Buildings seismic retrofit with FRCM Fiber Reinforced Cementitious Matrix composite

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1 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus ul ul TEchncal DIcton TECNICAL NOTEBOOK Bulngs ssc tot wth FCM Fb noc Cnttous Mat copost Conct an ason stuctus Jul 9

2 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus INTODUCTION Ths tchncal notbook as to onstat that ul X Msh C an ul X Msh Gol FCM ssts can b us o stng bulngs ssc tot (ason, conct an noc conct) b ncasng th stuctual uctlt. Ths ocunt s concptuall an tnson spccall ocusng on tals o th sgn cta o us o FCM contan n th: Instuctons o lannng Statc Consolaton ojcts wth us o Fb noc Cnttous Mat Copouns o FCM Followng sgn gulns o CN DT-4, ths ocunt taks a clos look at thotcal an sgn aspcts, suppot b a ang o apls n applcaton, o k pojcts o ssc tot o stng bulngs, such as sha nocnt o pllas, connnt, patton walls, tc.

3 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus TABLE OF CONTENTS. DELAMINATION DILATATION. EINFOCED CONCETE STUCTUES. nocnt wok wth FCM as. Bas an pllas sha nocnt.. nocnt Dsgn... Eapls Eapl. Sha nocnt o a plla. llas connnt.. Local ct: connnt o conct... Eapls Eapl. ctangula plla connnt: conct connnt.. Ect on scton: ont an bnng... Eapls Eapl. Connnt o a ctangula plla: ultat bnng an ultat ont.. Ect on th lnt: otaton ablt wth nc to th cho... Eapls Eapl. Connng a ctangula plla: otaton ablt wth nc to th cho. MASONY STUCTUES. As o nocnt wth FCM. Vault nocnt.. nocnt sgn... Eapls Eapl. nocnt o th taos o a bal vault. Unnoc stuctu ozontal collaps ultpl Locaton o pssu cnts Acclaton o th actvaton o th chans noc stuctu ozontal ultpl o collaps Locaton o th pssu cnts Acclaton o th actvaton o th chans Stsss (ont an noal oc) nocnt scton Sha 4. ATITION WALLS 4. As an cta o nocnt wth FCM 4.. nocnt sgn 4... Eapls Eapl. nocnt aganst out-o-plan ssc acton.

4 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus. DELAMINATION DILATION I w ollow th nstuctons [], wth nc to th aga appang n gu., au lanaton oc o th n o an tnal nocnt a b stat as: bu (.) p E A G cosponng to an n lanaton lataton o: wh: E A p G bu p G ε bu (.) E A E A s th oulus o lastct o th bs; s th aa o th coss scton o th bs; s th wth o th ntac suac; s th actu ng o th ntac suac. b b bu L b L b L Fgu.. Dlanaton o an tt. Intat lanaton laton a b stat as: p G ε b kc (.) E A wh k c s a cocnt to b calbat b copason wth pntal vnc. In th cas o th ul XMsh GOLD/M75 pouct, n accoanc wth th pnts conuct (gu.), w a assu: s n p ( n) nb k( n) k ( n) (.4).8 s n 4 J G k c.8 (.5) n whch n s th nub o las o sh la on on top o th oth, b s th wth o th nocnt an k(n) s an cnc cocnt pnng on th nub o las. 4

5 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus L b Dlanaton o an tt Int at lanaton b b b ε b ( ) Stato b ε b E 4 Stat A L () L () Fgu.. Dlanaton ocs an latons ε b ( ) Nuo stat, n 4 Consng th st o ths (.4) an takng nto account that A nt b,, (.) - (.) bco: bu nb k( n) E t G ε bu k( n) G E t wh t.46 s th thcknss o a sngl la o sh ( stong cton). k( n) G ε b k c (.6) E t Us o (.6) n th plan qus aopton o th calculaton popts o th atals: nb k( n) Et G ε k( n) G E t k c k( n) G ε (.7) E t wh: s th patal cocnt o th ahnc ol (to b assu to b.); G s th calculat actu ng o th ntac suac: G G (.8) g wh g s th patal sat cocnt (valus btwn. an.6 a suggst). Not that th lts (.6) on lanaton o tts an th cosponng calculat valus (.7) to a b anchoag lngth gat than ctv tans lngth, L (gu.). Fo th pouct un consaton ths lngth s about 5 (gu.). Moov, th lts (.6) an th cosponng calculaton valus (.7) hav bn stat on th bass o th sults o pnts wth spcns consstng o goo qualt conct ( ck > 5 Ma). In th vnt o applcaton on poo qualt conct, ths lts ust b uc appopatl.. EINFOCED CONCETE STUCTUES. As o nocnt wok wth FCM nocnt o stuctus wth a noc conct a wth FCM atals n ssc zons s patculal usul o achvng th ollowng as. ) Incasng sstanc to shang stss o bas an pllas to cat th coct hach o sstancs btwn agl chanss an uctl chanss. ) ) v) Incasng th uctlt o th tnal pats o bas an pllas whch a lkl to contan plastc hngs. Ipovng anchoag o longtunal bas n ovlappng aas. Catng an obstacl to wapng o longtunal bas n pllas. v) Incasng th stngth o nos. 5

6 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus Ths as t nto th contt o th o goal o ncasng ssc capact b ncasng stuctual uctlt. Stuctual uctlt, b whch w an th capact o stuctus to b o wll bon th lastc lt on atals, s n act an ssntal qunt o th suvval o stuctus subjct to ssc acton, as cogns b th ost cnt stanas an nstuctons. So o th as lst abov sult n an ncas n th collaps loas assocat wth agl chanss (cuttng, local no bakag, wthawal o nocnt bas, copsson o conct), akng th supo to th collaps loas assocat wth uctl chanss (bnng wth abunantl l nocnt). Th oth as, on th oth han, ncas local uctlt at th ponts cosponng to pats o th stuctu whch, upon collaps, ach th lts on sstanc (plastc hngs). Achvnt o ths as tho poots stuctual collaps u to oaton o plastc hngs an ncass th oatonal capact.. nocng sha stngth o bas an pllas Th sha stngth o a noc conct stuctu a b pov b applng FCM copost atals to ts s suacs, wth th bs lng acoss th longtunal as (gu.). Th ost qunt cas s ntl that n whch bs l at ght angls to th as o th lnt (gu.)... Dsgn o th nocnt Accong to th appoach scb n th gulns [], th sha stngth o a conct lnt noc wth copost atals a b stat as ollows: { V V V ; V } V n ct s (.) a wh Vct an Vs a th contbutons to sstanc assocat wth th conct an th coss stl nocnts, V a s th sstanc assocat wth bakag o th connctng os n th copss conct wall an V s th contbuton to sstanc assocat wth nocnt wth copost atal. Th quantts V an V a stat as usual n th cas o unnoc lnts. ct s nocnt nocnt nocnt noc nt nocnt Fgu.. nocnt o a g s sha stngth. nocnt Fgu.. nocnt o a g an a plla. Th contbuton assocat wth b nocnt s cat b: ( cot θ cot β) β t w V.9 E εv sn (.) v wh (gu.): v s th patal cocnt o th sstanc ol (assu to b qual to.); s th usul hght o th scton; w s th wth o ach ban o nocnt; s th cnt-to-cnt stanc btwn bans o nocnt; E s th oulus o lastct o th nocnt; ε v s th calculat lataton o nocnt o sha stngth (lnk wth lataton o th ns); θ s th nclnaton o copss conct connctng os n laton to th lnt s as; 6

