finite element analysis of reinforced concrete beams with large opening under flexure. The aim of this section is to verify the efficiency and accuracy of the model to simulate the load deflection response of reinforced concrete beams with large opening at the elastic, cracking and post-cracking stages of behaviour and the response at ultimate loads. The four rectangular simply supported beams with large opening were modelled. The beam dimension, amount and position of the load and longitudinal reinforcement was kept constant for all beams, where as opening size, its location and arrangement of transverse reinforcement was varied. In solid part of the beam, stirrup spacing was kept constant but in the regions below and above openings, the spacing of stirrups was varied for different specimen. It was found that the ultimate load capacity increases when the opening length decreases. The deflected shape along the beam length indicates that the maximum deflection of reinforced concrete beams with large opening occurs at the opening edge. As the distance between the applied load and the nearest end of the opening decreases the load carrying capacity was also decreased III. SCOPE OF PRESENT STUDY To develop analytical models and to investigate the relative importance of the nonlinear behavior of singly and doubly reinforced HSC beams under static loads. To obtain the cracking load of singly and doubly reinforced HSC beams using ANSYS. To compare the cracking load predicted by IS, ACI and ANSYS and to understand the deformation of the beams at the cracking load. To obtain the load deflection behavior of singly and doubly reinforced HSC beams. The comparison of working load deflection by IS, ACI and ANSYS. To obtain the ultimate load and failure criteria of the singly and doubly reinforced HSC beams and comparisons of ultimate moment by different codal provisions. To obtain the displacement ductility of singly and doubly reinforced HSC beams. IV. FINITE ELEMENT MODEL The ANSYS finite element program (ANSYS V12) [8], operating on a WINDOWS operating system was used in this study to simulate the behavior of the experimental beams. An eight noded Solid-65, element was used to model the concrete which has eight nodes with three degrees of freedom at each node translations in the nodal x, y, and z directions. The element is capable of plastic deformation, cracking and crushing. A Link8 element was used to model the steel reinforcement which has two nodes and each node has three degrees of freedom, translations in the nodal x, y, and z directions. The element is also capable of plastic deformation A. Fe Model Input Data For concrete, ANSYS requires input data for material properties as follows: elastic modulus E c, ultimate uniaxial compressive strength f ck, ultimate uniaxial tensile strength (modulus of rupture) f r, Poisson s ratio ν, shear transfer coefficient β and compressive uniaxial stress-strain relationship for concrete [9]. The shear transfer coefficient β, represents conditions of the crack face. The value of β ranges

3 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 23 rd June from 0 to 1.0, with 0 representing a smooth crack (complete loss of shear transfer) and 1.0 representing a rough crack (no loss of shear transfer) [8]. The value of β used in many studies of reinforced concrete structures, however, varied between 0.2 and 0.5.The shear transfer coefficient used in this study was equal to 0.3. B. Geometry and Beam Details The geometry and the material properties of nine HSC beams as reported by experiment [10] were used for this investigation. Details are tabulated in the table below in Table 1 Table 1: Details of Cracking Load for Different l/d Ratios for doubly reinforced beams for all l/d ratios. This increase is due to the result of lowering the neutral axis in the beams with the increase of the amount of reinforcement and the increase in the gross moment of inertia of the uncracked beam section. The cracking load has decreased with the increase in l/d ratios for all type of beams. The cracking loads obtained from experimental investigation are about 0.9 to 1 times that of ANSYS analysis, 1.2 to1.8 times that of IS code and 1.2 to 2 times that of ACI code respectively. The calculated cracking loads obtained from IS and ACI are less than the analytical and experimental cracking loads, this is because, the IS and ACI method does not consider the effect of reinforcement while calculating the cracking loads. The ratio of experimental results to that of ANSYS, IS and ACI were obtained for singly and doubly reinforced HSC beams. The mean, SD and COV was worked out in Table 3. It was observed that the codes underestimate the cracking load for most of the beams. In case of both singly and doubly reinforced beams ANSYS predicts better with least COV of Table 3: Ratio of Predicted Cracking Load to Experimental Cracking Load In the experiment, the loading and support were given with roller support to allow rotations of the beam. In finite element model the nodes at support was restrained in y direction and the loads were applied on directly on the nodes. The total load applied to a finite element model is divided into a series of load increments called load steps. At the completion of each incremental solution, the stiffness matrix of the model is adjusted to reflect nonlinear changes in structural stiffness before proceeding to the next load