ii T.C. %$/,.(6ø5h1ø9(56ø7(6ø )(1%ø/ø0/(5ø(167ø7h6h ø1ù$$70h+(1'ø6/øöø$1$%ø/ø0'$/,
<$3,/$5,1'(35(0'$95$1,ù,1,1%(/ø5/(10(6øødø1
d2.02'/88<$5/$0$/,<h.$57,0,<g17(0ø
'2.725$7(=ø øQú<N0K.DDQ7h5.(5 BDOÕNHVLU+D]LUDQ– 2005iii T.C. %$/,.(6ø5h1ø9(56ø7(6ø )(1%ø/ø0/(5ø(167ø7h6h ø1ù$$70h+(1'ø6/øöø$1$%ø/ø0'$/,
<$3,/$5,1'(35(0'$95$1,ù,1,1%(/ø5/(10(6øødø1
d2.02'/88<$5/$0$/,<h.$57,0,<g17(0ø
'2.725$7(=ø øQú<N0K.DDQ7h5.ER %DOÕNHVLU+D]LUDQ– 2005 %XoDOÕúPD%DOÕNHVLUhQLYHUVLWHVL5HNW|UO÷%LOLPVHO$UDúWÕUPD3URMHOHUL %LULPLWDUDIÕQGDQ%$3QROXSURMHLOHGHVWHNOHQPLúWLUii ÖZET YAPI/$5,1'(35(0'$95$1,ù,1,1%(/ø5/(10(6øødø1 d2.02'/88<$5/$0$/,<h.$57,0,<g17(0ø Kaan TÜRKER %DOÕNHVLUhQLYHUVLWHVL)HQ%LOLPOHUL(QVWLWV øQúDDW0KHQGLVOL÷L$QDELOLP'DOÕ 'RNWRUD7H]L7H]'DQÕúPDQÕ 'Ro'U(UGDOø57(0 %DOÕNHVLU dDOÕúPDGD\NVHNPRGODUÕQHWNLOLROGX÷XELQDODUÕQGHSUHPHWNLOHULDOWÕQGDNL OLQHHU ROPD\DQ GDYUDQÕúÕQÕQ EHOLUOHQHELOPHVL DPDFÕ\OD HWNLQ ELU dRN 0RGOX 8\DUODPDOÕ <N $UWÕPÕ <|QWHPL d08<$< JHOLúWLULOPLúWLU <|QWHPGH JHRPHWUL GH÷LúLPOHULQLQ GHQJH denklemlerine etkisi ve malzemenin elasto-plastik GDYUDQÕúÕ J|]|QQH DOÕQPDNWDGÕU 3ODVWLN úHNLOGH÷LúWLUPHOHULQ SODVWLN NHVLW DGÕ YHULOHQ EHOLUOL NHVLWOHUGH WRSODQGÕ÷Õ EXQXQ GÕúÕQGDNL E|OJHOHUGH GDYUDQÕúÕQ lineer-elastik ROGX÷X YDUVD\ÕOPDNWDGÕU ÇMUYAY’inGHVLVWHPLQEHOLUOLVDELWGúH\\NOHUYHDUWDQPRGDO \DWD\ \NOHU LoLQ KHVDEÕ \DSÕOPDNWDGÕU <|QWHPGH VDELW GúH\ \NOHU LoLQ KHVDS \DSÕOGÕ÷ÕQGDQikinci mertebeHWNLOHULOLQHHUOHúWLULOHELOPHNWHGLU$\UÕFDDNPDNRúXOODUÕ GD GR÷UX SDUoDODUÕQGDQ ROXúDFDN úHNLOGH OLQHHUOHúWLULOHUHN LGHDOOHúWLULOPHNWHGLU <|QWHPLQ EX |]HOOLNOHUL QHGHQL\OH SODVWLN NHVLWOHULQ ROXúXPX DUDVÕQGDNL OLQHHU GDYUDQÕúE|OJHOHULQGH\NDUWÕPÕX\JXODQPDVÕQDJHUHNNDOPDGDQKHUSODVWLNNHVLWLQ ROXúXPXQD NDUúÕ JHOHQ \DWD\ \N DUWÕPÕ YH GDYUDQÕú E\NONOHUL NHVLW WHVLUOHUL \HUGH÷LúWLUPHOHU SODVWLN G|QPHOHU YE GR÷UXGDQ GR÷UX\D EHOLUOHQHELOPHNWHGLU %|\OHFH EWQ SODVWLN NHVLWOHULQ ROXúXPX YH \DSÕ GDYUDQÕúÕ D\UÕQWÕOÕ RODUDN izlenebilmektedir. Yöntemde yüksek mod etkilerini gözönüne almDNDPDFÕ\ODDUGÕúÕN LNL SODVWLNOHúHQ NHVLW DUDVÕQGDNL OLQHHU GDYUDQÕú E|OJHVLQGH GDYUDQÕú VSHNWUXPX
analizi HVDVODUÕQGDQ \DUDUODQÕOPDNWDGÕU %XQD J|UH KHU SODVWLN NHVLW ROXúXPXQGDQ
VRQUD VLVWHPLQGH÷LúHQ PRGDO|]HOOLNOHUL J|]|QQHDOÕQDUDNEHOLUOHQHQPRGal yatay \N GD÷ÕOÕPODUÕ LoLQ DQDOL] \DSÕOPDNWDGÕU <|QWHPLQ EHWRQDUPH ELQDODU ]HULQGHNL VD\ÕVDOX\JXODPDODUÕQDRODQDNVD÷ODPDN]HUH0(3$5&6DGÕYHULOHQELUELOJLVD\DU SURJUDPÕ JHOLúWLULOPLúWLU *HOLúWLULOHQ \|QWHP /LQHHU 2OPD\DQ 'LQDPLN $QDOL] (LODA), PRG HVDVOÕ *HOHQHNVHO /LQHHU 2OPD\DQ 6WDWLN $QDOL] *-LOSA) ve )(0$¶GD|QHULOHQQLIRUPYHPRGDOGD÷ÕOÕPODUÕLoLQ/26$LOHNDUúÕODúWÕUÕODUDN GH÷HUOHQGLULOPLúWLU %X DPDoOD IDUNOÕ GHSUHP \HU KDUHNHWL ND\ÕWODUÕ LoLQ oHúLWOL periyotlara sahip betonarmH oHUoHYHOHU ]HULQGH VD\ÕVDO X\JXODPDODU \DSÕOPÕúWÕU 'H÷HUOHQGLUPHOHUNDW\DWD\\HUGH÷LúWLUPHOHULJ|UHOLNDW|WHOHPHOHULPDNVLPXPNLULú SODVWLN G|QPH GH÷HUOHUL NDW NHVPH NXYYHWOHUL NDSDVLWH H÷ULOHUL YH VLVWHPGHNL SODVWLNOHúHQ NHVLW GD÷ÕOÕPODUÕ LQFHOHQHUHN \DSÕOPÕúWÕU %XQD J|UH JHOLúWLULOHQ d08<$<¶QLQGL÷HUoGD÷ÕOÕPGDQ *-LOSA, LOSA-üniform ve modal) elde edilen VRQXoODUD J|UH /2'$¶H GDKD \DNÕQ VRQXoODU YHUGL÷L EHOLUOHQPLúWLU $\UÕFD d08<$<¶QGH VSHNWUDO |OoHNOHPHQLQ PRG VD\ÕVÕQÕQ YH ikinci mertebe etkilerinin DQDOL]VRQXoODUÕ]HULQGHNLHWNLOHULGHLQFHOHQPLúWLU
ANAHTAR SÖZCÜKLER: dRN PRGOX X\DUODPDOÕ \N DUWÕPÕ \|QWHPL oRN PRGOX X\DUODPDOÕ OLQHHU ROPD\DQ VWDWLN DQDOL] PDO]HPHQLQ OLQHHU ROPD\DQ GDYUDQÕúÕLNLQFLPHUWHEHHWNLOHUGHSUHPSHUIRUPDQVÕGH÷HUOHQGLUPHVLEHWRQDUPH bina
iii
ABSTRACT
MULTI MODAL ADAPTIVE LOAD INCREMENTS METHOD FOR DETERMINATION OF EARTHQUAKE RESPONSE OF STRUCTURES
Kaan TÜRKER
University of Balikesir, Institute of Science, Department of Civil Engineering
( Ph.D. Thesis / Supervisor : Assoc. 3URI'U(UGDOø57(0
Balikesir -Turkey, 2005
In this study, an effective Multi Modal Adaptive Load Increments Method (MMALIM) is developed for the determination of nonlinear behaviour of buildings affected by higher modes under earthquake loads. Elastic-plastic behaviour of material and second-order effects are considered in the method. It is assumed that plastic deformations are accumulated at certain sections defined as plastic sections and the other portions of the system remain linear-elastic. The system is analysed under factored constant gravity loads and increasing modal lateral loads in the method. The second-order effects can be linearilized due to the fact that the structure is analyzed under factored constant gravity loads. In addition, yield conditions are idealized as compose of linear segments. By these properties of the developed method, load increment for the formation of each plastic section and response quantities (internal forces, displacements, plastic rotations etc.) are determined directly without additional load increments in the linear regions between plastic sections. Formation of all plastic sections and behaviour of the system are tracked in detail. In the method, higher mode effects are considered by using response spectrum
analysis approach at linear region between the two successive plastic sections. Therefore, modal lateral loads obtained by using the modal properties of the system with plastic sections are used in the analysis. A computer program called MEPARCS is developed for analysis of reinforced concrete buildings by using MMALIM. The developed method is evaluated by comparing with Nonlinear Dynamic Analysis (NDA), Traditional Nonlinear Static Analysis (T-NSA) based on first mode and Nonlinear Static Analysis (NSA) proposed for uniform and modal distribution on FEMA 356. For this reason, reinforced concrete frames with different natural periods are analysed for different earthquake records. Floor lateral displacements, interstory drifts, maximum beam plastic rotations, story shears, capacity curves and distribution of plastic sections on the system are investigated in the evaluations. The results of the developed MMALIM are more closer to the results of NDA when compared with the results of other distributions (T-NSA, NSA-uniform and modal). Furthermore, effects of spectral scaling, number of modes and geometrical changes (second-order effects) on results of analysis are investigated in the developed MMALIM.
KEY WORDS: Multi modal adaptive load increments method / multi modal
adaptive nonlinear static (pushover) analysis / nonlinear behavior of material / second order effects / seismic performance evaluation / reinforced concrete building
iv
ødø1'(.ø/(5 Sayfa
ÖZET, ANAHTAR SÖZCÜKLER ii
ABSTRACT, KEY WORDS iii
ødø1'(.ø/(5 iv 6(0%2//ø67(6ø vi ù(.ø//ø67(6ø ix dø=(/*(/ø67(6ø xi ÖNSÖZ xiii 1. *ø5øù 1 1.1 Konu 1 1.2 .RQXLOHøOJLOL/LWHUDWUQøQFHOHQPHVL 4 1.3 dDOÕúPDQÕQ$PDFÕYH.DSVDPÕ 16 2. %ø1$/$5,1'(35(0'$95$1,ù,1,1%(/ø5/(10(6øødø1 (7.ø1%ø5d2.02'/88<$5/$0$/,<h.$57,0, <g17(0ø d08<$< 18 2.1 9DUVD\ÕPODU 18 2.2 YöntHPLQ(VDVODUÕ 20 2.3 $NPD.RúXOODUÕYH$NPD9HNW|U 22
2.4 Yöntemin Matematik Formülasyonu 25