7 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus β s th nclnaton o th nocnt bs n laton to th lnt s as. h w z L b Thcknss t θ β L w ζ ( ζ) ε ( ζ) V sn β E t b ζ φ tt E ε w E t () ζ ε b( ζ) ζ w ε ε b b V ε L L ε b ε L > L ε b ε L ε b b E w t L ε b Fgu.. Calculaton aga o nocnt o sha stngth. (.) ollows ctl o th Mösch s tlls appoach an a b appl to nocnt wth FCM atals, onc calculaton laton ε v an ctv tans lngth L hav bn n. Calculat laton o nocnt o sha stngth s qual to th avag laton o th bs that coss an al cack u to sha stss, un th contons o lanaton o th nocnt. In th cas o FCM nocnts aang n a U shap aoun th co o th ba (gu.), w ust tak nto account th act that not all th bs cossng a gnc cut caus b sha stss a ancho b o than L. An so, upon lanaton o th nocnt, not all th bs can ach th lataton o lanaton o th tt ε. In ths cas laton ε v s tn b laton o lanaton o th nocnt bs, as shown n gu.. Ths s th sa as ntoucng an cnc cocnt φ n as: L φ snβ (.) hw an tnng calculat laton o th nocnt o sha stngth as: ε v φ ε (.4) In th cas o pllas noc wth FCM (gu.), th bs wap aoun th nt scton, an w a suppos that th a all ancho b o than L. An so t ss asonabl to assu: ε v ε (.5) In th qunt cas o U-shap nocnt wth FCM aang contnuousl wth th bs at ght angls to th lnt s as, (.) an (.) bco:.9 V t E εv (.6) v L hw φ (.7)... Eapls Eapl. Sha nocnt o a plla (sstanc ach). Lt us cons a plla wth a scton asung 4, a hght o l p, consstng o conct wth ck Ma an th nocnts shown n gu.4, a o Fb44k stl. 7

8 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus M N S A s A s A s ϕ u () ε c ε cu ε s ε s c s () s () cc () c σ ε c ε cu ε ck Ma c. Ma ε c ε cu.5 c B 4 c B ε s A s 94 (φ) A s 68 (φ) A s 94 (φ) 7 ε u s () σ t ε ε - - t ε u ε k 4 Ma 74 Ma t 45 Ma ε.78 ε u 67.5 Fgu.4. lla: scton an atals. I w want to tn th scal o nocnt o sha stngth wth XMsh GOLD/M75 so as to sats th ato o th sstanc ach: V VE s M M lp wh: s th calculat sha stngth; s th sha stss us n calculaton, n accoanc wth th sstancs ach; M s th ont o sstanc o th top scton; V V E s M s th ont o sstanc o th botto scton; s th ov-sstanc cocnt, assu to b qual to. (CD B). Cobn copssv an bnng stss calculaton at th n sctons o th plla gvs us th sstanc oan (M, N ) shown n gu.5. B N S s M V E M () s M l p N S N () 5 no. V E no. - M N S M - Fgu.5. nocnt conguaton. Consng a noal actng oc o N S, un bakag contons (gus.4 an.5), w obtan: 56.4 εc.5 εs 4.77 ε s.97 stanc o th nutal as o th copss g au conct oaton oaton o nocnt on th lvls 8

9 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus ε s.8 M 78.7 calculat ont o sstanc An so th actng sha stss n accoanc wth th sstanc ach wll b: s M M VE..5 lp I w nglct th conct s contbuton an cons θ 45 (nclnaton o copss connctng os), th calculat sha stngth wll b: 4 A.5 V V.9 sw 5 s s. Consng that th plla s wapp n two las o XMsh GOLD nocnt (gu.5), th contbuton th nocnt gvs to sha stngth s: as V t E εv v. t t.9 wh t.45 s th nonal thcknss o th nvual la o nocnt, an havng assu, n accoanc wth (.7) an (.8): k( n) G E t ε 5. G 56 g.5 wh k().8,., G J/, g.5. Sha stngth wth nocnt s tho: V Vs V > VE.5 Not that th stats abov w a n a spl, pcautona ann, wthout takng nto account th ct o nocnt connng, scuss n th nt scton. G J. Connng pllas Connnt o a plla wth FCM copost atal s achv b wnng th copost atal aoun th u o th plla (gu.6). Th cts o ths nocnt conguaton a: - ncas n sha stngth (as scuss n th pvous pont); - ncas o oaton capablt o th copss conct; - ncas n th conct s copsson stngth. noc. noc. Fgu.6. Connnt o th ns o a plla. 9

10 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus.. Local ct: connnt o conct Connng wth copost atal poucs an obstacl to th tansvs lataton o conct assocat wth noal copsson oc an tho an ncas n th conct s sstanc an ultat oaton un copsson. avng tn ths ncass, w a ak stuctual assssnts consng th bnng lnk o th conn conct. Accong to th appoach st oth n th gulns [], th conn conct s calculat copsson stngth cc an ultat oaton un copsson ε ccu a: wh: c L L cc c.6 (.8) c ε ccu.5.5 L c s th calculat copsson stngth o th unconn conct; s th ctv connng pssu pouc b th nocnt. Ectv connng pssu L s th pouct o an cnc cocnt k whch pns on got to tn ncclng pssu L : L k L Connng pssu L (gu 7) a b calculat as: L ρe εc (.9) (.) (.) wh ε c s th calculat actual laton o th connng nocnt, whl th gotc nocnt pcntag s: 4t b D t B B ρ o ccula sctons o at D b ρ o ctangula sctons wth nsons B an (.) A c A c A c ε c E L ε c E b Ac Ac Ac kh kh.5.65 kh.7. 8 Atot Atot Atot ε c E L ε c E c b D B B B Fgu.7. Connnt o pllas. Th cnc cocnt pns on th shap o th scton an th got o th nocnt an s calculat as ollows:

