Analytical Confining Model of Square Reinforced Concrete Columns using External Steel Collars

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1 International Journal o ICT-aided Arhiteture and Civil Engineering, pp Analytial Conining Model o Square Reinored Conrete Columns using External Steel Collars Pamuda Pudjisuryadi 1, Tavio 2 and Priyo Suprobo 3 1,2,3 Sepuluh Nopember Institute o Tehnology (ITS), Surabaya, Indonesia 1 ppamuda@yahoo.om, 2 tavio@e.its.a.id, 3 priyo@e.its.a.id Abstrat Coninement in onrete olumn has been well known to improve its strength and dutility. Up to present, traditional transverse steel is still used as internal oninement in onrete olumn. Many researhers have proposed various stress-strain relationships or onined onrete under dierent onditions. In general, all these models suggested inreases both in ompressive strength and dutility. The improved dutility is haraterized by the inrease o ultimate ompressive strain and the latter post-peak desending branh o the urve. Reently, researh on onrete oninement has been developed urther rom internal to external tehniques. The inreasing demand o reinored onrete olumn retroits is the main reason to develop suh tehniques. Some external tehniques have been proven to be suessul in retroitting irular onrete olumns. Experimental programs as well as onining models or externally onined irular olumns have been developed. However, it is hard to provide an eetive onining stress by external retroit on square or retangular onrete olumn. The non-uniorm onining stress on olumn was due to high stress onentration at the olumn orners. Only a ew experimental and analytial studies addressed these issues. This paper proposes an analytial model or prediting the peak strength o square onrete olumns onined by external retroit as well as the shape o the improved stress-strain urve. Analytial study is also presented to provide a brie idea on the proposed analytial model in omparison with some developed models. The proposed model is also ompared with the experimental results by other researhers. It is shown that the proposed analytial model an predit the behavior o externally retroitted square onrete olumns reasonably well. Keywords: analytial model, external retroit, square onrete olumns, stress-strain urve 1. Introdution The oninement onventionally provided by transverse reinorement has been well known to signiiantly enhane the strength and dutility o the olumns [1-4]. Many analytial and experimental studies onduted to investigate the eets o oninement an be ound in literatures [1-19]. The studies over irular, retangular, and square olumn setions. The loadings on the speimens inlude axial and ombined axial and bending in monotoni and yli patterns. The analytial models predit only the envelope urves, in the ase o yli loading. It is generally onluded that the aeting variables o onined onrete behavior are the plain onrete ompressive strength, volumetri ratio o oninement steel to onrete ore, yield strength o onining reinorement, ratio o area o longitudinal steel around the ore perimeter and the resulting tie oniguration, and tie spaing. General agreements on the improved stress-strain relationship o onined onrete ISSN: IJIACE Copyright 2014 SERSC

2 International Journal o ICT-aided Arhiteture and Civil Engineering are the inrement o ompressive strength, latter post peak desending branh o the urve, and inrement o ultimate ompressive strain (inrement o dutility). Besides the onventional oninement studies, reent researh are extended to external oninement approah [5-8]. It is essential to develop suh approah due to the high demand o onrete olumns retroits. Early studies mainly deal with retroitting irular onrete olumns, and have been proven by experiments to be suessul. However, or retangular and square olumns, prediting eetive onining stress by external retroit is not a simple task. Similar to internal oninement on these setional shapes, the onining stress is not uniorm due to stress onentration in the orners. Some experimental and only a ew analytial studies are ound to address this problems [9-11]. The omplexity o external oninement inludes ailure mehanism, ontat behavior between onrete and external oninement elements, and distribution o onining stress in 3D spae, whih an be totally dierent to those o onventional stirrups. In this paper, an analytial model o axial stressstrain urve o square olumns onined by external steel ollars is proposed. The researh should provide better understanding o the external steel ollar oninement behavior whih aids a reliable use o this method on square onrete olumns. 2. Proposed Eetive Equivalent Uniorm Conining Pressure ( e ) In an externally onined onrete model, deinition o onining pressure an be modiied rom available deinitions whih were developed on the basis o internal oninement model. It is important to predit this onining stress, sine it is the basis to determine the peak strength and generate the stress strain urve. This paper proposes new model to deine eetive equivalent uniorm onining pressure or external oninement model ( e ). Firstly, onsider a typial square onrete olumn whih is externally retroitted by steel ollars (by steel angle setions in this explanation) as illustrated in Figure 1. The notations b, S, and S are the dimension o the square olumn, spaing o steel ollar elements, and lear spaing o steel ollar elements, respetively. In a plane aross the setion, the onining stress is not uniorm as shown in Figure 2(a). Normally, paraboli-shaped regions at the sides o the olumns (the shaded area) are assumed to be ineetive due to relatively weaker middle side oninement ompared to the stier orners. The expression o the ineetively onined area (A par ) is adopted rom Mander, Priestley, and Park [2, 3] and Lee, Hegemier, and Phillippi [11] as expressed in Eq. 1. A par 2 b 3 2 Similar ineetive onine regions are also assumed in vertial diretion between adjaent oninement elements as in Figure 2(b). With onsideration o both ineetive regions in horizontal and vertial diretions, and average eetively onined ross setional area, A e, an be adopted rom Mander, Priestley, and Park [2, 3] as expressed in Eq. 2. (1) A e 2 A par S A 1 1 A 2 b (2) where A is the ore area (whih is equal to the gross setion area o the olumn in the ase o externally onined olumns). Further, a ator desribing oninement eetiveness (k e ) an be expressed in Eq Copyright 2014 SERSC

