Numerical Analysis of RCC Beam Using ABAQUS

(1)

IOP Conference Series: Earth and Environmental Science

PAPER • OPEN ACCESS

Numerical Analysis of RCC Beam Using ABAQUS

To cite this article: A. Hemamathi et al 2022 IOP Conf. Ser.: Earth Environ. Sci. 1084 012077

View the article online for updates and enhancements.

Numerical Analysis of RCC Beam Using ABAQUS

Dr. A. Hemamathi^1,*, Dr. Binu Sukumar², and R.B. Hambrish Guru Chantrakant³

1Associate Professor, Department of Civil Engineering, R.M.K Engineering College, Tamil Nadu, India.

2 Professor, R.M.K Engineering College, Tamil Nadu, India

3UG Student, Department of Civil Engineering, R.M.K Engineering College, Tamil Nadu, India.

Corresponding [email protected]

Abstract. Experimental investigation of RCC beam provide an important understanding on its flexural properties. The stages involved from the design to casting, curing, testing and interpretation of results is time consuming and involves economy and labour. To reduce the above said challenges, numerical investigation seems to be an alternate without involvement of money and labour. Preliminary design stages involves design equation which are provided by the basic experiments conducted and they also give the basic information to develop the finite element model. This paper presents the numerical investigation of RCC beam to study the flexural properties using an effective finite element analysis tool ABAQUS. RCC beam prototypes were casted and their flexural properties were experimentally investigated. The results were validated through the finite element model by providing suitable properties for the material that are actually used for the prototype with the desired loading and support conditions. Beam of size 3000 x 230 x 300 mm of M20 grade concrete was casted and tested in the loading frame for flexure and deflection. The study focussed for under reinforced, balanced and over reinforced sections.

Numerical analysis was performed using ABAQUS for model geometry and the results were compared with the experimental results. The results agreed with both the experimental and numerical values. Numerical results helps in developing reliable models which can reduce the number of required test specimens for conducting experiments and the model can be used for various study. Also from the finite element results the propagation of cracks can be well understood for the actual specimen.

Keywords: RCC beam, Numerical investigation, ABAQUS,

1. Introduction

In general, structures are subjected to different types of loading condition. The primary structural element of RC structure is a beam and it is subjected to transverse loading condition. It is a flexural member subjected to bending action under the action of transverse load [1]. A RC beam is considered to be statically determinate when the analytical calculations are performed with known equilibrium equations and it may be considered as a homogeneous section with simple geometry until the concrete in the beam remains un cracked [2]. The individual beam element can be tested experimentally to study the effects of various loads and the behaviour of material. The experimental testing method of ordinary concrete beam is costly method to understand the behaviour under transverse loading. Also, it is time

(3)

ICSEEGT 2022

consuming process as the beam has to be cured for a period of time. This can be overcome by the use of computer software wherein the beam can be modelled at a swift pace making it a cost-effective process. Once the model is validated with the experimental results, it will be useful in refining analytical models, making good prediction on complex nonlinear behaviour of RC beams. [3]

ABAQUS is a powerful finite element tool to provide solution to engineering simulation programs. It can provide solution to simple linear analyses problems to the most challenging nonlinear simulations.

ABAQUS can model any geometry virtually from its available extensive library. Also, it contains number of material models to simulate any engineering materials such as metals, rubber, polymers, composites, reinforced concrete, crushable and resilient foams, and geotechnical materials such as soils and rock. ABAQUS tool not only provide solution to structural (stress/displacement) problems, but also it can simulate diversified problems such as heat transfer, mass diffusion, thermal management of electrical components (coupled thermal-electrical analyses), acoustics, soil mechanics (coupled pore fluid-stress analyses), piezoelectric analysis, electromagnetic analysis, and fluid dynamics. Also, ABAQUS can be used to model multiple components associating each geometry and defining each component with the appropriate material models and specifying component interactions. In nonlinear analysis ABAQUS is capable of choosing load increments and convergence tolerances and continually adjusts them during the analysis to ensure that an accurate solution is obtained efficiently [15].

The present study aims at comparing the experimental results with the ABAQUS results. The study started with experimental testing of beam of size 3000 x 230 x 300 mm of M20 grade concrete for under, balanced, over reinforced sections. The numerical study was performed for the model considered in the experimental study using Finite Element Analysis (FEA) tool, ABAQUS. The numerical results obtained from ABAQUS tool was compared with the experimental results which showed good agreement between the results.

1.1 Significance of study

The study focuses on the experimental study and numerical study of RC beam. The deflection parameter was investigated and checked with IS code specification. Experimental investigation on beam involves time, material and facility for testing. This paper provides a basic study on the RC beam where a numerical investigation was validated by experiment. Further the numerical procedure can be utilized further for RC beam with any grade of concrete, grade of steel, diameter and number of rebars and type of beam.

