Analytical simplified procedure for the evaluation of the RC buildings.

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1 Analytcal smplfed procedure for the evaluaton of the RC buldngs. N. Gattesco, R. Franceschns, F. Zorzn, Unversty of Treste, Italy SUMMARY: Numerous exstng buldngs are located n sesmc prone areas and many of them were not desgned consderng adequate sesmc provsons. Thus, for safety reasons, t s necessary to assess ther sesmc vulnerablty and to provde strengthenng nterventons f needed. To reduce gradually the sesmc vulnerablty, a prortzaton lst for the nterventon s requred. A new smplfed mechancal procedure for the assessment of the sesmc resstance of renforced concrete structures s heren presented (FIRSTEP-RC). The types of structures that may be assessed are varous: one-way frame, three-dmensonal frame, shear walls, mxed frame and shear walls, precast frames. The procedure related to the study of the frame structures s heren presented and dscussed. An example underlnes the effectveness and the smplcty of applcaton of the proposed procedure. eywords: Sesmc vulnerablty, Renforced concrete, Exstng buldngs.. INTRODUCTION A large porton of Italy s consdered to be sesmcally actve, but the sesmc classfcaton has been updated only after sesmc events. Snce the ssue of the OPCM 374 (003), the sesmc classfcaton has been extended to the whole natonal terrtory wth varyng degrees of hazard. Due to these updates, the changes are sgnfcant, n fact, some areas that were prevously consdered to have low sesmcty have now been classfed medum to hgh hazard (Manfred and Mas, 009). As a consequence, several exstng buldngs are located n areas that were not classfed as sesmcally actve at the tme of constructon and so they were bult wthout sesmc crtera. Thus, the vulnerablty of the exstng buldngs, n partcular the publc sector, has to be studed. A detaled analyss of all exstng constructons, however, requres very hgh economcal resources and so the problem may not be solved n the short term. The hugeness of the publc buldng stock requres the adopton of expedtous methods that allow the dentfcaton of potentally crtcal buldngs. It s necessary to defne a prortzaton lst for the strengthenng nterventons so to allow a gradual reducton of the sesmc vulnerablty and to ncrease the socal safety. The avalable methods for the assessment of the sesmc vulnerablty of buldngs are varous and are based on dfferent prncples, n functon of the result to be obtaned. The most common methodologes are the ndex-score methods that assocate a score to each buldng, n functon of some parameters that descrbe the ablty of the structure to survve to earthquakes. Among these methods, the most well known s that proposed n FEMA54 (00), as well as those methods nspred to the Hazus procedure (FEMA 366, 003). In these methodologes, a dsplacement capacty curve s assocated to each buldng, accordng to the structural typology, the number of floors and the year of constructon. The rato between the capacty and the demand (n term of spectral dsplacement) represents the ablty of the structure to support the expected earthquake and allows to have an ndex of comparson among structures. Other smplfed mechancal procedures allow to estmate the resstance of the structure and so they are sutable to acheve a prorty lst based on a quanttatve parameter. The smplfed mechancal methods developed untl now for the evaluaton of renforced concrete structures are lmted to some structural types (plane frame, shear walls). Further, the number