3 International Journal o ICT-aided Arhiteture and Civil Engineering k e A A e where A is the net ore area o the olumns (A minus the area o longitudinal bars, i any). This ator is used to modiy the equivalent uniorm onining pressure (, whih is explained later) into the eetive equivalent uniorm onining pressure, e as expressed in Eq. 4. (3) e k e (4) Figure 1. Three-dimensional Illustration o the Typial Columns Figure 2. The Paraboli-Shaped Ineetively Conined Region at: (a) Cross Setion; and (b) Along the Height o the Column In onventionally onined onrete by using internal transverse reinorement, oninement will tend to be higher in the orner due to higher stiness. This at is also observed in the ase o externally onined square onrete olumns. Xiao and Wu [9] Copyright 2014 SERSC 3

4 International Journal o ICT-aided Arhiteture and Civil Engineering observed that external steel ollars provide the onining pressure through ombined bending and axial mehanism. This phenomenon is dierent rom the assumption or internal transverse reinorement whih only depends on axial ation beause o the relatively small bending stiness. Consider a bulged externally retroitted onrete olumn under axial loading in Figure 3(a). The steel ollars are assumed to deorm suh a way that they maintain the ompatibility o outward expansion o the onrete olumn. This deormation is logially larger at the mid-sides than at the orners. The steel ollars are assumed to ail in ombined axial and bending mehanism at the orners and mid-sides o the olumns (plasti hinges are developed). With the assumption o uniorm generated onining pressure, the equilibrium o the ores in ross setional plane an be seen in Figure 3(b) (only a quarter o the model is analyzed due to double symmetri ondition). By using an equilibrium ondition o ores, the axial ore (p) and the bending moment (m) developed in the steel ollars an be expressed as a untion o equivalent uniorm onining pressure ( ), dimension o olumn (b), and spaing o steel ollars (S), as expressed in Eqs. 5 and 6. p m b S 2 b 2 16 S (5) (6) Figure 3. (a) Bulged Steel Collars Due to Lateral Expansion o Axially Loaded Conrete Column; and (b) Equilibrium o Fores Analyzed at a Quarter o the Cross Setion With nominal axial and bending apaities (p n and m n ) o steel ollars given, and adopting riteria o ombined axial and bending ailure o steel (Eq. 7), an be alulated. In alulating nominal apaity, the redution ators () in Eq. 7, shall be taken as 1.0. p 8 m p 1 o r 1.0 p 9 m p (7a) n n n 4 Copyright 2014 SERSC