2. Experimental Investigation

Mix design for M20 concrete was carried out as per IS 456: 2000 and IS 10262: 2019. Six cubes were casted and tested for 28 days. M20 grade of concrete was used for casting. After curing for 7 days, 3 cubes were tested for checking the initial strength of concrete which found to be 65% of the design value. The same procedure was done for the other 3 cubes after curing for 28 days. After the curing period of 28 days the beams were experimentally subjected to two-point loading by using hydraulic actuator as given in Figure 2A. Simply supported condition was used with a hinge on one side and roller on other side to attain an effective span of 3000 mm. The test specimen of dimension 230 x 300 mm was placed on the supports and mounted with the hydraulic actuator in the centre of test specimen.

An intermediate beam was placed for two-point load action between the load jack and the test specimen with two roller supports on the specimen top surface.

2.1 Beam casting and testing

Reinforced concrete beam was designed as per limit state method using IS 456: 2000 for mild exposure condition. The reinforcement provided in the beam as given below and detailing is shown in Figure 1.

Tension reinforcement: 2 nos. of 12 mm diameter Fe 415 steel

Transverse reinforcement: 2 legged 8 mm diameter stirrups at 150 mm c/c Cover to concrete: 40 mm

(4)

ICSEEGT 2022

Figure 1. Detailing of the beam specimen

After curing the beam for 28 days the specimen was subjected to two-point loading using hydraulic jacks. Simply supported condition was used with a hinge on one side and roller on other side for an effective span of 3000 mm. The test specimen having dimensions of 230 x 300 mm was placed on the supports and the hydraulic jacks was mounted in the centre of test specimen.

Figure 2A. Two point loading

Figure 2B. Testing of beam 2.1.1 Calculation of flexural strength from Lab Test

The beam is calculated for its flexural strength as per Indian standards. The Flexural Strength or Modulus of Rupture (𝑓_𝑏) is given in equation 1

𝑓_𝑏= ^𝑃𝑙

𝑏𝑑² (1)

Where, 𝑏 = width of specimen 𝑑 = effective depth

𝑙= supported length 𝑃 = Maximum Load taken by the specimen.

(5)

ICSEEGT 2022

2.1.2 Tensile Strength of Concrete

The flexural and splitting tensile strengths of the specimen was calculated as per the standard specification described in IS 516 and IS 5816 respectively. IS 456:2000 provides an estimate of the tensile strength from the compressive strength using the following formula given in equation 2

𝑓_𝑐𝑟 = 0.7 √𝑓_𝑐𝑘 (2)

Where 𝑓_𝑐𝑘 is the characteristic cube compressive strength of concrete in 𝑁/𝑚𝑚². 𝑓_𝑐𝑘= 20 𝑁/𝑚𝑚²

Flexural strength, 𝑓_𝑐𝑟= 0.7 √20 = 3.3 𝑁/𝑚𝑚² The test results of the beam are tabulated in Table 1

Table: 1 Beam test results

Beam ID Beam 1 Beam 2 Beam 3

Beam Size (mm)

230*300*3000 230*300*3000 230*300*3000

Effective Depth D (mm)

280 280 280

Age At Testing (Days)

31 31 31

Area (Sq.mm)

64,400 64,400 64,400

Flexure Load (N)

18500 17800 13500

Flexural Strength (Fb = Pl/Bd²) (MPa)

3.08 2.96 2.25

As Per IS 456

3.13 3.13 3.13

Nature Of Failure

FLEXURE FLEXURE FLEXURE

2.2 Theoretical calculation

The moment of resistance 𝑀_𝑢 is calculated as per IS 456: 2000 and is given in equation 3, where 𝑥_𝑢is the neutral axis depth, 𝑏 - width of specimen, 𝑑- effective depth and 𝑓_𝑐𝑘is the characteristic compressive strength of concrete

𝑀_𝑢= 0.36 𝑥_𝑢

𝑑 (1 − 0.42 𝑥_𝑢

𝑑) 𝑏𝑑²𝑓_𝑐𝑘

(3)

= 0.36 x 0.46(1 – 0.42 x 0.46) 230 x 280 x 280 x 20 Mu = 48.18 kN.m

𝑃_𝑢 = ^𝑀^𝑢

𝑙𝑒𝑣𝑒𝑟 𝑎𝑟𝑚 =^{48.18 ×10}

6 1000 = 4.8 t 2.3 Deflection

The deflection of the beam is calculated as per structural analysis calculation for the beam shown in Figure 3 and is given in equation 4.