6LVWHPLQ%LULP<N$UWÕPÕLoLQ/LQHHU2OPD\DQ+HVDEÕ 26 2.4.1.1 Denge Denklemleri 27 2.4.1.2 PODVWLNOHúHQ.HVLWOHUGHNL$NPD.RúXOODUÕ 32 2.4.1.3 'HQNOHP7DNÕPÕQÕQ*HQLúOHWLOPHVLYHd|]P 35 2.4.1.4 dXEXN8o.XYYHWOHULQLQYH'L÷HU.ULWLN.HVLW7HVLUOHULQLQ+HVDEÕ 35 2.4.1.5 3ODVWLNOHúHQ.HVLWLQYH<N$UWÕPÕQÕQ%HOLUOHQPHVL 36 2.4.1.6 <N$UWÕPÕQÕQ6RQODQGÕUÕOPDVÕ 38 2.4.2 6HUEHVW7LWUHúLP$QDOL]L 38 2.4.3 0RGDO<DWD\<N'D÷ÕOÕPODUÕQÕQ+HVDEÕ 39 2.4.4 %LULP0RGDO'DYUDQÕú%\NONOHULQLQ%LUOHúWLULOPHVL 40 dRN0RGOX8\DUODPDOÕ<N$UWÕPÕ<|QWHPLQLQ+HVDS$GÕPODUÕ 41 3. d08<$<¶1ø16$<,6$/8<*8/$0$/$5,ødø1*(/øù7ø5ø/(1 0(3$5&6%ø/*ø6$<$5352*5$0, 43 3URJUDPÕQ$PDFÕ.DSVDPÕYHdDOÕúPD']HQL 43 3.2 3URJUDPÕQ*LULú%LOJLOHUL 47 3.3 3URJUDPÕQdÕNÕú%LOJLOHUL 49
v %(721$50(d(5d(9(/(5'(12/8ù$1%ø1$/$5 h=(5ø1'(6$<,6$/ø1&(/(0(/(59(d08<$<¶1ø1 '(ö(5/(1'ø5ø/0(6ø 50 4.1 6D\ÕVDOøQFHOHPHOHUGH<DSÕODQ9DUVD\ÕPODUYH%HWRQDUPH.HVLWOHULQ 'DYUDQÕúÕQÕQøGHDOOHúWLULOPHVL 50 4.1.1 %DVLWYH%LOHúLN(÷LOPH(WNLVLQGHNL%HWRQDUPH.HVLWOHUGH øo.XYYHW-ùHNLOGH÷LúWLUPH%D÷ÕQWÕODUÕQÕQøGHDOOHúWLULOPHVL 52 4.1.2 %LOHúLN(÷LOPH(WNLVLQGHNL%HWRQDUPH.HVLWOHUGH$NPD .RúXOODUÕQÕQLGHDOOHúWLULOPHVL 53 4.2 $\UÕQWÕOÕ$oÕNODPDgUQH÷L '|UWNDWOÕ7HN$oÕNOÕNOÕ%HWRQDUPHdHUoHYH 54 $QDOL]6RQXoODUÕQDJ|UHd08<$<¶QLQ'H÷HUOHQGLULOPHVL 79 4.3.1 gUQHN%HWRQDUPHdHUoHYH%LQDODUÕQYH.XOODQÕODQ'HSUHP<HU +DUHNHWL.D\ÕWODUÕQÕQ Özellikleri 80 4.3.2 dHUoHYHOHULQ*HOLúWLULOHQd08<$<LOH$QDOL]L 86 4.3.3 Çerçevelerin Lineer Olmayan Dinamik Analizi (LODA) 86 4.3.4 dHUoHYHOHULQ0RQRWRQ$UWDQ)DUNOÕ<DWD\<N'D÷ÕOÕPODUÕLoLQ
Lineer Olmayan Statik Analizi (LOSA) 87 4.3.5 $QDOL]6RQXoODUÕQÕQ.DUúÕODúWÕUÕOPDVÕYH'H÷HUOHQGLULOPHVL 90 4.4 d08<$<¶QGH6SHNWUDOgOoHNOHPHQLQ(WNLVLQLQøQFHOHQPHVL 117 d08<$<¶QGH0RG6D\ÕVÕQÕQ(WNLVLQLQøQFHOHQPHVL 121 4.6 ÇMUYAY’nde øNLQFL0HUWHEH(WNLOHULQLQ'H÷erlendirilmesi 124 5. SONUÇLAR 9(g1(5ø/(5 129 KAYNAKLAR 134
vi 6(0%2//ø67(6ø
Sembol $GÕ Birimi
a1 , a2 , b $NPDYHNW|UúLGGHWLQLQELULPROPDVÕGXUXPXQGD OLQHHUOHúWLULOPLúDNPDNRúXOXNDWVD\ÕODUÕ
A1, A2, B /LQHHUOHúWLULOPLúDNPDNRúXOXNDWVD\ÕODUÕ Ao (WNLQ\HULYPHVLNDWVD\ÕVÕ
[d] '÷PQRNWDODUÕQÕQ\HUGH÷LúWLUPHELOHúHQOHULPDWULVL d (θ, ∆) 7HNHNVHQOLELOHúLNH÷LOPHGXUXPXQDDLWSODVWLN úHNLOGH÷LúWLUPHYHNW|U
Di dXEXNXo\HUGH÷LúWLUPHOHUL
Ec Beton elastisite modülü N/mm2
Es %HWRQoHOL÷LHODVWLVLWHPRGO N/mm2
EF Uzama rijitOL÷L kN
EI (÷LOPHULMLWOL÷L kNm2
fck %HWRQXQNDUDNWHULVWLNEDVÕQoGD\DQÕPÕ N/mm2 fyk %HWRQoHOL÷LQLQNDUDNWHULVWLNDNPDGD\DQÕPÕ N/mm2 Fij Modal kat kuvveti kN
g Yerçekimi ivmesi m/s2
I %LQD|QHPNDWVD\ÕVÕ
[k]ixix , [k]ixjx 6LVWHPHNVHQWDNÕPÕQGDLXFXQDDLWoXEXNULMLWOLNPDWULVOHUL
[k]jxix , [k]jxjx 6LVWHPHNVHQWDNÕPÕQGDMXFXQDDLWoXEXNULMLWOLNPDWULVOHUL K(M,N) = 0 7HNHNVHQOLELOHúLNH÷LOPHGXUXPXQDDLWDNPDNRúXOX L dXEXNX]XQOX÷X m m Kat kütlesi kNs2/m m 3ODVWLNOHúHQNHVLWVD\ÕVÕ M (÷LOPHPRPHQWL kNm Md %HWRQDUPHNHVLWWHGHQJHOLNÕUÕOPD\DNDUúÕOÕNJelen H÷LOPHPRPHQWL kNm Mo .HVLWLQEDVLWH÷LOPHHWNLVLQGHNLWDúÕPDJF kNm Mp 6DELWQRUPDONXYYHWHWNLVLQGHNLNHVLWLQH÷LOPHPRPHQWL kNm WDúÕPDJF M *|]|QQHDOÕQDQPRGVD\ÕVÕ [m] Kütle matrisi n '÷PQRNWDVÕVD\ÕVÕ n Kat adedi N Normal kuvvet kN Nd %HWRQDUPHNHVLWWHGHQJHOLNÕUÕOPD\DNDUúÕOÕNJHOHQ eksenel kuvvet kN Nob 6LPHWULNGRQDWÕOÕNHVLWOHULQWDúÕ\DELOHFH÷LHQE\N HNVHQHOEDVÕQoNXYYHWL kN Noç 6LPHWULNGRQDWÕOÕNHVLWOHULQWDúÕ\DELOHFH÷LHQE\N
vii
Sembol $GÕ Birimi
Np 6DELWH÷LOPHPRPHQWLDOWÕQGDNLNHVLWLQQRUPDONXYYHW
WDúÕPDJF kN
Pi Çubuk uç kuvvetleri
Pk NQROXDGÕPDDLW\DWD\\NSDUDPHWUHVL [P]i, [P]j dXEXNHNVHQWDNÕPÕQGDNLXoNXYYHWOHULPDWULVOHUL [P]ix, [P]jx 6LVWHPHNVHQWDNÕPÕQGDNLXoNuvvetleri matrisleri [Po]i, [Po]j dXEXNHNVHQWDNÕPÕQGDNL\NOHPHPDWULVOHUL [Po]ix, [Po]jx 6LVWHPHNVHQWDNÕPÕQGDNL\NOHPHPDWULVOHUL [Pφk]i, [Pφk]j 3ODVWLNOHúHQNHVLWOHUGHNLSODVWLNúHNLOGH÷LúWLUPH SDUDPHWUHOHULQLQELULPGH÷HULQGHQROXúDQoXEXNHNVHQ WDNÕPÕQGDNLXoNXYYHWOHULPDWULVOHUL [Pφk]ix, [Pφk]jx 3ODVWLNOHúHQNHVLWOHUGHNLSODVWLNúHNLOGH÷LúWLUPH SDUDPHWUHOHULQLQELULPGH÷HULQGHQROXúDQVLVWHPHNVHQ WDNÕPÕQGDNLXoNXYYHWOHULPDWULVOHUL [q] '÷PQRNWDODUÕQDHWNL\HQ\NPDWULVL R DavrDQÕúE\NO÷JHQHODGÕ
Sa Elastik spektral ivme m/s2
[S]D Dinamik rijitlik matrisi
[S]G 3ODVWLNOHúHQNHVLWOHUQHGHQL\OHJHQLúOHWLOPLúVLVWHPULMLWOLN matrisi
[Sdd] Elastik sistem rijitlik matrisi
[Sdφ] Plastik úHNLOGH÷LúWLUPHSDUDPHWUHOHULQLQELULPGH÷HUOHULQGHQ ROXúDQXoNXYYHWOHULQLQGHQJHGHQNOHPOHULQHNDWNÕVÕQÕ
ifade eden matris
[Sφd] %LULPSODVWLNúHNLOGH÷LúWLUPHOHUGHQROXúDQLoNXYYHWGH÷LúLP matrisi [Sφφ] 3ODVWLNOHúHQNHVLWWHNLSODVWLNúHNLOGH÷LúWLUPHSDUDPHWUHVLQLQ ELULPGH÷HULLoLQWPSODVWLNOHúHQNHVLWOHUGHNLLoNXYYHW GH÷LúLPLQLLIDGHHGHQPDWULV T Kesme kuvveti kN Tj Periyot s TA, TB 6SHNWUXPNDUDNWHULVWLNSHUL\RWODUÕ s wi .DWD÷ÕUOÕ÷Õ kN
χy %HWRQDUPHNHVLWWHDNPDQRNWDVÕQDNDUúÕOÕNJHOHQH÷ULOLN rad/m χmax %HWRQDUPHNHVLWWHL]LQYHULOHQPDNVLPXPH÷ULOLN rad/m δ .DW\DWD\\HUGH÷LúWLUPHVL m ∆ 8]DPDúHNLOGH÷LúWLUPHVLQLLIade eden plastik
úHNLOGH÷LúWLUPHELOHúHQL m ∆M (÷LOPHPRPHQWL GH÷LúLPL kNm ∆MC 0RGDOELUOHúWLUPHNXUDOÕLOHELUOHúWLULOPLúH÷LOPH PRPHQWLGH÷LúLPL kNm ∆N 1RUPDONXYYHWGH÷LúLPL kN ∆NC 0RGDOELUOHúWLUPHNXUDOÕLOHELUOHúWLULOPLúQRUPDO NXYYHWGH÷LúLPL kN [∆d] '÷PQRNWDODUÕQÕQ\HUGH÷LúWLUPHELOHúHQOHULGH÷LúLPL matrisi
viii Sembol $GÕ Birimi ∆Pk NQROXDGÕPDDLW\DWD\\NDUWÕPÕSDUDPHWUHVL ∆R 'DYUDQÕúE\NO÷DUWÕPÕQÕQJHQHODGÕ ∆RC 0RGDOELUOHúWLUPHNXUDOÕLOHELUOHúWLULOPLúGDYUDQÕú E\NO÷DUWÕPÕQÕQJHQHODGÕ εcu %HWRQGDL]LQYHULOHQHQE\NELULPNÕVDOPD
εco BetondDSODVWLNúHNLOGH÷LúWLUPHOHULQEDúODPDVÕQDNDUúÕ JHOHQELULPNÕVDOPD εsu %HWRQoHOL÷LQGHL]LQYHULOHQHQE\NELULPX]DPD εsy %HWRQoHOL÷LQGHDNPD\DNDUúÕOÕNJHOHQELULPX]DPD φ 3ODVWLNúHNLOGH÷LúWLUPHSDUDPHWUHVL [φ] 3ODVWLNúHNLOGH÷LúWLUPHSDUDPHWUHOHULQGHQROXúDQNRORQ matris Φij g]YHNW|UELOHúHQL Γj 0RGDONDWÕOÕPoDUSDQÕ θ (÷LOPHúHNLOGH÷LúWLUPHVLQLLIDGHHGHQSODVWLN úHNLOGH÷LúWLUPHELOHúHQL rad ij ρ dDSUD]NRUHODV\RQNDWVD\ÕVÕ ω $oÕVDOIUHNDQV rad/s ω2 g]GH÷HU rad2/s2 ξ 6|QPRUDQÕ
ix ù(.ø//ø67(6ø ùHNLO 1R$GÕ Sayfa ùHNLO LinHHUROPD\DQVWDWLNDQDOL]LOHEHOLUOHQHQNDSDVLWHH÷ULVL 2 ùHNLO øGHDOOHúWLULOPLúLoNXYYHW-úHNLOGH÷LúWLUPHED÷ÕQWÕVÕ 18 ùHNLO $NPDH÷ULVLYHSODVWLNúHNLOGH÷LúWLUPHYHNW|U 22 ùHNLO /LQHHUOHúWLULOPLúDNPDNRúXOXYHELULPDNPDYHNW|U 25
ùHNLO [Sdd] sistem rijitlik matrisinin elde edilmesi 27
ùHNLO [Sdφ] matrisinin elde edilmesi 29
ùHNLO 3ODVWLNúHNLOGH÷LúWLUPHSDUDPHWUHVLQLQELULPGH÷HULQGHQROXúDn uç kuvvetleri 30 ùHNLO h]HULQGHSODVWLNOHúHQNHVLWEXOXQDQoXEXN 33 ùHNLO 0(3$5&6SURJUDPÕQÕQJHQHODNÕúGL\DJUDPÕ 44 ùHNLO %HWRQYHEHWRQoHOL÷LQHDLWJHULOPH-úHNLOGH÷LúWLUPHED÷ÕQWÕODUÕ 51 ùHNLO%HWRQDUPHoXEXNODUGDLoNXYYHW-úHNLOGH÷LúWLUPHED÷ÕQWÕODUÕQÕQ LGHDOOHúWLULOPHVL 52 ùHNLO $NPDNRúXOODUÕQÕQGR÷UXSDUoDODUÕLOHLGHDOOHúWLULOPHVL 53 ùHNLO4 '|UWNDWOÕELQDQÕQJHRPHWULN|]HOOLNOHULYHGúH\\NOHUL 55 ùHNLO '|UWNDWOÕoHUoHYHGHNLNRORQODUÕQOLQHHUOHúWLULOPLúDNPDNRúXOODUÕ 56 ùHNLO '|UWNDWOÕoHUoHYHQLQDQDOL]LQGHNXOODQÕODQV|QPOHODVWLN ivme spektrumu 57 ùHNLO'|UWNDWOÕoHUoHYHQLQKHVDSPRGHOLQGHNLoXEXNYHG÷PQRNWDVÕ QXPDUDODUÕLOHoXEXNXoNXYYHWOHULQLQYH Xo\HUGH÷LúWLUPHOHULQLQ pozitif yönleri 57 ùHkil 4.8 '|UWNDWOÕoHUoHYHQLQKHVDSPRGHOLQHDLWVHUEHVWOLNOHU 58 ùHNLO '|UWNDWOÕoHUoHYHGHLON\NDUWÕPÕDGÕPÕQD HODVWLN DLW ELULPPRGDO\DWD\\NGD÷ÕOÕPODUÕ 62 ùHNLO'|UWNDWOÕoHUoHYHQLQNDSDVLWHH÷ULVLYHSODVWLNOHúHQNHVLWOHULQ GD÷ÕOÕPÕ 76 ùHNLO'|UWNDWOÕoHUoHYHGH\NDUWÕPODUÕQDDLWNDW\DWD\\HUGH÷LúWLUPHOHUL 78 ùHNLO'|UWNDWOÕoHUoHYHGH\NDUWÕPODUÕQDDLWJ|UHOLNDW|WHOHPHOHUL 78 ùHNLO'|UWNDWOÕoHUoHYHGH\NDUWÕPODUÕQDDLWPDNVLPXPNLULúSODVWLN dönmeleri 79 ùHNLO%LQDODUÕQWLSLNNDWSODQÕYHoHUoHYHGúH\HQNHVLWOHUL 81 ùHNLO$QDOL]OHUGHNXOODQÕODQGHSUHP\HUKDUHNHWOHULQHDLWLYPHND\ÕWODUÕ 84 ùHNLO $QDOL]OHUGHNXOODQÕODQGHSUHP\HUKDUHNHWOHULQHDLWHODVWLNLYPH VSHNWUXPODUÕ 85 ùHNLO$QDOL]OHUGHNXOODQÕODQMoment-Plastik Dönme (M-θ ) p ED÷ÕQWÕODUÕQDDLWPDWHPDWLNPRGHOOHU 87 ùHNLO<DWD\\NGD÷ÕOÕPODUÕQÕQúHPDWLNJ|VWHULPL 90 ùHNLO 5-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ (/&-180) 92 ùHNLO 5-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ (5=-DB) 93
