A new model for calculating impact force and energy dissipation based on the CR-factor and impact velocity

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1 Scientia Ianica A (015) (1), 59{68 Shaif Univesity of Technology Scientia Ianica Tansactions A: Civil Engineeing A new odel fo calculating ipact foce and enegy dissipation based on the -facto and ipact velocity H. Nadepoua;, R.C. Baosb and S.M. Khataia a. Faculty of Civil Engineeing, Senan Univesity, Senan, Ian. b. Faculty of Engineeing, Univesity of Poto, Poto, Potugal. Received 17 August 013; eceived in evised fo 7 Januay 014; accepted 7 July 014 KEYWORDS Abstact. Many eseaches have studied building pounding to calculate the dissipated 1. Intoduction daages wee due to the ipact of adjacent buildings. Investigation of building pounding has been divided into two pats: expeiental tests and nueical analyses. In this egad, Papadakakis and Mouzakis [3] conducted shaking table expeients on pounding between two-stoy einfoced concete buildings without sepaation distance unde eathquake ecods. Two steel buildings, with thee and eight stoies, wee tested by Filiatault using a shaking table [4]. The tests wee caied out with two di eent gaps, zeo and 15. The expeiental esults wee copaed with analytical pedictions based on the linea elastic sping theoy. The copaisons showed that acceleation at the contact level was not well pedicted. Watanaba and Kawashia [5] investigated the pounding of distibuted asses to odel colliding bidge decks. Cole et al. [6] indicated that building pounding and its ipact depend on the stuctual popeties and collision velocity of both buildings. They suggested a plan to contol the ipact. They deteined the Ipact; Coe cient of estitution; Velocity; Dissipated enegy; Daping. enegy and ipact foce between two buildings duing an eathquake. In this pape, a new equation is poposed to easue the ipact foce and enegy dissipation. The esults based on the poposed equation ae copaed with the esults of available equations. Using a suggested link eleent, a new foula is pesented to calculate the ipact foce and enegy dissipation. In ode to evaluate the esults of dissipated enegy, a new elation between and ipact velocity is also suggested. Since thee is a need to have a efeence cuve to select ipact velocity, based on the coe cient of estitution, seveal ipact velocities and s wee evaluated. By using the latte cuve, esults could be evaluated. A new equation of otion is assued to select the best ipact velocity and coe cient of estitution. Finally, based on the coe cient of estitution and using the steady-state esponse of a single degee of feedo syste, due to extenal foce, a new equation of otion is suggested to calculate the ipact daping atio. 015 Shaif Univesity of Technology. All ights eseved. Stuctual pounding, which ay occu duing an eathquake between two adjacent buildings with di eent dynaic chaacteistics, has been an inteesting eseach topic duing the last few decades in the eld of eathquake engineeing. Most eseaches have used nueical ethods to siulate the poble of eathquake-induced pounding between adjacent buildings [1]. All this eseach was caied out based on building pounding with di eent topics. Anagnostopolos [] was aong the st eseaches to explain possible danges due to building pounding. Between the, the 1985 Mexico City eathquake was the souce of excitation which caused sevee daage to buildings. Seveal epots showed that at least 15% of buildings *. Coesponding autho. Tel.: ; Fax: E-ail addess: nadepou@senan.ac.i (H. Nadepou)

2 60 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{68 theoetical axiu collision foce fo a syste with two distibuted asses. Velocity, ass and stiness at the tie of ipact have a elationship, and the nube and agnitude of the ipacts depend on these thee causes. Baos and Khatai [7] addessed soe coon isepesentations in the Ianian eathquake safety codes on the issue of the sepaation distance equied between two adjacent concete buildings unde nea-fault gound otions. In nueical analyses, link eleents ae located between the two investigated buildings. Koodoos et al. also took advantage of link eleents extensively in thei eseach [8]. Baos and Vasconcelos [9] investigated building pounding