2 of data requred for the assessment s too hgh. Among these methodologes, the VC procedure (Dolce e Moron, 007) allows to quantfy the base shear resstance of RC frame structures, assumng a shear-type behavour for each column and a soft storey collapse. In ths paper, a new smplfed mechancal procedure s proposed. Ths method s called "FIRSTEP- RC", that s the acronym of Frst Step Evaluaton Program for Renforced Concrete structures (Franceschns, 0). It was developed to assess the sesmc resstance of all the types of renforced concrete structures that may be found n the bult hertage: one-way frame, three-dmensonal frame, shear walls, mxed walls and frames, frames wth nfll walls. In FIRSTEP-RC the assessment of the structure takes nto account the varous types of falures that may occur: shear collapse, combned flexure and axal force collapse, local collapses. At the end of the process, the peak ground resstng acceleraton of the buldng, for each prncpal drecton (a ux, a uy ), s carred out. The lesser one (a u ) s taken to defne the sesmc safety ndex of the structure (I s ), n relaton to the sesmc acceleraton expected (a exp ): I s au a. (.) exp Ths procedure was developed durng the course of the Assess Project (008-0), fnanced by the Italan Regon Frul Veneza Gula and fnalzed to defne a prortzaton rankng to make nterventons n school buldngs so to reduce the sesmc rsk.. GENERAL PROCEDURE Varous structural types of renforced concrete buldngs may be assessed wth the FIRSTEP-RC procedure: one way frame, three dmensonal frame, precast frame, shear walls, mxed frame and shear walls, frames wth masonry nfll walls. The purpose s to develop a procedure characterzed by rapdty n applcaton, n whch the number of data requred for the evaluaton s lmted. Thus, some analytcal smplfcatons are needed. The most mportant smplfcaton s to study each buldng wth reference to the resstant elements at the ground floor only. To make relable ths smplfcaton and to dentfy the most sutable schematzatons of the varous structural types, n terms of stffness and resstance so to take nto consderaton the nfluence of the upper levels on the behavour at the ground floor, some specfc studes and parametrc analyss were performed. The results found wth ths procedure are relable for all the buldngs n whch the secton of the elements does not vary sgnfcantly from one floor to the others, and the sectons of the beams are the same at each level of the structure. The FIRSTEP-RC procedure, thanks to these smplfcatons, requres the graphc nput of the resstng element at the ground level only, the beams and the floors that pertan to each vertcal resstng element. A graphc nterface was mplemented n order to speed up the nput of the needed data startng from a CAD geometry. These data allow the numercal procedure to evaluate the nfluence area and the load that pertans to each vertcal element, and the centrod of the buldng. The steel percentage n each secton s evaluated by a smulated desgn procedure n functon of the nfluence area of the element and the hstorcal code provsons. The beam sectons are defned n functon of the type found durng the survey to the buldng: as for example deep beam or shallow beam. The dmensonal rato that characterzes each type of secton was obtaned through a parametrc study. The FIRSTEP-RC procedure concerns two parts that may be summarzed n the two functonal blocks n Fg... The former refers to the analyss of the structure and the latter to the evaluaton of the resstance of members. In the analyss, a untary force, appled on the centrod of the buldng, s dstrbuted among the resstng elements at the ground floor n functon of ther stffness and poston (f e ). A dedcate procedure allows to defne the stffness of each element. In case of structures made of frames and shear walls, a methodology to accurately estmate the nteracton between the frame and the equvalent shear wall was studed. These nteractons become much mportant at the ncrease of the

3 number of floors of the buldng. In partcular, the procedure mposes that the dsplacement at each level be the same for the frame and the equvalent wall and evaluates the fracton of base shear force that pertans to the frame (F F =α F TOT ) and to the walls (F W =(-α) F TOT ). The coeffcent α allows to estmate the stffness of the frame ( F ), wth respect to the total stffness of the structure ( F + W ), takng nto consderaton the nteracton wth the equvalent wall. Thus, t permts to establsh how to modfy the stffness of the columns of the frame ( F MOD ) and of the walls ( W MOD ) n order to correctly assess the dstrbuton of the base shear force. The dstrbuton of the force made wth the procedure takes nto consderaton the presence of a twstng effect n case of eccentrcty between the stffness centre and the centrod. Furthermore, the procedure allows to consderate, at the ground floor, the presence of squat columns. These rregulartes may lay, n fact, to a relevant eccentrcty. Fgure.: Flowchart of the general procedure of FIRSTEP CA. The second functonal block refers to the evaluaton of the resstng shear force of each element (F u ). Ths concdes wth the mnmum of the shear resstance force related to the most common type of collapse mechansms: combned flexure and axal force collapse (V resp ), sldng shear collapse (V ress ) and local collapse due to combned twstng and shear n the beam that supports the floor, n case of one way frame analysed n the weak drecton (V rest ). For each prncpal drecton, the total base shear resstng force of the buldng (F R ) concdes wth the base shear force that causes the collapse of the frst element that reaches ts ultmate lmt state: F R u e mn F f. (.) A behavor factor s defned for each vertcal element (q ), n functon of the domnant collapse mechansm. The value of the behavor factor s defned n the followng paragraphs for the cases of

