Non-Linear Finite Element Analysis of RC Slabs Strengthened with CFRP Laminates

8/12/2019 Non-Linear Finite Element Analysis of RC Slabs Strengthened with CFRP Laminates

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International Journal of Engineering Trends and Technology (IJETT) – volume 5 number 3- Nov 2013

ISSN: 2231-5381 http://www.ijettjournal.org Page 141

chosen for the purpose of analysing RC slabs with and without

external CFRP strengthening in this study due to its flexibility

in geometry and materials modelling . . The Five reinforcedconcrete slabs were loaded with a four point loading

configuration with a total length of 1530 mm an effectivelength of 1350 mm, and distance between loads of 450mm. All slabs were 125 mm thickness, 500 mm wide .

Concrete cover 25 mm, two types of flexural steel

reinforcement were used in the slabs , the first type consist of3 tor steel bars 10 mm in diameter and fy = 460 Mpa , the

second type consist of 4 mild steel bars 6 mm in diameter andfy = 250 Mpa . Slabs details with CFRP laminates are shown

in figures (1. , 2., 3., 4.) .

Figure 1. : slab loading pattern

Figure 2. : CST, SST Cross section

Figure 3. : CSM, SSM1 Cross section

Figure 4. : SSM2 Cross section

The following has been used for the materials idealization:

A. Concrete Idealization

SOLID65 was used to model the concrete. the geometry,node locations, and the coordinate system for this element are

shown in figure (5.).

B. Steel Reinforcement

LINK180 : is a 3-D spar that is useful in a variety ofengineering applications. LINK180was used to model the

steel reinforcement. The geometry, node locations, and thecoordinate system for this element are shown in Figure (6.).

C. Steel Plate

SOLID185 is used for 3-D modelling of solid structures.

It was used to model Steel plates were added at support and point of loading locations The geometry and node location for

this element type are shown in Figure (7.).

D. CFRP Laminates

SHELL41 A four node element was used to model CFRP

strips which is a 3-D element having membrane (in-plane)stiffness but no bending (out-of-plane) stiffness. The geometry

and node location of this element type are shown in Figure(8.).

FIGURE 5. : SOLID 65

GEOMETRY

FIGURE 6. : LINK 180

GEOMETRY





FIGURE 7. : SOLID 185

GEOMETRY

Figure 8. : SHELL 41

Geometry

RESULTS AND DISCUSSION

This chapter presents the results of Finite Element analysisof two control RC slabs, three RC slabs strengthened with

CFRP bonded at the bottom face. Finite element analysis(using ANSYS computer program version 13.0) of RC slabs

under the static incremental loads has been performed in the

present work. Subsequently these results are compared with

experimental results. The following comparisons are made

with regards to deflection values as well as the detailed overall behaviour of the of the slabs.

A. Loading And Boundary Conditions

In the experiment, the bearing plate of loading and support

dimensions are (50mm x 500mm). A 25 mm thick steel plate,modelled using Solid185 elements, is added at the support and

point of loading locations in order to avoid stressconcentration problems shown in figure (9.). This provides a

more even stress distribution over the support and point ofloading areas. Figure (10.) shows the distribution of the

applied load at nodes.

Figure 9.: Applied load and boundary conditions (a)Front view, (b) Top

Figure 10. : Distribution of applied load at nodes (a) nodes,

(b) elements

B. Results Of Finite Element Analysis I took the numerical load-deflection curves for the mild

reinforced strengthened slab strengthened by two laminates in

comparison with the experimental results, shown in figure(11.) as an example for the five models.

Figure 11. : Load-deflection curve for strengthened

slab_mild reinforcement2.

The deflection at (82 kN) obtained from the F.E. is a

flexural deflection of (6.2 mm), which is lower than the

experimental deflection of (8.2 mm) about 32.258%. Theother difference is the type of failure, where the experimental





model failed by debonding the CFRP laminate the thing that

not observed in F.E model.

C. Ultimate Loads And Ultimate Deflection

A comparison between the ultimate loads of the tested

beams and numerical ultimate loads from finite elementanalysis is shown in Table (1). The table shows, a goodagreement between the theoretical and experimental results,

and comparison between the ultimate deflections of the tested

beams and numerical ultimate loads from finite elementanalysis is shown in Table (2).