11 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus k kh kv kα (.) wh k h taks nto account th shap o th scton an s th ato btwn th ctvl ccl conct scton A c, th total scton A tot, kv taks nto account th stbuton o nocnts along th as o th plla an k α taks nto account th nclnaton α o th bs (gu.7): A k h A c tot k v n k α (.4) tan α as n s th nu cossws nson o th lnt (at D n ccula sctons), an th tnson o th unnoc aa btwn two conscutv stps, asu along th as o th lnt. In th cas o pllas wth a ctangula scton wth cons oun o an a ounng aus o c, th st o (.7) bcos: k h ( B c ) ( c ) (.5) A g wh A g s th aa o th coss scton (not nclung oun o cons). Th gulns [] suggst, n th cas o assssnt o sstanc to spl copsson o th conn plla, that w assu: ε c 4 an, o calculatng sstanc to l atgu an uctlt, that w assu: εc. 6 εk wh ε k s th nocnt s chaactstc bakag lataton. (.6) (.7) In th cas o FCM XMsh GOLD/M75 nocnt, takng nto account css caus b lanaton, n th scon cas t s asonabl to assu: εc ε (.8)... Eapls Eapl. Connng a ctangula plla: conn conct. I w cons a plla wth a ctangula scton asung 4 c consstng o conct wth a chaactstc sstanc to clncal copsson o ck Ma, an suppos that w aopt a con cuv aus o c (gu.8) an nccl th scton wth two contnuous las o XMsh GOLD nocnt, lang th bs hozontall (th sh s stong cton) an vtcall, th unconn conct s calculat copsson stngth, accong to [], wll b: α.85 c c ck. Ma c.5 Th gotc nocnt pcntag s: ( B ) b.9 ( 4). 5 t ρ B 4 wh t.9 (oubl la) an b / (contnuous wappng along th as). Th cnc cocnts a: ( B c ) ( c ) ( 6) ( 4 6). 56 kh Ag π 4 4 k v n

12 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus k α tan α as n ths cas α an. Connng pssu wll b:.5 5. L ρe εc 7.75 Ma an ctv connng pssu wll b: L k L kh kv kα L Ma Th calculat copsson stngth an ultat oaton o th conn conct wll tho b:.87.6 L cc c Ma c..87 ε.5.5 L ccu c. As w can s, connng has a uch gat pact on ultat oaton (a 79.% ncas) than on stngth (a 7.4% ncas). Appn D to th guln [] also suggsts that whn ollng th chancal bhavou o conn lnts w shoul aopt a consttutv laton consstng o an ntal paabolc scton, up to oaton, an a scon scton at a constant slop up to a oaton o ε ccu (gu.9). B B cc σ Conn σ c π/4 c Unconn c ε c ε cu ε ck Ma c. Ma ε c ε cu.5 Fgu.8. nocnt conguaton. B 4 c ε c ε cu.5 ε cc u ε ( ) Fgu.9. Lnk consttutng conn an unconn conct. In th cas un consaton, w appl th pocu llustat, w obtan th consttutv latons shown n gu., ptanng to aopton o a nub o las o nocnt, cosponng to th ultat stngths an oatons shown n tabl.. Copsson stngth, cc Ultat oaton εccu (Ma) cc / c ( ) ε ccu /ε cu Unnoc la las las las Tabl.. Ect o connng on th conct s bhavou un copsson. c : calculat copsson stngth wthout nocnt; ε cu: ultat oaton wthout nocnt.

13 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus σ (Ma) 4 las 5 l a c Conn 5 B Unconn B B 4 c ε ( ) Fgu.. Consttutv laton n conct wth nt gs o connng... Sctonal ct: ont an bnng Th consttutv latons n gu. a b us n a consvaton ol o lat sctons (gu.) o tnaton o calculat ont o sstanc an ultat bnng o th scton. A s ε sc ε c σ c sc() cc() cc c σ σ cc(ε) M ϕ u() ε c ε cu ε ε ccu c A s B ε st st() ε u t ε σ σ s(ε) ε ε ε u - - t Fgu.. Daga o tnaton o ultat ont an ultat bnng. Th ultat bnng o th conn scton s: ϕ ϕ u εu εccu u n th cas o bakag u to achng th stl s ultat oaton pont n th cas o bakag u to ultat oaton o conn conct (.9) wh th stanc o th nutal as o th copss g s th soluton to th qulbu quaton: cc sc st NS (.) as cc sc, st an N S a, spctvl, th sult o copsson tnsons n th conct, th sults o copsson an th sults o tnsl stss n th stl an th noal calculat actng oc. Ths sults a b calculat as ollows: A σ ( ϕ ( c) ) A σ ( ϕ ( ) ) sc cc s s u B σ ( ϕ z) z cc u wh σ (ε) an σ cc s(ε) a th consttutv latons o conn conct an stl (gu ). Th calculat ont o sstanc o th conn scton s gvn b th qulbu quaton: st s s u (.)

14 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus M B σ A s cc ( ) ( ) ϕ u z z z A s σs ϕu c c ( ) σ s ϕu (.)... Eapls Eapl. Connng a ctangula plla: ultat bnng an ultat ont. I w onc agan cons th plla takn n th pvous apl, t s conn wth two las o XMsh GOLD w hav th consttutv laton n th conn conct shown n gu.. Consng N S 5 an th nocnts shown n gu., th soluton to th qulbu quaton (.) gvs us:.5 whch cospons to th css u to achng th nccl conct s ultat oaton pont, an tho ultat cuv: ϕ u εccu.6 Upon bakag th atals oaton ponts a as ollows: ε c a εcccu ϕu ε s ϕu ( ).6 (.7.4) 6. 6 ε ϕ ( c).6 (.4.) 4. s u Th sults o tnsl stss an copsson a:.5 cc B σcc ( ϕu z) z. σcc (.6 z) z As σs( ϕu ( c) ) 4 σ s As σs( ϕu ( ) ) 4 σ s 57. sc st Lastl, b applng (.), w a obtan calculat ont o sstanc: M 7.9 I w pat th calculaton o unconn conct (gu.), that s, patng th oulas abov wth th consttutv laton o unconn conct n plac o that o conn conct, w hav: 7.8 ϕ ε c a ϕu ε s ϕu ( ).7 (.7.78) 6. 6 ε ϕ ( c).7 (.78.). 68 s u M. u.5.78 εcu.7 Copason o th bakag pont o th conn scton an th unconn scton s shown n gu.. As w a s, n ts o sctons too, th ct o connng s uch gat whn t cos to ultat oaton (a 6% ncas) than sstanc (a 4.5% ncas). Tabl. shows th onts an ultat bnngs tn o th scton un consaton as scb abov, o nt las o nocnt. 4

15 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus M () ϕu M /M ϕ /ϕ (/) u u Unnoc la las las las Tabl.. Calculat ont o sstanc an ultat bnng. M : calculat ont o sstanc wthout nocnt (cosponng ton S); ϕu: ultat bnng wthout nocnt. A s ε c ε cu ε sc σ c c sc() cc () ck Ma c. Ma ε c ε cu.5 M ϕ u() cc 4.4 Ma ε cu 6.7 c A s B ε st st() M A s ϕ u() ε c ε ccu ε sc σ c cc sc() cc() k 4 Ma 74 Ma t 45 Ma ε.78 ε u 67.5 A s c B σ ε st st() σ B 4 c A s 4 (φ6) A s 4 (φ6) 7 cc c ε c σ cc(ε) ε cu ε ε ccu ε u t ε ε - - t Fgu.. Copason o conn scton an unconn scton at th bakag pont. σ s(ε) ε u ε I w pat th calculaton o nt valus o noal actng oc, w obtan th sstanc oans (M, N ) o th noc scton shown n gu.. M () Unconn Conn N S 4 stat N () Fgu.. sstanc oans upon vaaton o th g o connng. 5