between two adjacent concete buildings by nueical analyses. They pesented the esults of analyses using dieent stiness and daping atios. Two concete buildings, with eight and ten stoies, have been odeled by Raj pant and Wijeyewickea [10]. Dieent types of sping with dieent stiness, o vaious dapes with dieent daping atios, have also been used in ecent nueical studies at FEUP by Codeio [11] and Vasconcelos [1] in thei paaetic studies of pounding between adjacent buildings. Baos and Khatai [13] estiate the eect of daping atio on the nueical study of ipact foces between two adjacent concete buildings subjected to pounding. In yet anothe study, Baos and Khatai [14] copaed esults of two SDOF faes with dieent link eleents based on atheatical elations. In soe of thei analyses, stuctues wee odeled as SDOF systes, and a collision was siulated using linea visco-elastic odels of ipact foce. Many eseaches have epesented seveal atheatic elations to siulate kinetic enegy loss. They have suggested dieent foulas in tes of daping coecient, and developed a efeence elation to get the best equation of otion. In this pape, based on a cyclic pocess, a new daping coecient is suggested to calculate ipact foce, and is checked to con dissipated enegy.. Ipact philosophy Investigation of building pounding can be addessed in two dieent paths: expeiental analyses and analytical analyses. To easue the ipact foce duing collisions and the lateal displaceent of adjacent stuctues, softwae is needed to dene a specic link eleent at the connection level between the buildings analyzed. These link eleents can be signicantly dieent, so as to insue a coplete ageeent between analytical and expeiental esults, based on type of link eleent. Matheatical equations coesponding to odeling by distinct link eleents can be calculated by dieent appoaches. The ain concepts used on link eleents coespond to the appopiate use Figue 1. Scheatic ipact odel between two bodies. Figue. Scheatic SDOF odel. of gap, sping and dape in the. As peiods of the adjacent colliding buildings ae conceptually dieent, the link eleents should be able to allow and tanslate the dieent behavio of buildings duing seisic excitations [13]. In the dynaics of stuctues, the explanation and undestanding of the ipact odel focus on the usual case of two bodies. The ipact foces and the consequences between two colliding bodies (Figue 1) depend on thei ass and acceleation. 3. Dynaic odel Two special building cases of an oiginal n-building foulation subject to eathquake excitation ae investigated. This captues the essence of oe geneal esponse foulation by allowing the exaination of both inteio and exteio buildings. As shown in Figue, the adjacent buildings wee odeled as a Single Degee Of Feedo (SDOF) syste, with luped asses, 1 and. Thee is a distance (d) assued between two adjacent buildings. The stiness of the two buildings ae k 1 and k, and the linea viscose dape constants fo the buildings ae c 1 and c, espectively. The ipact between the two buildings was odeled by intoducing a sping and a linea viscose dashpot between the colliding buildings. The stiness of the sping between the buildings is s. these eleents act only when a collision occus. The coecient of dape has been shown by c. In ode to descibe the ipact between two colliding bodies using atheatical equations, the odel in Figue 3 can be equivalently odeled as the esponse of a SDOF syste. In Figue 3, V 1 and V ae velocities of both

3 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{68 61 Figue 3. Equivalently odel of SDOF odel. collided asses. The equation of otion of this SDOF syste is witten as: u + c _u + ku = f(t); (1) whee u is acceleation, and _u and u ae the velocity and lateal displaceent of the syste, espectively. All entioned options ae assued to be linea in ode to conveniently seach the appoxiate elationship between velocity and lateal displaceent using the knowledge of stuctual dynaics. The sping constants can be obtained as a function of the stiness of the colliding buildings. The dynaic equation fo the pounding between single degee of feedo systes can be witten as: u1 u + k1 + s + s 4. Link eleents c1 + c c _u1 c c _u s f1 = : () u f k u Linea ipact odel The st investigated odel is based