5 International Journal o ICT-aided Arhiteture and Civil Engineering p m p 1 o r 1.0 p m p 2 n n n (7b) Moreover, or bolted orners, there are hanes that the bolts ail beore the steel ollars [10]. In this ase, the plasti moment generated in Figure 3(b), should be modiied. I the plasti moment apaities o bolts and steel ollars are deined as m, and k m respetively, the new equilibrium ondition an be seen in Figure 4. Fator k deines the ratio o plasti moment apaities o steel ollars with respet to that o bolts (> 1.0). It an be shown that the moment generated in bolts an still be expressed as a untion o previous known variables (Eq. 8) and Eqs. 5 to 7 still an be used to alulate. m b S k (8) I the bolts are pre-tensioned signiiantly that they provide ative initial oninement pressure, urther modiiations are neessary. The inal equivalent uniorm onining pressure ( ) should be the resultant o initial onining pressure ( 0 ) and the alulated onining pressure rom Eqs. 5 to 8. In this ase, the nominal axial apaity o the bolts (p n ) in Eq. 7 should be redued by the initial pretension ore (F b ). With the assumption that pretension ores applied with inlined angle o 45 degrees (Figure 5(a)), the initial onining pressure ( 0 ) in Figure 5(b), an be expressed in Eq b S 2 F b (9) The alulated equivalent uniorm onining pressures ( ) is then modiied by using Eq. 4, into eetive equivalent uniorm onining pressures ( e ). The peak strength ( ) an be determined by using available analytial model in terms o unonined onrete strength ), and the proposed eetive equivalent uniorm onining pressure ( e ). ( 0 Figure 4. Equilibrium o Fores at a Cross Setional Plane (Modiied) Copyright 2014 SERSC 5

6 International Journal o ICT-aided Arhiteture and Civil Engineering Figure 5. (a) Pretension Fores in Bolts Conneting the Steel Collars at Corners; and (b) the Resulting Initial Conining Pressure 3. Proposed stress-strain Model or Externally Conined Conrete As explained in previous setion, one the onining pressure and orresponding peak strength determined, the stress strain urve an be generated by using available models. Many models have been developed, and mainly based on internally onined onrete. To develop suh model or externally onined onrete an be a very hallenging task. The shape o the stress strain urve will highly depend on the harateristis (ailure mehanism, dutility, et.) o external onining element. This setion will review some well established models developed or internally onined onrete. The models are then ompared to available experimental results o externally retroitted onined onrete by using steel ollars [10], and the neessary modiiations are proposed Mander et.al. Model [2] The widely used model proposed by Mander, Priestley, and Park [2, 3] expresses the stress-strain relationship with a single untion. Eqs. 10 to 16 show the orresponding model e r E E se E E E se x 0 e 0 (10) (11) (12) (13) (14) (15) 6 Copyright 2014 SERSC

7 International Journal o ICT-aided Arhiteture and Civil Engineering where 0 xr 2 r 1 x = ompressive strength o onined onrete (MPa) = ompressive strength o unonined onrete (MPa) = ompressive strain o onined onrete orresponding to = onrete strain E se = seant modulus (MPa) r = a onstant E = modulus o elastiity o plain onrete (MPa) = onrete stress as a untion o onrete strain (MPa) (16) 3.2. Razvi and Saatioglu Model [14] The Razvi and Saatioglu [14] proposed stress strain relationship o onined onrete with non linear asending branh and linear desending branh as expressed in Eqs. 17 to 24. where k k K k 1 0 e e 1 e K K = ompressive strain o onined onrete orresponding to = ompressive strain o unonined onrete orresponding to 01 0 = ompressive strain o onined onrete orresponding to = ompressive strain o unonined onrete orresponding to = volumetri ratio o oninement element with respet to onrete ore (17) (18) (19) (20) (21) (22) (23) (24) It should be noted that the values o 01 and 085 is valid or unonined onrete strength below 40 MPa, and the yield strength o onining element below 500 MPa. Otherwise, the expressions or the ase an be seen in literature [14]. Copyright 2014 SERSC 7

8 International Journal o ICT-aided Arhiteture and Civil Engineering 3.3. Modiied Tabsh Model [12] The model proposed by Tabsh [12] ombines Mander model [2, 3] and Hoshikusuma model [13] or the asending and desending branhes o stress-strain urve, respetively. The peak strength is determined exatly the same as Mander model (Eq. 10). The stressstrain urve an be generated using expressions given in Eqs. 25 to 29. E se r E E E se 6. 5 r s r r 1 E 1 1 r r 1 (25) (26) (27) (28) (29) where = ompressive strain o unonined onrete orresponding to 0 0 = volumetri ratio o external steel ollar with respet o onrete ore s A modiiation is proposed to stimulate the harater o externally onine onrete olumns. Strain orresponding to the peak stress in Eq. 25 seems to be quite large rom model proposed by Tabsh [12] whih was originally developed or high strength onrete olumn 6.5 onined by welded wire abri (WWF). The expression in Eq. 25 is modiied rom 3.8 original to take into aount the dierent eet o internal WWF and external Hollow s Square Setion (HSS) ollars oninement. 4. Comparison o Analytial Stress-Strain Models In order to give lear view o the models desribed in previous setion, some typial square onrete olumns externally retroitted by steel ollars are analyzed. The data o the mentioned speimens (namely S1, S2, and S3) as well as the resulting eetive equivalent 6.5 uniorm onining pressure ( e ) and peak strength ( ) are presented in Table 1. Stress-strain urves (normalized to ) are then generated analytially or eah desribed model. In this simulation, the unonined onrete strength ( ) is assumed as large as 85 perent o 0 ylinder ompressive strength ( ). It is assumed that there is no signiiant pretension ore in the bolts. s s 8 Copyright 2014 SERSC

