Analisi sismica non lineare di edifici in muratura con il programma TREMURI S. Lagomarsino, A. Penna, A. Galasco e S. Cattari Dipartimento di Ingegneria Strutturale e Geotecnica Università degli Studi di Genova
Strategie di modellazione Analisi limite Metodo POR Elementi finiti Macroelementi l F 2 (Podestà, 21) Como & Grimaldi Tomaževic, Braga & Dolce Gambarotta & Lagomarsino, Anthoine, Maier et al., Lourenço spandrel beam pier l F 1 joint Pagano et al. Braga & Liberatore D Asdia & Viskovic Magenes & Della Fontana
3D model of a masonry building Hypotheses: Earthquake Resistant Structure: walls + floors Walls are bearing elements Floors share vertical loads to the walls and are planar stiffening elements (orthotropic membrane) Walls out-of-plane behaviour and flexural floors response negligible with respect to global one Wall in-plane model: Frame-type model 2 nodes macro-elements: piers and lintels Joints: rigid bodies Tie-rods (no compression spar) and stringcourses (beam) elements included
Macro-element wall models Nodo Rigido Fascia Maschio Earthquake Damage Observation FEM Non-linear Continuum Model
The non-linear macro-element (Gambarotta & Lagomarsino, 1996) 3 ϕ j w j u j j 2 ϕ w 2 2 u 2 M 2 2 N 2 T 2 3 M j M 2 N j j T j 2 T 2 N 2 h 2 δ φ 2 n m w 1 (a) 1 ϕ 1 1 i w i b u 1 u i ϕ i s 1 T 1 M 1 N 1 (b) 1 N 1 M 1 1 T 1 i T i M i N i
The non-linear macro-element (Gambarotta & Lagomarsino, 1996) Shear-sliding (friction) Bending-rocking
b Crushing with degrade?b s w z x f w o w R w max = µ w R w R w s s R s R el * N = N N el M = M M * µ 1 µ ζ 1 M ( µζ,, wmax ) = bn 3 2 * N ( µζ,, wmax) = k ζbswmax * * w Vertical displacement rotation interaction: with and w/o crushing j
3D Building Model Plane structures Orthotropic floors 5 dof 3D nodes Mass sharing q, E 1, E 2, G
3D Building Model Plane structures Orthotropic floors 5 dof 3D nodes Mass sharing uz = w f x f y f u u y u x 3 dof nodes (2D) 5 dof nodes (3D) Z? Y X
3D Building Model l J Mx My x Plane structures Orthotropic floors 5 dof 3D nodes Mass sharing m Mx I My I I l M = M + m(1 cos α ) x x I I l M = M + m(1 sinα ) y y x l x l Y Z α X
TREMURI Program Implemented non-linear analysis procedures STATIC INCREMENTAL (FORCE / DISPLACEMENT) DYNAMIC (Newmark integration, Rayleigh viscous damping) 1 8 6 4 2-2 -4-6 -8-1 Influence of the vertical vibrations 1 8 6 4 2-2 -4-6 -8 -.3 -.25 -.2 -.15 -.1 -.5.5.1.15.2.25.3
TREMURI Program Implemented non-linear analysis procedures STATIC INCREMENTAL (FORCE / DISPLACEMENT) DYNAMIC (Newmark integration, Rayleigh viscous damping) PUSHOVER (analisi statica non lineare p.to 4.5.4) K k K x λf FF Fm FC F F T T k kfm mm kcm xm = λ fm K CF kcm KCC xc rc K k K x FF Fm FC F T T kfm kmm kcm xm = λ fm K CF kcm KCC xc rc f i f i f i ki1 km 1 x1 +... + kim kmm xm +... + kin kmn xn = fm fm fm
3D Pushover Analysis Parete 1 Parete 4 Parete 2 Parete 3
3D Pushover Analysis 35 35 3 3 25 2 15 1 5.2.4.6.8.1.12.14.16 Rigid floors Parete 1 Parete 2 Globale Taglio alla base [N] 25 2 15 1 5.2.4.6.8.1.12 Spostamento 2 piano [m] Flexible floors Parete 1 Parete 2 Globale P2 P2 P3 P4 P3 P4 P1 P1
3D Dynamic Analysis 3 2 1-1 a [m/s 2 ],9,6,3 -,3-2 -3 -,6 T [s] -,9 2 4 6 8 1 12 14 16 18 2 3 2 1-1 -2-3 -,9 -,6 -,3,3,6,9 -,9 -,6 -,3,3,6,9 -,9 -,6 -,3,3,6,9 Wall 1 Wall 2 Global