on a linea ipact sping, which povides an elastic ipact foce on the link eleent, and siulates ipact foce using linea cuve stiness (Figue 4). The equation of the contact collision foce duing pounding, evaluated by the linea elastic odel, is given by: F c (t) = k k :(t); (3) in which k k is the stiness of the linea ipact sping, and (t) is the lateal displaceent of the colliding bodies. In this odel, the nueical value of ipact foce is based on a linea constant stiness, which cannot be accuately deteined, consideing that the chaacteistics of the studied buildings ae dieent and that they also povide axial stiness fo the distinct ipacts. This odel of the link eleent also is not Figue 4. Linea elastic odel. Figue 5. Hetz daped odel. able to calculate enegy losses duing ipact, which constitutes the ain disadvantage of the linea elastic odel. 4.. Nonlinea ipact odels The ipact odel between two bodies duing an eathquake has been shown using a sping and dape, which ae located paallel to each othe. The explanation of the ipact odel focuses on two stuctues next to each othe when they collide duing seisic excitation (Figue 5). The ipact foce between two bodies depends signicantly on collided asses, velocity and acceleation. In this pat, soe used odels ae deonstated to get a bette iage fo contact. To calculate the value of the enegy dissipation, soe eseaches have suggested dieent elations to siulate the daping atio. They have tied to get the ost appopiate assuption fo evaluating dissipated enegy duing collisions. A suay of pevious studies about the ipact daping atio of pounding shows that the suggested foula by Anagnostopolus [1] and two epesented foulas by Jankowski [15] ae based on the Coecient of Restitution () and calculating the ipact daping atio by atheatical elations. The coecient of estitution is a facto that siulates a elation between velocities befoe and afte collision. This elation could be witten as: 0 < = v befoe v afte < 1: (4) As shown, the coecient of estitution is calculated to be in the ange of 0 and 1. If becoes equal to 0, collision is pefectly plastic, and if becoes equal to 1, collision shows an elastic behavio Kelvin odel The st elation of the ipact odel is the Kelvin odel. This odel was poved by a linea viscoelastic ipact odel, in ode to calculate enegy loss duing ipact. In this odel, ipact foce at tie t is siulated by the following equation: F c (t) = k k :(t) + c _ (t); (5) whee k k is stiness, c is the ipact viscous daping coecient, (t) is lateal displaceent and (t) is elative velocity between the luped asses in contact at tie t. In this equation, the ipact viscous daping

4 6 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{68 coecient, c, is elated to the coecient of estitution,, which is explained by: 1 c = k k ; (6) 1 + = ln p + (ln ) : (7) In the above elation, c depends on, which has been descibed by the second witten elation. is a vecto fo 0 to 1, which descibes elastic and plastic ipact and is explained in the next pat. This foula was based on the assuption of an equivalent SDOF dynaic syste that epesents two bodies in contact and the consevation of enegy befoe and afte ipact Nonlinea viscoelastic odel To ipove the ipact odel, Jankowski [15] pesented an idea, wheein a nonlinea viscose dape is located paallel to the sping in ode to absob the enegy dissipation echanis. The equation of the nonlinea viscoelastic odel can be witten by: F c (t) = k h :(t) + c h _ (t); (8) c h = = k h p (t) ; (9) p 5 1 : (10) Hetz daped odel The ost ipotant used elation to calculate the ipact foce and dissipated enegy is called Hetz Daped, as witten in a geneal fo below: F c (t) = k h :(t) n + c _ (t): (11) The second te of the entioned foula descibes the ipact daping coecient, which is calculated by c = :(t) n. In ecent yeas, Ye Kun [16] suggested two atheatical foulas fo the estiation of ipact daping based on Coecient of Restitution (), stiness of sping (k) and ipact velocity (v ip ). In ode to evaluate dissipated enegy duing ipact, Lankaani [17] suggested a atheatic elation to calculate the ipact daping atio, which is deteined by: = 3k h(1 ) 4v ip : (1) By using a SDOF syste, Ye Kun (008) [16] assued that the daping coecient and stiness of equivalent ae linea to