International Journal of Steel Structures 15(3): 671-680 (2015) DOI 10.1007/s13296-015-9013-7 ISSN 1598-2351 (Print) ISSN 2093-6311 (Online) www.springer.com/journal/13296
Non-Linear Finite Element Investigation on the Behavior of CFRP Strengthened Steel Square HSS Columns under Compression Urmi Devi* and Khan Mahmud Amanat Department of Civil Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, 1000, Bangladesh
Abstract This paper presents a numerical finite element investigation on the behavior of steel square hollow structural section (HSS) columns strengthened with CFRP. Three dimensional finite element (FE) models of square HSS sections were developed using shell elements considering both material and geometric nonlinearities whereas CFRP strengthening was incorporated with additional layers of shell elements. The developed FE models were used to simulate experimental studies done by past researchers. Good agreement has been found between numerical analysis and past experimental results, which has validated the acceptability of the FE model to carry out further investigation. Study is then focused on some selected non-compact AISC square HSS columns and the effects of number of CFRP layers, slenderness ratio and cross-sectional geometry on the strength gain of those columns has been observed. It is observed that CFRP strengthening is comparatively effective for higher slenderness ratios. For smaller sections strengthening tends to be effective at smaller slenderness ratios as well. For relatively large AISC square HSS columns, with increasing number of CFRP layers (from 1 to 5 layers) the axial strength gain is only approximately by about 1 to 20%. For medium and small square HSS sections, effectiveness of CFRP strengthening increases approximately by about 10 to 90%. The findings of the present study provide us a better understanding of the behavior of HSS sections strengthened with CFRP and shall be useful to engineers in applying CFRP retrofitting techniques to strengthen steel columns. Keywords: CFRP strengthening, steel square HSS columns, material and geometric nonlinearities, axial strength gain
1. Introduction The use of Carbon Fiber Reinforced Polymer (CFRP) materials is gaining popularity day by day for repairing and strengthening of steel structures (Zhao, 2013; Teng et al., 2012; Zhao and Zhang, 2007) compared to other retrofitting techniques (Di Sarno and Elnashai, 2005). With the use of CFRP materials, it may be possible to overcome the problems associated with the conventional retrofitting techniques such as added dead weight, long installation time, corrosion, reduced fatigue life etc. due to having high strength and high stiffness-to-weight ratios and excellent corrosion resistance (Raj and Nirmalkumar, 2014) along with fatigue properties (Al-Hammoud et al., 2011; Badawi and Soudki, 2010). Implementation of repair strategies using CFRP is faster, lighter, causes less nuisance and aesthetically more pleasing than other repair Received July 9, 2014; accepted May 13, 2015; published online September 30, 2015 © KSSC and Springer 2015 *Corresponding author Tel: +8801677545209 E-mail:
[email protected]
techniques (Shaat and Fam, 2007). Satisfactory results have been obtained by conducting research on upgrading metallic structures with advanced polymer composites (Hollaway and Cadei, 2002), strengthening steel bridge girder with CFRP plates (Puurula et al., 2015; Peiris and Harik, 2014; Illig and White, 2010; Schnerch and Rizkalla, 2008; Millar et al., 2001) and rehabilitating the reinforced concrete beam-column joints with CFRP polymers (Garcia et al., 2014) and also about upgrading reinforced concrete structures by jacketing with CFRP sheets (Darwish, 2000; Gajdosova and Bilcik, 2013; Zilch et al., 2014; Wu et al., 2014; El-Saikaly et al., 2014; Sadeghian et al., 2010; Balaguru et al., 2009; Oehlers and Seracino, 2004). Aging and overburdened structures need retrofitting to comply with the modified and more stringent design codes and specifications of the recent years. Columns are generally the most important elements in a structure that need to be strengthened. Through strengthening of steel columns using CFRP, the whole structure may perform better than that of rebuilding them. By retrofitting the columns, vertical extension of floors, design fault removal, damage reduction due to lateral loads may even be possible. In recent years, steel hollow structural section (HSS)
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columns have become increasingly popular in the steel construction industry (Bambach, 2014; Law and Gardner, 2013; Zhao and Zhang, 2007; Gardner and Nethercot, 2004a,b). Bambach et al. (2009a,b) and Bambach and Elchalakani (2007) strengthened short HSS sections with different fiber layouts and were able to achieve axial capacities up to two times that of control columns. Key and Hencock (1985) investigated the column behavior of cold formed square hollow sections with slenderness ratio ranging from 66 to 98. Shaat and Fam (2006) experimented steel square HSS slender columns of constant slenderness ratio strengthened with high modulus CFRP sheets and had been able to increase the column axial strength by up to 23%. An analytical model