16 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus.. Ect on th lnt: capact o otaton wth spct to th cho Th ncas n th scton s capact o oaton poucs an ncas n th stuctu s ovall capact o oaton. Ths ncas capact a b calculat on th bass o capact o otaton wth spct to a cho, n as th ato btwn tansvs sht o a scton wth a ont o null an th sha span L v (gu.4). Accong to [], otaton capact wth spct to th cho o th conn plla a b calculat as ollows: wh: l θ ϕ u ϕ L pl L v θ u l θ L L pl ( ϕ ϕ ) L u V pl s a acto qual to.5 o th an stuctual lnts an. o th scona ons; s otaton wth spct to th cho upon lng o tns longtunal bas; th scton s ultat bnng; th scton s cuv whn th stl bas l; th lngth o th plastc hng; th sha span. (.) δ θ L v En δ t θu L v En L pl z M L v δ δ M θ pl δ t δ δ δ t δ θ pl L v, L v: δ, δ: θ, θ : L pl, L pl: θ pl, θ pl : δ t, δ t : θ u, θ u : Sha spans. Shts upon lng. otaton wth spct to th co upon lng. Lngth o th plastc hngs. otaton o th plastc hngs. Shts upon bakag. otaton capact wth spct to th co. L v En δ θ L v L pl M( z) M En δ θ t u Lv Fgu.4. otaton wth spct to th cho. Also n accoanc wth [], otaton wth spct to th cho upon lng o tns longtunal bas, θ, an th lngth o th plastc hng L p a b calculat as ollows: wh: b c LV b θ ϕ..5. ϕ (.4) L L pl c V b.lv.7.4 (.5) s th avag at o th longtunal bas; s th l tnson o th longtunal bas; s th conct s copsson stngth. c 6

17 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus... Eapls Eapl. Connng a ctangula plla: capact o otaton wth spct to th cho. Onc agan consng th plla n th pvous apl, n th cas o connnt wth two las o XMsh GOLD w hav: b.6 74 Lpl.LV c 4.4 L V b θ ϕ..5. ϕ LV c wh bnng an bnng ont upon lng o th tns stl bas a: ϕ.9 an consng th sha span L v to b.5. otaton capact wth spct to th cho wll tho b: θu θ u l ( ϕ ϕ ) w cons.5. l Th sa quantts o th unconn scton a: M 97.9 L pl Lpl LV ( ) b.6 74 Lpl.L V θ ϕ LV θu θ u l ( ϕ ϕ ) c L V. ϕ b c.5 L pl Lpl LV ( ) wh bnng an bnng ont upon lng o th tns stl bas a: ϕ.95 M I w pat th sa calculatons wth to 4 las o nocnt, w wll obtan th sults shown n tabl. an th ont-otaton agas shown n gu.5. 7

18 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus Mont, M(k N) 8 B Unconn c Conn 4 las Lpl ϕ θ M θ () ( - ) ( ) () ( ) θ u /θ u Unn la las las las Tabl 4. otaton capact wth spct to th cho. θ u : otaton capact wth spct to th cho wthout nocnt. 6 4 Yl N S otaton wth spct to th co, θ( ) B B 4 c Fgu.5. Dagas llustatng ont-otaton wth spct to th cho wth nt gs o connnt 8

19 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus. MASONY STUCTUES. As o nocnt wth FCM nocnt o ason stuctus n ssc zons wth FCM copost atals s patculal ctv o th ollowng puposs: ) Incasng tnsl stngth n plan an out o plan o ason panls (vtcal wall lnts an hozontal blts). ) Incasng sha stngth n plan o ason panls (vtcal wall lnts an hozontal blts). ) v) Inhbton o local collaps chanss. Mocaton o th o o local collaps chanss, wth a consqunt ncas n hozontal acclaton o th actvaton.. Vault nocnt nocnt o th ntaos o taos o a ason vault subjct to ssc ocs wth FCM copost atals a sult, pnng on th got o th nocnt, n ocaton o pvnton o th collaps chans o th unnoc vault. In th st cas, th noc stuctu wll stll collaps u to th chans, wth acclaton o actvaton gat than that o th unnoc stuctu; n th scon cas, th stuctu wll collaps bcaus t has ach th lt on th stngth o th atals... nocnt sgn I nocnt s nstall n such a wa that th noc stuctu wll stll collaps u to th chans, th tnt o nocnt a b sgn to nsu that th spctal acclaton o actvaton o th nw chans cs an, pss n ts o spctal acclaton, whch a b calculat on th bass o th st, th sol popts an th got o th stuctu, accong to th ncatons contan n pont C8A.4 o []. Th nocnt scton (nub o las) a lat b sgn b assssng th stss caus b noal oc an th lng ont assocat wth th acclaton o actvaton o th nw collaps chans. In th cas o nocnt nstall n such a wa as to p all th collaps chanss, th nocnt scton (nub o las) a b sgn on th bass o th stss caus b th noal oc an bnng ont assocat wth th ssc acton takn nto account n th pojct. In both cass, on th bass o th ncatons contan n [] th ont o sstanc o a noc ason scton a b assss b consng a consttutv laton o th ason consstng o an ntal lna lastc banch, up to a calculat copsson stngth o, ollow b a scton subjct to constant tnson up to th pont o oaton ε u.5 an nocnt o a lna lastc consttutv laton up to th substat s lanaton laton (o, sall, th nocnt s calculat tnsl stngth). Altnatvl, w a spl us a stss-block appoach.... Eapls Eapl. nocnt o th taos o a bal vault Lt us cons th vault-p sst shown n gu.. k Ma s th copsson stngth o th ason. Th calculaton s po wth nc to unta pth. Th stuctu s subjct not onl to ts own wght an th wght o th suppot, but to th loa p stbut on th taos o th suppot an stuat n a ssc zon. W ntall calculat th acclaton o actvaton o th collaps chans n th unnoc stuctu an thn tn th sz o nocnt wth FCM ul XMsh C/M5 to ncas t. 9

20 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus p s v Dnst n Dnst.5.. sp. s v.5 p / 8 kg/ n 6 kg/ s p s p Fgu.. Vault-p sst. Unnoc stuctu ozontal collaps ultpl Actng on th bass o th hpothss that th ason has nnt copsson stngth, wth nc to gus. an., cons a collaps chans nt b th psnc o 4 hngs. Th stuctu thus ans subv nto quons to b otat wth spct to th cnts o otaton. Vtcal loas a cons to b appl to ach o th quons (assocat wth th own wght, wth suppot an wth th unol stbut loa) an a sst o hozontal ocs popotonat to th vtcal loas though th unknown ultpl λ. Th stuctu s n a conton o balanc o as long as λ s sall nough; t s not n balanc λ s sucntl lag. W a lookng o th ctcal ultpl λ λ c ov whch th stuctu no long ts th conton o balanc. p Ssc acton 4 Fgu.. Collaps chans. Th sst a achv balanc though th ncpl o Vtual Wok; th sst s n qulbu o as long as: η η η λ δ δ δ that s, as long as: (.)