get a elation between lateal displaceent and velocity. He consideed the oentu and enegy balance between the stat and end of the collision to be equal. By this assuption, he suggested a new elation to calculate the ipact daping atio, which is witten by: = 3k k(1 ) : (13) ::v ip In ode to ipove the entioned foula, a developed equation was noted by Ye Kun (009) [18]. Based on a atheatical elation and consideing a oe accuate ethod, he calculated a new equation fo the ipact daping atio to incease the dissipated enegy. The poposed foula can be descibed by: = 8k h(1 ) : (14) 5::v ip Finally, using Table 1, dieent odels of pounding have been epesented. The advantages and disadvantage of the odels ae pesented. 5. Poposed nonlinea ipact odel Fo getting a efeence elation to cove the thee entioned ipact daping elations, a new equation of otion is suggested based on thee paaetes. c ip = f(k; ; v ip ): (15) As noted befoe, it is assued that the ipact daping coecient is a atheatical function, which calculates the enegy dissipation by using: c ip = k v ip n (1 ) : (16) Based on a cyclic pocess, c ip was calculated and checked to con the accuacy of the suggested foula. In this case, a cyclic pocess has been used to siulate the ipact of two assued bodies. Based on this pocess and using the coecient of estitution, two paaetes wee selected. Finally, the epesented foula was obtained by selecting n and. In ode to check accuacy and con the suggested elation, the enegy dissipation was calculated and copaed with kinetic enegy loss, which is pesented in Figue 6. Consequently, n and can be selected fo Table. Fo this elation, ipact foce is epesented by: F ip = 1:5 (k + c ip ): (17) By having SDOF asses ( = ipact foce can be calculated ), k and v ip,

5 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{68 63 Linea sping Table 1. Suay of pounding odel. Model Foula Advantage Disadvantage F c(t) = k k :(t) Easy ipleent in softwae Dissipated enegy cannot be odeled Kelvin- Voight F c(t) = k h :(t) + c _ (t) The constant of the dashpot deteines the aount of enegy dissipated The viscous eleent eains activated when the stuctues tend to be sepaated. Hetz daped F c (t) = k h :(t) n + c _ (t) The constant of the dashpot deteines the aount of enegy dissipated Table. Thee used unknown paaetes. E N M Figue 6. Copaison of esults of fou dieent foulas. Afte selecting, c ip is calculated and the hysteesis loop is depicted. In ode to exaine the eects of using dieent ipact odels, an analytical odel has been used to calculate the kinetic enegy loss and copae it with othe entioned elations. Fo exaple, the SDOF ass of two bodies is assued to be kn. The ipact stiness fo the used link eleent and ipact velocity is calculated as and 9.976, espectively. Fo siplifying the siulation of ipact, a suitable estiation of k and v ip is taken to be equal to and 10, in ode to be used in all foulas fo estiation of the ipact daping. The coecient of estitution is also assued to be Nueical analyses to investigate the accuacy of foula To evaluate and con the suggested equation, two single degee of feedo systes ae assued. In this evaluation, two bodies ae connected with each othe by a link eleent, which is odeled by a sping and dape. Two entioned eleents ae located paallel with each othe to calculate the ipact foce and also dissipated enegy. The ass of two bodies is assued to be 100 and 150 ton fo buildings A and B, espectively. The stiness of the sping is 000 and the ipact velocity is also estiated to be equal to 15. Coecients of estitution ae selected fo 0.1 to 0.9. A efeence lateal displaceent is used and its deivation is calculated to be the velocity of the SDOF systes. The suggested equation of otion is siulated to get the esults of the ipact and dissipated enegy. By using dieent e, the ipact cuve is depicted and dissipated enegy is calculated due to the hysteetic behavio of ipact. In ode to investigate the accuacy of the suggested foula, dissipated enegy is copaed with kinetic enegy loss, as pesented in Figues 7 and 8. Kinetic enegy can be descibed as [19]: E = 1 1 (1 )( ip ) : (18) 1 + In this siulation, assued coecients of estitution ae copaed with calculated coecients of estitution. In Table 3, the pecentage of eo is pesented.