x ùHNLO 1R$GÕ Sayfa ùHNLO 5-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ 6.5-090) 94 ùHNLO 5-NDWOÕoHUoHYHGHNDSDVLWHH÷ULOHULQLQNDUúÕODúWÕUÕOPDVÕ 95 ùHNLO-NDWOÕoHUoHYHGHSODVWLNOHúHQNHVLWGD÷ÕOÕPODUÕQÕQNDUúÕODúWÕUÕOPDVÕ 96 ùHNLO 10-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ (/&-180) 98 ùHNLO 10-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ (RZ-DB) 99 ùHNLO 10-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ 6.5-090) 100 ùHNLO-NDWOÕoHUoHYHGHNDSDVLWHH÷ULOHULQLQNDUúÕODúWÕUÕOPDVÕ 101 ùHNLO-NDWOÕoHUoHYHGHSODVWLNOHúHQNHVLWGD÷ÕOÕPODUÕQÕQNDUúÕODúWÕUÕOPDVÕ ùHNLO 15-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ (/&-180) 104 ùHNLO-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ (5=-DB) 105 ùHNLO 15-NDWOÕ oHUoHYHGH DQDOL] VRQXoODUÕQÕQ NDUúÕODúWÕUÕOPDVÕ 6.5-090) 106 ùHNLO 15-NDWOÕoHUoHYHGHNDSDVLWHH÷ULOHULQLQNDUúÕODúWÕUÕOPDVÕ 107 ùHNLO 15-NDWOÕoHUoHYHGHSODVWLNOHúHQNHVLWGD÷ÕOÕPODUÕQÕQNDUúÕODúWÕUÕOPDVÕ ùHNLO 20-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ (/&-180) 111 ùHNLO 20-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ (5=-DB) 112 ùHNLO 20-NDWOÕoHUoHYHGHDQDOL]VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ 6.5-090) 113 ùHNLO 20-NDWOÕoHUoHYHGHNDSDVLWHH÷ULOHULQLQNDUúÕODúWÕUÕOPDVÕ 114 ùHNLO 20-NDWOÕoHUoHYHGHSODVWLNOHúHQNHVLWGD÷ÕOÕPODUÕQÕQNDUúÕODúWÕUÕOPDVÕ ùHNLO 15-NDWOÕoHUoHYHGHLONG|UWPRGLoLQSHUL\RWYHVSHNWUDOLYPHQLQ SODVWLNOHúPHLOHGH÷LúLPOHUL (5Z-DB) 119 ùHNLO-NDWOÕoHUoHYHGHLONG|UWPRGLoLQPRGDO\DWD\\NGD÷ÕOÕPODUÕQÕQ SODVWLNOHúPHLOHGH÷LúLPOHUL (5=-DB) 120 ùHNLO-NDWOÕoHUoHYHGHJ|]|QQHDOÕQDQPRGVD\ÕVÕQÕQDQDOL]VRQXoODUÕ üzerideki etkileri (ERZ-DB) 122 ùHNLO 20-NDWOÕoHUoHYHGHJ|]|QQHDOÕQDQPRGVD\ÕVÕQÕQNDSDVLWHH÷ULVL
üzerindeki etkisi (ERZ-DB) 123 ùHNLO 20-NDWOÕoHUoHYHGHJ|]|QQHDOÕQDQPRGVD\ÕVÕQÕQSODVWLNOHúHQNHVLW GD÷ÕOÕPODUÕ]HULQGHNLHWNLVL (5=-DB) 123 ùHNLO 10-NDWOÕoHUoHYHGHbirinci ve ikinci mertebe elasto-plastik analiz
VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ 125 ùHNLO 20-NDWOÕoHUoHYHGHbirinci ve ikinci mertebe elasto-plastik analiz
VRQXoODUÕQÕQNDUúÕODúWÕUÕOPDVÕ 126 ùHNLOYH-NDWOÕoHUoHYHOHUGHbirinci ve ikinci mertebe
elasto-plastik DQDOL]OHUGHQHOGHHGLOHQNDSDVLWHH÷ULOHULQLQ
NDUúÕODúWÕUÕOPDVÕ 127 ùHNLO 20-NDWOÕoHUoHYHQLQbirinci ve ikinci mertebe elasto-plastik
DQDOL]OHULQGHSHUL\RGXQSODVWLNOHúPHLOHGH÷LúLPOHULQLQ
xi dø=(/*(/ø67(6ø
Çizelge No $GÕ Sayfa
Çizelge 4.1 '|UWNDWOÕELQDQÕQPDO]HPH|]HOOLNOHULYHGHSUHP KHVDEÕQD ait parametreler 55 Çizelge 4.2 '|UWNDWOÕoHUoHYHGHNLNLULúOHULQGRQDWÕODUÕH÷LOPHPRPHQWL WDúÕPDNDSDVLWHOHULYHH÷LOPHULMLtlikleri 55 Çizelge 4.3 '|UWNDWOÕoHUoHYHGHNLNRORQODUÕQGRQDWÕODUÕH÷LOPHYH uzama rijitlikleri 56 Çizelge 4.4 '|UWNDWOÕoHUoHYHQLQVLVWHPULMLWOLNPDWULVL HODVWLN 59 Çizelge 4.5 '|UWNDWOÕoHUoHYHGHGúH\KHVDS yüklerine ait uç kuvvetleri 60 Çizelge 4.6 '|UWNDWOÕoHUoHYHGHLON\NDUWÕPÕDGÕPÕQD HODVWLN DLWPRGDO
büyüklükler ve spektral ivmeler 61 Çizelge 4.7 '|UWNDWOÕoHUoHYHGHLON\NDUWÕPÕDGÕPÕQD HODVWLN DLW
özvektörler (Φij) 62 Çizelge 4.8 '|UWNDWOÕoHUoHYHGHLON\NDUWÕPÕDGÕPÕQD HODVWLN DLWELULP
modal uç kuvvetleri 64 Çizelge 4.9 '|UWNDWOÕoHUoHYHGHLON\NDUWÕPÕDGÕPÕQD HODVWLN DLWELULP
PRGDONDW\DWD\\HUGH÷LúWirmeleri 64
Çizelge 4.10 '|UWNDWOÕoHUoHYHGHLON\NDUWÕPÕDGÕPÕQD HODVWLN DLWELULP
modal göreli kat ötelemeleri 65 Çizelge 4.11 '|UWNDWOÕoHUoHYHGH∆P1=1 yüklemesine ait uç kuvvetleri 65
Çizelge 4.12 '|UWNDWOÕoHUoHYHGH∆P1 LoLQNDW\DWD\\HUGH÷LúWLUPHOHULYH
göreli kat ötelemeleri 66 Çizelge 4.13 '|UWNDWOÕoHUoHYHGHLON\NDUWÕPÕVRQXQGDNLWRSODPXoNXYYHWOHUL 68 Çizelge 4.14 '|UWNDWOÕoHUoHYHGHLON\NDUWÕPÕVRQXQGDNLNDW\DWD\ \HUGH÷LúWLUPHOHULYHJ|UHOLNDW|WHOHPHOHUL 68 dL]HOJH'|UWNDWOÕoHUoHYHGHLONSODVWLNNHVLWROXúXPXQGDQVRQUD JHQLúOHWLOPLúVLVWHPULMLWOLNPDWULVL 72 dL]HOJH'|UWNDWOÕoHUoHYHGHLNLQFL\NDUWÕPÕDGÕPÕQDDLWPRGDO
büyüklükler ve spektral ivmeler 73 Çizelge 4.17 '|UWNDWOÕoHUoHYHGHLNLQFL\NDUWÕPÕDGÕPÕQDDLWPRGDO \DWD\\NGD÷ÕOÕPODUÕ 73 dL]HOJH'|UWNDWOÕoHUoHYHGHLONSODVWLNNHVLWWHNLSODVWLNúHNLOGH÷LúWLUPH SDUDPHWUHVLYHSODVWLNG|QPHGH÷HUL 74 dL]HOJH '|UWNDWOÕoHUoHYHGHLNLQFL\NDUWÕPÕQDDLWNDW\DWD\ \HUGH÷LúWLUPHOHUL 75 Çizelge 4.20 '|UWNDWOÕoHUoHYHGHLNLQFL\NDUWÕPÕQDDLWJ|UHOLNDW|WHOHPHOHUL 75 dL]HOJH'|UWNDWOÕoHUoHYHGHLNLQFL\NDUWÕPÕVRQXQGDNLWRSODP uç kuvvetleri 75 Çizelge 4.22 '|UWNDWOÕoHUoHYHGHVRQ\NDUWÕPÕQDDLWJHQLúOHWLOPLú
xii Çizelge No $GÕ Sayfa Çizelge 4.23 %LQDODUÕQJHQHO|]HOOLNOHULYHGHSUHPKHVDEÕQGDNXOODQÕODQ parametreler 80 Çizelge 4.24 gUQHNEHWRQDUPHoHUoHYHOHULQNDWNWOHOHULYHSHUL\RWODUÕ 81 Çizelge 4.25 dHUoHYHOHUGHNLNLULúHQNHVLWER\XWODUÕYHGRQDWÕODUÕ 82 Çizelge 4.26 ÇerçevelHUGHNLNRORQHQNHVLWER\XWODUÕYHGRQDWÕODUÕ 83 Çizelge 4.27 $QDOL]OHUGHNXOODQÕODQGHSUHPOHULQ|]HOOLNOHUL 83
xiii
ÖNSÖZ
'RNWRUD WH]L RODUDN VXQXODQ EX oDOÕúPDGD \NVHN PRGODUÕQ HWNLOL ROGX÷X binDODUÕQ GHSUHP HWNLOHUL DOWÕQGDNL OLQHHU ROPD\DQ GDYUDQÕúÕQÕQ HWNLQ RODUDN EHOLUOHQHELOPHVL DPDFÕ\OD oRN PRGOX X\DUODPDOÕ ELU \N DUWÕPÕ \|QWHPL JHOLúWLULOPLúWLU
dDOÕúPDODUÕPVÕUDVÕQGDoRNGH÷HUOLELOJLYHWHFUEHOHULQLEHQLPOHSD\ODúDQWH] GDQÕúPDQÕP 6D\ÕQ 'Ro'U (UGDO øUWHP¶H oRN GH÷HUOL ELOJL YH \RUXPODUÕQGDQ
ID\GDODQGÕ÷ÕP 6D\ÕQ 3URI'U (UNDQ g]HU¶H YH WH]LPH NDWNÕODUÕQGDQ GROD\Õ 6D\ÕQ<'Ro'U.RQXUDOS*LUJLQ¶HWHúHNNUOHULPLVXQDUÕP
$\UÕFD WH] oDOÕúPDODUÕP VÕUDVÕQGD YHUGL÷L E\N GHVWHNWHQ GROD\Õ oDOÕúPD
DUNDGDúÕP$UDú*|U<N0K8PXW+DVJOEDúWDROPDN]HUHGH÷HUOLDUNDGDúODUÕP $UDú*|U'U 1XUD\ *HGLN¶H $UDú*|U'U $OWX÷ <DYDú¶D YH GL÷HU DUDúWÕUPD
J|UHYOLVLDUNDGDúODUÕPDGDWHúHNNUHGHULP
Her dönHPGHROGX÷XJLELEXWH]oDOÕúPDPVÕUDVÕQGDGDEDQDoRNE\NGHVWHN YHUHQVHYJLOLDQQHPHEDEDPDYHDEODPDúNUDQODUÕPÕVXQDUÕP
7H]oDOÕúPDODUÕPQHGHQL\OHoRN\R÷XQoDOÕúPDWHPSRVXLOHJHoHQHYOLOL÷LPLQ EXLON\ÕOODUÕQGDE\NIHGDNDUOÕNJ|VWHUHQYHEDna her yönden destek olan sevgili HúLP%XUFX7UNHU¶HHQLoWHQWHúHNNUOHULPLVXQDUÕP
%DOÕNHVLU Kaan TÜRKER
1
1. *ø5øù
1.1 Konu
6RQ RQ \ÕO LoLQGH SHUIRUPDQVD GD\DOÕ WDVDUÕP YH GH÷HUOHQGLUPH \DNODúÕPÕQÕQ RUWD\D NRQPDVÕ YH \D\JÕQODúPDVÕ LOH \DSÕODUÕQ GHSUHP HWNLOHUL DOWÕQGDNL OLQHHU ROPD\DQGDYUDQÕúÕQÕJ|]|QQHDODQLOHULKHVDS\|QWHPOHUL]HULQGHNLoDOÕúPDODUKÕ] YH|QHPND]DQPÕúWÕU
3HUIRUPDQVD GD\DOÕ WDVDUÕP YH GH÷HUOHQGLUPH \DNODúÕPÕQGD HVDV DOÕQDQ ELU GHSUHPLoLQ\DSÕQÕQSODVWLNúHNLOGH÷LúWLUPHWDOHELQLQ LVWHPLQLQ EHOLUOHQPHVLYHEX talep gözönünde tutularak, hasar düzeyinin kontrol edilmesi öngörülmektedir. %|\OHFHIDUNOÕGHSUHPWHKOLNH ULVN VHYL\HOHULLoLQKHGHIOHQHQSHUIRUPans düzeyine VDKLSRODQ\DSÕWDVDUÕPÕ\DSÕODELOPHNWHYH\DPHYFXWELU\DSÕQÕQSHUIRUPDQVG]H\L GH÷HUOHQGLULOHELOPHNWHGLU
<DSÕODUÕQ GHSUHP HWNLOHUL DOWÕQGDNL SODVWLN úHNLOGH÷LúWLUPHOHULQLQ EHOLUOHQHELOPHVL LoLQ PDO]HPH YH JHRPHWUL GH÷LúLPL EDNÕPÕQGDQ Oineer olmayan GDYUDQÕúÕQJ|]|QQHDOÕQGÕ÷ÕGLQDPLNYH\DVWDWLNDQDOL]\|QWHPOHULQLQNXOODQÕOPDVÕ gerekmektedir.