increment. The ANSYS program [8] provide convergence at the end of each load increment within tolerance limits V. DISCUSSION ON RESULTS A. Cracking Load After Analysis the FE beam model, at some initial stages of loading, first crack was observed. The load was noted at the cracking point. An attempt has been done to compare the analytical cracking load, experimental values and cracking load using IS code and ACI code using linear stress relationship of the uncracked section as shown in Table 2. Table 2: Details of Cracking Load for Different l/d Ratios B. Load Deflection Behaviour In the analytical analysis carried out using ANSYS, a gradual load of 0.2 kn was applied at each step and corresponding deflection were noted down. The experimental and numerical load-deflection curves obtained for all the beams Figure 1 and 2. The curves show good agreement in finite element analysis with the experimental results throughout the entire range of behaviour and failure mode, for all beams, the finite element model is stiffer than the actual beam in the linear range. The micro cracks produced by drying shrinkage and handling are present in the concrete to some degree. These would reduce the stiffness of the actual beams, while the finite element models do not include micro cracks due to factors that are not incorporated into the models. After the initiation of flexural cracks, the beam stiffness was reduced and the linear load deflection behaviour ended when the internal steel reinforcement began to yield. It has been observed from the Table 1 that the cracking load has increased with the increase in compression reinforcement Figure 1: Combined Load vs. Deflection Curve for l/d =15and l/d=20 Using ANSYS It has been observed that the deflection of HSC/20/30 is more than HSC/20/70 and HSC/20/BS. The load vs. deflection show same trend till yield point and then there is a deviation in the curves and HSC/20/BS has shown good post ductility

4 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 23 rd June compared over other curves. There is considerable difference in the ultimate load carrying capacity of HSC/15/30 and HSC/15/70 beams compared over HSC/15/BS. The load deflection curves of HSC/15/30 and HSC/15/70 are steeper compared to HSC/15/BS. The deflection at ultimate load for HSC/15/30 and HSC/15/70 is large compared to HSC/15/BS. Similarly, the graph can be plotted for l/d=25. Table 4: Comparison of Ultimate Moment It has been observed from the Table 4 that the ultimate moment carrying capacity of doubly reinforced beams is higher than that of singly reinforced beams. In case of doubly reinforced beams the ultimate moment carrying capacity is increased for about 1.3 times with increase in steel reinforcement. Ultimate moment carrying capacity of experimental beams are about 0.8 to 0.9 times that of ANSYS, 1.8 to 1.9 times that of IS Code and 1.5 to 1.8 times that of ACI Code respectively. Table 5: Ratio of Predicted Ultimate Moment to Experimental Moment Figure 2: Load vs. Deflection Curves for Different l/d=15 and l/d=20 C. Ultimate Moment Ultimate moment carrying capacity is very important factor. The code gives same moment carrying capacity formulae for any grade of concrete. In this section, investigation has been done by means of using different equations and expressions regarding ultimate moment carrying capacity (M u ) of the section and compared with the analytical and experimental data. After analysis of the data it was observed that (vide Table 5 ) the codes underestimate the moment of resistance for most of the beams. In case of singly reinforced beams ANSYS predicts better with least COV of In case of doubly reinforced beams both ANSYS and ACI predicts better than IS code as COV was 0.04 Figure 3: M U (EXP) vs. M U (ANSYS, ACI, IS) for Singly and Doubly Reinforced Beams A 45 degree line was drawn to ascertain the accuracy of predictions of experimental values as shown in Figure 3. It was observed from the graph most of the values lie close to 45 degree line for ANSYS.

5 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 23 rd June D. Ductility Ductility can be defined as the ability of the material to undergo large deformations without rupture before failure. Displacement ductility is the ratio of deflection at the ultimate load to the deflection at the first yielding of the tensile steel. The yield point is located by equating the area under the actual load deflection diagrams to the bilinear system keeping the initial angel same in both the conditions. (Bilinear method)[11]. Table 5: Comparison of Displacement Ductility It has been observed from the Table 5 calculated ductility values decreased with increase in the l/d ratio. Also the admissible ductility (>3) is achieved only with the l/d ratio 15. The Experimental ductility values were lower than that values obtained ANSYS analysis. This is due to the fact the ANSYS model is stiffer than the experimental specimen. With the increase in percentage of tension reinforcement, ductility factor is reduced, (vide Fig 4) since the yielding of reinforcement occurs at later stages. With the increase in percentage of Compression reinforcement, ductility factor is increased. Figure 4: Ductility vs. l/d Ratio for Singly and Doubly Reinforced Beams It can be observed that the ductility factor increases as l/d ratio decreases. This is due the fact that strength and initial stiffness increase greatly as l/d decreases (vide Figure 4). However, the flexural failure of the concrete member with shorter l/d on the compressive side occurs rapidly, showing that the concrete beam member becomes more brittle after the maximum loading for the member with shorter l/d. VI. CONCLUSIONS 1. The analytical and calculated cracking loads were compared with experimental cracking loads. 