4 combned flexure and axal force, sldng shear and local brttle mechansms. For each prncpal drecton, the behavor factor of the buldng q, concdes wth the lower value that derves from the rato between the structural factor q of each vertcal element and ts load rate: q mn q F ( F f ). (.) u R e At the end of ths procedure, the shear force that pertans to each element s known (F R f e ). The followng step s to evaluate f these forces may lead to the brttle collapse of one or more beamcolumn jonts. If t s the case, the resstng force of the buldng has to be reduced (F R F ) and the behavor factor s taken equal to.5 (brttle collapse - NTC 008). The resstng acceleraton s evaluated through the equaton: a u F FR q g (.3) W S F 0 n whch a u s the peak ground resstng acceleraton at the base of the buldng, q s the behavor factor, W/g s the mass of the buldng, S s the sol factor, F 0 s the buldng amplfer factor of the sesmc acton. For brevty, only the aspects related to the study of the frame structures are presented the followng. 3. STRUCTURAL ANALYSIS: SCHEMATIZATION OF THE FRAMES. To analyze the real structure, the stffness of each vertcal element s separately evaluated n each of the two prncpal drectons. In ths step, the behavor of the element (column or shear wall), the base restrant (fxed or hnged), the grade of restrant at the upper end of the column at the ground floor and the number of levels of the consdered element are taken nto account. The models adopted to analyze the frame structures refer to the portal method (Fg. 3.a). Ths method assumes that, for a group of horzontal forces appled to the frame, the dagram of the bendng moment has hs contraflexure ponts n the mddle of each column and of each beam. Placng hnges n these ponts, the structure, ntally hyperstatc, may be studed as a sum of sostatc substructures. The generc column, n functon of ts stffness, has to support a rate ψ of the total base shear force (Fg. 3.b). Fgure 3.: Portal method: (a) Mult-level frame wth contraflexure ponts; (b) forces and sgnfcant dmensons on the generc column; (c) structural smplfcaton for the column wth fxed end at the base and wth an elastc rotatonal restrant at the top. In the FIRSTEP-RC procedure, the poston of beam hnges (λ l, λ l ) and column hnge at the frst floor (βh ) are not placed n the mddle of the elements, as n the portal method, but result from parametrc analyses performed on frame structures wth dfferent number of floors, length and sectons of the beams and floors (Fg. 3.b). The nfluence of the horzontal beams and the presence of the upper floors are taken nto account through a sprng wth rotatonal stffness, whch leads to the

5 defnton of the smplfed schematzaton n Fg. 3.c. In Fg. 3.a and Fg. 3.b, the force F A corresponds to the quantty ψ P of Fg. 3.b, nstead F B s equal to ψ(p +P 3 ). For each element, to evaluate the stffness of the rotatonal sprng, a dstrbuton of horzontal loads concentrated at each floor and varyng n proporton to the heght, s consdered. The nterstory heght and the mass of the floor are assumed constant at each level. A untary total force s appled to each element (F tot =). Thus, the force at the -th level (F ) s assumed proportonal to the number n of the plan: F =Cn, wth C constant. The value of the constant C s equal to: n tot n C, (3.) tot where n tot s the total number of floors. Wth these assumptons, the force F A (Fg. 3.b) s equal to C, nstead the force F B s equal to the sum of the forces due to the upper floors (F B =-C). Ths procedure allows to model all the restrant confguraton that may characterze the columns at the ground floor of a real frame (Fg. 3.): (a) fxed end at the base, elastc rotatonal restrant wth free translaton at the top, (b) hnge at the base, elastc rotatonal restrant wth free translaton at the top, (c) fxed end at the base and hnge wth free translaton at the top. The frst case (a) represents, n the plane, the confguraton of frames that has a sound foundaton and bearng beams at the upper floors. The second case (b) concerns the cases wth a weak restrant at the foundaton level (weak footngs or plane of acton perpendcular to the drecton of the beam foundaton) and a bearng beam or a one way slab at the upper levels. The last case (c) represents the confguraton of nverse pendulum structures (prefabrcaton or columns wth strong foundaton but very weak beams at the top. The rotatonal sprng at the top of the element n the cases (a) and (b) of Fg. 3., represents the rotatonal nerta guaranteed by the beams that pertan to the jont; t takes nto account the degree of restrant offered by the beams and the number of levels of the vertcal element. Fgure 3.: Representatve models of actual cases. 3.. Stffness of a column fxed at the base and wth an elastc rotatonal restrant at the top. The problem concerns the model of the column n Fg. 3.c. In ths fgure, λ l, λ l and βh are respectvely the lengths of the horzontal beams and of the column at the frst level up to the pont of zero moment (hnge). The horzontal loads actng on the structure are characterzed by the rules descrbed n the prevous chapter (F =Cn, wth C constant). The stffness of the rotatonal sprng s obtaned mposng the same dsplacement at the top of the systems evdenced n Fg. 3.b and Fg. 3.c: ( h (3.) 4 l l ) ( C) h ( C) l 3EI l, l 3EI l, 4EI h, (3.3)