/LQHHUROPD\DQGLQDPLNDQDOL]\|QWHPOHUL\DSÕODUÕQGHSUHPHWNLOHULDOWÕQGDNL GDYUDQÕúÕQÕQ JHUoH÷H HQ \DNÕQ RODUDN EHOLUOHQHELOGL÷L \öntemlerdir. Bu yöntemler JHQHO RODUDN J|]|QQH DOÕQDQ GHSUHP \HU KDUHNHWLQH DLW LYPH ND\GÕ LoLQ DWDOHW NXYYHWOHULGH÷LúLPLQLYHV|QPGHLoHUHUHN\DSÕQÕQ]DPDQWDQÕPDODQÕQGDKHVDEÕQÕ HVDV DOPDNWDGÕU $QFDN EX \|QWHPOHU oRN NDUPDúÕN ]DPDQ DOÕFÕ oRN Iazla yerel GHSUHP \HU KDUHNHWL ND\GÕ YH GHQH\LP JHUHNWLUGL÷LQGHQ JQP]GH ELOLPVHO DUDúWÕUPDODUGÕúÕQGDVDGHFHoRN|]HO\DSÕODULoLQNXOODQÕODELOPHNWHGLU
2
/LQHHU ROPD\DQ GLQDPLN DQDOL] \|QWHPOHULQLQ VÕQÕUOÕ NXOODQÕP DODQÕ ROPDVÕ nedeniyle, bunlara görH GDKD EDVLWOHúWLULOPLú RODQ OLQHHU ROPD\DQ VWDWLN DQDOL] SXVKRYHU DQDOL] \|QWHPOHUL JHQLú NXOODQÕP DODQÕ EXOPDNWDGÕU /LQHHU ROPD\DQ VWDWLN DQDOL] \ÕOÕQGDQ LWLEDUHQ ED]Õ VWDQGDUWODUGD -DSDQHVH 35(666 >@ (XURFRGH>@ \HUDOPD\DEDúODPÕúKDWta Japonya’da belirli özellikteki betonarme \DSÕODUÕQWDVDUÕPÕLoLQDQD\|QWHPRODUDNNDEXOHGLOPLúWLU$\UÕFD$%'¶GHELQDODUÕQ SHUIRUPDQVDGD\DOÕWDVDUÕPÕYHGH÷HUOHQGLULOPHVLDPDFÕ\ODKD]ÕUODQDQoHúLWOLUDSRUYH ön standartlarda (VISION 2000 [3], ATC 40 [4,5], FEMA 273[6], FEMA 356 [7]) OLQHHU ROPD\DQ VWDWLN DQDOL]L HVDV DODQ GH÷HUOHQGLUPH \|QWHPOHULQH |QHPOL \HU YHULOPLúWLU
/LQHHUROPD\DQVWDWLNDQDOL]\|QWHPOHULJHQHORODUDNEHOLUOLVDELWGúH\\NOHU ve deprem etkisini temsil eden artan yatay yükOHU DOWÕQGD PDO]HPH YH JHRPHWUL GH÷LúLPL EDNÕPÕQGDQ OLQHHU ROPD\DQ WHRUL\H J|UH \DSÕQÕQ yatay kuvvet-tepe \HUGH÷LúWLUPHVL ED÷ÕQWÕVÕQÕQ EHOLUOHQPHVLQL HVDV DOPDNWDGÕU ùHNLO <DSÕQÕQ \DWD\GHSUHP\NWDúÕPDNDSDVLWHVLQLLIDGHHGHQEXED÷ÕQWÕNDSDVLWHH÷ULVL SXVKRYHU H÷ULVL RODUDNDGODQGÕUÕOPDNWDGÕU>@
ùHNLO/LQHHUROPD\DQVWDWLNDQDOL]LOHEHOLUOHQHQNDSDVLWHH÷ULVL
.DSDVLWH H÷ULVLQLQHOGH HGLOPHVLLOH KHU\NDUWÕPÕLoLQ\DSÕGDNLHOHPDQODUÕQ GD\DQÕPYHúHNLOGH÷LúWLUPHWDOHSOHUL\DSÕQÕQ]D\ÕIHOHPDQODUÕYH\HUOHULRODELOHFHN NÕVPLYH\DWRSWDQJ|oPHPHNDQL]PDVÕGXUXPODUÕGLUHNWRODUDNEHOLUOHQHELOPHNWHGLU >@$\UÕFDNDSDVLWHH÷ULVLLOHGDYUDQÕúVSHNWUXPDQDOL]LQLQELUOHúWLULOPHVLQHGD\DQDQ δδmax VT 7HSH\HUGH÷LúWLUPHVL δδmax) T ab an ke sm e kuv ve ti (V T ) .DSDVLWHH÷ULVL SistemdHNLSODVWLNOHúPH QRNWDODUÕ
3
oHúLWOL \|QWHPOHU .DSDVLWH 6SHNWUXPX <|QWHPL >@ <HUGH÷LúWLUPH .DWVD\ÕODUÕ <|QWHPL >@ 1 <|QWHPL > @ $NPD 1RNWDVÕ 6SHNWUXPX <|QWHPL >@ YE NXOODQÕODUDN J|]|QQH DOÕQDQ GHSUHP LoLQ\DSÕQÕQJHQHO GD\DQÕP YH\HUGH÷LúWLUPH talepleri belirlenebilmekte, böylece istenilen deprem seviyeOHUL LoLQ \DSÕODUÕQ SHUIRUPDQVG]H\OHULGH÷HUOHQGLULOHELOPHNWHGLU
Lineer olmayan statik analiz yöntemlerinde (LOSA), deprem etkilerini temsil HWPHN ]HUH JHQHO RODUDN \DSÕQÕQ ELULQFL WHPHO WLWUHúLP PRGXQD NDUúÕOÕN JHOHQ DWDOHW NXYYHWOHUL GD÷ÕOÕPÕ YH\D \|QHWPHOLNOHUGH |QJ|UOHQ HúGH÷HU GHSUHP \N GD÷ÕOÕPÕ NXOODQÕOPDNWDGÕU %X GD÷ÕOÕPGDNL \NOHU DUDODUÕQGDNL RUDQ VDELW NDODFDN úHNLOGH PRQRWRQ RODUDN DUWWÕUÕODUDN DQDOL] \DSÕOPDNWDGÕU %X \N GD÷ÕOÕPODUÕQÕQ PRQRWRQDUWWÕUÕOPDVÕQÕHVDVDODQ*HOHQHNsel Lineer Olmayan Statik Analiz (G-LOSA) \DNODúÕPODUÕQÕQ SODQGD YH GúH\GH G]HQVL]OL÷L EXOXQPD\DQ D] NDWOÕ \DSÕODU LoLQ JHUoHN GDYUDQÕúD ROGXNoD \DNÕQ VRQXoODU YHUGL÷L ELOLQPHNWHGLU >-16]. Buna NDUúÕOÕN D] NDWOÕ G]HQVL] YH oRN NDWOÕ G]HQOL YH\D G]HQVL] \DSÕODU ]HULQGHNL DUDúWÕUPDODU V|] NRQXVX *-/26$ \DNODúÕPODUÕQÕQ JHUoHN GDYUDQÕúÕ EHOLUOHPHGH \HWHUVL] NDOGÕ÷ÕQÕ J|VWHUPHNWHGLU >-@ %XQXQ QHGHQL HVDVHQ GHSUHP VÕUDVÕQGD ROXúDQDWDOHWNXYYHWOHULQLQ \DWD\\NGD÷ÕOÕPÕQÕQ GHSUHP|]HOOLNOHULQHYH\DSÕGDNL SODVWLNOHúPHQLQ G]H\LQH SODVWLNOHúHQ NHVLW VD\ÕVÕQD ED÷OÕ RODUDN VUHNOL GH÷LúLP J|VWHUPHVLYHWHPHOPRGGÕúÕQGDNL\NVHNPRGODUÕQGDGDYUDQÕúWDHWNLQROPDVÕGÕU
%X QHGHQOH D] NDWOÕ G]HQVL] YH oRN NDWOÕ G]HQOL YH\D G]HQVL] \DSÕODUÕQ deSUHP HWNLOHUL DOWÕQGDNL JHUoHN GDYUDQÕúÕQÕQ EHOLUOHQHELOPHVL LoLQ OLQHHU ROPD\DQ VWDWLN DQDOL] \|QWHPOHULQGH VLVWHPLQ GH÷LúHQ GLQDPLN |]HOOLNOHULQLQ \NVHN PRG HWNLOHULQLQPRGúHNOLGH÷LúLPLQLQYE GHJ|]|QQGHEXOXQGXUXOPDVÕJHUHNPHNWHGLU Bunun için aQDOL] \|QWHPOHULQGH VLVWHPLQ GLQDPLN |]HOOLNOHULQLQ GH÷LúLPLQLQ L]OHQPHVL YH EXQD ED÷OÕ RODUDN DQDOL] ER\XQFD IDUNOÕ |]HOOLNOHUGHNL \HQL \DWD\\N GD÷ÕOÕPODUÕQÕQ NXOODQÕOPDVÕ JHUHNPHNWHGLU %X GXUXPGD OLQHHU ROPD\DQ VWDWLN analiz yöntemlerindeki hesap ]RUODúPDNWDYHKDFPLoRNE\NRUDQGDDUWPDNWDGÕU g]HOOLNOH DUGÕúÕN \DNODúÕPÕ YH\D DGÕP-DGÕP DQDOL]L HVDV DODQ \N DUWÕPÕ yöntemlerinde [17-@ LVWHQLOHQ KDVVDVL\HWH GH ED÷OÕ RODUDN KHVDS KDFPL oRN GDKD E\N RUDQGD DUWPDNWDGÕU $\UÕFD EX \|QWHPOHUGH \N DUWÕPÕ VÕUDVÕQGD |QFHNL
4
DGÕPGDNL\NOHUGHQED÷ÕPVÕ]\NOHULQNXOODQÕOPDVÕQGDED]Õ]RUOXNODUODNDUúÕODúÕOGÕ÷Õ bilinmektedir [11,21].
6RQXoRODUDN\NVHNPRGHWNLOHULQLYHSODVWLNOHúPHOHULQQHGHQROGX÷X\DWD\ \NGD÷ÕOÕPÕGH÷LúLPOHULQLJ|]|QQHDOPDNDPDFÕ\ODSODVWLNOHúHQNHVLWOHULQD\UÕQWÕOÕ RODUDN EHOLUOHQHELOGL÷L YH KHU \N DUWÕPÕQGD ED÷ÕPVÕ] \N GD÷ÕOÕPÕ NXOODQÕPÕQD RODQDN YHUHQ YH D\QÕ ]DPDQGD HWNLQ DQDOL] \|QWHPOHULQH LKWL\Do GX\XOGX÷X görülmektedir.
.RQXLOHøOJLOL/LWHUDWUQøQFHOenmesi
Bu bölümde, “Geleneksel Lineer Olmayan Statik Analiz (G-LOSA) \|QWHPOHUL EX \|QWHPOHUGH NXOODQÕODQ IDUNOÕ \DWD\ \N GD÷ÕOÕPODUÕQÕQ DQDOL] VRQXoODUÕQD HWNLOHUL /26$¶L HVDV DODQ SHUIRUPDQV GH÷HUOHQGLUPH \|QWHPOHUL oRN modlu ve uyarlDPDOÕ SODVWLNOHúPHOHU LOH GH÷LúHQ \DWD\ \N GD÷ÕOÕPÕQÕ HVDV DODQ /26$\|QWHPOHUL´NRQXODUÕQÕLoHUHQOLWHUDWULQFHOHPHVL|]HWOHQPLúWLU
Özer (1987), çelik düzlem çerçevelerde ikinci mertebe limit yükQKHVDEÕLoLQ JHQHOELU\NDUWÕPÕ\|QWHPLJHOLúWLUPLúWLU0DO]HPHQLQHODVWR-SODVWLNGDYUDQÕúÕQÕQ YH JHRPHWUL GH÷LúLPOHULQLQ GHQJH GHQNOHPOHULQH HWNLVLQLQ J|]|QQH DOÕQGÕ÷Õ EX oDOÕúPDGDSODVWLNPDIVDOKLSRWH]LELOHúLNLoNXYYHWGXUXPXQXGDNDSVD\DFDNúHNLOGH JHQLúOHWLOPHNWHGLU<|QWHPGHVDELWGúH\\NOHUYHDUWDQ\DWD\\NOHUDOWÕQGDKHVDS \DSÕODUDNGúH\\NOHUHED÷OÕRODUDNKHVDSODQDQQRUPDONXYYHWOHULoLQikinci mertebe HWNLOHUL OLQHHUOHúWLULOPHNWHGLU 6LVWHPGH KHU SODVWLN NHVLWLQ ROXúXPXQGDQ VRQUD R kesitteki plastik dönme yeni bir bilinmeyenRODUDNDOÕQPDNWDYHSODVWLNOHúHQNHVLWWHNL DNPD NRúXOXQX LIDGH HGHQ \HQL ELU GHQNOHP PHYFXW GHQNOHP WDNÕPÕQD LODYH HGLOPHNWHGLU%|\OHFHKHU\NDUWÕPÕQGD KHUSODVWLNNHVLWLQROXúXPXQGD GHQNOHP WDNÕPÕQÕQ\HQLGHQNXUXOXSo|]OPHVLQHJHUHNNDOPDGDQ\HQLELOLQPH\HQHDLWVDWÕUYH NRORQXQ LQGLUJHQPHVL VXUHWL\OH SODVWLNOHúHQ NHVLWOHUGHNL SODVWLN úHNLOGH÷LúWLUPHOHUL GH LoHUHQ o|]P HOGH HGLOPHNWHGLU dDOÕúPDGD SODVWLNOHúHQ NHVLWOHUGHNL Lo NXYYHW GXUXPODUÕQÕQ\|QGH÷LúWLUHUHNDNPDH÷ULVLQLQLoE|OJHVLQH\|QHOPHVLYHDNPDH÷ULVL ]HULQGHE|OJH GR÷UX GH÷LúWLUPHVLJLEL|]HOGXUXPODUGD\|QWHPLQX\JXODPDHVDVODUÕ
5
DoÕNODQPÕúWÕU $\UÕFD JHOLúWLULOHQ \|QWHPGHQ \DUDUODQDUDN \DWD\ \NOHU LOH ELUOLNWH GúH\ \NOHULQ GH D\QÕ RUDQGD DUWWÕUÕOGÕ÷Õ RUDQWÕOÕ \NOHPH GXUXPXna ait çözümün \DSÕODELOPHVLLoLQELUo|]P\ROX|QHULOPLúWLU>@
øUWHP >@¶GHHVDVODUÕDoÕNODQDQ\NDUWÕPÕ\|QWHPLQGHQ\DUDUODQDUDN uzay çubuk sistemlerin ikinci mertebe limit yüküQQEHOLUOHQPHVLDPDFÕ\ODELU\N DUWÕPÕ\|QWHPLJHOLúWLUPLúWLU*HOLúWLULOHQ\|QWHPGHVDELWGúH\\NOHUYHDUWDQ\DWD\ \NOHU GHSUHP U]JDU YE LoLQ KHVDS \DSÕOPDNWDGÕU dDOÕúPDGD DNPD NRúXOX RODUDN ELOHúLN H÷LN H÷LOPH HWNLVLQGHNL oHOLN NXWX NHVLW YH EHQ]HUL NHVLWOHU LoLQ G]OHPOHUOH OLQHHUOHúWLULOPLú o ER\XWOX DNPD \]H\OHUL |QHULOPLú YH JHOLúWLULOHQ \|QWHPLQEXWLSNHVLWOHUGHQROXúDQX]D\oHUoHYHOHU]HULQGHX\JXODPDVÕ\DSÕOPÕúWÕU dDOÕúPDGD SODVWLNOHúHQ NHVLWOHUGHNL Lo NXYYHW GXUXPODUÕQÕQ \|Q GH÷LúWLUHUHN DNPD yüzeyinin iç bölgesine yönelmesi, akma y]H\L]HULQGHE|OJH G]OHP GH÷LúWLUPHVL YHRUDQWÕOÕ\NOHPHJLEL|]HOGXUXPODUGD\|QWHPLQX\JXODPDHVDVODUÕDoÕNODQPÕúWÕU <|QWHPLQ VD\ÕVDO X\JXODPDODUÕQD RODQDN VD÷ODPDN LoLQ RWRPDWLN ELU ELOJLVD\DU SURJUDPÕGD ø0(3-' JHOLúWLULOPLúWLU>@
