Rev. Téc. Ing. Univ. Zulia. Vol. 37, Nº, 97-05, 04 Pobabilistic assessment of the stuctual safety of a type of bolted and welded connections fo seismic zones David De León, Alfedo Reyes, Cheng Yu 3 Facultad de Ingenieía, Univesidad Autónoma del Estado de México. Ciudad Univesitaia, Toluca, Estado de México. daviddeleonescobedo@yahoo.com.mx Facultad de Ingenieía, Univesidad Autónoma de Sinaloa. aeyes@uas.uasnet 3 Depatment of Engineeing Technology, Univesity of Noth Texas, USA. Cheng.Yu@unt.edu Abstact The findings about the fagile behavio of steel welded connections afte the Nothidge 994 eathquake, specially fo fames designed to withstand lateal foce, has bought an amount of new attention to the design and safety issues of the welded connections fo stuctues located on seismic zones. In México, pactitiones and designes ae facing the poblem of the seismic effectiveness of the seveal kinds of connections as cuently poposed fo the design of steel stuctues. A decision must be made to balance the safety equied with the costs incued afte exceeding the seviceability limit state. Stuctual eliability techniques povide the pope famewok to include the inheent uncetainties into the design pocess. Registeed motions afte the 985 Mexico City eathquake ae popely scaled accoding to the seismic hazad cuve fo soft soil in Mexico City. Eathquake occuence is modeled as a Poisson pocess and the expected life-cycle cost is taken as the decision citeia. Paametic analyses allow the identification of dominant vaiables and anges whee one option is moe ecommendable than the othe one. The poposed fomulation may suppot designes and buildes on the analyses and justification pocess towads the selection of the convenient connection type fo the seismic zones with soft soil in Mexico City. Key wods: bolted and welded connections, seismic esponse, life-cycle expected cost, seismic isk. Evaluación pobabilista de la seguidad estuctual de un tipo de conexiones atonilladas y soldadas paa zonas sísmicas Resumen Los hallazgos del compotamiento fágil de conexiones soldadas de aceo después del temblo de Nothidge de 994, especialmente paa macos diseñados paa esisti cagas lateales, ha taído la atención en los aspectos de seguidad y diseño de conexiones soldadas paa estuctuas localizadas en zonas sísmicas. En México, ingenieos de la páctica y diseñadoes se están peguntando cuál seá la efectividad sísmica de vaias altenativas de conexiones utilizadas en estuctuas de aceo. Se deben toma decisiones paa equiliba el nivel equeido de seguidad con los costos en que se incue cuando se excede un estado límite. Las técnicas de confiabilidad estuctual poveen del maco adecuado paa inclui explícitamente las incetidumbes inheentes al poceso de diseño. Movimientos del teeno egistados en el temblo de la Ciudad de México de 985 se escalan apopiadamente de acuedo a la cuva de iesgo sísmico de la zona de suelo blando de México, DF. La ocuencia de tembloes se modela de acuedo a un poceso de Poisson y se toma como citeio de decisión el costo espeado en el ciclo de vida. El análisis paamético pemite
98 De León et al.. la identificación de vaiables dominantes y se identifican angos en los que una opción, de las conexiones popuestas, es más ecomendable que la ota. La fomulación popuesta puede apoya a diseñadoes y constuctoes en el poceso de toma de decisiones aceca de la selección del tipo conveniente de conexión paa zonas sísmicas como la Ciudad de México. Palabas clave: conexiones atonilladas y soldadas, espuesta sísmica, costo espeado en el ciclo de vida, iesgo sísmico. Intoduction Steel buildings ae a common design solution fo seismic zones. Howeve, the selection of the appopiate connection type is still an issue in Mexico. Special inteest has been aised about the fagile behavio of welded connections, especially afte the amount of damages expeienced due to the Nothidge eathquake [] occued in Califonia in 994. The SAC Poject [], developed in the US unde FEMA s coodination, povided some insight to impove the undestanding of the seismic behavio of welded connections [3, 4]. In Mexico, some effots have been made to deive pactical ecommendations fo steel connections [5-8]. Altenate loading is an impotant facto to poduce cumulative damage [9] and, ecently, the factue mechanism of typical connections has been studied unde the light of eliability analyses [0]. Usually the collapse limit state is emphasized to povide design ecommendations [, ] but, given the chaacte and extension of the damage poduced by some eathquakes and the time the stuctue is off-sevice duing epais, the seviceability condition is also a concen. Stuctual eliability and life-cycle costing [3] seve as the measuing tools to weigh the cost/benefit elevance of the vaious connection altenatives and to balance the tade-off between equied safety and costs of the damage consequences. A seismic hazad cuve, peviously developed fo Mexico City [4] is used with scaling factos to assess the seismic vulneability of the stuctues. Given the uncetain natue of the foces at the connection, as a consequence that the seismic envionment is also uncetain, esponses