of this experimental study has also been proposed (Shaat and Fam, 2007). The study was then extended to include high modulus CFRP of 313 GPa and showed that effectiveness of the CFRP increases as slenderness ratio (KL/r) of long columns increase (Shaat and Fam, 2009), where gains in axial capacity of up to 70% were achieved for columns with 93 slenderness ratio and axial stiffness ranged from 10 to 17% were also achieved. Ritchie et al. (2014) investigated CFRP strengthening of long steel columns of 197 slenderness ratio that is close to the upper limit of 200 permitted by code against global buckling around weak axis using CFRP plates of various moduli. Kalavagunta et al. (2014) observed that bonding CFRP to cold-formed lipped steel channels can increase their axial capacity by 17%. Such experimental studies provide useful results regarding strengthening, however more research is still required in this field. Though laboratory experiments provide firsthand experience and knowledge, cost of such lab procedures sometimes prohibits conducting extensive testing scheme. A reliable numerical finite element analysis is often regarded as an alternative to costly experimental procedures (Jama et al., 2009; Patton and Singh, 2012). This paper focused on developing a three dimensional finite element model to investigate the behavior and axial strength of steel square column of Hollow Structural Section (HSS) strengthened using Carbon Fiber Reinforced Polymer (CFRP) considering both the geometric and
material nonlinearities. Verification of this finite element model has been demonstrated with reference to the experiment of Shaat and Fam (2007). The proposed model is then used to examine the effects of number of CFRP layers, slenderness ratios, cross sectional geometry of non-compact square HSS column sections from AISC Manual, 13th edition (2005) and also to examine the different potential failure modes of CFRP strengthened square HSS columns of different slenderness ratios and CFRP configurations.
2. Methodology for Finite Element Analysis This section describes a finite element model to predict the responses of CFRP retrofitted steel HSS columns. The model accounts for both material and geometric nonlinearities. Geometric non-linearity is triggered by providing a slight imperfection in the initial straightness of the column as was adopted by Shaat and Fam (2007). To perform the modeling in a generalized way, a hollow square section is chosen in such a way that can help to ease the modeling procedure. For example, round corners of a general square HSS section are considered chamfered in the proposed model. It will not affect the results since the CFRP sheets were provided only at the straight portions of the cross section of a steel HSS column. Since this study is concerned with thin plated structural sections, shell element is the best option for finite element modeling. On account of this, four noded finite strain shell element having six degrees of freedom at each node has been used for steel square HSS column. Retrofitting materials involving CFRP, GFRP (Glass Fiber Reinforced Polymer) along with bonding material epoxy resin have been modeled with an additional equivalent layer of similar shell elements. Here, full bonding has been assumed between different layers of retrofitting materials and steel. If the cross-sectional area and modulus of elasticity of different layers are A1, A2, A3 ……… An and E1, E2, E3 ……En respectively then the equivalence of different retrofitting layers (based on strain compatibility) may be achieved as follows.
Figure 1. Actual test features (Shaat and Fam, 2007). Figure 2. Equivalent idealization of the retrofitting materials.
Non-Linear Finite Element Investigation on the Behavior of CFRP Strengthened Steel Square HSS Columns under Compression 673
Figure 3. Finite element mesh of steel HSS column along with boundary conditions and loading.
Figure 4. Finite element mesh of column initial imperfection (exaggeration).
Equivalency of the materials can also be understood from Fig. 1 and Fig. 2. It may be mentioned that such equivalency of material holds true mainly in the elastic regime. When the material non-linearity begins, such equivalency only holds approximately. Restraints are provided in the model in accordance with
the test setup of steel column’s compression test (Shaat and Fam, 2007). Longitudinal dimension has been considered along the z direction whereas cross sectional dimensions have been considered along x and y directions. One end of the column is kept restrained for translation in all the x, y and z direction while the other end of the column is kept restrained in x and y direction translation. To prevent twisting of column about z axis, a corner node of column is additionally restrained in x and y translation. To force buckling about y-y axis only as was done in the experiment (Shaat and Fam, 2007) additional restraint against movement in y direction has been applied at mid height of the column. For load application, elastic and stiff steel plates are modeled at both ends of the column using the same
Figure 5. Close view of 4-sided layered retrofitting materials.
Figure 6. Close view of the equivalent 4-sided retrofitting materials.