GirgiQ >@¶GHHVDVODUÕDoÕNODQDQ\NDUWÕPÕ\|QWHPLQGHQ\DUDUODQDUDN betonarme uzay çubuk sistemlerin ikinci mertebe limit yükünün ve göçme JYHQOL÷LQLQEHOLUOHQPHVLDPDFÕ\ODELU\NDUWÕPÕ\|QWHPLJHOLúWLUPLúWLUdDOÕúPDGD ELOHúLN H÷LN H÷LOPH HWNLVLndeki betonarme çubuk elemanlar için lineer bölgelerden ROXúDQLGHDOOHúWLULOPLúoER\XWOXELUDNPD\]H\L|QHULOPLúYHEXúHNLOGHPDO]HPH EDNÕPÕQGDQ OLQHHU ROPD\DQ EHWRQDUPH VLVWHPOHUGH DNPD NRúXOODUÕQÕQ OLQHHU GHQNOHPOHUH G|QúWUOPHVL VD÷ODQPÕúWÕU /LQeer olmayan burulma úHNLOGH÷LúWLUPHOHULQLQVLVWHPGDYUDQÕúÕQDHWNLVLGHJ|]|QQHDOÕQPÕúWÕUdDOÕúPDGD D\UÕFD JHOLúWLULOHQ \|QWHPLQ oRN NDWOÕ E\N EHWRQDUPH \DSÕ VLVWHPOHULQLQ ikinci
mertebe elasto-plastik KHVDEÕQD HWNLQ RODUDN X\JXODQPDVÕQÕ VD÷ODPDN DPDFÕ\OD
ELOLQPH\HQ VD\ÕVÕQÕQ D]DOWÕOPDVÕQÕ YH NDWVD\ÕODU PDWULVLQLQ LQGLUJHQPH LúOHPLQLQ KÕ]ODQGÕUÕOPDVÕQÕ VD÷OD\DQ ELU DOJRULWPD |QHULOPLúWLU <|QWHPLQ VD\ÕVDO X\JXODPDODUÕQD RODQDN VD÷ODPDN DPDFÕ\OD o DGHW ELOJLVD\DU SURJUDPÕ %(.(-3, PARCS, CHECK) ha]ÕUODQPÕúWÕU>@
6
.LODUYH)DMIDU DVLPHWULN\DSÕODUÕQOLQHHUROPD\DQVWDWLNDQDOL]LLoLQ ELU\|QWHPJHOLúWLUPLúOHUGLUhoER\XWOX\DSÕODUÕQoHúLWOLG]OHPPDNURHOHPDQODUOD DOW VLVWHPOHUOH WHPVLO HGLOGL÷L EX \|QWHPGH \DSÕ\D DLW NDSDVLWH H÷Uisinin basit bir úHNLOGH HOGH HGLOPHVL DPDoODQPÕúWÕU *HOLúWLULOHQ \|QWHP LOH VLPHWULN YH DVLPHWULN \DSÕODU LQFHOHQPLú YH EXUXOPDQÕQ \DSÕ GDYUDQÕúÕ ]HULQGHNL HWNLOHUL GH÷HUOHQGLULOPLúWLU>@
Moghadam ve Tso (1997), elastik dinamik analiz verilerinden yararlanarak üç ER\XWOX \DSÕODUÕQ OLQHHU ROPD\DQ VWDWLN DQDOL]LQLQ \DSÕOGÕ÷Õ ELU \|QWHP JHOLúWLUPLúOHUGLU <|QWHPGH \DWD\ \N GD÷ÕOÕPÕ YH KHGHI \HUGH÷LúWLPHVL GH÷HUOHUL elastik dinamik analizden elde edilmektedir. Bu yöntemden elde edilen sonuçlar lineeUROPD\DQGLQDPLNDQDOL]VRQXoODUÕLOHNDUúÕODúWÕUÕODUDNGH÷HUOHQGLULOPLúWLU>@
)DHOOD YH .LODU EXUXOPD G]HQVL]OL÷L EXOXQDQ \DSÕODUÕQ GHSUHP \NOHUL DOWÕQGDNL GDYUDQÕúÕQÕQ EHOLUOHQPHVL LoLQ o ER\XWOX OLQHHU ROPD\DQ VWDWLN analizin uygulanDELOLUOL÷LQL LQFHOHPLúOHUGLU %XQXQ LoLQ NWOH PHUNH]L ND\GÕUÕODUDN EXUXOPD G]HQVL]OL÷L ROXúWXUXODQ G|UW NDWOÕ ELU \DSÕ HOH DOÕQPÕú YH \DWD\ \NOHULQ SODQGDIDUNOÕHWNLPHQRNWDODUÕLoLQOLQHHUROPD\DQVWDWLNDQDOL]OHUL\DSÕOPÕúWÕU(OGH edilen sonuçlar lLQHHU ROPD\DQ GLQDPLN DQDOL] VRQXoODUÕ LOH NDUúÕODúWÕUÕODUDN GH÷HUOHQGLULOPLúWLU>@
3HQHOLV YH .DSSRV ELQDODUÕQ EXUXOPD GDYUDQÕúÕQÕQ GD J|]|QQH DOÕQGÕ÷Õ ELU OLQHHU ROPD\DQ VWDWLN DQDOL] \|QWHPL JHOLúWLUPLúOHUGLU <|QWHPGH NXOODQÕODQ \DWD\ \N GD÷ÕOÕPÕ HODVWLN VSHNWUDO DQDOL] NXOODQÕODUDN EHOLUOHQPHNWH YH \DSÕQÕQGLQDPLNNDUDNWHULVWLNOHULQLQEHOLUOHQPHVLQGHEXUXOPDYH|WHOHPHPRGODUÕQÕQ ELUOHúWLULOGL÷L HúGH÷HU WHN VHUEHVWOLN GHUHFHOL VLVWHP \DNODúÕPÕ NXOODQÕOPDNWDGÕU *HOLúWLULOHQ\|QWHPWHNNDWOÕWHNGR÷UXOWXGDVLPHWULNELU\DSÕ]HULQGHX\JXODQPÕúYH HOGH HGLOHQ VRQXoODU OLQHHU ROPD\DQ GLQDPLN DQDOL] VRQXoODUÕ LOH NDUúÕODúWÕUÕODUDN GH÷HUOHQGLULOPLúWLU>@
Mwafy ve Elnashai (2001), Lineer Olmayan Statik Analizin (LOSA) GR÷UXOX÷XQX YH X\JXODQDELOLUOL÷L DUDúWÕUPÕúODUGÕU %X DPDoOD IDUNOÕ VQHNOLN |]HOOLNOHULQH VDKLS G]HQOL YH G]HQVL] oHUoHYH \DSÕODU LOH G]HQOL SHUGH-çerçeve
7
\DSÕODUVHoLOPLúYHEX\DSÕODU]HULQGHGHSUHP\NQWHPVLOHGHQIDUNOÕ\DWD\\N GD÷ÕOÕPODUÕ LoLQ WHUV oJHQ GD÷ÕOÕP QLIRUP GD÷ÕOÕP YH oRN PRGOX GD÷ÕOÕP /26$¶OHU \DSÕODUDN oRN VD\ÕGD GHSUHP \HU KDUHNHWL LoLQ \DSÕODQ /LQHHU 2OPD\DQ 'LQDPLN$QDOL] /2'$ VRQXoODUÕLOHNDUúÕODúWÕUÕOPÕúWÕU<DSÕQÕQ\HWHUOLGR÷UXOXNWD PRGHOOHQPHVL \DWD\ \N GD÷ÕOÕPÕQÕQ GLNNDWOL VHoLOPHVL YH VRQXoODUÕQ GR÷UX \RUXPODQPDVÕGXUXPXQGD/26$¶LQHODVWLNYHHODVWLNROPD\DQE|OJHGHNLGDYUDQÕúODU KDNNÕQGD |QHPOL ELOJLOHU YHUGL÷L EHOLUWLOPLúWLU /26$¶LQ D] NDWOÕ YH NÕVD SHUL\RWOX oHUoHYH\DSÕODULoLQoRNX\JXQROGX÷XEHOLUOHQPLúWLUg]HOYHX]XQSHUL\RWOX\DSÕODU LoLQ/26$YH/2'$¶GHQHOGHHGLOHQVRQXoODUÕQELUELULQGHQIDUNOÕROGX÷XEHOLUOHQPLú YH EXQXQ QHGHQL VDELW \DWD\ \N GD÷ÕOÕPÕQÕQ HODVWLN VRQUDVÕ E|OJHGH \NVHN PRG HWNLOHULQLJ|]|QQHDODPDPDVÕRODUDNDoÕNODQPÕúWÕU%XQXJLGHUPek için birden fazla \DWD\ \N GD÷ÕOÕPÕ LoLQ D\UÕ D\UÕ DQDOL]OHU \DSÕODUDN NDSDVLWH YH WDOHSOHULQ EHOLUOHQPHVLQLQ X\JXQ RODFD÷Õ EHOLUWLOPLúWLU $\UÕFD \NVHN PRG HWNLOHULQL YH G]HQVL]\DSÕHWNLOHULQLJ|]|QQHDODELOHFHNVSHNWUXPHVDVOÕHWNLQ\HQL\|QWHPlerin JHUHNOLOL÷LGH÷HUOHQGLULOPLúWLU>@
Lew ve Kunnath (2001), FEMA 273’de önerilen lineer olmayan statik analiz SURVHGUOHULQLQ HWNLQOL÷LQL LQFHOHPLúOHUGLU %XQXQ LoLQ 1RUWKULGJH GHSUHPLQH DLW JoO GHSUHP \HU KDUHNHWL ND\ÕWODUÕ EXOXQDQ LNL oHOLN Ye iki betonarme bina NXOODQÕOPÕúWÕU %LQDODUGDQ GHSUHP VÕUDVÕQGD DOÕQDQ |OoPOHUGHQ \DUDUODQDUDN
EHOLUOHQHQ \HUGH÷LúWLUPH GDYUDQÕúÕ LoLQ OLQHHU ROPD\DQ GLQDPLN DQDOL] \DSÕOPÕú YH )(0$¶GH|QHULOHQoIDUNOÕ\DWD\\NGD÷ÕOÕPÕLoLQ\DSÕODQOLneer olmayan statik
DQDOL] VRQXoODUÕ LOH NDUúÕODúWÕUÕOPÕúWÕU 3ODVWLNOHúHQ NHVLWOHULQ VLVWHP ]HULQGHNL GD÷ÕOÕPÕ YH J|UHOL NDW |WHOHPHOHUL LoLQ \DSÕODQ NDUúÕODúWÕUPDODUGDQ OLQHHU ROPD\DQ VWDWLN DQDOL] \|QWHPOHULQLQ VW NDWODUGDNL SODVWLNOHúPHOHUL YH J|UHOi kat ötelemesi WDOHSOHULQLEHOLUOHPHGH\HWHUVL]NDOGÕNODUÕEHOLUOHQPLúWLU> @
Freeman (1998), lineer olmayan statik analiz ile GDYUDQÕúVSHNWUXPDQDOL]Lnin ELUOHúWLULOPHVLQH GD\DQDQ Kapasite Spektrum Yönteminin HVDVODUÕQÕ JHOLúLPLQL YH G]OHúWLULOPLúVSHNWUXPODULOHJHUoHNGHSUHP\HUKDUHNHWLND\ÕWODUÕQDDLWVSHNWUXPODU LoLQ NXOODQÕPÕQÕ DoÕNODPÕúWÕU dDOÕúPDGD D\UÕFD EX \|QWHP EHQ]HU \|QWHPOHULQ HVDVODUÕEDNÕPÕQGDQNDUúÕODúWÕUÕOPÕúWÕU>@
8
)DMIDU \DSÕODUÕQ GHSUHP \NOHUL DOWÕQGD DQDlizi için, N2 olarak DGODQGÕUÕODQEDVLWELUOLQHHUROPD\DQDQDOL]\|QWHPLJHOLúWLUPLúWLU<|QWHPGHoRN VHUEHVWOLNGHUHFHOLELUVLVWHPLQ/LQHHU2OPD\DQ6WDWLN$QDOL]L /26$ HúGH÷HUWHN serbestlik dereceli sistemin GDYUDQÕú VSHNWUXP DQDOL]L LOH ELUOHúWirilmektedir. <|QWHPLYPH\HUGH÷LúWLUPHIRUPDWÕQGDIRUPOHHGLOPLúE|\OHFHGHSUHPGDYUDQÕúÕQÕ NRQWURO HGHQ WHPHO GDYUDQÕú E\NONOHULQLQ J|UVHO GH÷HUOHQGLUPH \DSÕOPDVÕQD RODQDNYHULOPLúWLU<|QWHPGHKapasite Spektrumu YöntemiQGHQIDUNOÕRODUDNHODVWik VSHNWUXP\HULQHHODVWLNROPD\DQVSHNWUXPNXOODQÕOPDNWDGÕU%XúHNLOGHLWHUDV\RQD JHUHNNDOPDGDQJHUHNOLWDOHSE\NONOHULEHOLUOHQHELOPHNWHGLU<|QWHPG|UWNDWOÕ ELU EHWRQDUPH \DSÕ ]HULQGH X\JXODQDUDN VRQXoODU D\QÕ \DSÕ LoLQ JHUoHNOHúWLULOHQ dene\ VRQXoODUÕ LOH NDUúÕODúWÕUÕOPÕúWÕU %LULQFL PRGXQ HWNLQ ROGX÷X EX \DSÕ LoLQ VRQXoODUÕQ \HWHUL NHVLQOLNWH ROGX÷X EHOLUOHQPLúWLU dDOÕúPDGD D\UÕFD JHOLúWLULOHQ \|QWHP$7&YH)(0$¶GHYHULOHQ/26$HVDVOÕGH÷HUOHQGLUPH\|QWHPOHULLOH NDUúÕODúWÕUÕOPÕúWÕU> @
$VFKKHLP YH %ODFN \DSÕODUÕQ GHSUHP \NOHUL DOWÕQGDNL GDYUDQÕúÕQÕ EHOLUOHPHN YH GH÷HUOHQGLUPHN DPDFÕ\OD OLQHHU ROPD\DQ VWDWLN DQDOL]L HVDV DODQ YH “$NPD 1RNWDVÕ 6SHNWUXPX´ RODUDN DGODQGÕUÕODQ \HQL ELU \|QWHP JHOLúWLUPLúOHUGLU <|QWHPGHNDSDVLWHH÷ULVLLNLGR÷UXSDUoDVÕLOHLGHDOOHúWLULOHUHNWHNVHUEHVWOLNGHUHFHOL VLVWHPH G|QúWUOPHNWH YH J|]|QQH DOÕQDQ GHSUHP \HU KDUHNHWLQH DLW HODVWLN
ROPD\DQLYPHVSHNWUXPX VDELWVQHNOLNRUDQOÕ LOHELUOLNWHDNPDGD\DQÕPÕNDWVD\ÕVÕ-akma \HUGH÷LúWLUPHVL IRUPDWÕQGD D\QÕ JUDILN ]HULQGH oL]LOPHNWHGLU 'DKD VRQUD
IDUNOÕ VQHNOLN RUDQÕQD VDKLS HODVWLN ROPD\DQ LYPH VSHNWUXPODUÕQGDQ VLVWHP DNPD QRNWDVÕQÕ NHVHQ LYPH VSHNWUXPXQD DLW VQHNOLN RUDQÕ NXOODQÕODUDN PDNVLPXP \HUGH÷LúWLUPHWDOHELEHOLUOHQPHNWHGLUdDOÕúPDGDD\UÕFDDNPDQRNWDVÕQÕQGD\DQÕP YH ULMLWOLNOH GH÷LúLPL GH÷HUOHQGLULOPLú YH JHOLúWLULOHQ \|QWHPLQ SHUIRUPDQVD GD\DOÕ WDVDUÕPYHGH÷HUOHQGLUPHGHNXOODQÕPÕQDLOLúNLQSURVHGUOHUDQODWÕOPÕúWÕU>@
Albanesi vd. (2002), lineer olma\DQ VWDWLN DQDOL]L HVDV DODQ GH÷HUOHQGLUPH \|QWHPOHULQGHQ.DSDVLWH6SHNWUXP<|QWHPLQL<HUGH÷LúWLUPH.DWVD\ÕODUÕ<|QWHPLQL YH1\|QWHPLQL\HUGH÷LúWLUPHYHGD\DQÕPWDOHSOHULEDNÕPÕQGDQGDYUDQÕúVSHNWUXP
analizi HúLW HQHUML YH HúLW \HUGH÷LúWLUPH \DNODúÕPODUÕ YH OLQHHU ROPD\DQ GLQDPLN
9