2. It was found that the calculated cracking loads obtained from IS and ACI are less than the analytical and experimental cracking loads, this is because, the IS and ACI method does not consider the effect of compression reinforcement while calculating the cracking loads. 3. The cracking load has been decreased with increase in l/d ratio but corresponding deflection has increased for all l/d ratios in both singly and doubly reinforced beams 4. Deflections at service loads which is taken as 2/3 rd of ultimate load was obtained from IS-456 and ACI-318 codes. It has been observed that as the l/d ratio increases deflection at working load increases. 5. In case of doubly reinforced beams, with increase in percentage of reinforcement deflections at working load are almost similar for Analytical, IS and ACI methods. 6. The load deflection behaviour observed to be linear up to cracking load and non-linearity starts thereafter. The comparisons of the analytical load-deflection and the experimental values were made and shown in form of tables and figures. 7. It was observed that code underestimates the prediction of ultimate moment. The ratios experimental moment to analytical and calculated moments were worked out and averages were 0.93,1.89 and 1.63 and coefficient of variance was 9%, 11% and 10% respectively for singly reinforced beams. Similarly the averages were 0.92, 1.88 and 1.58 and coefficient of variance was 4%, 9% and 4% respectively for doubly reinforced beams. Considering the coefficient of variance, the best prediction was done by ANSYS for both singly and doubly reinforced beams. 8. It was found that available deflection ductility index decreases as the longitudinal reinforcement increases and deflection ductility increases as the percentage of compression reinforcement increase. 9. It was observed that the ductility factor increases as l/d ratio decreases. This is due the fact that strength and initial stiffness increase greatly as l/d decreases. 10. In ANSYS, the tolerances in convergence criteria should carefully be defined in a nonlinear analysis. With load adjustment, tolerance may need to be relaxed to avoid a diverged solution. Scope of Future Investigation 1. In the present study, analysis of flexural behaviour of HSC beams was done using ANSYS FE package by varying the l/d ratio & percentage of reinforcement. Similarly studies can be extended by varying the grade of concrete of HSC. 2. The analytical studies can be carried out by considering other parameters such as shear and torsional behaviour. 3. The similar analytical studies can be made by varying the material properties and percentage of compression reinforcement of doubly reinforced HSC beams. 4. A steel plates needs to be included in the model at the support locations to represent the actual support condition in the full size beams. The steel plate also provides a more even stress distribution over the

6 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 23 rd June support area to avoid problems of stress concentration. 5. A relation to express the correlation between the experimental results & analytical study using computer FEM packages should be established by considering all other parameters such as shear, torsion etc. so that one can rely only on analytical studies instead of conducting experimental studies. REFERENCES [1] State of art report on HSC American concrete institute ACI363 r [2] Maghsoudi, A.A Ductility of High Strength Concrete Heavily Steel Reinforced Members, Shahid Bahonar University Publications, Kerman, Iran. (2010) [3] Antonio F, Barbosa, A.F. and Ribeiro, G.O. Analysis of reinforced concrete structures using ANSYS nonlinear concrete Model, Proc. of Conf on Computational Mechanics, Trends and Applications, 1998, pp. 1 7 [4] Saifullah, M.A.Hossain, S.M.K.Uddin, M.R.A.Khan and M.A.Amin Nonlinear Analysis of RC Beam for Different Shear Reinforcement Patterns by Finite Element Analysis International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01,2011. [5] Farked Kais Ibrahim Nonlinear Finite Element Analysis of High Strength Lightweight Concrete Beam, Building and Construction Engineering Department, University of Technology, Baghdad. (2010). [6] L.Dahmani, A. Khennane, and S. Kaci Crack identification in reinforced concrete beams using ANSYS software Strength of Materials, Vol. 42, No. 2, [7] Dr. Ihsan A. S. Al-Shaarbaf, Nabil A-M. J. Al-Bayati, Dhar I. A. Al- Kaisy Nonlinear Finite Element Analysis of Reinforced Concrete Beams with Large Opening under Flexure Eng. & Technology, Vol.25, No.2, 2007 [8] ANSYS, ANSYS User s Manual Revision V12, ANSYS, Inc., Canonsburg, Pennsylvania [9] Desayi P. and Krishnan S., Equation for the Stress-Strain Curve of Concrete, Journal of the American Concrete Institute, 61, pp , March [10] Satish Chandra. H.B Flexural behaviour of doubly reinforced HSC beams M.Tech thesis, MSRIT, Bangalore. [11] Prabhakara R., Muthu K.U. and Meenakshi R., Investigation on ultimate flexural strength and Ductility behaviour of HSC beams, The Indian Concrete Journal, Oct 2006, pp