6 where I s the second moment of area of the cross secton and E s the Young modulus, the subscrpts and dentfy the beam at the left and rght of the jont, respectvely. On observe that the value of the stffness depends on the stffness of the beams and the load dstrbuton along the heght. The stffness of the smplfed element n Fg. 3. s equal to: EI 6 h EI element 3 3. (3.4) EI The bendng moment dagram on the column at the ground floor s lnear and the pont of zero moment (h F ) s evaluated wth the relatonshp: h F 3 6EI 3 EI. (3.5) Stffness of a column wth a hnge at the base and an elastc rotatonal restrant at the top. The modellng s smlar to that n Fg. 3. wth a hnge at the base. The procedure for the evaluaton of the rotatonal sprng s the same adopted n the prevous chapter. Ths modellng refers to all the frames wth a weak restrant at the base. The resstant mechansm to horzontal actons whch occurs n ths case s guaranteed by the slab resstance to bendng and by the combned shear-torsonal strength of the bearng beam. The FIRSTEP-RC procedure takes nto account both the flexural stffness flex, due to the beams l and l that represent the one way slabs, and the torsonal stffness of the beam that supports the slabs ( glob ) (Fg. 3.3a). The two rotatonal sprngs are n seres and thus the equvalent stffness becomes:. (3.6) glob flex To evaluate the torsonal stffness provded by the beam n global terms ( glob ), a unform dstrbuton of torques (m t ) on the beam was assumed, whch represents the contrbuton of the floor josts. The constant dstrbuton of torsonal moment s not the real one, but leads to a good approxmaton of the torsonal stffness of the beam. The strategy s to mpose, for the two systems n Fg. 3.3b, the same deformaton energy due to the torsonal moments: a 0 * p * m z dz M t, (3.7) GI glob where M t * s the torsonal moment at the fxed end, G I p * s the torsonal stffness of the beam n the uncracked state of the secton. The dstrbuton of the torque s assumed to be constant, thus the torsonal stffness of the sprng s: glob * GI p 3, (3.8) a where a s half of the beam length (Fg. 3.3b). In ths confguraton, the bendng moment dagram on the column at the ground floor results to be trangular wth zero value at the base. The shear acton V (constant) and the maxmum bendng moment on the element (M max ), are lnked by the relatonshp: M max = h F V, where h F, n ths case, concdes wth the heght of the column (h ).

7 (a) Fgure 3.3: (a) Stffenng effect of the slabs and the beam that supports them n respect to the acton of horzontal forces; (b) schemes to evaluate the torsonal moment on the beam. (b) 3.3. Stffness of a column fxed at the base and hnged at the top. In the case of precast frame buldngs wth columns fxed at the foundaton and hnged at the floor levels (nverted pendulum), the followng changes wth respect to the model n Fg. 3. were done. In partcular, t s assumed that the hnges are located at the ends of the beams. The horzontal loads actng on the structure are characterzed by the same rules adopted n the prevous chapters (F =Cn, wth C constant). The translatonal stffness of the element s evaluated by the followng relatonshp: M tot F y( 3 tot M tot ) h 3 E I 3 C h n tot n tot j 3 h E I G A, (3.9) n. (3.0) In the equatons, h s the nterstorey heght of the -th level, A s the cross secton of the element, G s the shear modulus of concrete, χ s the shear factor of the secton, F tot s the sum of the forces appled on the element at each level (F tot =), M tot s the overturnng moment on the top of the column at the ground floor derved from the forces appled at the upper floors. In ths confguraton, the poston of the contraflexure pont (h F ) n the equvalent element s assumed to be equal to that obtaned by relatng the maxmum moment at the base of the element wth the shear acton n the same secton: h F M T max max C h n tot n tot j n. (3.)