9 International Journal o ICT-aided Arhiteture and Civil Engineering Table 1. Data o Column Speimens Desription Speimen S1 S2 S3 Column dimension, d (mm) 150 Steel ollar spaing, S (mm) Steel ollar setion, leg leg thikness (mm) HSS Volumetri ratio o onining element, Yield strength o steel ollar, (MPa) y (%) s Unonined onrete strength, (MPa) 0 20 Strain at unonined onrete strength, Modulus o elastiity, E (MPa) Eetive equivalent uniorm onining pressure, e (MPa) Peak strength o onined onrete, (MPa) Mander [2] & Tabsh [12] Peak strength o onined onrete, 240 (MPa) Razvi & Saatioglu [14] Figure 6. Stress-strain Curves o Speimens S1, S2, and S3 (Mander Model) Copyright 2014 SERSC 9

10 International Journal o ICT-aided Arhiteture and Civil Engineering Figure 7. Stress-strain Curves o Speimens S1, S2, and S3 (Razvi and Saatioglu Model) Figure 8. Stress-strain Curves o Speimens S1, S2, and S3 (Tabsh Model) 10 Copyright 2014 SERSC

11 International Journal o ICT-aided Arhiteture and Civil Engineering Figure 9. Stress-strain Curves o Speimens S1, S2, and S3 (Proposed Model) It an be seen in Figures 6 and 7 that the stress-strain model proposed by Mander, Priestley, and Park [2, 3] as well as Ravzi and Satioglu [4, 14], whih were developed using the extensive onventionally onined onrete olumns, possessed similar harateristis. The desending branhes in both models depend on the level o oninement. Steeper desending slopes are seen in speimens with lower oninement. This harater is widely aepted among researhers. More models ommonly emphasize on the shapes o the desending branh o the urves. Many models have been proposed or dierent onditions. To it the stress strain urve o olumns externally retroitted by steel ollars, vast experimental data are needed. Only a ew researhes have been done in this area. One o them is experiment done by Hussain and Driver [10]. The stress strain urves o these externally onined olumns are haraterized by relatively larger peak strain. Model proposed by Tabsh [12] seems to have suh riteria (Figure 8). This paper proposed a modiiation to Tabsh model by reduing the value o peak strain as explained in Setion 3.3 (Figure 9) to it the available experimental results. Comparisons o the disussed models with the experimental results are presented in Setion Stress-strain Comparison with Experimental Results Experimental results o other authors are used to veriy the analytial models. Hussain and Driver [10] onduted a ompression test o square olumns externally retroitted by Hollow Square Setion (HSS) steel ollars. Figure 10 shows the typial speimens and steel ollars, respetively. Eleven olumns were tested with desription as shown in Table 2. Other mehanial properties are available in Re. 10. In the experiment, the bolts used in Speimens C02 to C05 were pre-tensioned with dierent levels. Figure 11 shows the axial stress-strain urve o the olumns. Speimens C01, C02, C03, and C04 are analytially analyzed by the disussed analytial model desribed in Setion 3. Speimen C05 is exluded beause the test was not ompleted Copyright 2014 SERSC 11

12 International Journal o ICT-aided Arhiteture and Civil Engineering due to mahine apaity limitation. Speimens applied with welded orners are also exluded in this study (C06 to C09). Normalized analytial stress-strain urves are plotted against the experimental results. The omparison o analytial and experimental results is presented in Figures 12 to 15. Figure 10. Typial Collared Column Speimens: (a) Elevation View; (b) Bolted; and () Welded [10] Table 2. Desription o Column Speimens [10] 12 Copyright 2014 SERSC