to scenaio spectal acceleation demands ae obtained, at the connection location, fo the typical building consideed hee. These esponses ae calculated thoughout a Monte Calo simulation pocess unde scenaio spectal acceleations. The Monte Calo simulation pocess, the scenaio acceleations, the esponse statistics and the connection models, ae detailed ahead in the following sections. Maximum moment and maximum shea foces histogams ae obtained with these statistics and, by using the appopiate limit state function fo the given connection type, pobabilities of failue and damage ae obtained fo both demand levels: exteme and opeational eathquakes. These pobabilities ae intoduced into the life-cycle cost/benefit elationship fo seveal connection types and the optimal type is obtained by compaing the expected life-cycle costs. The minimum expected life-cycle cost coesponds to the optimal connection type. Damage costs include the epai cost and losses elated to the potential fatalities, injuies and business inteuption. The appopiate limit state function will coespond to whethe the maximum moment exceeds its coesponding esistance o the maximum shea foce exceeds its esisting foce. The esults may also be used, afte futhe efinements, to update the design specifications fo seismic zones in Mexico. Fomulation of the decision citeia The expected life-cycle cost is usually calculated to assess the economic effectiveness of potential stuctual solutions and come up to optimal decisions unde uncetain loading conditions [5, 6]. Two altenative connection types ae poposed and thei pefomances ae compaed fom the viewpoints of stuctual eliability and costs. The expected life-cycle cost E[C T ] is composed by the initial cost C i and the expected damage costs E[C D ]: E C ] = C + E[ C ] () [ T i D The expected damage costs include the components of damage cost: expected epai E[C ], injuy E[C inj ] and fatality E[C fat ] costs and each one depends on the pobabilities of damage and
Evaluación de la seguidad estuctual de conexiones atonilladas y soldadas paa zonas sísmicas 99 failue of the stuctue. These component costs of damage ae defined as: E [ C ] = C ( PVF) P () whee C = aveage epai cost, which includes the business inteuption loss, C bi. The aveage epai cost includes the mateial epais and loss due to business inteuption while the epai woks ae pefomed. PVF = pesent value function [6] PVF [ n = Γ n= k = k ( k, γl) / Γ( k, υl)( υ / γ ) ]( υl) / n!exp( υl) (3) whee k is the numbe of eathquakes and n the numbe of eathquakes consideed in the nth.- tem composing the function in ode to conside any numbe of eathquakes with Poissonian occuence pobability. Also, n = mean occuence ate of eathquakes that may damage the stuctue, g = net annual discount ate, L= stuctue life and P = pobability of epai, defined in a simplified way, as a the pobability to each the allowable limit state, which is in tems of the allowable stess fo eithe the bolted o the welded connection. Similaly, the business inteuption cost, C bi, is expessed in tems of the loss of evenue due to the epais o econstuction woks afte the eathquake, assumed to last T yeas: Cbi = LR (T ) (4) whee L R = loss of evenues pe yea. The expected cost of injuies is poposed to be: E [ C ] = C ( N ) P (5) inj IL in f whee C IL = aveage injuy cost fo an individual, N in = aveage numbe of injuies on a typical steel building in Mexico given an eathquake with a mean occuence ate n and P f is the annual failue pobability. n Fo the expected cost elated to loss of human lives, the cost coesponding to a life loss, C L, and the expected numbe of fatalities, N D ae consideed. The cost associated with a life loss may be estimated in tems of the human capital appoach, which consists in the calculation of the contibution lost, due to the death of an individual, to the Goss Domestic Poduct duing his expected emaining life. The expected age of the individual, assumed to die duing the eathquake, is simulated fom the pobabilistic distibution of ages fo the population of Mexico City, as obtained fom national statistics, and the estimated distibution of building occupants (with vaying ages) at the time of the eathquake. The emaining life is estimated as the diffeence between the aveage life expectancy fo Mexico City and this expected age. Moe details of this calculation ae given in a pevious wok [3]. The expected numbe of fatalities is estimated fom a cuve peviously developed fo typical buildings in Mexico, in tems of thei plan aeas, given an eathquake with a mean occuence ate n [3]. E = ( N ) P (6) [ C fat ] CL D f In the next section, all the figues ae estimated fo typical costs in USD fo Mexico. A typical building fame, see Figue, located on the soft soil of Mexico City is selected to analyze its citical fame unde seismic loads. A seies of esponse analyses wee pefomed to identify the maximum moments and shea foces unde scenaio spectal acceleations. Eathquakes ae assumed to occu accoding to a Poisson pocesses (with mean occuence ate n), with spectal acceleations which ae scaled fom the seismic hazad cuve fo Mexico City [4]. Fom the acceleations exceedance ate found in this efeence, it is obtained the annual cumulative distibution of spectal acceleations fo the soft soil of Mexico City (see Figue ). The above descibed esponse statistics ae used as an input to the (Finite Element Method) FEM models of the altenative connections and a Monte Calo simulation pocess [8] is pefomed fo each connection model in ode to get the statistics of maximum shea foce and moment. With these statistics and the limit state function of each connection, the coesponding failue pobabilities ae calculated. As an example, g M and g M ae the limit state functions fo maximum moment and fo each one of the two altenative connections. g M = M M (7)