A 1 E 1 + A 2 E2 + ··········· + A n E n E e = -------------------------------------------------------------------A1 + A 2 + ··········· + A n
(1)
A 1 F y1 + A2 F y2 + ··········· + A n Fyn F yeqv = -------------------------------------------------------------------------A1 + A 2 + ··········· + A n
(2)
A eqv = A 1 + A2 + ··········· + A n
(3)
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Figure 7. (a) 3D view of typical deformed shape for square HSS column specimen (b) Close view of deformed shape for square HSS column at point where maximum lateral deflection occurs (for compact section) (c) Close view of deformed shape (for non-compact section).
type of shell element as steel HSS column. The details of boundary conditions and loading are shown in Fig. 3. Also some sketches of finite element mesh are shown in Figs. 4, 5 and 6. For steel HSS columns and equivalent retrofitting materials, non-linear behavior has been incorporated in the model. For obtaining the load deflection diagram, nonlinear analysis has been performed both by considering NewtonRaphson method (Bathe, 1976) and Arc-Length Method (Crisfield, 1991). It has been observed that in detailed study of noncompact section, arc-length method (Crisfield, 1991) gives better post-peak load deflection curve showing the snap-back effect (if any) whereas Newton-Raphson method (Bathe, 1976) stops at the peak. But for both methods peak occurs at the same point, so there will be no problem in determining the maximum strength gains if we want to continue in either of the method. The typical deformed shape for the proposed model has been obtained as shown in Fig. 7.
3. Simulation of Experiments The finite element model needed to be verified against previously done experiments for its reliability and acceptability. For this purpose, experimental study performed by Shaat and Fam (2007) has been taken into consideration. Table 1 and Table 2 list some basic data relevant to the experiments of Shaat and Fam (2007). A comparison between the results of numerical analysis and the experiment (Shaat and Fam, 2007) are given in Table 3 as well as in Figs. 8 and 9. In the post peak regime, some deviation between the experimental and analysis results are observed. The reason for such deviation may lie in the fact that an equivalent material has been used for CFRP and GFRP layers. When material non-linearity begins different materials (e.g. CFRP, GFRP, epoxy resin etc.) undergoes incompatible strain followed by de-bonding and tensile failure. The equivalency of materials under such highly complex non-linear state holds only approximately true. However, considering the overall load vs.
Table 1. Material Properties used in Shaat and Fam (2007) Properties
Steel HSS Column
CFRP Sheets
GFRP Sheets
Epoxy Resin
200 480
230 510
14 269
3.18 72.4
Modulus of Elasticity (GPa) Tensile Strength (MPa)
Table 2. Geometric Properties used in Shaat and Fam (2007) Properties
Steel HSS Column
CFRP Sheets
GFRP Sheets
Epoxy Resin
Thickness (mm) Length (mm) No. of Layers Cross Section
3.2 2380 89×89 mm
0.54 2380 n=1, 3 and 5 74×0.54×n layers
1.46 2380 1 74×1.46×1 layer
0.5 2380 74×0.5×1 layer
Non-Linear Finite Element Investigation on the Behavior of CFRP Strengthened Steel Square HSS Columns under Compression 675
Figure 8. Load vs. Axial Displacement behavior for axially loaded unstrengthened/strengthened HSS column specimen.
displacement responses, it can be said that a reasonably good agreement exists between test results and finite element analysis from the observation of Figs. 8 and 9.
Figure 9. Load vs. Lateral Displacement behavior for axially loaded unstrengthened/strengthened HSS column specimen.
Thus the proposed finite element modeling scheme can be reliably used as a replacement procedure for costly lab experiments.
Table 3. Comparison between Experimental and Numerical Model Results Specimen Identification
KL/r
89×89×3.2 (Control) 89×89×3.2 (1L-2S) 89×89×3.2 (3L-2S)
68
Maximum Load Out of Straightness e’ (Numerical Analysis/ Exp. of Shaat and Fam (mm) Exp.) Ratio Numerical Analysis (2007) 6.60 0.92 7.04
295 355 335
268 400 364
0.91 1.13 1.09
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4. Parametric Study and Discussion A parametric study on AISC square HSS (Hollow Structural Section) column sections available in the AISC manual of Steel Construction (13th edition 2005) has been carried out using the proposed finite element model. Preference has been given on the study of non-compact sections, since such sections are more susceptible to local buckling. Seven HSS sections chosen for parametric study are HSS16×16×5/16, HSS14×14×5/16, HSS12×12×3/16, HSS9×9×1/8, HSS7×7×1/8, HSS5×5×1/8, and HSS3×3×1/8. A total of 168 square HSS column sections, 24 of each, varying the slenderness ratios (from 0.25Cc to 1.5Cc with an increment of 0.25Cc) and number of CFRP layers (control, 1, 3, and 5 layers), are considered for conducting the parametric study. Material properties are taken same
as those used in the experimental analysis of Shaat and Fam (2007). Results obtained from the numerical simulation are shown in Fig. 10(a) to 10(f).