21 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus η η η λ δ δ δ th ctcal ultpl o th chans takn nto consaton s tho: (.) wh (gu.): η η η λ c δ δ δ s th wght o th -th block (,, ); s th wght o th suppot on th -th block (,, ); s th sult o th loa unol stbut on th -th block (,, ); η s th vtcal vtual sht n th applcaton pont o (,, ); η s th vtcal vtual sht n th applcaton pont o (,, ); η s th vtcal vtual sht n th applcaton pont o (,, ); δ s th hozontal vtual sht n th applcaton pont o (,, ); δ s th hozontal vtual sht n th applcaton pont o (,, ); s th hozontal vtual sht n th applcaton pont o (,, ). δ In vw o th chans shown n gus. an. o th hngs n th sctons nt b: (.) (.4) th hngs a locat at th coonats: cos.88 sn.69 cos.5 sn. cos. 5 4 cos 4. 5 sn.9 4 sn4 th wghts o th th ach quons an th coonats o th applcaton ponts a gvn b: ( ) (.5) (.6) 4 sn cos g ( ) 4 sn sn g an a qual to: (.7)

22 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus (X, Y ) (, ) (, ) λ (, ) λ (, ) (, ) λ ϕ ozontal vtual shts δ δ δ (, ) (, ) λ ( g, g ) λ (g, g) 4 λ λ (, ) (g, g) (, ) λ λ ( 4, 4 ) δ δ δ ϕ δ δ ϕ δ V tual vtc al shts ϕ η η η η η η η ϕ η η ϕ Fgu.. Sst o actng ocs an vtual shts g.6 g.6 g.95 g.5 g.6 g.7 (.8) th wght o th suppot on th th ach quons an th coonats o th applcaton ponts a gvn b an a qual to: n ( sn sn ) n ( sn sn ) n sn cos ( sn) (.9) (.) th sults o th loa stbut on th th ach quons an th coonats o th applcaton ponts a b calculat as ollows: ( cos cos ) p ( cos cos ) (.)

23 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus an a qual to: th cnt o otaton o th scon block has th ollowng coonats (gu.): ( 4 )[ ( ) ( )( ) ] ( 4 )( ) X.4 ( )( 4 ) ( 4 )( ) Y ( X ).4 (.) (.) I w abtal tn th otaton ϕ o th st block, th otaton o th scon an th block wll b (gu.): ϕ. 4 ϕ X ass ϕ ϕ. ϕ X 4 ϕ (.4) th shts n th applcaton ponts o ocs a: η η η ( g ). ϕ ( g X ). ϕ ( g 4 ). ϕ ϕ 5 ϕ 8 ϕ 6 η ϕ ( n ). 4 ϕ η φ ( n ass ). 8 φ η ϕ ( n 4 ). 49 ϕ η ϕ ( ). 56 ϕ η ϕ ( ass ). ϕ η ϕ ( 4 ). 58 ϕ I w appl (.) w tho hav th ultpl: λ c.96 δ δ δ ( g ). ϕ ( g ass ). ϕ ( g 4 ). ϕ ϕ 84 ϕ 87 ϕ 5 δ ϕ ( n ). 6 ϕ δ ϕ ( n ass ). 7 ϕ (.5) δ ϕ ( n 4 ). 4 ϕ δ ϕ ( ). 56 ϕ δ ϕ ( ass ). 4 ϕ δ ϕ ( 4 ) ϕ (.6) Ths ultpl s pnnt on th chans cons, an tho th poston o th hngs. In oth wos, w chang th poston o th hngs (.4) an pat th pocu, w wll gt a nt ultpl o th valu (.6). Th stuctu s actual collaps ultpl s th sallst o all thos cosponng to th kntcall assbl collaps chanss. It s tho ncssa to pat th pocu scb to obtan postons,,, 4 o th hngs tnng th nu collaps ultpl. Ths ptton has ala bn po, so that th on psnt b th hngs (.4) s th ctv collaps chans an th on pss b (.6) s th stuctu s ctv collaps ultpl. Locaton o pssu ponts To con ths, w a tn th locaton o pssu cnts on th sctons o th stuctu an chck that t s alwas n th thcknss o, n hng sctons, on th g. Constanng actons n th t hngs ( 4 ) can b tn usng th sst o qulbu quatons (gu.4):

24 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus ( [ ] [ ( ] λ λ λ c s v vs g g c g g 4 4 v g c g s vs ) ) (.7) an a qual to: 9.7 vs v 9.84 s (.8) λ c λ c λ c λ c λ c λ c λ c λc λ c (, ) (g, g) ( g, g ) (, ) (, ) (, ) (, ) ( g, g ) (, ) (, ) (, ) (, ) (4, 4) vs s v Fgu.4. actons n th t hngs. Bnng ont n laton to th taos o a gnc scton nt b s: [ ] g g c g g s vs M λ (.9) wh. Noal oc, cons postv t s copsson oc, n th gnc scton nt b s: [ ] [ ] ψ λ ψ sn cos N c s vs (.) Th unctons o that appa n (.9) an (.) a (gu.5): 4

25 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus : () uncton assocatng th angl wth th abscssa o th taos o th scton nt b ; : () uncton assocatng th angl wth th onat o th taos o th scton nt b ; : () uncton assocatng th angl wth th wght o th stuctu btwn th ntal scton an th scton nt b ; : () uncton assocatng th angl wth th wght o th suppot btwn th ntal scton an th scton nt b ; : () uncton assocatng th angl wth th sult o th loa stbut btwn th ntal scton an th scton nt b ; : g () uncton assocatng th angl wth th abscssa o th pont o applcaton o (); : g () uncton assocatng th angl wth th onat o th pont o applcaton o (); : () uncton assocatng th angl wth th abscssa o th pont o applcaton o (); : () uncton assocatng th angl wth th onat o th pont o applcaton o (); : () uncton assocatng th angl wth th abscssa o th pont o applcaton o (); : ψ() uncton assocatng th angl wth th nclnaton o th scton nt b ; an a b pss as: < < n p n p s s π π π cos < < n π π π tan sn tan (.) < < n p v p p n p s s s s π π π (.) < < n p π π π n sn h n [ ] < < gp p gp p p gp p n gp g s π π cos sn 4 < < p gv v gp p p gp p n g s π π π sn 4 (.) 5