00 De León et al.. g M = M M (8) whee M and M ae the maximum moments and M and M the esisting moments fo the altenative connections and, espectively. The coesponding functions fo shea foce and fo the epai pobability level ae simila. The expected life-cycle cost of each connection is obtained though the calculated failue pobabilities, and Eqs. () to (6). The connection type to be ecommended will be the one with the minimum lifecycle cost. Application to a steel building in Mexico Figue. Typical fame fo a steel building in Mexico. The plan of the consideed building is shown in Figue 3 and the building belongs to goup B, 0.8 FY (y) 0.6 0.4 0. 0 0 00 00 300 400 500 y (cm/s ) Figue. Cumulative annual pobability of seismic spectal acceleations. Figue 3. Plan of analized building.
Evaluación de la seguidad estuctual de conexiones atonilladas y soldadas paa zonas sísmicas 0 accoding to the Mexico City building code []. The building is a egula, famed stuctue without bacings and the study is made with fixed coss sections, thee is no paametic study with vaiable coss sections. The use of the bulding is fo hotel ooms and the stuctue natual peiod is 0.58 s. The coss sections of beam and column at citical joint ae: section W4X90 and box section 6 X6 X/, espectively. The joint is designed fo two options: bolted (connection ) and welded (connection ). The bolted option is shown in Figue 4 wheeas the welded connection is sketched in Figue 5. The welded connection only consists on 5 cm filets on both sides of the web. The only joint consideed was the edge one. The second altenative connection is a welded set of fillets with 5cm length and ¼ thickness with electodes E70 to join the beam web to the column flanges. The designs wee made to meet standad pactices and assuming the application of conventional constuction pocedues. The annual mean occuence ate of significant eathquakes is 0.4/yea. Significant ae consideed to be those events that might poduce enough damage in the consideed building (coesponding to intensities lage than 0.5g). In ode to simplify the Monte Calo simulation pocess, a seies of peliminay stuctual esponse analyses wee pefomed fo specified spectal acceleation coefficients coesponding to the spectal acceleations given in the X-coodinates of the cuve in Figue. The whole ange of scenaio spectal acceleations was divided into 4 pats: 0 to 0.5g, 0.5g to 0.5g, 0.5g to 0.35g and 0.35g to 0.45g and the maximum moment and maximum shea foce wee identified fo each of the 4 limits. In all cases the citical joints wee found to be the fist floo connections. These maximum esponses wee fitted to nonlinea piecewise deteministic functions. Many tials wee pefomed by andomly geneating spectal acceleations (Figue ) and by calculating the atio between this acceleation and the closest limit. The maximum moment and shea foce ae estimated by multiplying the maximum moment and shea foce obseved fo that limit, times the atio between acceleations. The pdf (pobability density function) of these maximums is calculated by conventional statistics and shifted gamma distibutions [7] wee fitted to the calculated maximum foces (see Figues 6 and 7). The epai and failue pobability of both connections ae calculated though the aea unde the cuves. The epai limit states wee consideed on the basis to Figue 4. Views of citial joint, bolted option of connection.
0 De León et al.. Table Costs data (USD) Connection Ci 0000 000 C 8000 0000 Figue 5. Altenative welded connection. exceed the allowable moment and shea foce at each connection and these thesholds wee calculated fo the bolt o welding esistance fom the 0.60 of the ultimate stess fo the bolt o welding. Specific epai techniques wee not consideed but, instead of that, the limit state function compaed the maximum foce (moment o shea foce) to the coesponding esistance. The costs and othe economic data, fo the building, ae shown in Tables and. It was consideed that the wost scenaio of human af- LR 0000 0000 CIL 0000 0000 CL 80000 80000 Table Othe economic data g 0.08 N in 0 N D 60 L 50 yeas 0. 0.5 Calculated Shifted gamma pdf 0. 0.05 0 6 8 0 4 6 8 30 3 34 36 38 40 4 44 46 48 Mmax (tn-m) Figue 6. Annual maximum moment distibution fo welded connection. 0.08 0.06 Calculated Shifted gamma pdf 0.04 0.0 0 0.00 8.00 6.00 4.00 3.00 40.00 48.00 56.00 64.00 7.00 80.00 88.00 96.00 Vmax (tn) Figue 7. Annual maximum shea foce distibution fo welded connection.