13 International Journal o ICT-aided Arhiteture and Civil Engineering Figure 11. Normalized Stress-Strain Curves [10] Figure 12. Comparison o Normalized Stress-Strain Curves or Speimen C01 Copyright 2014 SERSC 13

14 International Journal o ICT-aided Arhiteture and Civil Engineering Figure 13. Comparison o Normalized Stress-Strain Curves or Speimen C02 Figure 14. Comparison O Normalized Stress-Strain Curves or Speimen C03 14 Copyright 2014 SERSC

15 International Journal o ICT-aided Arhiteture and Civil Engineering Figure 15. Comparison o Normalized Stress-Strain Curves or Speimen C04 It is shown in Figures 12 to 15 that the peak strength an be predited reasonably well. The igures also show that the proposed derivation o eetive equivalent uniorm onining stress is reliable. Only Speimen C03 indiates slightly higher deviation. Prediting peak strain is proven to be a more diiult task. Both Mander and Saatioglu models predit the peak strain onsiderably lower. The rate o strength degradation in both models also did not math the experimental results. Meanwhile, Tabsh model predit the peak strain signiiantly higher suh that the rate o degradation annot be observed. However, by modiying the value o the peak strain o Tabsh model (proposed model), it an be seen that the Tabsh model an predit the behavior o the speimen muh better than the other models. Strength degradations o Speimens C01 and C04 an be simulated by the proposed model, while all the other models ail to do so. Moreover, the post peak behavior o speimens observed rom the experimental results did not show any ertain pattern. Some speimens showed earlier ailure (C03 and C04), while test on C05 was not ompleted due to the limitation o the testing mahine apaity. 6. Conluding Remarks From above observations and disussions, some points an be onluded. Firstly, the proposed ormulation to alulate the eetive equivalent uniorm onining stress ( e ) an exellently predit the peak strength. Seondly, the basi shape o stress strain urves is best predited using Tabsh model. However, or externally onined onrete olumns, the peak strain suggested by Tabsh should be adjusted to lower values. The modiiation o expression in Eq. 25 to in this study might only be good or external Hollow Square Setion s s (HSS) ollars oninement. Furthermore, sine results rom Hussain and Driver [10] did not provide very lear pattern, more experimental programs (on square onrete olumns retroitted externally using steel ollars) are needed to urther veriy the proposed model. Copyright 2014 SERSC 15