26 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus n h n h g ( ) ( ) ( ) ( ) sn h n < π π < π ( ) sn n n < (.4) π π < π ( ) cos n < π π < π n n < ψ ( ) π π π < π wh h () s th hght o th suppot on th scton nt b (gu.5): n h ( ) ( ) n < π π < π s th valu o cosponng to th bas scton o th lt p: n (.5) (.6) a tan n 56. (.7) () ((), ()) ( (), ()) () h n () p n ((), ()) () Fgu.5. Functons o. p an gp psnt th wght o ach p an th abscssa o th cnt o gavt o th lt p, spctvl: 6

27 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus sp p sp 5.96 gp.5 (.8) v an gv psnt th wght o th vault an th onat o ts cnt o gavt: t π 4 v 9.46 gv.5 (.9) π an psnt th total wght o th suppot an th onat o th cnt o gavt o ts volu: g n ( 4 π) n 4.9 g.75 t (.) t Th stanc o th cnt o pssu o th taos n th scton s: M u (.) N whl th locaton o pssu cnts on th stuctu s plan s gvn b th paatc quatons: p u cos( ψ ) u sn( ψ ) (.) Th locaton o th pssu cnts pss b (.) s tac n gu.6.. () u() ( p (), p ()) λ c.96 (). λ c Fgu.6. Locaton o pssu cnts. Acclaton o actvaton o th chans On th bass o th st-up n pont C8A.4 o [], th ass patcpatng n th collaps chans shown n gu. s th pouct o: δ δ δ M g δ δ δ g (.) wh th wghts, an (,, ) an th cosponng hozontal shts a gvn b (.8) (.5). Th acton o ass patcpatng s tho: gm.8 (.4) tot wh tot s th total wght o th asss nvolv n th chans: 7

28 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus tot Lastl, spctal acclaton o actvaton o th chans shown n gu. s: a (.5) λcg.9 g (.6) FC wh th connc acto FC s assu to b.5. noc stuctu W ntn to noc th stuctu so as to chang ts collaps chans an ncas th cosponng hozontal ultpl. Not that th collaps chans n th unnoc stuctu (gu.) os not nvolv th ps, whch a capabl o supplng th vault wth th ncssa hozontal acton (thust) wthout ovtunng. Lt us cons th nocnt vc shown n gu.7, n whch ul XMsh/M5 copost atal s appl all ov th taos o th vault. Ths nsus that th cannot b ntaos hngs n th sctons o th vault, but onl n thos o th ps, whch wll tho b nvolv n th nw collaps chans. Th collaps ultpl o th noc stuctu a tho stll b tn usng (.) n whch th quantts (wghts an shts) a consstnt wth a nw collaps chans n whch th ntaos hngs a onl b locat n th scton o th ps, whl th taos hngs, whch a not p b th nocnt, a b plac n an poston. p Spcc wght n Spcc wght s nocnt wth FCM XMsh C/M5.5.. s p. s.5 p / 8 kg/ n 6 kg/ s p s p Fgu.7. Locaton o FCM nocnt. ozontal collaps chans Lt us thn cons th collaps chans shown n gus.8 an.9, wth th hngs n th sctons: π n 6. 4 (.7) 8

29 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus p Ssc acton 4 Fgu.8. Collaps chans o th stuctu wth FCM nocnt. In laton to ths chans, th hngs a locat at th coonats (gu.9):.. cos.4 4 sp. sn (.8) th wghts an cnts o gavt o th st two quons a also tn accong to (.6), whl th wght an cnt o gavt o th th block a latv to th ght p onl: 9.8 g.8.8 g.8 g.97 g.5 sp 5.96 sp g.5 (.9) g.5 th wghts o th suppot on th st two quons a also tn b (.9), whl th wght o th suppot on th th block s null: (.4) th sults o th loa stbut on th st two quons an th coonats o th ponts o applcaton a also tn b (.), whl th loa stbut on th th block s null: th cnt o otaton o th scon s also tn accong to (.): X. (.4) Y 5.4 (.4) 9

30 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus (X, Y ) ϕ ozontal vtual shts (, ) λ (, ) (, ) λ (, ) λ δ δ (, ) (g, g) λ λ (g, g) 4 λ δ δ δ δ ϕ (, ) (, ) ( g, g ) λ δ ϕ Vtc al vtual shts (4, 4) η ϕ η ϕ ϕ η η η η η Fgu.9. Sst o actng ocs an vtual shts o th FCM noc stuctu. avng abtal tn th otaton ϕ o th st block, th otatons o th scon an th block can also b tn wth (.4): ϕ. 5 ϕ 96 ϕ ϕ (.4) th shts n th ponts o applcaton o ocs, onc agan tn accong to (.5), a tho: η. ϕ η. 4 ϕ η. 48 ϕ η. ϕ η. 66 ϕ η. 6 ϕ η. 7 ϕ δ. 97 ϕ δ. 7 ϕ δ. 44 ϕ δ. 69 ϕ δ. 9 ϕ δ. 5 ϕ δ. 68 ϕ I w appl (.) w tho obtan th ultpl: λ c.97 (.44) (.45) whch s about oubl th on o th unnoc stuctu (th chans n gu.). too, th ultpl pns on th chans takn nto consaton, an tho th poston o th hngs. I w chang th poston o th hngs (.7), alwas coplng wth th stctons pos b th nocnt, an patng th pocu scb, w wll n a nt ultpl o th valu o (.45). Th ctv collaps ultpl o th noc stuctu a b oun b nsng th collaps

31 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus ultpl wth spct to th postons o th hngs,,, 4, alwas n coplanc wth th stctons cat b th nocnt. Ths opaton was po bo, an so th on psnt b th hngs (.7) s th ctv collaps chans o th noc stuctu an th on pss b (.45) s th ctv collaps ultpl. Locaton o pssu cnts To con ths, w a tn th locaton o cnts o pssu on th sctons o th stuctu an chck that t: ) alwas ls n th thcknss n unnoc sctons o on th g o hng sctons; ) ls n th thcknss o ntaos o sctons wth a noc taos; n th latt cas, tnsl n th nocnt can guaant qulbu. Th constanng actons (gu.) n th n hngs ( 4 ) can also b tn usng th sst (.7) an ntng th quantts o th collaps chans n t (.7), qual to: vs. v s.9 9. (.46) (, ) λ (, ) (, ) λ λ (, ) λ (, ) ( g, g ) λ s (g, g) (, ) vs λ (, ) (g, g) λ ( 4, 4 ) Fgu.. actons n th n hngs o a stuctu noc wth FCM. Bnng ont n laton to th taos an noal oc n th gnc scton nt b a also pss b (.9) an (.), wth th paats cosponng to th nw collaps chans. Th sultng locaton o th pssu cnts, onc agan pss b (.) an (.), s shown n gu.. v