6 64 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{68 Table 3. Eo in calculated coecient of estitution. Assued Calculated Eo Figue 7. Copaison of hysteesis loops by using dieent fo poposed nonlinea ipact foce. Figue 9. The pocedue that has been followed in ode to deive the foula that povides optiu and v ip. Figue 8. Eo estiation fo poposed nonlinea ipact foce. 6. Relation between coecient of estitution and ipact velocity Fo nueical analyses, the coecient of estitution,, is calculated. It sees that thee is a need to have a efeence cuve to select v ip based on the coecient of estitution, which is able to show the optiu esults in tes of dissipated enegy. To evaluate the ipact velocity, it is assued that the efeence velocity is 10 and the value of is 0.5. The pocedue that has been followed fo the deivation of the ipact velocity is deonstated in Figue 9. Fistly, the value of v ip is selected and the coecient of estitution is also assued. Afte each siulation, the kinetic enegy loss is checked as to whethe it equals the aea of the hysteesis loop Figue 10. The copaison of two dieent popeties. obtained fo the analysis, and, if not, the constant is odied and a new analysis is pefoed (Figue 10). Fo instance, analyses have shown that the dissipated enegy of the hysteesis loop, using v ip = 11 and =0.45 and the efeence odel, ae appoxiately equal. Kinetic enegy losses ae and in the efeence and second odels, espectively. By tting the nueical data, using the en-

7 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{68 65 Z f D d = Z =w o (c k _ ) _ dt = 0:5 _ nal ; (3) whee _ nal denotes the nal velocity and is an equivalent of two asses ( = ). In ode to solve Eq. (3) fo, the following equation is used: ax = 4k : _ nal : (4) Figue 11. Suggested cuve fo and v ip. tioned ethod in the chat, the following foula has been obtained elating the coecient of estitution. The estiated foula can be witten by: v ip =494: : :67: (19) It can be seen fo Figue 11 that Eq. (19) siulates quite pecisely the elation between the coecient of estitution and ipact velocity. It is woth entioning that the deceased tend in the ipact velocity fo inceasing the value of the coecient of estitution has been coned by Jankowsky [15]. 7. Relation between coecient of estitution and ipact daping atio () As noted in Eq. (19), the loss in kinetic enegy depends on ass, coecient of estitution and ipact velocity. The steady state esponse of the single degee of feedo syste, due to the extenal foce, p(t) = p 0 sin(wt), has been evaluated. Based on the entioned foce, the dissipated enegy due to the viscose dape in haonic excitation can be witten by the following the elation: E = Z f D d = Z =w 0 (c k _ ) _ dt: (0) Also, by focusing stongly on the daping te of equation of otion the following is obtained: E = Z ax 0 c k _ d: (1) Based on the equations of dynaics of stuctues [0]: E = w w n k ; () in which, w is adial fequency and w n is daped adial fequency. The elation between w and w n could be assued to be 1. Consideing nal velocity and ass, it could be witten as: Fo each value of defoation duing ipact, as the enegy tansfes fo elastic stain enegy to kinetic enegy, the elative velocity can be calculated as follows: k + 0:5 _ = 0:5 _ nal: (5) Solving Eq. (5), the following elation is obtained: 0:5 _ = 0:5 _ nal k : (6) Consequently, velocity would be: nal 4k : (7) Dening Relation (4) and consideing the displaceent of zeo ( = 0), it is an assuption that Eq. (7) can be changed by using the coecient of estitution to deteine the velocity duing collision fo _ > 0 and _ < 0. _ = _ nal 4k fo _ < 0 _ = 1 _ 4k nal fo _ > 0: (8) Using the dissipated enegy fo the dape and efeing to Eq. (0), it could be calculated by: E = p k: Z _d: (9) Consideing the above elations and subitting Eq. (8) into Eq. (9), the following is obtained: E = p k: Z _ nal by substituting Eq. (3) into Eq. (30): 4k ax E = p Z ax k: 0 4k d: (30) 4k The elation is siplied to Eq. (31): E = p 4k!Z ax p k: ax 0 d: (31) d; (3)