Table (1) Comparison between experimental andNumerical ultimate loads

Slab’ssymbol

(Pu)exp.(kN)

Pu)num.(kN)

Difference%

cs t 29.17 26.65 9.455

ss t 82.16 123.8 33.634

cs m 18.24 25.25 27.762

ss m 1 48.56 71.8 32.367

ss m 2 85.6 123 30.398

Table (2): Comparison between experimental and

Numerical ultimate Deflection

Slab’sSymbol

(Δu)exp.(mm)

(Δu)num.(mm)

Difference(%)

cs t 5.68 3.25 74.769

ss t 13.95 15.3 8.823

cs m 1.30 0.58 125.137

ss m 1 8.90 12.9 31.007

ss m 2 8.66 11.2 22.678

IV. CONCLUSION

The following conclusions can be drawn from the present

study

1)The behaviour of slab represented by the load-deflectioncurves in ANSYS show close agreement with the

experimental data from the full-scale RC slab tests.2)It has been concluded that strengthening the slab with

CFRP, the slab also bears larger deflection and strengthening

the slab with CFRP sheet also increases the ultimate load

carrying capacity of the slab.

3) The analytical load carrying capacity of the control slabwas in close agreement with the experimental work.

4) The cracks start appearing at the centre and move from

centre towards the free edges of the slab. Major damage

occurred at the centre of the slab and negligible damageoccurred at corners.

5) Because of the strengthening techniques , the strengthenedslabs sst , ssm1 and ssm2 are shows high load carryingcapacity about 78.758% , 95.503% and 94.821% respectively

in comparison with control slabs.

6) The difference between numerical and experimental valuesfor loads and deflections gives negative values for the two

control slabs and positive values for the other strengthenedslabs and the reason for that is the existing of CFRP with

strengthened models in ANSYS program that makes the program solving for long time.

REFERENCES

[1] ACI committee 363R, (1997) “State of The Art Report on High-

Strength Concrete“, American Concrete Institute. Detroit, Vol. 81,

No.4[2] ACI Committee 318, (2008) "Building Code Requirements for

Structural Concrete (ACI 318-08) and Commentary", American

Concrete Institute, Detroit, U.S.A.

[3] A., P. Godat, Labossière, and K. W. Neale., 2011 "Numericalinvestigation of the parameters inf luencing the behavior of FRP

shear-strengthened beams". Constr. and Build. Mat.,.In Press.

[4] Chen, W. F. and Saleeb, A. F., (1981) "Constitutive Equations for

Engineering Materials", West Lafayette, Indiana, , pp. 580 December

[5] Chen, W. F. and Saleeb, A. F., (1981) "Constitutive Equations for

Engineering Materials", West Lafayette, Indiana, , pp. 580 December

[6] Chen, W. F.,( 1982) "Plasticity in Reinforced Concrete", McGraw-

Hill, , 471pp.

[7] Elsayed, W., Usama A. E., and Kenneth W. N. (2007). "Interfacial

behavior and debonding failures in FRP-strengthened concrete slabs" .

Journal of Composites for Construction 11.6: 619-628.

[8] Gopalaratnam , V.S. and Shah. (1985) ,"Softening Response of Plain

Concrete in Direct Tension", ACI Journal ,Vol. 82,No.3, , pp, 310-323.

[9] Kenneth, W. N., Ahmed, G., Hussien, M. A. B., Walid, E. E., and

Usama, A. E. (2011) "Approaches for finite element simulations of

FRP-strengthened concrete beams and slabs." Architecture, 4.4: 59-72.[10] Kim, Y. J., Longworth, J. M., Wight, R. G., & Green, M. F. (2008)

"Flexure of two-way slabs strengthened with prestressed or non prestressed CFRP sheets" Journal of Composites for Constructi on, 12.4:366-374.

ACKNOWLEDGMENT

Foremost, I would like to thank my God for Hisgraciousness, unlimited kindness and with the blessings of

whom the good deeds are fulfilled.Finally I would like to dedicate this work to my family

and all my beloveds

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Non-Linear Finite Element Analysis of RC Slabs Strengthened with CFRP Laminates