]HULQGH IDUNOÕ \DWD\ \N GD÷ÕOÕPODUÕ QLIRUP ELUOHúWLULOPLú PRGDO NDW NHVPH NXYYHWOHUL GD÷ÕOÕPÕ YH PRGDO X\DUODPDOÕ GD÷ÕOÕP LoLQ HOGH HGLOHQ NDSDVLWH H÷ULOHUL NXOODQÕODUDN EHOLUOHQHQ GDYUDQÕú E\NONOHUL GH÷HUOHQGLULOPLúWLU <DSÕODQ NDUúÕODúWÕUPDODUGDQ LQFHOHQHQ \|QWHPOHULQ \NVHN PRGODUÕQ HWNLQ ROGX÷X \NVHN \DSÕGDWDEDQNHVPHNXYYHWLWDOHSOHULQLROGXNoDGúNYHUGL÷LQLJ|VWHUPLúWLU)DUNOÕ \DWD\\NGD÷ÕOÕPODUÕQÕQ\HUGH÷LúWLUPHGDYUDQÕúÕQÕGH÷LúWLUPHGL÷LDQFDNWDEDQNHVPH NXYYHWLQGHNLE\NIDUNODUÕD]DOWWÕ÷ÕJ|UOPúWU>@
$OEDQHVLYG HQHUMLHúLWOL÷LLONHVLQHGD\DQDQ\HQLELUOLQHHUROPD\DQ VWDWLNDQDOL]\|QWHPLJHOLúWLUPLúOHUGLU%XHQHUML\HGD\DOÕ\|QWHPGHGLQDPLNDQDOL] YH\D \DUÕ-VWDWLN X\DUODPDOÕ DQDOL] HVDV DOÕQPDNWDGÕU *HOLúWLULOHQ \|QWHP .DSDVLWH Spektrum Yöntemi, elastik GDYUDQÕúVSHNWUXPDQDOL]LYHGLQDPLNDQDOL]VRQXoODUÕLOH NDUúÕODúWÕUÕODUDNGH÷HUOHQGLULOPLúWLU>@
5HLQKRUQ \DSÕODUÕQ OLQHHU ROPD\DQ VWDWLN DQDOL]LQGH NXOODQÕOPDN ]HUH\DSÕQÕQGLQDPLNNDUDNWHULVWLNOHULQLQYHGHSUHPLQNDUDNWHULVWLNOHULQLQJ|]|QQH DOÕQGÕ÷Õ ELU \DWD\ \N GD÷ÕOÕPÕ IRUPODV\RQX WDQÕPODPÕúWÕU ³0RGDO 8\DUODPDOÕ
DD÷ÕOÕP´ RODUDN LVLPOHQGLULOHQ GD÷ÕOÕPGDSODVWLNOHúPH SODVWLN NHVLWOHULQ ROXúXPX
LOHGH÷LúHQPRGúHNLOOHULPRGDONDWÕOÕPoDUSDQODUÕYHHODVWLNVSHNWUDOLYPHGH÷HUOHUL J|]|QQHDOÕQPDNWDGÕU$\UÕFDWDQÕPODQDQEXIRUPODV\RQ,'$5&-2D bilgisayar SURJUDPÕQDDGDSWHHGLOHUHNVD\ÕVDOX\JXODPDODUDRODQDNVD÷ODQPÕúWÕU>@
%UDFFL YG D] YH RUWD NDWOÕ \DSÕODUÕQ GHSUHP \NOHUL DOWÕQGDNL SHUIRUPDQVÕQÕ EHOLUOHPHN YH EXQGDQ \DUDODQDUDN \DSÕODUÕ JoOHQGLUPHN LoLQ ELU \|QWHP JHOLúWLUPLúOHUGLU <|QWHP Kapasite Spektrumu Yöntemi¶QGHQ WUHWLOPLúWLU <|QWHPGH\DSÕQÕQHODVWLNDúDPDGDQJ|oPHDúDPDVÕQDNDGDURODQE|OJHGHGLQDPLN NDUDNWHULVWLNOHULQLQGH÷LúLPLQLLoHUHQNDWWDOHSH÷ULOHULHOGHHGLOPHNWHGLU%XWDOHSOHU ED÷ÕPVÕ] RODUDN /LQHHU 2OPD\DQ 6WDWLN $QDOL] (LOSA) ile belirlenen yatay kat NDSDVLWHOHUL LOH NDUúÕODúWÕUÕOPDNWDGÕU /26$¶GH NXOODQÕODQ \DWD\ \NOHULQ GD÷ÕOÕPÕ ULMLWOL÷HED÷OÕDUWÕPVDONDWNHVPHWDOHSOHULQHGD\DQPDNWDGÕU*HOLúWLULOHQ\|QWHP |OoHNOL ELU \DSÕ PRGHOLQH X\JXODQPÕúWÕU %X PRGHO D\QÕ ]DPDQGD ODEDURWXYDUGD VDUPD WDEODVÕ LOH WHVW HGLOPLúWLU <DSÕ EHOLUOL G]H\GH KDVDU J|UGNWHQ VRQUD JoOHQGLULOPLúYHWHNUDUWHVWHGLOPLúWLU(OGHHGLOHQDQDOL]VRQXoODUÕLOHWHVWVRQXoODUÕ
10
NDUúÕODúWÕUÕODUDN SURVHGU GH÷HUOHQGLULOPLúWLU dDOÕúPDGD JHOLúWLULOHQ \|QWHPLQ \DSÕODUÕQGHSUHP\NOHULDOWÕQGDNLSHUIRUPDQVÕQÕEHOLUOHPHGHYHGH÷HUOHQGLUPHGHNDW WDOHSOHUL YH EXQD NDUúÕOÕN JHOHQ NDW NDSDVLWHOHUL LoLQ JYHQLOLU GH÷HUOHU YHUGL÷L J|UOPúWU %D]Õ \DSÕVDO G]HQVL]OLNOHU LoHUHQ D] NDWOÕ \DSÕODUÕQ GHSUHm yükleri DOWÕQGDNL SHUIRUPDQVÕQÕ EHOLUOHUNHQJHOHQHNVHO PRQRWRQDUWDQ\DWD\\NGD÷ÕOÕPÕQÕ HVDVDODQ /26$\HULQH\DSÕQÕQGLQDPLN|]HOOLNOHULQLQ|QHPOLGH÷LúLPOHUJ|VWHUGL÷L E|OJHOHUGH EX GH÷LúLPOHUL LoHUHQ \HQL \DWD\ \N GD÷ÕOÕPODUÕQÕQ NXOODQÕOPDVÕQÕQ \HULQGHRODFD÷ÕEHOLUWLOPLúWLU>@
3DUHWYG YH6DVDNLYG \NVHNPRGODUQHGHQL\OHROXúDQJ|oPH PHNDQL]PDODUÕQÕ EHOLUOH\HELOPHN LoLQ ³Çok-Modlu Pushover Analiz” olarak DGODQGÕUÕODQ ELU /LQHHU 2OPD\DQ 6WDWLN $QDOL] /26$ \|QWHPL JHOLúWLUPLúOHUGLU <|QWHPGHJHOHQHNVHO/26$EDVLWOL÷LNRUXQDUDN\NVHNPRGHWNLOHULQLGHJ|]|QQH DODFDNúHNLOGHJHQLúOHWLOPHNWHGLU*HOLúWLULOHQSURVHGUQHVDVÕ|]HOWLWUHúLPPRGODUÕ LoLQ \DSÕQÕQ GDYUDQÕúÕQÕ WHPVLO HGHQ NDSDVLWH H÷ULOHUL ROXúWXUPDNWÕU %X kapasite H÷ULOHULQLQEHOLUOHQPHVLQGHLOJLOLPRGDDLWHODVWLNPRGúHNOLQHGD\DQDQ\DWD\GD÷ÕOÕP NXOODQÕOPDNWDYHKHUELULLoLQD\UÕD\UÕJHOHQHNVHO(g6ø$\DSÕOPDNWDGÕU'DKDVRQUD KHUELUNDSDVLWHH÷ULVLKapasite Spektrumu YöntemiHVDVODUÕNXOODQÕODUDNLOJili talep VSHNWUXPX LOH NDUúÕODúWÕUÕOPDNWD YH HWNLQ RODQ GL÷HU PRGODU GD EHOLUOHQPHNWHGLU dHúLWOL GHSUHPOHULQ HWNLVL\OH KDVDU J|UPú IDUNOÕ \DSÕODU ]HULQGH SURVHGU X\JXODQPÕú HOGH HGLOHQ VRQXoODU J|]OHQHQ KDVDUODU LOH NDUúÕODúWÕUÕODUDN \|QWHP GH÷HUOHQGLULOPLúWLU *HOLúWLULOHQ \|QWHP LOH \NVHN PRGODUÕQ HWNLOL ROGX÷X \DSÕODUGD güvenlik ve hasar kontrolünün geleneksel yöntemlere oranla daha gerçekçi olarak EHOLUOHQHELOGL÷LEHOLUWLOPLúWLU>@
9DOOH\ YH +DUULV GúH\GH YH SODQGD G]HQVL]OL÷L Qedeniyle yüksek PRGODUÕQ HWNLQ ROGX÷X LNL NDWOÕ ELU EHWRQDUPH ELQDQÕQ ]HULQGH PRGDO X\DUODPDOÕ OLQHHUROPD\DQVWDWLNDQDOL]X\JXODPÕúODUGÕU/LQHHU-elastik analiz özelliklerine sahip SURJUDP NXOODQÕODUDN JHUoHNOHúWLULOHQ DQDOL]GH HOHPDQODUGD SODVWLNOHúPe meydana JHOGLNoH ULMLWOLNOHU GH÷LúWLULOPHNWH YH\D LOJLOL HOHPDQ VLVWHPGHQ oÕNDUÕOPDNWD GDKD VRQUDGLQDPLNDQDOL]LOH\HQL\NGD÷ÕOÕPÕEHOLUOHQPHNWHGLU%XDQDOL]\DSÕQÕQLOJLOL LWPHDGÕPÕQGDNLELUOHúWLULOPLúPRGDO\HUGH÷LúWLUPHGH÷HULQHXODúÕOÕQFD\DYeya toptan J|oPHPHNDQL]PDVÕROXúXQFD\DNDGDUVUGUOPúWU>@
11
Moghadam (1998), yüksek mod etkilerini içeren “3XVKRYHU 6RQXoODUÕ %LUOHúWLUPHVL´ LVLPOL ELU \|QWHP JHOLúWLUPLúWLU <|QWHP HODVWLN PRG úHNLOOHULQH GD\DQDQ\DWD\\NGD÷ÕOÕPODUÕLoLQ\DSÕODQOLQHHUROPD\DQVWDWLNDQDOL]VRQXoODUÕQÕQ |QHULOHQ ELU NRPELQDV\RQ LIDGHVL LOH ELUOHúWLULOPHVLQH GD\DQPDNWDGÕU *HOLúWLULOHQ \|QWHP \LUPL NDWOÕ ELU G]OHP oHOLN oHUoHYH \DSÕ\D X\JXODQDUDN PDNVLPXP \HUGH÷LúWLUPHOHU YH NDW |WHOHPHOHUL EDNÕPÕQGDQ OLQHHU olmayan dinamik analiz VRQXoODUÕLOHNDUúÕODúWÕUÕOPÕúWÕU>@
<DQJ YH :DQJ \NVHN PRG HWNLOHULQL YH \DSÕGD PH\GDQD JHOHQ SODVWLNOHúPHOHULQ HWNLVLQL LoHUHQ ELU \DWD\ \N GD÷ÕOÕPÕQÕQ OLQHHU ROPD\DQ VWDWLN DQDOL] VRQXoODUÕQD HWNLVLQL LQFHOHPLúOHUGLU øQFHOHQHQ GD÷ÕOÕP ED]Õ G]HQVL]OLNOHU LoHUHQ o IDUNOÕ G]OHP EHWRQDUPHoHUoHYH ]HULQGH X\JXODQPÕúYHVRQXoODUOLQHHU ROPD\DQGLQDPLNDQDOL]VRQXoODUÕLOHNDUúÕODúWÕUÕOPÕúWÕU$\UÕFDHOGHHGLOHQVRQXoODU FEMA 273’de önerilen ters üçgen yatay yükGD÷ÕOÕPÕYHPRGDOGD÷ÕOÕPNXOODQÕODUDN \DSÕODQOLQHHUROPD\DQVWDWLNDQDOL]VRQXoODUÕLOHNDUúÕODúWÕUÕOPÕúYH|QHULOHQGD÷ÕOÕP GH÷HUOHQGLULOPLúWLU>@
*XSWD YH .XQQDWK \DSÕGD PH\GDQD JHOHQ SODVWLNOHúPHOHULOH \DWD\\NGD÷ÕOÕPÕQGDNLGH÷LúLPLYH\NVHNPRGHWNLOHULQLLoHUHQVSHNWUXPHVDVOÕELU /LQHHU2OPD\DQ6WDWLN$QDOL] /26$ \|QWHPLJHOLúWLUPLúOHUGLU<|QWHPGHVDGHFH PDO]HPHQLQ OLQHHU ROPD\DQ GDYUDQÕúÕ J|]|QQH DOÕQPÕúWÕU dDOÕúPDGD |QFHOLNOH deprem etkilerini ölçen aletler ilH GRQDWÕOPÕú oHúLWOL ELQDODUÕQ 1RUWKULGJH GHSUHPLHVQDVÕQGDNLGDYUDQÕúODUÕLQFHOHQPLúWLU%XLQFHOHPHGHGHSUHPVÕUDVÕQGDNL NDW\HUGH÷LúWLUPHOHULQGHQ\DUDUODQÕODUDNDWDOHWNXYYHWOHULQLQGH÷LúLPLEHOLUOHQPLúWLU $]NDWOÕ\DSÕODUGDDWDOHWNXYYHWOHULQLQGD÷ÕOÕPÕQÕQELULQFLPRGúHNOLQHX\GX÷XDQFDN \DSÕ\NVHNOL÷LDUWWÕNoDGD÷ÕOÕPODUÕQLNLQFLPRGúHNLOOHULQHEHQ]HGL÷LEHOLUOHQPLúWLU 'DKD VRQUD EX GDYUDQÕúODUGDQ \DUDODQDUDN JHOHQHNVHO /26$ \|QWHPOHULQLQ HNVLNOLNOHULQLJLGHUHFHN\HQLELU\|QWHPJHOLúWLULOPLúWLU<|QWHP\DSÕQÕQGLQDPLN |]HOOLNOHULQH YH J|]|QQH DOÕQDQ GHSUHP |]HOOLNOHULQH ED÷OÕ RODUDN KHU ELU WLWUHúLP SHUL\RGX LoLQ KHVDSODQDQ PRGDO NDW NXYYHWOHULQLQ ELUELULQGHQ ED÷ÕPVÕ] RODUDN VLVWHPH HWNLWLOPHVLQLYHHOGHHGLOHQGDYUDQÕúE\NONOHULQLn ilgili mod için uygun RODQNRPELQDV\RQNXUDOÕLOHELUOHúWLULOPHVLQLHVDVDOPDNWDGÕU$QDOL]VÕUDVÕQGDKHU ELU \N DUWÕPÕ LoLQ \DSÕ HOHPDQODUÕQGD PH\GDQD JHOHQ ULMLWOLN GH÷LúLPOHULQGHQ
12
(çatlama, akma vb.) sonra sistemin modal özellikleri yeniden belirlenmekte ve belirli ELUVÕQÕUGH÷HUHXODúÕOÕQFD\DNDGDUEXúHNLOGHDQDOL]HGHYDPHGLOPHNWHGLU<|QWHPGH HOHPDQODUÕQSODVWLNOHúPHGH÷HUOHULQLQEHOLUOHQPHVLQGHWPPRGODUGDQPH\GDQDJHOHQ NHVLW WHVLUOHUL NXOODQÕODUDN PRGODUÕQ HWNLOHúLPL J|]|QQH DOÕQPDNWDGÕU Modal kat NXYYHWOHULQLQEHOLUOHQPHVLQGHHODVWLNVSHNWUDOLYPHOHUNXOODQÕOPDNWDGÕU*HOLúWLULOHQ SURVHGU D] YH oRN NDWOÕ D\UÕFD ULMLWOLN YH GD\DQÕP G]HQVL]OL÷L EXOXQDQ G]OHP oHUoHYH \DSÕODU ]HULQGH X\JXODQPÕúWÕU (OGH HGLOHQ VRQXoODU )(0$ PRdal \DWD\ \N GD÷ÕOÕPÕ YH QLIRUP \DWD\ \N GD÷ÕOÕPÕ NXOODQÕODUDN \DSÕODQ /26$ VRQXoODUÕ YH /LQHHU 2OPD\DQ 'LQDPLN $QDOL] VRQXoODUÕ /2'$ LOH NDUúÕODúWÕUÕOPÕúWÕU(OGHHGLOHQVRQXoODUNDSDVLWHH÷ULOHULU|ODWLINDW|WHOHQPHOHULYH SODVWLNOHúHQ NHVLWOHULQ \DSÕGDNL GD÷ÕOÕPÕ EDNÕPÕQGDQ /2'$ VRQXoODUÕQD ROGXNoD \DNÕQ EXOXQPXúWXU <NVHN PRG HWNLOHULQLQ |QHPOL ROGX÷X YH GD\DQÕP YH ULMLWOLN G]HQVL]OL÷L EXOXQDQ \DSÕODUGD JHOHQHNVHO /26$ \HULQH JHOLúWLULOHQ \|QWHPLQ NXOODQÕOPDVÕQÕQX\JXQRODFD÷ÕEHOLUWLOPLúWLU [19,38].