Evaluación de la seguidad estuctual de conexiones atonilladas y soldadas paa zonas sísmicas 03 fectation is when all the building occupantsdie and thee ae no injuies. The bending mode was found to goven the connection failue. The capacities fo moment and shea foce, fo failue (f) and epai (ep) and fo both connections ae shown in Table 3. The epai and failue pobabilities, fo both connections, ae shown in Table 4. With the above obtained failue pobabilities, the expected life-cycle costs ae calculated and the esults ae shown in Table 5. Paametic studies Two types of connections, bolted and welded, have been designed in such a way that the bending and shea esistances ae simila, accoding to Table 3. The connections capacity is lage than the capacity of the beam and column and thee might be some inelastic behavio in beam and column. This is included into the esults as they conside the maximum acting foce and the capacity of the connections. The ultimate capacity of the connections has been consideed hee although the full nonlinea moment-cuvatue behavio and ductility is not explicitly included at this stage of the study. Fom inspection of the esults, it is obseved that the initial, epai and economic loss ae the costs that dominate the selection of connection type. Theefoe, the expected life-cycle cost is assessed fo vaious values of these paametes. The esults fo seveal combinations of initial (constuction) costs ae shown in Figue 8. If the cost of welding emains below 0.97 times the cost of the bolted connection, the welded connection is the ecommended one. Howeve, if the welding exceeds that limit, the connection should be bolted fo the minimum expected lifecycle cost. Now, as fa as the epai cost is concened, the compaison of expected life-cycle costs, fo a few combinations of epai costs fo the bolted and welded connections poposed, is shown in Figue 9. Table 3 Capacities fo altenative connections M f (tn-m) V f (tn) 69.65 08.3 M ep (tn-m) V ep (tn) 6.9 64.99 M f (tn-m) V f (tn) 70.58 5.8 M ep (tn-m) V ep (tn) 38.75 8.48 Table 4 Repai and failue pobabilities fo altenative connections P M P M 0.007 E-06 P f M P fm E-07 E-08 Wheneve the welded connection costs less than 0.4 times the bolted one, it is moe economical to do the welded one and, if this cost exceeds that limit, the bolted one is the one to be ecommended. Finally, fo losses due to business inteuption (ent, fo example) up to 00,000 USD, the bolted connection is pefeed but, fo losses highe than that, the welded connection is ecommended (see Figue 0). Discussion of esults Fo the two specific connections consideed hee, it is obseved that ecommended one is the bolted connection. The most impotant cost items wee the initial (constuction) cost, the epai cost and the losses due to sevice (business) inteuption. The bending effect is the one that govens the connection design fo the case teated hee and Table 5 Expected life-cycle costs fo altenative connections Altenative E[C f ] E[C fat ] E[L ] C i E[C D ] E[C T ] 630.87 E0 000 77.87 077.87 0.7 0.09 3E-0 000 0.9 000.9
04 De León et al.. E[CT] 4000 000 0000 Bolt Weld C i bolt = 0000 USD 8000 0.9 0.95.05. C i weld /C i bolt Figue 8. Expected lifecycle cost fo seveal initial costs of welded connection. The cost diffeences egading the initial and epai costs may be explained because, fo the bolted connection, pat of the wok is made on a wokshop and the est in situ and no vey specialized wokmanship is equied wheeas, the welded one makes use of a moe qualified cetified (moe expensive) wokmanship. It is inteesting to note that, fo expensive sevice inteuption losses, the gain on safety by the welded connection offsets the moe expensive initial and epai cost. But, fo cheape sevice losses, the bolted connection is ecommended. Two simple options wee included hee fo illustation puposes and the findings apply only to this case. The esults ae useful fo the hazad and site consideed. Othe conditions equie an adaptation of data like, hazad type, seismicity and costs. Conclusions and ecommendations E[CT] E[CT] 4000 000 C weld = 0000 USD 0000 Bolt Weld 8000 0. 0.3 0.4 0.5 0.6 C weld /C bolt Figue 9. Expected lifecycle cost fo seveal epai costs of bolted connection. 