16 International Journal o ICT-aided Arhiteture and Civil Engineering Aknowledgements This study is supported by the Department o Civil Engineering, Sepuluh Nopember Institute o Tehnology (ITS), Surabaya, Indonesia. The authors greatly aknowledge or all the support reeived. Reerenes [1] S. A. Sheikh, A Comparative Study on Coninement Models, ACI Journal, vol. 79, no. 4, (1982) July- August, pp [2] J. B. Mander, M. J. N. Priestley and R. Park, Theoretial Stress-Strain Model or Conined Conrete, Journal o Strutural Engineering, ASCE, vol. 114, no. 8, (1988), August 1, pp [3] J. B. Mander, M. J. N. Priestley and R. Park, Observed Stress-Strain Behavior o Conined Conrete, Journal o Strutural Engineering, ASCE, vol. 114, no. 8, (1988) August, pp [4] M. Saatioglu and S. R. Razvi, Strength and Dutility o Conined Conrete, Journal o Strutural Engineering, ASCE, vol. 118, no. 6, (1992) June, pp [5] Y. H. Chai, M. J. N. Priestley and F. Seible, Analytial Model or Steel-Jaketed RC Cirular Bridge Columns, Journal o Strutural Engineering, ASCE, vol. 120, no. 8, (1994) August, pp [6] M. Saai, H. A. Toutanji and Z. Li, Behavior o Conrete Columns Conined with Fiber-Reinored Polymer Tubes, ACI Material Journal, vol. 96, no. 4, (1999) July-August, pp [7] A. Z. Fam and S. H. Rizkalla, Coninement Model or Axially Loaded Conrete Conined by Cirular Fiber-Reinored Polymer Tubes, ACI Strutural Journal, vol. 98, no. 4, (2001) July-August, pp [8] S. A. Carey and K. A. Harries, Axial Behavior and Modeling o Conined Small-, Medium-, and Large- Sale Cirular Setions with Carbon Fiber-Reinored Polymer Jakets, ACI Strutural Journal, vol. 102, no. 4, (2005) July-August, pp [9] Y. Xiao and H. Wu, Retroit o Reinored Conrete Columns using Partially Stiened Steel Jakets, Journal o Strutural Engineering, ASCE, vol. 129, no. 6, (2003) June, pp [10] M. A. Hussain and R. G. Driver, Experimental Investigation o External Coninement o Reinored Conrete Columns by Hollow Strutural Setion Collars, ACI Strutural Journal, vol. 102, no. 2, (2005) Marh-April, pp [11] C. S. Lee, G. A. Hegemier and D. J. Phillippi, Analytial Model or Fiber-Reinored Polymer-Jaketed Square Conrete Columns in Axial Compression, ACI Strutural Journal, vol. 107, no. 2, (2010) Marh- April, pp [12] S. W. Tabsh, Stress-Strain Model or High-Strength Conrete Conined by Welded Wire Fabri, Journal o Materials in Civil Engineering, ASCE, vol. 19, no. 4, (2007) April, pp [13] J. Hoshikusuma, K. Kawashima, K. Nagaya and A. W. Taylor, Stress-Strain Model or Conined Reinored Conrete in Brigde Piers, Journal o Strutural Engineering, ASCE, vol. 123, no. 5, (1997) May, pp [14] S. Rasvi and M. Saatioglu, Coninement Model or High Strength Conrete, Journal o Strutural Engineering, ASCE, vol. 125, no. 3, (1999) Marh, pp [15] T. and B. Kusuma, Stress-Strain Model or High-Strength Conrete Conined by Welded Wire Fabri, Journal o Material in Civil Engineering, ASCE, Disussion, vol. 21, no. 1, (2009) January, pp [16] T., B. Kusuma and P. Suprobo, Experimental Behavior o Conrete Columns Conined by Welded Wire Fabri as Transverse Reinorement under Axial Compression, ACI Strutural Journal, vol. 109, no. 3, (2012) May-June, pp [17] T., I. N. Budiantara and B. Kusuma, Spline Nonparametri Regression Analysis o Stress-Strain Curve o Conined Conrete, Civil Engineering Dimension, Petra Christian University, vol. 10, no. 1, (2008) Marh, pp [18] T. and A. Tata, Prediting Nonlinear Behavior and Stress-Strain Relationship o Retangular Conined Conrete Columns with ANSYS, Civil Engineering Dimension, Petra Christian University, vol. 11, no. 1, (2009) Marh, pp [19] T., I. Wimbadi, A. K. Negara and R. Tirtajaya, Eet o Coninement on Interation Diagrams o Square Reinored Conrete Columns, Civil Engineering Dimension, Petra Christian University, vol. 11, no. 2, (2009) September, pp Copyright 2014 SERSC

17 International Journal o ICT-aided Arhiteture and Civil Engineering Authors Pamuda Pudjisuryadi, is a Ph.D. Candidate in the Department o Civil Engineering, Sepuluh Nopember Institute o Tehnology (ITS), Surabaya, Indonesia. He reeived his Master Degree rom the Shool o Civil Engineering at Asian Institute o Tehnology (AIT), Bangkok, Thailand. His researh interests inlude strutural analysis, earthquake engineering, and retroitting method o reinored onrete strutures. Tavio, is a Proessor o Civil Engineering at ITS. He reeived his Ph.D. rom the Shool o Civil and Environmental Engineering at Nanyang Tehnologial University (NTU), Singapore. He is a Member o the Joint ACI-ASCE Committee 441: Reinored Conrete Columns, International Assoiation or Lie-Cyle Civil Engineering (IALCCE), Amerian Conrete Institute (ACI), and Preast/Prestressed Conrete Institute (PCI). His researh interests inlude numerial modeling o reinored onrete strutures, behavior o lat plates, preast and prestressed onrete strutures, and behavior o onined onrete olumns under seismi loading. Priyo Suprobo, is a Proessor o Civil Engineering at ITS. He reeived his Ph.D. in ivil engineering rom Purdue University. His researh interests inlude inite element modeling, strutural analysis, and strutural reliability. Copyright 2014 SERSC 17

18 International Journal o ICT-aided Arhiteture and Civil Engineering 18 Copyright 2014 SERSC