/HIRUW >@¶GHJHOLúWLULOHQ0RGDO8\DUODPDOÕ'D÷ÕOÕP¶GDDQOÕNHODVWLN VSHNWUDOLYPHOHULOH|OoHNOHPHQLQHWNLVLQLLQFHOHPLúWLU$\UÕFD\NDUWÕPÕVÕUDVÕQGD \DWD\\NOHUL|OoHNOHPHúHNOLQLQ VDGHFHVRQ\NDUWÕPÕQÕ|OoHNOHPHYHWRSODP yatay \N |OoHNOHPH HWNLVLQL LQFHOHPLúWLU dDOÕúPDGD G]HQOL ULMLWOLN YH GD\DQÕP G]HQVL]OL÷L EXOXQDQ \DSÕODU LQFHOHQPLúWLU /LQHHU ROPD\DQ VWDWLN DQDOL] /26$ VRQXFXQGDHOGHHGLOHQNDSDVLWHH÷ULOHULQLIRUPGD÷ÕOÕPYHWHUVoJHQGD÷ÕOÕPLoLQ yaSÕODQ /26$ YH DUWÕPVDO GLQDPLN DQDOL] VRQXoODUÕ LOH NDUúÕODúWÕUÕODUDN GH÷HUOHQGLULOPLúWLU> @
&KRSUD YH *RHO VDELW \DWD\ \N GD÷ÕOÕPÕQÕ HVDV DODQ JHOHQHNVHO \|QWHPOHULQ KHVDSVDO YH NDYUDPVDO EDVLWOL÷LQLQ NRUXQGX÷X \DSÕ GLQDPL÷L WHRULVLQH da\DQDQ \HQL ELU /LQHHU 2OPD\DQ 6WDWLN $QDOL] /26$ \|QWHPL JHOLúWLUPLúOHUGLU “Modal Pushover Analiz´ RODUDN DGODQGÕUÕODQ \|QWHPGH KHU ELU PRG LoLQ DWDOHW NXYYHWL GD÷ÕOÕPÕ NXOODQÕODUDN /26$ LOH NDSDVLWH H÷ULOHUL EHOLUOHQPHNWH YH EX H÷ULOHUGHQ\DUDUODQDUDk modlara ait deprem talepleri elde edilmektedir. Daha sonra EXPRGDOWDOHSGH÷HUOHULX\JXQNRPELQDV\RQNXUDOÕLOHELUOHúWLULOHUHNOLQHHUROPD\DQ WRSODPGHSUHPWDOHELEHOLUOHQPHNWHGLU<|QWHPGHKHUELUPRGLoLQED÷ÕPVÕ]/26$ \DSÕOGÕ÷ÕQGDQ PRGODUÕQ HWNLOHúLPL J|]|QQH DOÕQPDPDNWDGÕU *HOLúWLULOHQ\|QWHP
13
GRNX] NDWOÕ oHOLN G]OHP ELU oHUoHYH ]HULQGH X\JXODQPÕú YH VRQXoODU /LQHHU 2OPD\DQ 'LQDPLN $QDOL] /2'$ LOH NDUúÕODúWÕUÕOPÕúWÕU <DSÕQÕQ NDW \HUGH÷LúWLUPHOHULNDW|WHOHQPHOHULYHSODVWLNPDIVDOODUÕQGD÷ÕOÕPÕEDNÕPÕQGDQ/2'$ LOH X\XPOX VRQXoODU HOGH HGLOPLú DQFDN SODVWLN PDIVDOODUGDNL G|QPH GH÷HUOHULQGH E\N KDWDODU EHOLUOHQPLúWLU $\UÕFD JHOLúWLULOHQ \|QWHP )(0$ ¶GH |QHULOHQ \DWD\ \N GD÷ÕOÕPODUÕ LoLQ \DSÕODQ /26$ LOH GH NDUúÕODúWÕUÕOPÕúWÕU *HOLúWLULOHQ \|QWHPLQ )(0$ ¶GH |QHULOHQ GD÷ÕOÕPODUÕQ WPQGHQ GDKD L\L VRQXoODU YHUGL÷L EHOLUOHQPLúWLU6RQXoODUDJ|UHJHOLúWLULOHQ\|QWHPLQELQDODUÕGH÷HUOHQGLUPHYHGL]D\Q HWPHGHSUDWLNX\JXODPDODULoLQ\HWHULNDGDUNHVLQROGX÷XEHOLUWLOPLúWLU>-42].
Elnashai (2001, 2002), mevcut geleneksel lineer olmayan statik analiz yöntemlerinin eksikliklerini ve çok-PRGOX X\DUODPDOÕ \HQL \|QWHPOHUL GH÷HUOHQGLUPLúWLU%X\HQL\|QWHPOHUGHVSHNWUDO|OoHNOHPHQLQHWNLVLQLYHLWPHDQDOL]L VÕUDVÕQGD \N GD÷ÕOÕPÕQÕQ DUWÕPVDO YH WRSODP |OoHNOHQPHVLQLQ IDUNODUÕQÕ DUWÕPVDO GLQDPLN DQDOL] GLQDPLN SXVKRYHU SURVHGU LOH NDUúÕODúWÕUPDODU \DSDUDN LQFHOHPLúWLUg]HOOLNOH\NVHNPRGODUÕQHWNLQROGX÷X\DSÕODUGD|QHPOLRODQGHSUHP NDUDNWHULVWLNOHULQLQ J|]|QQH DOÕQPDVÕ LoLQ VSHNWUDO |OoHNOHPHQLQ JHUHNOL ROGX÷XQX YH WRSODP |OoHNOHPHQLQ DUWÕPVDO |OoHNOHPH\H RUDQOD \DSÕQÕQ GHSUHP VÕUDVÕQGDNL GDYUDQÕúÕQÕGDKDL\L\DQVÕWWÕ÷ÕQÕJ|VWHUPLúWLU>@
$QWRQLRX YG GHSUHPL WHPVLO HGHQ \DWD\ NXYYHWOHULQ \DSÕQÕQ PRGDO özellLNOHULQHED÷OÕRODUDNKHUKHVDSDGÕPÕQGDGH÷LúWLULOGL÷L³7DP2ODUDN8\DUODPDOÕ
Pushover Prosedürü´ LVLPOL ELU \|QWHP JHOLúWLUPLúOHUGLU <|QWHPGH \DSÕ
HOHPDQODUÕQGDNLKHUULMLWOLNGH÷LúLPLQGHQ oDWODPDDNPDYE VRQUD\DSÕQÕQGLQDPLN özelliklerine göre mRGDO NDW NXYYHWOHUL EHOLUOHQPHNWH YH R DGÕP LoLQ X\JXQ RODQ PRGDONRPELQDV\RQNXUDOÕLOHELUOHúWLULOHQNDWNXYYHWOHUL\DSÕ\DHWNLWLOHUHNLVWHQLOHQ GDYUDQÕú E\NONOHUL EHOLUOHQPHNWHGLU $QDOL] LVWHQLOHQ ELU VÕQÕU GXUXPD NDGDU VUGUOPHNWHGLU *HOLúWLULOHn yöntemde, modal kat kuvvetleri elastik spektral LYPHOHU LOH |OoHNOHQPHNWHGLU $\UÕFD PRGDO |]HOOLNOHUGHNL GH÷LúLPH ED÷OÕ RODUDN KHVDSODQDQ \DWD\ \NOHU DUWÕPVDO |OoHNOHPH YH\D WRSODP |OoHNOHPH NXOODQÕODUDN VLVWHPH HWNLWLOHELOPHNWHGLU *HOLúWLULOHQ \|QWHP oHúLWOL VQHNOLN G]H\OHULQH VDKLS G]HQOL YH G]HQVL] oHUoHYH \DSÕODU YH G]HQOL SHUGH-oHUoHYH \DSÕ ]HULQGH X\JXODQPÕú YH HOGH HGLOHQ NDSDVLWH H÷ULOHUL OLQHHU ROPD\DQ GLQDPLN DQDOL] LOH
14
NDUúÕODúWÕUÕODUDN GH÷HUOHQGLULOPLúWLU $\UÕFD D\QÕ \DSÕODU Loin üniform ve üçgen GD÷ÕOÕPNXOODQÕODUDNJHOHQHNVHOOLQHHUROPD\DQVWDWLNDQDOL]OHU\DSÕOPÕúYHVRQXoODU NDUúÕODúWÕUÕOPÕúWÕU *HOLúWLULOHQ \|QWHPLQ JHOHQHNVHO \|QWHPOHUH J|UH OLQHHU ROPD\DQ GLQDPLNDQDOL]VRQXoODUÕQDGDKD\DNÕQVRQXoODUYHUGL÷LEHOLUWLOPLútir [20].
$\GÕQR÷OX oRN PRGOX GDYUDQÕúÕ J|]|QQH DODELOHQ SUDWLN YH D\QÕ ]DPDQGD WHRULN WXWDUOÕOÕ÷Õ GD RODQ \HQL OLQHHU ROPD\DQ VWDWLN DQDOL] \|QWHPL JHOLúWLUPLúWLU ³$UWÕPVDO 'DYUDQÕú 6SHNWUXP $QDOL]L´ RODUDN DGODQGÕUÕODQ \|QWHP modal kapasitH GL\DJUDPODUÕ DGÕ YHULOHQ GL\DJUDPODUÕQ \DNODúÕN RODUDN HOGH HGLOPHVLQH GD\DQPDNWDGÕU 0RGDO KLVWHUHVLV H÷ULOHULQLQ LVNHOHW H÷ULOHUL RODUDN WDQÕPODQDQEXGL\DJUDPODUoRNPRGOXLWPHDQDOL]LQLQKHUDGÕPÕQGDJ|]|QQHDOÕQDQ deprem için hesaplanan lineer olPD\DQVSHNWUDO\HUGH÷LúWLUPHOHUHED÷OÕRODUDNHOGH HGLOPHNWHGLU %|\OHFH EX \|QWHP LOH \DSÕODQ DQDOL] VRQXFXQGD J|]|QQH DOÕQDQ GHSUHP LoLQ WP E\NONOHUH DLW WDOHSOHU GR÷UXGDQ GR÷UX\D NDSDVLWH H÷ULVL NXOODQÕOPDGDQ EHOLUOHQHELOPHNWHGLU <|QWHPGH OLQHHr olmayan spektral \HUGH÷LúWLUPHOHULQEHOLUOHQPHVLLoLQKHUDGÕPGDPRGDONDSDVLWHGL\DJUDPODUÕQÕQLNL GR÷UX SDUoDVÕ LOH LGHDOOHúWLULOPHVL YH EXQD DLW |]HOOLNOHUL HVDV DODQ WHN VHUEHVWOLN dereceli sistemin dinamik hareket denkleminin çözülmesi öngörülmektedir. dDOÕúPDGDD\UÕFDPKHQGLVOLNX\JXODPDODUÕQGDNXOODQÕOPDN]HUH\|QHWPHOLNOHUGH WDQÕPODQDQ VWDQGDUW GDYUDQÕú VSHNWUXPXQGDQ \DUDUODQDUDN oRN PRGOX SHUIRUPDQV GH÷HUOHQGLULOPHVL \DSÕODELOPHVL LoLQ HúLW GHSODVPDQ NXUDOÕQÕ esas alan bir pratik versiyon gHOLúWLULOPLúWLU *HOLúWLULOHQ SURVHGU VDGHFH PDO]HPHQLQ OLQHHU ROPD\DQ GDYUDQÕúÕQÕQ J|]|QQH DOÕQGÕ÷Õ GRNX] NDWOÕ oHOLN ELU oHUoHYH ]HULQGH X\JXODQDUDN HOGH HGLOHQ VRQXoODU OLQHHU ROPD\DQ GLQDPLN DQDOL] VRQXoODUÕ LOH NDUúÕODúWÕUÕOPÕúWÕU Prosedürün, öWHOHPH RUDQODUÕ NLULú SODVWLN G|QPHOHUL NDW NHVPH NXYYHWOHUL YH GHYLUPHPRPHQWOHULLoLQ\HWHUOLNHVLQOLNWHVRQXoODUYHUGL÷LJ|VWHULOPLúWLU>@
øQHO YG SUDWLNWH OLQHHU ROPD\DQ VWDWLN DQDOL] \|QWHPOHULQGH NXOODQÕODQ EHú IDUNOÕ \DWD\ \N GD÷ÕOÕPÕQÕ QLIRUP GD÷ÕOÕP WHUV oJHQ GD÷ÕOÕP )(0$PRGDOGD÷ÕOÕPÕELULQFLPRGGD÷ÕOÕPÕYHX\DUODPDOÕELULQFLPRGGD÷ÕOÕPÕ ve [40-@¶GHNL \|QWHPGH ED]Õ GH÷LúLNOLNOHU \DSDUDN X\JXODGÕNODUÕ ³Çok-Modlu
Pushover Analiz´\|QWHPLQLGH÷HUOHQGLUPLúOHUGLUBunun için, iki adet düzenli, iki
15
VD\ÕGD GHSUHP LoLQ \DSÕODQ OLQHHU ROPD\DQ GLQDPLN DQDOL] VRQXoODUÕ LOH NDUúÕODúWÕUÕOPÕúWÕU 7P GD÷ÕOÕPODUÕQ PDNVLPXP \HUGH÷LúWLUPH GDYUDQÕúÕQÕ NDEXO HGLOHELOLU NHVLQOLNWH YHUGL÷L DQFDN J|UHOL NDW |WHOHPHOHUL YH NDW NHVPH NXYYHWOHULQGHNLKDWDODUÕQoRNE\NPHUWHEHGHROGX÷XEHOLUOHQPLúWLU³Çok-Modlu
Pushover Analiz´ GHQ HOGH HGLOHQ VRQXoODUÕQ LVH GL÷HU GD÷ÕOÕPODUD J|UH GDKD L\L
sonuçODUYHUGL÷LEHOLUOHQPLúWLU>@
Chopra ve Goel (2004), [21-@¶GH HVDVODUÕ DQODWÕODQ ³Modal Pushover
Analiz´\|QWHPLQLoER\XWOX\DSÕODUÕLoHUHFHNúHNLOGHJHOLúWLUPLúOHUGLU'DKDVRQUD
SURVHGUoER\XWOXSODQGDG]HQVL]OL÷LEXOXQDQYHEXOXQPD\DQ\DSÕVLVWHPOHULQH X\JXODPÕúODU YH OLQHHU ROPD\DQ GLQDPLN DQDOL] LOH NDUúÕODúWÕUPDODU \DSDUDN GR÷UXOX÷XQXGH÷HUOHQGLUPLúOHUGLU>@
-DQYG \NVHNPRGHWNLOHULQLJ|]|QQHDODQEDVLWOHúWLULOPLúELUVW VÕQÕU/LQHHU2OPD\DQ6WDWLN$QDOL] /26$ \|QWHPLJHOLúWLUPLúOHUGLU<|QWHPGH |QHULOHQELUIRUPODV\RQLOHKHUPRGLoLQ\NVHNPRG\HUGH÷LúWLUPHNDWÕOÕPRUDQODUÕ KHVDSODQPDNWDYHEXRUDQODUDED÷OÕRODUDN\LQHYHULOHQELUIRUPODV\RQLOH\DWD\\N GD÷ÕOÕPÕ YH PDNVLPXP HODVWLN ROPD\DQ \HUGH÷LúWLUPH WDOHEL KHVDSODQPDNWDGÕU %X \DWD\ \N GD÷ÕOÕPÕ NXOODQÕODUDN KHVDSODQDQ KHGHI WHSH \HUGH÷LúWLUPHVL GH÷HULQH XODúÕOÕQFD\D NDGDU PRQRWRQ DUWDQ GD÷ÕOÕP LOH DQDOL] \DSÕOPDNWDGÕU *HOLúWLULOHQ \|QWHP EHú IDUNOÕ \DSÕ ]HULQGH X\JXODQPÕú YH D\QÕ \DSÕODU LoLQ JHUoHNOHúWLULOHQ oJHQGD÷ÕOÕPOÕ/26$³modal pushover analiz” ve lineer olmayan dinamik analiz VRQXoODUÕ LOH NDUúÕODúWÕUÕODUDN GH÷HUOHQGLULOPLúWLU .DW \HUGH÷LúWLUPHOHUL J|UHOL NDW |WHOHPHOHUL YH SODVWLN G|QPH GH÷HUOHUL LoLQ JHOLúWLULOHQ \|QWHPLQ D] NDWOÕ \DSÕODUGD GL÷HU \|QWHPOHUH J|UH KDWDOÕ VRQXoODU YHUGL÷L oRN NDWOÕ \DSÕODUGD LVH GL÷HU WP \|QWHPOHUHRUDQODL\LVRQXoODUYHUGL÷LEHOLUOHQPLúWLU>@
$\GÕQR÷OX >@¶GHHVDVODUÕDoÕNODQDQ³$UWÕPVDO'DYUDQÕú6SHNWUXP
Analizi” yönteminin üç boyutlu ve ikinci mertebe HWNLOHUL LoHUHQ X\JXODPDODUÕQÕ \DSPÕúWÕU%XQXQLoLQGRNX]NDWOÕNWOHHNVDQWULNOL÷LQHGHQL\OHEXUXOPDG]HQVL]OL÷L EXOXQDQoHOLNELUoHUoHYHYHRQG|UWDoÕNOÕ÷ÕEXOXQDQELUYL\DGNVLVWHPLLQFHOHPLúWLU dDOÕúPDGD JHOLúWLULOHQ \|QWHPLQ \NVHN PRGODUÕQ HWNLQ ROGX÷X EXUXOPD G]HQVL]OL÷LQHVDKLSELQDODUYHN|SUOHULoLQNXOODQÕODELOHFH÷LEHOLUWLOPLúWLU> @
16
dDOÕúPDQÕQ$PDFÕYH.DSVDPÕ
%X oDOÕúPDGD \NVHN PRGODUÕQ HWNLOL ROGX÷X ELQDODUÕQ GHSUHP HWNLOeri DOWÕQGDNL OLQHHU ROPD\DQ GDYUDQÕúÕQÕQ EHOLUOHQHELOPHVL LoLQ HWNLQ ELU dRN 0RGOX 8\DUODPDOÕ <N $UWÕPÕ <|QWHPL d08<$< JHOLúWLULOPHVL DPDoODQPÕúWÕU *HOLúWLULOHQ\|QWHP%|OP¶GHYHULOHQNRúXOODUÕVD÷OD\DQEWQ\DSÕVLVWHPOHULQH uygulanabilmektedir.