8 4. BASE SHEAR RESISTANCE OF THE BUILDING Wth the procedure descrbed n the left block of the dagram n Fg.. the quote of the untary shear force that pertans to each resstng element can be evaluated. To assess the resstng shear force of the buldng t s necessary to evaluate the resstance of each element n terms of shear acton. The resstng shear force of each element s the mnmum among those relatve to the collapse due to the followng mechansms (Fg..): () combned flexure and axal force collapse (V resp ); () collapse due to sldng shear (V ress ); (3) collapse due to combned twstng and shear n the bearng beam that supports the slab, n case of one way frame consdered n the weak drecton (V rest ). The possblty of actvaton of a local collapse mechansm n beam-column jonts (V resl ) s studed by the procedure through a check a posteror. 4.. Combned bendng moment and axal force resstance. The resstance of the element related to the collapse mechansm of combned bendng moment and axal force s evaluated trough the study of the stran felds, defned n functon of the axal force on the element. The poston of the neutral axs and the resstng moment of the secton (M res ), n the prncpal drectons, are evaluated by the procedure n functon of the axal force, the percentage of renforcement n the cross secton and the stran dstrbuton at the ultmate lmt state. The resstng shear force assocated to ths resstng moment s V resp =M res /h F. The dstance h F correlates the bendng moment actng on the element and the acton of shear, t s evaluated n a dfferent way for the three basc confguratons n Fg. 3., as descrbed n the prevous Sectons. The behavor factor assocated to ths type of collapse ("ductle") s lnearly varable from.5 to 3, dependng on the stress level of concrete (NTC 008). In partcular, for the -th element, the behavor factor q s evaluated n functon of the rato between the axal force on the member N Ed and the maxmum axal resstng force N Res : q 3.5 N N. (4.) Ed Res 4.. Sldng-shear resstance. The resstance related to the sldng shear mechansm of the column (V ress ) s evaluated wthout consderng the strrups effect, whch may be assumed neglgble for exstng RC buldngs bult before seventes. The shear strength per unt area s taken equal to the maxmum between v rd and v rd, as recommended by the NTC (008): v rd 00 l fck k 0. 5 cp, v k 0. 5 FC c 3 rd f ck cp, (4.) where k s the lesser between +(00/d) 0.5 and ; d s the effectve depth of the concrete secton n mm; ρ l s the geometrcal rato of longtudnal renforcement; FC s the confdence factor; f ck s the characterstc compressve resstance of concrete; γ c s the partal securty factor of concrete; σ cp s the average stress n the concrete secton. Ths type of collapse s brttle and thus the relatve behavor factor s equal to.5 (NTC 008) Shear resstance related to the torsonal collapse of the beam that supports the floor. In one way frames, the weakest drecton s the transversal one. The resstant mechansm n ths drecton takes n consderaton the bendng resstance of the floors and the torsonal resstance of the bearng beam that supports the floors. In general, the dsspatve capacty of floors s greater than the beam and thus the attenton s focused on the beam. In fact, the bearng beam s subjected to shear and torson, thus t s necessary to verfy the capacty relatve to the combnaton of both actons (NTC 008):

9 T T Ed Rcd V V Ed Rcd. (4.3) In the equaton T Ed s the desgn value of the torsonal moment actng on the beam, T Rcd s the torsonal resstng moment related to the collapse of concrete, V Ed s the shear acton due to gravtatonal loads and V Rcd s the resstance related to the mechansm of shear and compresson of concrete. The resstng torsonal moment of the bearng beam (T Ed res ) s obtaned through the Eqn. 4.3, after the evaluaton of V Ed, V Rcd and T Rcd. The shear acton on the column (V rest ) s evaluated at the presence of that torsonal moment on the beam, usng the smplfed models above descrbed (Fg. 3.). Ths value of shear acton s equal to the resstng shear of the column related to the torsonal collapse of the beam. Ths type of collapse s brttle and so the behavor factor s equal to.5 (NTC 008). 5. BEAM-COLUMN JOINT COLLAPSE. For the vertcal elements wth unconfned jont n one or both prncpal drectons, the maxmum shear that the element may support wthout the collapse of the node s evaluated. In the procedure FIRSTEP- RC ths type of control s performed at the end of the process. In partcular, the shear acton on the node has to be lower than the resstng shear force of the node. The shear acton on each node V ned s evaluated through the node equlbrum. In Fg. 5. the actons on the node are dsplayed: V s the shear force on the element at the ground level, and t s estmated on the bass of the shear capacty of the structure F R, that s evaluated takng nto consderaton the possble actvaton of the collapse mechansms descrbed above (V = F R f e ). Moreover, F A s the quote of the external shear force on the element, appled at the frst floor (F A =C V, wth C constant (Eq. 3.)), whle F B s the quote of the shear acton on the element due to the horzontal forces appled at the upper levels (F B =F A -V ). M R and M L are the bendng moments on the beams at the rght and at the left of the node, C R, C L and T R, T L form the couples (compresson and tenson forces) n the beams, related to the presence of M R and M L. M and M o are the flexural moments at the summt of the column at the ground level and at the bottom end of the column at the second level, respectvely. The shear resstance of the node V n s evaluated takng nto account both the compresson falure and the tenson falure of concrete (NTC 008). If the shear resstance of the node V n s lower than that requred (V ned ), the demand has to be reduced by a factor equal to the rato between V n and V ned, and the shear resstance of the vertcal element (V resl ) has to be reduced by the same factor. In ths case the shear resstance of the column s F ux =V resl, so that the acton on the node s wthn the lmts of verfcaton. The factor Rd s evaluated wth the Eq. 5.. If ths factor s less than one, the brttle collapse mechansm of the node s decsve and the shear resstance of the structure has to be reduced for ths factor. In ths case the behavor factor s equal to.5 (brttle collapse (NTC 008)). Rd mn ( Rd ) mn F ( F f ). (5.) ux Rx ex Fgure 5.: Equlbrum of an nternal node.