4000 000 0000 8000 0000 80000 40000 00000 60000 L (USD) Bolt Weld Figue 0. Expected lifecycle cost fo seveal losses elated to business inteuption. fo the seismic conditions illustated. This is not always the case and, fo othe cases of stuctual type, joints and seismic envionment, the govening failue mode should be identified. A isk-based decision tool has been pesented to select a connection between poposed types in a steel building unde seismic loads. Fo the paticula building consideed hee, the bolted connection is pefeed, fom the cost effectiveness point of view, ove the welded one. The bolted connection is pefeed when the initial cost of the welded one exceeds, at least 0.97 times, the cost of the bolted one, if the epai cost of the welded one exceeds, at least 0.4 times, the one of the bolted one and if the losses due to sevice inteuption ae less than 00,000 USD. Maximum moments and maximum shea foces ae bette chaacteized though shifted gamma distibutions. Futhe eseach, with the analysis of many othe stuctual types, numbe of stoies, natual peiods of buildings and a whole ange of connection types and joints (including combinations of bolts and welding fillets), may help to update the Mexican code fo design and etofit specifications. In addition to that, the nonlinea behavio of bolted and welded connections should be included. Refeences. Buneau, M.; Whitakke, A. and Uang, Ch. M. Ductile Design of Steel Stuctues. McGaw Hill. 987.. SAC poject (994): http://quive.eec.bekeley.edu:8080/libay/index.html 3. FEMA 73 (997) NEHRP Guidelines fo the seismic ehabilitation of buildings 4. Wen, Y. K. and Fouth, D. A. (997) Poposed statistical and Reliability Famewok fo compaing and evaluating pedictive models fo Evaluation and Design and Citical Issues
Evaluación de la seguidad estuctual de conexiones atonilladas y soldadas paa zonas sísmicas 05 in developing such Famewok. Repot No. SAC/BD-97/03, SAC Joint ventue, Sacamento Califonia. 5. IMCA, Memoias V Simposio Intenacional de Estuctuas de Aceo, Guadalajaa, Jal. 997. 6. Mianda, E.: Plate-end connection fo steel buildings in Mexico Memoias V Simposio Intenacional de Estuctuas de Aceo, Guadalajaa, Jal. 997a. 7. Mianda, E.: Seismic design of beam-column connections. Memoias V Simposio Intenacional de Estuctuas de Aceo, IMCA, Guadalajaa, Jal. 997b. 8. Mianda, E. and Matínez R., E.: Seismic design ecommendations fo steel stuctues with eccentically-baced fames in México Memoias VI Simposio Intenacional de Estuctuas de Aceo, Puebla.999. 9. Esteva, L.: Behavio Unde Altenating Loads of Masony Diaphagms Famed by Reinfoced Concete Membes, Poc. Intenational Symposium on the Effects of Repeated Loading of Mateials and Stuctues. RILEM, México City.996. 0. Righiniotis, T. D. and Imam, B.: Factue eliability of a typical Nothidge steel moment esisting connection Engineeing Stuctues, School of Engineeing, Univesity of Suey, Guildfod, Suey GU 7XH, UK, Vol. 6, Issue 3(004)38-390. Gobieno del D. F., Nomas Técnicas Complementaias paa Diseño y Constucción de Estuctuas Metálicas, México DF, 004.. AISC, Specification fo Stuctual Steel Buildings. Chicago Illinois, E.U. 005. 3. Ang, A. H-S. and De León, D.,: Detemination of optimal eliabilities fo design and upgading of stuctues, Stuctual Safety, Vol. 9, No,(997) 9-03. 4. Esteva, L. and Ruiz, S.: Seismic failue ates of multistoy fames. Jounal of Stuctual Engineeing, ASCE, Vol. 5, No., (989) 68-84. 5. Neves, L. C.; Fangopol, D. M. and Hogg, V. Condition-eliability-cost inteaction in bidge maintenance. ICASP9, San Fancisco, CA.003. 6. Ang, A. H-S. and De León, D.: Modelling and analysis of uncetainties fo isk-infomed decisions in infastuctues engineeing, Jounal of Stuctue and Infastuctue Engineeing, Vol., Nº, (005) 9-3. 7. Ang, Alfedo H-S and Tang, W. H.: Pobability Concepts in Engineeing Planning and Design, Basic Pinciples, nd. Edition. John Wiley and Sons, New Yok. Vol. I, (007). 8. Ang, Alfedo H-S and Tang, W. H.: Pobability Concepts in Engineeing Planning and Design Vol. II - Risk, Reliability and Decisions. John Wiley and Sons, Vol. II, New Yok, 984. Recibido el 0 de Eneo de 03 En foma evisada el 8 de Abil de 04