4.1. Effect of number of CFRP layers on Strength The effect of number of CFRP layers on the behavior of AISC HSS column sections under compressive load have been observed by using bar charts presented in Fig. 11 which clearly shows that the application of CFRP materials to the unstrengthened square HSS column sections is capable of increasing their strength. This axial strength gain increases with the increase in the number of CFRP layers (Figs. 12, 13, and Fig. 14). Whenever the steel HSS column is subjected to deformation due to axial loading, the external bonding of CFRP strips provides sufficient restraining effect against
Figure 10. (a) Maximum load obtained with varying slenderness ratio and varying no. of CFRP layers for AISC steel column HSS 3×3×1/8.
Figure 10. (b) Maximum load obtained with varying slenderness ratio and varying no. of CFRP layers for AISC steel column HSS 7×7×1/8.
Figure 10. (c) Maximum load obtained with varying slenderness ratio and varying no. of CFRP layers for AISC steel column HSS 9×9×1/8.
Non-Linear Finite Element Investigation on the Behavior of CFRP Strengthened Steel Square HSS Columns under Compression 677
Figure 10. (d) Maximum load obtained with varying slenderness ratio and varying no. of CFRP layers for AISC steel column HSS 12×12×3/16.
Figure 10. (e) Maximum load obtained with varying slenderness ratio and varying no. of CFRP layers for AISC steel column HSS 14×14×5/16.
Figure 10. (f) Maximum load obtained with varying slenderness ratio and varying no. of CFRP layers for AISC steel column HSS 16×16×5/16.
elastic deformation and also delayed the local buckling and as a result the ultimate strength capacity is increased. Application of CFRP causes an increase in effective thickness which reduces the width-to-thickness ratio of cross sectional elements. This decrease in the slenderness of crosssectional elements actually results in a delayed local buckling which ultimately enhances overall buckling strength of columns.
4.2. Effect of Cross Sectional Geometry on Strength For relatively large AISC square HSS columns, such as for HSS16×16×5/16 and HSS14×14×5/16, the percentage gain in axial strength is only approximately by about 1 to 20% due to CFRP strengthening with increasing number of layers (1, 3 and 5) (Fig. 12). Addition of CFRP layers
does not significantly contribute in increasing the effective thickness or reducing the width-thickness ratio of the elements of the section. The axial load carrying capacity is generally governed by the local buckling which depends on the width-thickness ratio of cross-sectional elements. Since width-thickness ratio does not decrease significantly, therefore strength gain is also not very significant. On the other hand, for comparatively medium and small AISC square HSS sections, addition of CFRP layers can significantly increase the effective thickness or decrease the width-thickness ratio of the cross sectional elements. This prevents or delays the onset of local buckling, resulting in a significant increase in strength by upto 90% (Figs. 13 and 14).
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Figure 11. Effect of number of CFRP layers on the strength of AISC HSS column sections for different slenderness ratio.
5. Conclusion In this study, a three dimensional finite element model of HSS steel column has been developed for the purpose of predicting the axial strength of column strengthened using CFRP materials. Verification of this finite element model has been demonstrated with reference to the experiment of Shaat and Fam (2007) and good agreement has been found. This authenticates the validity and acceptability of performing further study using this numerical model instead of conducting comparatively expensive experimental study. For this reason, the proposed model is then used for performing the parametric study on some of the non-compact square HSS column sections from
AISC Manual (13th edition, 2005) with varying CFRP layers and slenderness ratios. Based on the parametric study the following conclusions are drawn. (1) Carbon Fiber Reinforced Polymer (CFRP) materials are capable of increasing the axial load capacity of the steel HSS columns. The axial strength of column specimens can even be possible to increase up to two times to that of control/unstrengthened specimens irrespective of number of CFRP layers and slenderness ratios. (2) The capacity increases with the increase in the number of CFRP layers. The application of CFRP strips increases the effective thickness of the steel HSS column reducing the slenderness value of the cross-sectional elements which ultimately results in a delayed local
Non-Linear Finite Element Investigation on the Behavior of CFRP Strengthened Steel Square HSS Columns under Compression 679
Figure 12. Percentage gain in axial strength for a larger section HSS 16×16×5/16.
Figure 13. Percentage gain in axial strength for a relatively smaller section HSS 9×9×1/8.
Figure 14. Percentage gain in axial strength for a relatively smaller section HSS 3×3×1/8.
buckling as well as increasing the overall buckling strength of columns. (3) For relatively large AISC square HSS columns, the axial strength gain is only approximately by up to 20% due to CFRP strengthening with increasing number of layers (1, 3 and 5). On the other hand, for comparatively medium to small AISC square HSS sections, there is a significant increase in strength due to CFRP strengthening by up to 90% with the increasing number of CFRP layers.
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