10 6. WORED EXAMPLE. An example of the applcaton of the procedure s shown n the follow (Franceschns, 0). The analysed buldng (958) s a one way frame structure wth beam foundaton and deep bearng beams n the longtudnal drecton. The buldng has 4 levels above the ground, the nterstorey heght s 3 m. It has a rectangular shape, of about 60 x 5m (floor plan n Fg. 6.). The red elements n Fg. 6. are squat column n X drecton, whle blu elements are squat columns n Y drecton (free heght equal to m). The strength of materals and the steel percentage were evaluated n functon of the year of constructon (concrete: f cm =0 MPa, steel: f ym =30 MPa, FC=). The base shear resstance of the buldng was carred out through the FIRSTEP-RC procedure and through a lnear statc analyss usng a fnte element program. The comparson of results n Table 6. underlnes the good accuracy of the smplfed procedure wth respect to a lnear analyss; the most crtcal elements are the same for both procedures. The falure s due, n both drectons, to sldng shear collapse of a squat column. Secton: Dr X [m] Dr Y [m] Steel [%] A, A, D, D B C Fgure 6.: Plan of the ground level of the school buldng consdered n the example. Table 6.: Peak ground resstng acceleraton. FIRSPEP-RC Lnear-Analyss Collapse PGA a u X drecton 0.045g 0.047g Sldng shear q=.5 (El.) Y drecton 0.05g 0.06g Sldng shear q=.5 (El.) 6. CONCLUSIONS. A new smplfed mechancal procedure for the sesmc assessment of renforced concrete buldngs n terms of peak ground acceleraton was presented (FIRSTEP-RC). The few data requred for the assessment may be gathered durng a rapd survey of the buldng. A worked example puts n evdence the relablty of the methodology. The presented procedure was appled to a large number of buldngs durng the Assess Project, fnalzed to the prortzaton of strengthenng nterventons on school buldngs n Frul Veneza Gula Regon n Italy. REFERENCES Dolce M., Moron C. (007). Le procedure VC e VM per la valutazone della vulnerabltà e del rscho ssmco degl edfc pubblc. Congresso Ands 007, Psa, IT (In Italan). FEMA 54 (00). Rapd Vsual Screenng of Buldngs for Potental Sesmc Hazards: A Handbook. Federal Emergency Management Agency. FEMA 366, (003). Hazus - Techncal manual. Federal Emergency Management Agency. Franceschns R. (0). Procedure for the assessment of the sesmc vulnerablty of exstng renforced concrete school buldngs (In Italan), PhD Thess, Bresca, IT. Manfred V., Mas A., (009). Le azon ssmche prevste nelle NTC008, anals e confront con precedent norme ssmche. 8 Convegno nazonale GNGTS, Treste, IT (In Italan). NTC 008 (008). D. M. 4/0/008, (Italan Code Provsons) Nuove Norme tecnche per le costruzon. O.P.C.M. 374 (003) (Italan Code Provsons) Prm element n matera d crter general per la classfcazone ssmca del terrtoro nazonale e d normatve tecnche per le costruzon n zona ssmca.

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