ATC-40(996) (Capacity Spectrum Method (Capacity Curve) Acceleration)(Spectral Displacement) (Performance Point) ETAB 93 2 94 7 8 ETABS
(999;2000) ETABS ATC-40(996) Pushover ETAB ETABS 93 2 94 7 8 ETABS ( ) V roof
i F F = [ w φ / Σw φ V () i i i i i ] w ( ) φ i i i i () φ i hi ATC-40(996) V S S a d i roof PF N i= = N i= w φ i i w φ i 2 i (2) N wiφi i= α = (3) N 2 W w φ α i= i 2 i V W S a = (4) S d roof = (5) PFφ roof PF α W (d p,a p ) A c ATC-40
Kawashima(986) C A C C = a (6) c d p C A c C 2005 7 C S S C S 0.4S DS DS ad = (7) C T T e d a p ad T e d p 2 a p g (8) = π C ξ Kawashima(986). (T 0.03 ) C =.0 d d eq 2. ( T > 0.5 T > 0.2 ).5 C d = + 0.5 (9) 40ξ + eq 3. ξ ATC-40 eq ξ eq = 5% + κξ (0) 0 κ 0.33 ξ 0 Chopra(995) ED ξ 0 = () 4π E S 0 E ED S 0 a p d p E D 2 E = 4A (2) D 0 A0 + A+ A2 + A3 = A e (3)
A + A2 + A3 = a pd p Ae (4) A 0 = 2Ae a pd p (5) ξ 4A 2a d e p p 0 = (6) π a pd p MAX A e = a pd p (7) 2µ 2 µ MAX ξ 0 = (8) π µ µ C d (6) A c a p = (9) C C d ETAB ( ) () (Axial hinge) (2) (P-M-M hinge) (3) (Moment hinge) (4) (Shear hinge) RC (shell element) RC
RC Moehle (Elwood and Moehle, 2005a; 2005b) P V s (Ductile shear failure) (Flexure-shear failure) a (Axial failure) (Drift ratio) (Elwood and Moehle, 2005a) s L = 3 00 '' ν P + 4ρ (Mpa units) (20) ' 40 ' f 40 Ag fc 00 c '' L ρ ν = V bd b d ' h 0.8 f A (20) c (Elwood and Moehle, 2005b) g y a L = 4 00 2 + (tanθ ) s tanθ + P A f d st yt c tanθ (2) s A f d st yt θ 65 tan ( L / h) (2) (Sezen and Moehle, 2004) V V k n V m a Moehle (Elwood and Moehle, 2005a; 2005b) (20) (2) s s m s a k a c
k 3 = 2( EI) c L (22) ( EI) c ATC-40 0.5E c I g 0.7EcI g Ec I g Vn Moehle (Sezen and Moehle, 2004) 0.5 f = A (23) ' Ast fstd c P Vn + s + 0. 8 a / d ' 0.5 fc A g g a (Shear span) L / 2 2 a / d 4 V V m = M L (24) m 2 n (Nominal moment strength) (ACI M n Committee 38, 2005) V V n k V n (Elwood and Moehle, 2005b) (2) a 0.04L V V m k m ( Clear Length) L - - Moment SF Rotation SF M n m a
a L s y = (25) L a s b = max, L L (26) 3 = Vm VmL y k = 2( EI) (27) c ( Clear Length) L - - Force SF V Disp. SF L a c = min,0.04 (28) L n RC (2004) RC RC RC RC RC RC RC RC RC RC RC RC (2005) RC (, 2000) θ
93 2 6 ETABS 94 7 8 2 30% ETABS-Nonlinear ETABS
ATC-40 ETABS ACT-40, 996. Seismic evaluation and retrofit of concrete buildings. Report No. SSC 96-0, Applied Technology Council., 999.,,.,,,. 2000.,,. Kawashima, K., and Aizawa, K., 986. Modification of Earthquake Response Spectra with Respect to Damping Ratio. Proceedings of the third U.S. National Conference on Earthquake Engineering, South Carolina, 07-6. Chopra, A. K., 995. Dynamics of structures - theory and applications to earthquake engineering. Prentice-Hall, Inc., Englewood Cliffs, New Jersey. Elwood, K. J., and Moehle, J. P., 2005a. Drift capacity of reinforced concrete columns with light transverse reinforcement. Earthquake Spectra, Vol. 2, No., 7-89. Elwood, K. J., and Moehle, J. P., 2005b. Axial capacity model for shear-damaged columns. ACI Structural Journal, Vol. 02, No. 4, 578-587. Sezen, H. and Moehle, J. P., 2004. Shear strength model for lightly reinforced concrete columns. Journal of Structural Engineering, ASCE, Vol. 30, No., 692-703. ACI Committee 38, 2005. Building code requirements for structural concrete (ACI 38-05) and commentary (ACI 38R-05). American Concrete Institute, Farmington Hills, MI.., 2004. 価 ( ) (Guidelines for Performance Evaluation of Earthquake Resistant Reinforced Concrete Buildings(Draft)).., 2005. RC.,,.,,,, 2000.,,. (M3 Type) Points Moment/SF Rotation/SF A 0 0 B 0 C a D 0 b E 0 b
(V2 Type) Points Force/SF Disp/SF A 0 0 B 0 C 0 c D 0 c E 0 c V roof V roof
roof α W/g S d = roof /PF V F=α WS a V V=F S a a c (dp,ap) S d
S a (d p,a p ) E S0 S d E D S a A e (d p,a p ) A A 3 A 2 A 0 A 2 A 3 A S d
P V M L M V P M = y = s = a
V V n V=2M/L V m k s a V V m V n V=2M/L k a
V V n V=2M/L V m M P V m a b θ y s a -
P P V n c y min ( a,0.04) - RC
2F B
Base shear (kn) 4000 3000 2000 In-site Test ETABS calculated 000 0 0 40 80 20 60 200 Deflection (mm)
2 3 P 5 4 P 3 2 3 P 8 7 P 3 2 3 P P 3 2
Base shear (kn) 2500 2000 500 In-site Test ETABS calculated 000 500 0 0 00 200 300 400 500 Deflection (mm)
Base shear (kn) 3000 2000 In-site Test ETABS calculated 000 0 0 00 200 300 400 500 Deflection (mm)
Base shear (kn) 4000 3000 2000 In-site Test ETABS calculated 000 0 0 00 200 300 400 500 Deflection (mm)