(6)

ICSEEGT 2022

Figure 3. Loading on the beam 𝛿_𝑚𝑎𝑥 = 𝑃𝑎

24 𝐸𝐼(3𝐿²− 4𝑎²)

(4)

= 4.14 mm

The deflection of beam may be generally limited to the following:

The final deflection due to all loads including the effects of temperature, creep and shrinkage and measured from the base level of the supports of Floors, roofs and all other horizontal members, should not normally exceed span / 250.

Span = 3000mm

Permissible deflection = 3000/250 = 12 mm 3. ABAQUS Modelling

ABAQUS is a finite element analysis software suite, and was introduced in 1978. It is a commercial software package for performing linear and nonlinear analysis. Based on the main objectives of this study, finite element model of reinforced concrete beam was developed three dimensionally and the process of ABAQUS is explained in the Figure 4 given below:

Figure 4. Flowchart of steps adopted in ABAQUS modelling

(7)

ICSEEGT 2022

3.1 Creating part

The beam is modelled as a deformable solid body by creating part in two-dimensional profile.

Then it was converted to three dimensions by extrusion. Three new part is created in the model BEAM_CONCRETE, REBAR_STEEL, STIRUPPS_STEEL. The extruded part is shown in figure 5. In this study concrete is modelled as eight noded element, steel is modelled as two noded beam element.

Figure 5. Extruded part

Beam of length 3 m and width 230 mm and depth 300 mm is created. Plane stress elements are commonly used to model beams in 2D as the beam is relatively long compared to its width. The reinforcement can be modelled with 2D and 1D elements as embedded reinforcement. The rebars were modelled as two –node beam elements connected to the nodes of adjacent solid elements.

3.2 Material property

The property of material used are defined as below in ABAQUS

1. Young’s modulus of 22360 MPa for concrete and Young’s modulus of 215000 MPa for steel.

2. Poisson’s ratio of 0.3 for steel and 0.2 for concrete

3. Mass Density of 2400 kg/m³ for concrete and Mass Density of 7460 kg/m³ for steel.

3.3 Assigning section

A homogeneous solid section is created and assigned to the beam. The solid section created in the previous step was assigned as concrete and the two nodded beam element created for reinforcements were assigned to Steel. The assigned section is shown figure 6.

(8)

ICSEEGT 2022

Figure 6. Material property assigned section 3.4 Step creation and assembling the model

In this simulation the static response of the simply supported beam is subjected to pressure load applied over the beam top. Consequently, this model will consist of two steps and the model is assembled as shown figure 7.

• An initial step, in which the boundary condition are applied that constraints two and of the simply supported beam.

• A general, static analysis step is applied with pressure load on top face of the beam

Figure 7. Assembling the model

(9)

ICSEEGT 2022

3.5 Applying boundary condition and loading on the model

A new load is created in the model tree and load dialog box appears. In the dialog box, load is selected as POINT LOAD. Load will be selected a step 1 and load will be applied. In the selected Step list, Pressure (as the point load in this case is distributed throughout the surface area of the beam in contact) is applied on the beam. The magnitude of the load is selected as -50000 (CF2) and the negative sign indicates that load is applied along Y- axis. The beam with boundary condition is shown in figure 8.

Figure 8. Applying boundary condition 3.6 Meshing the model

The process of generating nodes and elements is called Meshing. Elements are defined by generating nodes and connecting them to form a mesh.The finite element meshing is used to generate the mesh module. The meshing technique can be selected from ABAQUS that is used to create the mesh, the element shape, and the element type. Number of meshing techniques are available in ABAQUS to arrive at most converging solution. The default meshing technique assigned to the model is indicated by the colour of the model. If the model displays orange colour, it indicates that it cannot be meshed without assistance from the user. The meshed model is shown in figure 9.

(10)

ICSEEGT 2022

Figure 9. Meshed model 3.7 Creating and submitting an analysis

The model is created with all properties defined, assigned and meshed. The model is then analysed by running the analysis. Figure 10 shows the modelled specimen.

(11)

ICSEEGT 2022

4. Evaluation of results

The beam was analysed by assigning the properties to the model. The analysis without aborting indicates the error free model. The results of the analysis are viewed in the Visualization module.

The deflected shape is shown in figure 11. The results of deflection was then compared with the analytical and experimental results.

Figure 11. Deflected beam 5. Comparison of results

The analysed beam from ABAQUS was compared with the experimental and theoretical values as described in the work. It was found that the results have proved to be in par with the theoretical calculation and the properties assigned for both concrete and steel well behaved in the model and the results are tabulated in the table 2. The model was then re-assigned with two different tension reinforcement; viz, 2 # of 16 mm diameter bars and 2 # of 20 mm diameter bars. In both the cases the beam has shown the expected results.