32 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus. () u() ( p (), p ()) λ c.96 (). λ c Fgu.. Acclaton o th actvaton o th chans Followng th st-up o pont C8A.4 n [] o th noc scton too, th ass patcpatng n th collaps chans n gu.9 s calculat as ollows: δ δ δ M g δ δ δ 5.4 g (.47) wh wghts, (,, ) an th cosponng hozontal shts a th pouct o (.9) - (.44). Th acton o th ass patcpatng s tho: gm.97 (.48) tot wh s th total wght o th asss nvolv n th chans shown n gu.9: tot tot. Spctal acclaton o actvaton o th chans n th gu s tho: a (.49) λ g c.5 g (.5) FC wh th connc acto FC s onc o assu to b.5. Ths acclaton o actvaton s 67% gat than that o th unnoc stuctu. Not that, n o to ncas th hozontal collaps ultpl vn o, an tho spctal acclaton o actvaton o th chans, t woul b ncssa to ntvn b nocng th ntaos o th vault o th ps as wll. At ths pont w a pss an opnon as to th sutablt o acclaton o actvaton o th chans b copang ths acclaton wth an, whch bascall pns on th st on whch th constucton stans, as scb n pont C8A.4 o []. Stss (ont an noal oc) Th bnng ont an noal oc scb n (.9) an (.) appa n gus. an.. Fgu. also shows bnng ont M S (), calculat wth spct to th cnt o gavt o th sctons pouc b:

33 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus MS s M N wth s s p n < sv π s p π < π n (.5) In ach o th noc sctons, th scton o th nocnt ust b tn n laton to ths stss. Fo apl, cons th ollowng whn chckng: ) th scton n whch th ccntct o noal oc s gatst (n th oulus); ) th scton n whch ont M S () s gatst (n th oulus). I w stu th locaton o th pssu cnts (.) w a c that th scton n whch noal oc acts wth au ccntct wll b nt b (gu,): v (.5) th cosponng stss s: MSD( v ).56 NS N( v) 9.8 (.5) MS I w an th ont aga (.5) w a tn that th scton wth au bnng ont s nt b (gu.): v 54 (.54) th cosponng stsss a: MSD( v ) 5.69 NS N( v ) 8. (.55) MS () () () Mont (/) v v () Mont (/) 6 4 () () MsD() - M() M() MsD() - λ c M S - M() M S() Mont (/) MS () () λ c Fgu.. Bnng ont.

34 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus v () () N() Noal oc (/) v () () N() Noal oc (/) - Noal oc (/) N S λ c N() N S () () 8 λ c Fgu.. Noal oc. nocnt scton Supposng w noc th vault taos as shown n gu.7, wth two las o FCM ul XMsh C/M5. Th nocnt scton s tho: A t wh t.47 s th nonal thcknss o th nvual la o nocnt. (.56) Takng nto account th phnonon o lanaton, w cons a calculat laton o th nocnt o ε. W thn tn th scton o th vault noc aganst stsss (.5) an (.55). I w aopt th stss-block appoach, an supposng th scton to hav bokn whn th nocnt s ultat laton pont was ach (gu.4), o scton w wll hav: v αβ s M ( s β) Eε 6.9 (.57) wh s th stanc o th nutal as o th copss g: A E N ε S 85.8 (.58) αβ an as α an β a n n gu.4, E 4 Ma th oulus o lastct o th nocnt bs s: k.5 Ma (.59) M th calculat copsson stngth o th ason, assss takng nto account a patal sat cocnt o M. wth a au ason oaton o: ε ε.57 (.6) s lss than ε u.5, w a con th assupton o bakag on th noc s. 4

35 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus N S M Q uon c β/ s ε u ε ε /(s-) β α /(s-) α.85 β. 8 E ε E 4 Ma ε 7 Ma ε u. 5 t ε Doatons Tnsons Fgu.4. Tnson status o th scton. In laton to scton v, w wll hav: αβ s M ( s β) Eε 7. (.6) wh th stanc o th nutal as o th copss g s: A Eε NS.9 (.6) αβ In ths cas, th au oaton o th ason s: ε ε. (.6) s whch s onc agan lss than ε u.5. Fgu.5 llustats vcaton o all th noc sctons o th vault. It shows on th plan (N, M) th onon o sstanc o th noc scton an th locaton o ponts (N S (), M S ()), wth btwn an π. 5 Noal oc (/) Vault stss (N S (), M ()) (N, M ) π Mont (/) -5 (N, M ) v v Unnoc scton noc t scton Fgu.5. Doan o sstanc an locaton o stsss on th vault. Sha In laton to th noc stuctu, un th chans conton sha o th gnc scton nt b wll b: V [ vs ( )] sn ψ [ λ ( ( ) ( ) ( ))] cos ψ s c (.64) 5

36 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus Consng th contbuton o both cton an cohson to sha stngth, th sha stngth o th gnc scton nt a b stat as: wh: μ V k.9 s v c (.65) M μ s th patal ol cocnt, assu to b.; s() s th thcknss o th stuctu n scton (th scon o (.5)); v s th calculat sha stngth o th ason n th absnc o noal oc; s th chaactstc valu o th ason cton cocnt; k M s th patal sat cocnt o th ason ( M ); c () s th sult o copsson o th ason, whch a b stat as appoatl: c ( ) N N ( ) s( ) u( ) u ( ) s( ) u( ) < s( ) (cnt o pssu n th scton) (cnt o pssu outs th scton) (.66) Sha stngth (.65) ust b gat than th sha stss actng n ach scton (.64). Copason o sha stss an sha stngth (.65) obtan b assung v.6 Ma an μk.4 s shown n gu () () 6 Taglo (/) -6 - () () 6 - V -V() - V() -V() - - V() Shang (/) - - V λ c V () () () λ c V S () -V () - Fgu.6. 6

37 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus 4. ATITION WALLS 4. As an cta o nocnt wth FCM Mason patton walls subjct to ssc acton a spla th tpcal local chanss o collaps shown n th aga n gu 4.. In th contt o analss o th local collaps chanss nt n pont C8A.4 o [], spctal acclaton o actvaton o a collaps chans s: a α g (4.) FC wh s th patcpatng acton o th ass, calculat as ollows: n gm M n δ g (4.) tot δ wh M s th ass patcpatng n th chans: h t t (a) (b) Fgu 4.. Out-o-plan collaps chanss n wall pattons. In (4.)-(4.): α s th hozontal ultpl o actvaton o th chans (gu 5), to b tn b posng th au qulbu contons on th sst; g s th acclaton o gavt; FC s th Connc Facto, assu to b.5 th ason s copsson stngth s cons to b nnt; tot s th total wght o th asss nvolv n th chans; s th wght o th -th ass nvolv n th chans,,,,n; s th vtual hozontal sht n th pont o applcaton o th wght,,,,n. δ In th cas o th collaps chanss shown n gu 4., th sst s qulbu suppls th ultpls: t ht t 4 ht α o th chans n gu 4. (a); α o th chans n gu 4. (b); I th blocks akng up th chans a not stng on th goun, vcaton o th Lt Stat o th Saguang o L s sats th spctal acclaton o actvaton a satss: (4.) wh: a ad (4.4) 7