Simulazione numerica delle prove sperimentali su un prototipo in scala reale di edificio in muratura (Università di Pavia Magenes & Calvi, 1997) -25-2 -15-1 -5 5 1 15 2 25 Numerical results
Damage n8 9 3 n5 1 4 n9 4 5 6 n6 7 1 n4 8 2 n7 1 2 3 n1 n2 n3
Earthquake response prediction 3D building model Pushover Analysis: Load pattern: P = pm? Capacity Curve 1 Cyclic Pushover Analysis: Modal Analysis: T 1 =.16 s (= experimental value) ξ c, eff = ξ v + 2π Equivalent hysteretic damping
Curva di Capacità ed energia dissipata 3 2 1 Window wall Door wall Global Pushover Base shear [kn] -1-2 -3-3 -2-1 1 2 Second floor displacement [mm]
Analisi Dinamica PGA.2 g.4 g.6 g Base shear [N] 3 2 1-1 -2-3 Displacement [cm] 1.5 1.5 -.5-1 -1.5-2.5-2 -1.5-1 -.5.5 1 1.5 2 2.5 Second floor displacement [cm] Time [s] 2 4 6 8 1 12 14 16 18 2
Risultati delle analisi dinamiche 4.2 g.6 g.4 g 3.5 3 Sa [m/s2] 2.5 2 1.5 1.5.5 1 1.5 2 2.5 3 3.5 Sd [cm]
Analisi sismica di edifici reali Osservatorio Sismico delle Strutture Servizio Sismico Nazionale SSN Modal analysis P2 Modal testing Dynamic Identification by Modal Testing T 1 T 1 P6 P5 P4 P3 P7.139.139 P1 P2 T 2 T 2 P6 P5 P7 P4 P3.119.12 P1 P2 T 3 T 3 P6 P5 P7 P4 P3.15.95 P1 Seismic Analysis Acceleration [ms -2 ] 4,5 4 3,5 3 2,5 2 1,5 1 SDOF Structure,5,5,1,15,2,25,3,35,4,45,5 Displacement [m]
Analisi sismica di edifici reali Eixample district, Barcelona (Bonet et al., 22) - RISK-UE Project
Analisi di edifici reali Castelnuovo Belbo Hall, Piedmont Monferrato Earthquake 2
Municipio Castelnuovo Belbo Monferrato Earthquake 2 Analisi di edifici reali N9 48 n33 52 n28 56 n37 59 N41 32 35 39 42 45 N8 47 n32 51 n27 55 n36 58 N4 31 34 38 41 44 N7 46 N31 5 n26 54 N35 57 N39 33 36 37 4 43 N2 N29 49 n25 53 N34 N38
Seismic analysis of real buildings Pushover Analysis Dynamic Analysis 4 Direzione X Tbase (kn) 35 3 25 2 15 1 5 5 1 15 2 25 3 35 4 45 5 Umedio sommità (mm) T (kn) 4 3 2 1-3 -2-1 -1 1 2 3-2 -3-4 -5 s (mm) 4 Direzione Y Tbase (kn) 35 3 25 2 15 1 5 5 1 15 2 25 3 35 4 45 5 T (kn) 4 3 2 1-3 -2-1 -1 1 2 3-2 -3-4 -5 Umedio sommità (mm) s (mm)
Analisi di edifici reali Municipio Castelnuovo Damage simulation BelboMonferrato Earthquake 2 N15 219 N13 2 34 n128 n127 39 4 n126 n125 322 n129 33 336 337 339 38 37 338 41 N97 N197 5 N94222 N74 N174 29 212 217 N14 218 N96 6 N93 7 N73 28 211 214 216 N13 31 N95 N92 22 221 N72 27 21 213 215 N23 N98 N91 N71 N1 42 344 N17 n121 14 N11 43 317 1317 342 318 n1211 343 15 N16 13 N762 n7762 N62 N111 162 51 159 1156 156 N761 n7761 161 5 N61 158 1155 155 N76 n776 16 49 N6 157 1154 154 N759 n7759 N59
Simulazione del danno osservato Municipio Castelnuovo Damage simulation BelboMonferrato Earthquake 2 N15 219 N13 2 34 n128 n127 39 4 n126 n125 322 n129 33 336 337 339 38 37 338 41 N97 N197 5 N94222 N74 N174 29 212 217 N14 218 N96 6 N93 7 N73 28 211 214 216 N13 31 N95 N92 22 221 N72 27 21 213 215 N23 N98 N91 N71 N1 42 344 N17 n121 14 N11 43 317 1317 342 318 n1211 343 15 N16 13 N762 n7762 N62 N111 162 51 159 1156 156 N761 n7761 161 5 N61 158 1155 155 N76 n776 16 49 N6 157 1154 154 Observed damage N759 n7759 N59 Numerical simulation