8 66 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{68 E = 4k 1:5 p Z ax p ax d: (33) 0 Solving Eq. (33), it can be epesented that the dissipated enegy will be: E = 4k 1:5 p (0:5 ax ): (34) Kinetic enegy loss, noted in Eq. (31), can be equal to the dissipated enegy fo the dape duing ipact, as: 1 1 (1 )( ip ) =4k 1:5 p (0:5 1 + ax ): (35) Figue 1. Copaison aong dieent foulations by using dieent values fo. Modifying ax fo Eq. (3) into Eq. (35), the following would be obtained: 1 1 (1 )( ip ) 1 + = 4k 1:5 p _ 0:5 nal 1 4k 1 +! : (36) Eq. (36) could be witten as: p (1 c )( ip ) : = : ( _ nal): (37) And, nally, the elation fo giving will be: Figue 13. Copaison of ipact foces aong thee dieent types of ipact daping atios. = : p (1 ) : (38) Consideing thee dieent, calculated fo past studies, a nueical analysis was caied out to copae thee ipact daping atios. In ode to investigate the calculated, a single degee of feedo is siulated to evaluate the ipact foce between two asses. Thee used dieent ipact daping atios fo Jankowski [15], Seyed Mahoud [1] and the entioned equation of otion, ae seen in Table 4. The esults of a copaison between ipact daping atios, based on the coecient of estitution, ae shown in Figue 1. The ipact daping atio is stated fo 61, 3.5 and 3. fo the poposed odel, Jankowski's odel, and Seyed Mahoud's odel, espectively. The esults tend to zeo fo all investigated odels. It sees that the suggested equation of otion Table 4. Utilized ipact daping atios. Jankowski's equation p 5 1 Seyed Mahoud's equation 1 1 Poposed equation = : p (1 ) Figue 14. Copaison of ipact foces aong thee coecients of estitution. in this pape can show an acceptable cuve between the two othe foulas. The cuve of this odel akes it sensible to get the ipact daping atio based on the coecient of estitution, as the esults ae close to each othe, fo =0.4 to =0.9 (Figue 13). To bette expess this, selecting dieent coecients of estitution fo 0.4 to 0.9 will have siila esponses, in tes of ipact daping atio and ipact foces (Figue 14). 8. Conclusion In this pape, building pounding duing seisic excitation has been investigated. Fistly, the concept of

9 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{68 67 ipact between two asses has been descibed to get a bette iage of collisions duing an eathquake. Two dieent types of link eleent have been explained. The st has a sping and the second has a sping and dape, which ae located paallel to each othe. Shown in Table 1, the advantages and disadvantages of link eleents have been investigated. The ajoity of equations of otion in tes of ipact foce have been collected, and ipact daping in tes of these elations has been deonstated. A new elation to calculate the value of daping has been suggested to get the best esults in tes of dissipated enegy. To evaluate the accuacy of the suggested foula, the elationship between the selected coecient of estitution and the calculated coecient of estitution has been plotted in a cuve. The esults show good accuacy in copaison with othe foulas. As thee is a need to have a efeence cuve to select v ip based on the coecient of estitution, a cyclic pocess was siulated to suggest the optiu elation between ipact velocity and coecient of estitution. To each this goal, the ipact velocity and coecient of estitution wee assued to be efeences. Based on this assuption, anothe ipact velocity and