38 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus wth: S (T ): T : an as: wh: ( T ) ψ( Z) S (4.5) q a D onat o th spctu o lastc spons n laton to th pobablt o cng th nc po V, cosponng to po T, b %; st natual po o th nt stuctu; ψ Z Z N (4.6) N Z: s hght, wth spct to th ounaton o th cnt o gavt o th constants btwn th blocks nvolv n th chans; : s th stuctu s hght abov th ounaton; N: s th nub o loos n th bulng. I conton (5) s not t, t s possbl to ntvn wth FCM an connctos to noc th patton wall. 4.. Dsgn o nocnt To pvnt th chans llustat n gu 4. (a) wth a spctal acclaton o acton bnng th upp n o th patton wall qual to: a p h D t (4.7) g To pvnt th chans llustat n gu 4. (b) wth a spctal acclaton o a D, w n a w ust aang th copost nocnt on th suac o th patton wall, sgn n o to ak su that th scton has a calculat ont o sstanc o o than: a D M S ad p h g 8 t (4.8) Th ont o sstanc o th noc scton a b stat as: M.9 t E A ε wh t s th thcknss o th patton wall, E th oulus o lastct, A th aa o th scton an ε th calculat lataton o th nocnt (lnk wth th phnonon o lanaton). Copason o (4.8) wth (4.9) gvs us th ncssa nocnt scton: A MS.9 t E ε (4.9) (4.) 8

39 t Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus h t t (a) Connctos (b) nocnt Fgu 4.. nocnt wth FCM to pvnt out-o-plan collaps chanss. W a conuct a o tal nvstgaton on th bass o th gulns []. Th ont o sstanc o th noc scton a b stat takng nto consaton a stss-block appoach o th ason wth a copsson tnson o.85 tn ov th scton wth a pth o.8, wh s th ason s calculat copsson stngth an s th stanc o th nutal as o th copss g (gu 4.). Vw ε?.85.8 () b t () A L nocnts A Scton Fgu 4.. Tnsons on th scton. In th absnc o noal oc, th calculat ont o sstanc s tho: ( t.4 ) M ε E A (4.) wh s th stanc o th nutal as o th copss g, calculat as ollows: ( t ) E A ε.8.85 u.8.85 ε E A n th cas o bakag whn th ason achs ts ultat oaton pont n th cas o bakag whn th nocnt achs ts calculat ultat laton (4.) 4... Eapls Eapl. nocnt o a patton wall aganst out-o-plan ssc acton. Lt us cons th patton wall shown n gu 4.4, consstng o ason wth a calculat copsson stngth o.5 Ma. W tn th acclaton o actvaton o th chanss n gu 4. an tn th aount o nocnt wth FCM ul XshC/M5 qu to ncas t. W cons th spons spctu o th Lt Stat o th Saguang o L shown n gu

40 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus t h t..5 Ma S (T), g h t.6.4. ag sηfo.7 g a g.5g η S S TS S.5 F o.5 T(s) 4 t Fgu 4.4. atton wall subjct to ssc actons at ght angls to th plan. Th sst s qulbu n laton to th collaps chans llustat n gu 4. (a) povs us wth th hozontal ultpl o actvaton: t α. ht an tho th chans s spctal acclaton: a αg.g FC.5.5 g as, o th chans un consaton,, an takng nto account a connc acto o FC.5, as qu b []. Dan, psnt b a D, s: a S ( T ) ψ Z.7.8. g.4 g D q takng nto consaton th au onat o th spctu an Z, an N 4 n (7). Th stngth o th connctos qu to pvnt ths chans s: D a p h t.4. g.66 Consng applcaton o ul XJont connctos wth a at o φ c, wth an stat b scton o: πφc A c an a calculat conncto laton o ε, stngth wll b: con A c εcon E Fconn conn 9 Th sst s qulbu n laton to th collaps chans llustat n gu 4. (b) gvs us th hozontal actvaton ultpl: t α 4. ht an tho a spctal acclaton o chans actvaton o: 4

41 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus a αg. g FC.5.96 g as, o th chans takn nto consaton, an w hav cons FC.5. Dan, psnt b a D, s onc agan: S( T ) ψ( Z).7.8. g q a D Th ont o sstanc qu to t ths an s: M t S ad p h g 8.4 g. g 8.4 g.495 Consng that ul XMsh C/M5 nocnt has a calculat nocnt laton o ε, th nocnt scton qu s appoatl: MS A n t E ε I w appl vtcal stps w wth a cnt-to-cnt stanc o (gu 4.5), th nocnt scton wll b: A h t h t 5 t nocnt b Fgu 4.5. nocnt conguaton o a patton wall wth FCM. Wth ths nocnt conguaton, supposng that bakag s on th tnsl s (achng ε n th bs), th stanc o th nutal as o th copss g wll b: ε E A an th au oaton o th ason wll b: ε ε.47 t Ths valu cons th assupton o bakag n th tnsl aa. Fnall, th scton s calculat ont o sstanc wll b: M ε E A ( t.4 ) (..4.8).97 Fo btt vson o stsss, th aga n gu 4.5 also conss a hozontal nocnt 5 w. 4

42 Tchncal notbook Bulngs Ssc tot wth FCM Conct an ason stuctus ncs [] CN DT/4 Instuctons o th Dsgn, Ecuton an Contol o Statc Consolaton Wok usng Fb noc Coposts, 4. [] Janua 4 8 Mnstal Dc. Tchncal gulatons o constucton. [] Fbua 9 oanu no. 67. Instuctons o applcaton o th tchncal stanas o constuctons contan n th Janua 4 8 nstal c. Basc bblogaph Copost a atc cntza p l nozo volt n uatua [F. Focacc, G. Mantgazza, Stu a on Monuntal stoaton n th Ega Islans, alazzo Floo, Favgnana, Octob 7 FCM vs. F copost to stngthn C bas: a copaatv analss [a. D Toaso, F. Focacc, G. Mantgazza, A. Gatt, FCS-8 Unvst o atas, atas, Gc, Jul 6-8, 7] ow uabl s F-plat conct un ostu? [O. Buukoztuk, FCS-8 Unvst o atas, atas, Gc, Kul 6-8, 7] Etnall bon F nocnt o C stuctus [FIB Bulltns n. 4] F nocnt n C stuctus [FIB Bulltns n. 4] Gu o th Dsgn an Constucton o Etnall Bon F Ssts o Stngthnng Conct Stuctus. [ACI 44.] Istuzon p la pogttazon ntvnt consolanto statco ant l utlzzo copost bonozat a atc cntza FCM (Instuctons o plannng statc consolaton pojcts usng b noc cnttous at copouns) 4