*HOLúWLULOHQ\|QWHPGHJHRPHWULGH÷LúLPOHULQLQGHQJHGHQNOHPOHULQHHWNLVLYH malzemenin elasto-plastikGDYUDQÕúÕJ|]|QQHDOÕQDUDNVLVWHPLQEHOLUOLVDELWGúH\ \NOHU YH DUWDQ PRGDO \DWD\ \NOHU LoLQ DQDOL]L \DSÕOPDNWDGÕU 3ODVWLN úHNLOGH÷LúWLUPHOHULQ plastik kesit DGÕ YHULOHQ EHOLUOL NHVLWOHUGH WRSODQGÕ÷Õ EXQXQ GÕúÕQGDNL E|OJHOHUGH GDYUDQÕúÕQ lineer-elastik ROGX÷X YDUVD\ÕOPDNWDGÕU <|QWHPGH VDELW GúH\ \NOHU LoLQ KHVDS \DSÕOPDVÕQGDQ \DUDUODQDUDN ikinci mertebe etkileri OLQHHUOHúWLULOPHNWHGLU$\UÕFDDNPDNRúXOODUÕQÕLIDGHHGHQH÷ULOHUGHGR÷UXSDUoDODUÕ LOHLGHDOOHúWLULOHUHNOLQHHUOHúWLULOPHNWHGLU
<|QWHPLQ \XNDUÕGD NÕVDFD LIDGH HGLOHQ |]HOOLNOHUL QHGHQL\OH SODVWLNOHúHQ NHVLWOHU DUDVÕQGDNL OLQHHU GDYUDQÕú E|OJHOHULQGH \N DUWÕPÕ X\JXODQPDVÕQD gerek NDOPDGDQ KHU SODVWLN NHVLWLQ ROXúXPXQD NDUúÕ JHOHQ \DWD\ \N DUWÕPÕ YH GDYUDQÕú E\NONOHUL NHVLW WHVLUOHUL \HUGH÷LúWLUPHOHU SODVWLN úHNLOGH÷LúWLUPHOHU YE GR÷UXGDQ GR÷UX\D EHOLUOHQHELOPHNWHGLU %|\OHFH d08<$< LOH \DSÕODQ DQDOL]GH plastik kesLWOHULQ ROXúXPXQXQ YH \DSÕ GDYUDQÕúÕQÕQ D\UÕQWÕOÕ RODUDN L]OHQHELOPHVL VD÷ODQPDNWDGÕU
*HOLúWLULOHQ \|QWHPGHKHUSODVWLN NHVLWLQ ROXúXPXQGDQ VRQUDRNHVLWWHNLELU SODVWLNúHNLOGH÷LúWLUPHELOHúHQL\HQLELUELOLQPH\HQRODUDNDOÕQPDNWDYHSODVWLNOHúHQ kHVLWWHNL DNPD NRúXOXQX LIDGH HGHQ \HQL ELU OLQHHU GHQNOHP ELU |QFHNL GHQNOHP WDNÕPÕQD LODYH HGLOPHNWHGLU %|\OHFH KHU \N DUWÕPÕQGD KHU SODVWLN NHVLWLQ ROXúXPXQGD GHQNOHPWDNÕPÕQÕQ\HQLGHQNXUXOXSo|]OPHVLQHJHUHNNDOPDGDQ\HQL ELOLQPH\HQHDLWVDWÕUYHNRORQXQLQGLUJHQPHVLLOHSODVWLNúHNLOGH÷LúWLUPHELOHúHQLQLGH LoHUHQ o|]P HWNLQ RODUDN HOGH HGLOPHNWHGLU $\UÕFD Lo NXYYHW GXUXPXQXQ DNPD NRúXOXQX VD÷ODGÕ÷ÕQÕ LIDGH HGHQ LODYH GHQNOHPOHULQ NXOODQÕOPDVÕ LOH ELOHúLN H÷LOPH
17
etkisindeki plastik kesitlerdH H÷LOPH YH X]DPD úHNLOGH÷LúWLUPHOHUL YH EXQODU DUDVÕQGDNLHWNLOHúLPGHJ|]|QQHDOÕQPÕúROPDNWDGÕU
<|QWHPGH \NVHN PRG HWNLOHULQL J|]|QQH DOPDN DPDFÕ\OD DUGÕúÕN LNL SODVWLNOHúHQNHVLWDUDVÕQGDNLOLQHHUGDYUDQÕúE|OJHVLQGHGDYUDQÕúVSHNWUXPXDQDOL]L esDVODUÕQGDQ \DUDUODQÕOPDNWDGÕU %XQD J|UHKHUSODVWLNNHVLWLQROXúXPXQGDQVRQUD VLVWHPLQ GH÷LúHQ PRGDO |]HOOLNOHUL YH |QFHNL DGÕPGDNL ELULP PRGDO \DWD\ \N GD÷ÕOÕPODUÕJ|]|QQGHEXOXQGXUXODUDNEHOLUOHQHQELULPPRGDO\DWD\\NGD÷ÕOÕPODUÕ LoLQ KHVDS \DSÕOPDNWDGÕU +HU DGÕPD DLW ELULP PRGDO \DWD\ \N GD÷ÕOÕPODUÕ LOJLOL DGÕPODUDDLWHODVWLNVSHNWUDOLYPHOHULOH|OoHNOHQPHNWHE|\OHFHGHSUHP|]HOOLNOHULYH PRGODUÕQ ELUELULQH J|UH HWNLQOL÷LQLQ SODVWLNOHúPH\H SODVWLN NHVLWOHULQ ROXúXPXQD ED÷OÕRODUDNGH÷LúLPLGHJ|]|QQHDOÕQDELOPHNWHGLU
dDOÕúPDGD JHOLúWLULOHQ \|QWHPLQ EHWRQDUPH ELQDODU ]HULQGHNL VD\ÕVDO X\JXODPDODUÕQD RODQDN VD÷ODPDN ]HUH ELU ELOJLVD\DU SURJUDPÕ 0(3$5&6 JHOLúWLULOPLúWLU
*HOLúWLULOHQ d08<$<¶QGHQ HOGH HGLOHQ VRQXoODUÕQ GH÷HUOHQGLULOPesi DPDFÕ\ODoGH÷LúLNGHSUHP\HUKDUHNHWLND\GÕLoLQIDUNOÕSHUL\RWE|OJHOHULQLWHPVLO HWPHN ]HUH |UQHN RODUDN HOH DOÕQDQ YH -NDWOÕ EHWRQDUPH oHUoHYHOHU üzerinde, ÇMUYAY ile LOSA, Lineer Olmayan Dinamik Analiz (LODA), 1. mod HVDVOÕJHOHQHNVHO/26$)(0$¶GD|QHULOHQQLIRUPYHPRGDOGD÷ÕOÕPODUÕLoLQ /26$ \DSÕOPÕúWÕU /2'$ VRQXoODUÕ NHVLQ o|]P NDEXO HGLOHUHN NDUúÕODúWÕUPDODU \DSÕOPÕú YH d08<$< GH÷HUOHQGLULOPLúWLU 'H÷HUOHQGLUPHOHU NDW \DWD\ \HUGH÷LúWLUPHOHUL J|UHOL NDW |WHOHPHOHUL PDNVLPXP NLULú SODVWLN G|QPHOHUL NDW NHVPH NXYYHWOHUL NDSDVLWH H÷ULOHUL YH VLVWHPGHNL SODVWLNOHúHQ NHVLW GD÷ÕOÕPODUÕ LQFHOHQHUHN\DSÕOPÕúWÕU
$\UÕFD JHOLúWLULOHQ \|QWHPGH VSHNWUDO |OoHNOHPHQLQ J|]|QQH DOÕQDQ PRG VD\ÕVÕQÕQ YH ikinci mertebe etkilerinin DQDOL] VRQXoODUÕ ]HULQGHNL HWNLOHUL GH LQFHOHQPLúWLU
18
%ø1$/$5,1 '(35(0 '$95$1,ù,1,1 %(/ø5/(10(6ø ødø1 (7.ø1 %ø5 d2. 02'/8 8<$5/$0$/, <h. $57,0, <g17(0ø d08<$<
%X E|OPGH \NVHN PRGODUÕQ HWNLOL ROGX÷X ELQDODUÕQ GHSUHP HWNLOHUL DOWÕQGDNLOLQHHUROPD\DQGDYUDQÕúÕQÕQEHOLUOHQPHVLDPDFÕ\ODJHOLúWLULOHQdRN0RGOX 8\DUODPDOÕ <N $UWÕPÕ <|QWHPLQLQ d08<$< YDUVD\ÕPODUÕ HVDVODUÕ PDWHPDWLN IRUPODV\RQX YH KHVDS DGÕPODUÕ D\UÕQWÕOÕ RODUDN DoÕNODQPÕúWÕU *HOLúWLULOHQ d08<$<EHOLUOLVDELWGúH\\kler ve artan modal yatay yükler için sistemin ikinci
mertebe elasto-plastik teori\H J|UH KHVDEÕQÕ HVDV DOPDNWD YH PRGDO \DWD\ \NOHULQ
NXOODQÕOPDVÕQHGHQL\OHVHUEHVWWLWUHúLPDQDOL]Lni de içermektedir.
2.1 9DUVD\ÕPODU
%XE|OPGH\|QWHPLQJHOLúWLULOPHVLQGH\DSÕODQYDUVD\ÕPODUYHULOPLúWLU • Sistem, düzlem çubuk sistemdir.
• Bernoulli-Navier hipotezi geçerlidir. Buna göre düzlem kesitler úHNLOGH÷LúWLUGLNWHQVRQUDGDG]OHPNDOÕUODU • (NVHQHONXYYHWYHH÷LOPHPRPHQWLHWNLVLQGHNLoXEXNHOHPDQODUGDiç kuvvet-úHNLOGH÷LúWLUPHED÷ÕQWÕODUÕQÕQùHNLO¶GHJ|UOG÷JLELLNLGR÷UXSDUoDVÕLOH LGHDOOHúWLULOHELOHFH÷LYDUVD\ÕOPDNWDGÕU ùHNLOøGHDOOHúWLULOPLúLoNXYYHW-úHNLOGH÷LúWLUPHED÷ÕQWÕVÕ øoNXYYHW ùHNLOGH÷LúWLUPH Plastik úHNLOGH÷LúWLUPH kapasitesi rijitlik 7DúÕPD kapasitesi
19
• /LQHHU ROPD\DQ H÷LOPH YH X]DPD úHNLOGH÷LúWLUPHOHULQLQ SODVWLN NHVLW DGÕ YHULOHQEHOLUOLNHVLWOHUGHWRSODQGÕ÷ÕEXNHVLWOHUGÕúÕQGDNLE|OJHOHUGHYHNHVPH NXYYHWL HWNLVL DOWÕQGD VLVWHPLQ OLQHHU-HODVWLN GDYUDQGÕ÷Õ YDUVD\ÕOPDNWDGÕU %|\OHFH WHN HNVHQOL EDVLW H÷LOPH HWNLVLQGHNL G]OHP oXEXN VLVWHPOHUH uygulanDELOHQSODVWLNPDIVDOKLSRWH]LELOHúLNLoNXYYHWGXUXPXQXGDLoHUHFHN úHNLOGHJHQLúOHWLOPLúROPDNWDGÕU
• $NPD NRúXOODUÕQÕQ H÷LOPH PRPHQWLQH YH QRUPDO NXYYHWH ED÷OÕ ROGX÷X NHVPH NXYYHWLQLQ DNPD NRúXOODUÕQD HWNLVLQLQ WHUN HGLOHELOHFH÷L YDUVD\ÕOPDNWDGÕU%LOHúLNH÷LOPHHWNLVLQGHNLHODPDQODUDDLWDNPDNRúXOODUÕ GR÷UXSDUoDODUÕQGDQROXúDFDNúHNLOGHLGHDOOHúWLULOPHNWHYHDNPDYHNW|UQQ DNPD\]H\LQHGLNROGX÷XYDUVD\ÕOPDNWDGÕU
• .RORQHOHPDQODUÕLoLQikinci mertebe teorisi,QRUPDONXYYHWLQNoNROGX÷X NLULú HOHPDQODUÕ LoLQ LVH birinci mertebe teorisi X\JXODQPDNWDGÕU øNLQFL
mertebe teorisiQGH JHRPHWUL GH÷LúLPOHULQLQ GHQJH GHQNOHPOHULQH HWNLVL
J|]|QQHDOÕQPDNWDJHRPHWULNX\JXQOXNNRúXOODUÕQDHWNLVLWHUNHGLOPHNWHGLU • 6LVWHPLQ úHNLOGH÷LúWLUPHVL VÕUDVÕQGD \NOHULQ GR÷UXOWXODUÕQÕQ GH÷LúPHGL÷L
YDUVD\ÕOPDNWDGÕU
• 6LVWHPLROXúWXUDQoXEXNODUGR÷UXHNVHQOLVDELWHQNHVLWOLGLUYHQRUPDONXYYHW oXEXNER\XQFDVDELWWLU%XNRúXOODUDX\PD\DQoXEXNODU\HWHUGHUHFHGHNoN SDUoDODUDD\UÕODUDNV|]NRQXVXNRúXOODU\DNODúÕNRODUDNVD÷ODWÕODELOLU
• <D\ÕOÕ \NOHU \HWHU VD\ÕGD VWDWLNoH HúGH÷HU WHNLO NXYYHWOHUH G|QúWUOHUHN KHVDS\DSÕOPDNWDGÕU • .D\PDúHNLOGH÷LúWLUPHOHULQLQHWNLVLLKPDOHGLOPHNWHGLU $\UÕFDVHUEHVWWLWUHúLPDQDOL]LQGH\DSÕODQYDUVD\ÕPODUDúD÷ÕGDYHULOPLúWLU • .WOHOHULQNDWG|úHPHOHULVHYL\HVLQGHWRSODQDELOHFH÷LYDUVD\ÕOPDNWDGÕU • $WDOHWNXYYHWOHULQLQ\DWD\|WHOHPHELOHúHQLJ|]|QQHDOÕQPDNWDGúH\DWDOHW NXYYHWOHULLOHDoÕVDODWDOHWNXYYHWOHULWHUNHGLOPHNWHGLU