coecient of estitution is estiated and its hysteesis loop is depicted. Dissipated enegy is calculated and copaed with the enegy pinciple. If both ae equal, the assued velocity and coecient of estitution ae coned. If not, the pocess is epeated to get the best selection. Finally, a elation between the two investigated paaetes was epesented to pedict ipact velocity. Consideing the coecient of estitution, ipact velocity is calculated to have a siila esponse using dieent ipacts and coecients of estitution. A new elation between coecient of estitution and ipact daping atio has been pesented to evaluate linea and nonlinea ipact odels. Using atheatical elations and consideing the steady state esponse of single degee of feedo systes due to extenal foce, based on haonic foce, a new elation was suggested and copaed with othe suggested foulas. The calculated ipact daping atio depends signicantly on the coecient of estitution and shows bette esults in copaison with othe elations. Refeences 1. Yaghaei-Sabegh, S. and Jalali-Milani, N. \Pounding foce esponse spectu fo nea-eld and fa-eld eathquakes", Scientia Ianica, 19(5), pp (01).. Anagnostopouls, S.A. \Pounding of building in seies duing eathquakes", Eathquake Engineeing and Stuctual Dynaics, 16(3), pp (1998). 3. Papadakakis, M. and Mouzakis, H. \A Lagange ultiplie solution ethod fo pounding of building duing eathquakes", Jounal of Eathquake Engineeing and Stuctual Dynaics, 0, pp (1991). 4. Filiatault, A. and Wagne, P. \Analytical pediction of expeiental building pounding", Jounal of Eathquake Engineeing and Stuctual Dynaics, 4, pp (1995). 5. Kavashia, C.G. and Watanaba, K. \Eathquake induced inteaction between adjacent einfoced concete stuctual with non-equal heights", Eathquake Engineeing and Stuctual Dynaics, 34(1), pp. 1-0 (005). 6. Cole, G.L. and Dhakal, R.P. \The eect of diaphag wave popagation on the analysis of pounding stuctues", Poc. nd Int. Confeence on Coputational Method in Stuctual Dynaic an Eathquake Engineeing (COMPADYN), Geece (009). 7. Baos, R. and Khatai, S.M. \Ipotance of sepaation distance on building pounding unde nea-fault gound otion, using the Ianian eathquake code", 9th Intenational Congess on Civil Engineeing, Isfahan Univesity of Technology (IUT), Isfahan, Ian (01). 8. Koodoos, P. and Polycapou, P. \On the nueical siulation of ipact fo the investigation of eathquake-induced pounding of building", Tenth Intenational Confeence on Coputational Stuctues Technology, Civil-Cop Pess, Stilingshie, Scotland (010). 9. Vasconcelos, H. \Study about collision between einfoced concete building and copaison of thei esistance envelope by push ove analysis", MSc Thesis, FEUP, Potugal (011). 10. Raj, P. and Wijeyewickea, C., Seisic Pounding Between Reinfoced Concete Buildings: A Study Using two ecently poposed Contact Eleent Models, 14ECEE, Ohid, Macedonia (010). 11. Codeio, J.M.C. \Study of the collision between buildings without and with base isolation", MSc Thesis in Civil Engineeing, Poto, Potugal (011). 1. Vasconcelos, H.E. \Study of the collision between einfoced concete buildings and copaison of thei pushove capacities", MSc Thesis in Civil Engineeing, Poto, Potugal (011). 13. Baos, R.C. and Khatai, S.M. \An estiation of daping atio fo the nueical study of ipact foces between two adjacent concete buildings, subjected to pounding", 15th Intenational Confeence on Expeiental Mechanics (15th ICEM), Syposiu on \Dynaics and Stability", FEUP, pp. -7, Poto, Potugal (July 01). 14. Baos, R.C. and Khatai, S.M. \Building pounding foces fo dieent link eleent odels", Poceedings of the Eleventh Intenational Confeence on Coputational Stuctues Technology, Dubovnik, Coatia, pp. 4-7 (Septebe 01).