Table: 2 Comparison of results

Beam ID Beam 1 Beam 2 Beam 3

Beam Size (mm) 230*300*3000 230*300*3000 230*300*3000

Diameter of rod 12 16 20

Ast of rod mm2 226.1 402.1 628.3

Theoretical displacement (mm) 4.14 4.14 4.14

Numerical displacement (MPa) 3.925 3.743 3.457

Experimental strength (mm) 2.76 - -

Permissible displacement (mm) 12 12 12

(12)

ICSEEGT 2022

6. Conclusions & Discussions

A RC beam of length 3 m, 230 mm wide and 300 mm deep was casted with 2 # 12 mm diameter bars as tension reinforcement and 2-legged 8 mm stirrups at 150 mm c/c was provided as transverse reinforcement on the beam. The beam was analysed theoretically as per specifications given in IS 456:2000 and numerically using finite element tool ABAQUS. The following conclusions have been arrived from the experimental testing and numerical evaluation:

● The beam was applied with two-point loading and the flexural strength of the beam was found experimentally which was in par with the specification given in IS 456: 2000

● The Experimental displacement and Numerical displacement for the beam reinforced with 12 mm diameter bar was studied and compared and they found to be similar.

● From the results of the 12 mm diameter bars used as tension reinforcement, numerical displacement for 16mm and 20mm reinforcement bars was done numerically using ABAQUS Modelling.

● The failure mechanism of a reinforced concrete beam is modelled quite well using FEA and the failure load predicted is very close to the failure the load measured during experimental testing.

References

[1] Sayed Mohamad Soleimani and Sajjad Sayyar Roudsari, “Analytical Study of Reinforced Concrete Beams Tested under Quasi-Static and Impact Loadings” Journal of Applied Sciences, Volume 9, 2019

[2] Dimosthenis Floros Olafur Agust Ingason, “Modelling and simulation of reinforced concrete beams” Department of Applied Mechanics Division of Solid Mechanics Chalmers University Of Technology, 2013

[3] T. Tejaswini, Dr.M.V.Rama Raju, “Analysis of RCC Beams using ABAQUS”, International Journal of Innovations in Engineering and Technology (IJIET), Volume 5 Issue 3, June 2015.

[4] A.Hemamathi, Sanjith Murugavel , Binu Sukumar , M.Usha Rani, “Numerical Investigation of Precast Grouted Sleeve Connection under Cyclic Loading Using ABAQUS”, Journal of Physics: Conference Series, 2070 (2021) 012178

[5] Sayed M S and Sajjad S R, “Analytical Study of Reinforced Concrete Beams Tested under Quasi-Static and Impact Loadings”, Applied Science, 2019.

[6] S.V.Chaudhari, M.A.Chakrabarti, “Modeling of concrete for nonlinear analysis Using Finite Element Code ABAQUS”, International Journal of Computer Applications (0975 – 8887), Volume 44– No.7, April 2012.

[7] T.S.Vishnu Kumar, N.Rushwanth Chowdary, “FINITE ELEMENT MODELING OF RCC BEAM BY USING ABAQUS”, International Journal of Creative Research Thoughts (IJCRT), Volume 8, Issue 7 July 2020.

[8] Hamid S, Mahdi S, Amir H A, Mohammad A and Ali S, “Evaluation of reinforced concrete beam behaviour using finite element analysis by ABAQUS”, Scientific Research and Essays Vol.

7(21), pp. 2002-2009, 7 June 2012.

[9] I. Saifullah, M. Nasir-uz-zaman, S.M.K. Uddin, M.A. Hossain and M.H. Rashid,

“Experimental and Analytical Investigation of Flexural Behavior of Reinforced Concrete Beam”, International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: 01, February 2011.

[10] Swoo H L, Ali A, Kyung J, Hee D, “ABAQUS modeling for post-tensioned reinforced concrete beams”, Journal of Building Engineering Volume 30, July 2020.

[11] Workshop 1, “Linear Static Analysis of a Cantilever Beam, Introduction to Abaqus”, D’s Simulia

[12] Indian Standard Plain and Reinforced Concrete - Code of Practice, Is. 456: 2000.

[13] Indian Standard Concrete Mix Proportioning – Guidelines (Second revision) IS 10262: 2019.

[14] Indian Standard Methods of Tests for Strength of Concrete IS 516: 2004.

[15] Dassault Systems “Getting Started with Abaqus/CAE Abaqus 2016”.

Numerical Analysis of RCC Beam Using ABAQUS

IOP Conference Series: Earth and Environmental Science

Numerical Analysis of RCC Beam Using ABAQUS

You may also like

Numerical Analysis of RCC Beam Using ABAQUS