10 68 H. Nadepou et al./scientia Ianica, Tansactions A: Civil Engineeing (015) 59{ Jankowski, R. \Non-linea viscoelastic odeling of eathquake-induced stuctual pounding", Eathquake Engineeing and Stuctual Dynaics, 34, pp (005). 16. Ye, K. and Zhu, H. \A note on the Hetz contact odel with nonlinea daping fo pounding siulation", Eathquake Engineeing and Stuctual Dynaics., 38(9), pp (008). 17. Lankaani, S. \A Hetz contact odel with nonlinea daping fo pounding siulation", Eathquake Engineeing and Stuctual Dynaics., 35, pp (006). 18. Ye, K. and Zhu, H. \A odied Kelvin ipact odel fo pounding siulation of base-isolated building with adjacent stuctue", Eathquake Engineeing and Engineeing Vibation, 8, pp (009). 19. Goldsith, W. \Ipact: The theoy and physical behavio of colliding solids", Edwad Anold: London, U.K. (1960). 0. Chopa, A.K., Dynaics of Stuctues, Theoy and Applications to Eathquake Engineeing, Univesity of Califonia at Bekeley (1995). 1. Mahoud, S. and Jankowski, R. \Modied linea viscoelastic odel of eathquake induced stuctual pounding", Ianian Jounal of Science & Technology, 35(C1), pp (011). Biogaphies Hosein Nadepou was bon in 1981 in Tehan, Ian. He obtained his BSc, MSc and PhD degees in Civil and Stuctual Engineeing in 003, 006 and 010, espectively. He then joined Senan Univesity whee he is pesently assistant pofesso of Stuctual Engineeing. He is also the diecto of eseach aais in Senan Univesity. D. Nadepou is autho of 30 papes published in jounals and 70 papes pesented at national and intenational confeences. He has given seveal speeches in Switzeland, China, Austalia, Canada, Belgiu, Potugal, Spain, Geany, Italy and Fance. His eseach inteests include: aticial intelligence, coposite stuctues, stuctual eliability, stuctual optiization, design and constuction of extenally bonded FRP systes fo stengthening concete stuctues and base isolation systes. Rui Manuel de Menezes e Caneio de Baos was gaduated in Civil Engineeing fo Faculty of Engineeing Univesity of Poto (FEUP), Potugal (l974). He eceived his MSc degee in Ocean Engineeing at the Univesity College, London, England (l976), and his PhD degee in Civil Engineeing at the Univesity of Akon, Ohio, USA (1983). Since 1983, he has been a Pofesso in the Civil Engineeing Depatent of the Univesity of Poto (FEUP). He is the autho of oe than 0 published scientic papes (70than 90 intenal technical epots, and nueous handwitten and pinted couse-notes fo undegaduate and gaduate use. Pesently, he is the FEUP univesity scientic coodinato of an industial collaboative poject with the Metalogalva (Poject VHSS-Poles fo duation of 3 yeas, and a total budget of aound 1 illion euo), fo addessing the constuction and cetication of an expeiental station on an industial plant at nothen Potugal. Besides, he had 11 invited speeches in Potugal, has given 5 invited speeches in Chile, Bazil, Thailand, China, Singapoe, Lithuania, Italy, Ieland, Malta and Denak. Duing May 005 and also duing July 010, he has been `Exchange Pofesso', espectively, at Kaunas Technical Univesity and Vilnius Gediinas Technical Univesity, both in Lithuania, unde an Easus Mobility Gant fo Pofessos. Seyed Mohaad Khatai was bon in 198 in Senan, Ian. He obtained his BS and MS degees in Stuctual Engineeing in 007 and 010, espectively. His eseach inteests include: dynaics of stuctues, building pounding, and nonlinea analysis of RC stuctues. He is pesently a PhD student in Senan Univesity. M. Khatai is autho of 5 papes published in jounals and 30 papes pesented at national and intenational confeences.