Analisi sismica non lineare di edifici in muratura con il programma TREMURI

Transcription

1 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

2 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

3 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

4 Macro-element wall models Nodo Rigido Fascia Maschio Earthquake Damage Observation FEM Non-linear Continuum Model

5 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

6 The non-linear macro-element (Gambarotta & Lagomarsino, 1996) Shear-sliding (friction) Bending-rocking

7 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

8 3D Building Model Plane structures Orthotropic floors 5 dof 3D nodes Mass sharing q, E 1, E 2, G

9 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

10 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

11 TREMURI Program Implemented non-linear analysis procedures STATIC INCREMENTAL (FORCE / DISPLACEMENT) DYNAMIC (Newmark integration, Rayleigh viscous damping) Influence of the vertical vibrations

12 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 x kim kmm xm kin kmn xn = fm fm fm

13 3D Pushover Analysis Parete 1 Parete 4 Parete 2 Parete 3

14 3D Pushover Analysis Rigid floors Parete 1 Parete 2 Globale Taglio alla base [N] Spostamento 2 piano [m] Flexible floors Parete 1 Parete 2 Globale P2 P2 P3 P4 P3 P4 P1 P1

15 3D Dynamic Analysis a [m/s 2 ],9,6,3 -, ,6 T [s] -, ,9 -,6 -,3,3,6,9 -,9 -,6 -,3,3,6,9 -,9 -,6 -,3,3,6,9 Wall 1 Wall 2 Global

16 Simulazione numerica delle prove sperimentali su un prototipo in scala reale di edificio in muratura (Università di Pavia Magenes & Calvi, 1997) Numerical results

17 Damage n8 9 3 n5 1 4 n n6 7 1 n4 8 2 n n1 n2 n3

18 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

19 Curva di Capacità ed energia dissipata Window wall Door wall Global Pushover Base shear [kn] Second floor displacement [mm]

20 Analisi Dinamica PGA.2 g.4 g.6 g Base shear [N] Displacement [cm] Second floor displacement [cm] Time [s]

21 Risultati delle analisi dinamiche 4.2 g.6 g.4 g Sa [m/s2] Sd [cm]

22 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 P P1 P2 T 2 T 2 P6 P5 P7 P4 P P1 P2 T 3 T 3 P6 P5 P7 P4 P 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]

23 Analisi sismica di edifici reali Eixample district, Barcelona (Bonet et al., 22) - RISK-UE Project

24 Analisi di edifici reali Castelnuovo Belbo Hall, Piedmont Monferrato Earthquake 2

25 Municipio Castelnuovo Belbo Monferrato Earthquake 2 Analisi di edifici reali N9 48 n33 52 n28 56 n37 59 N N8 47 n32 51 n27 55 n36 58 N N7 46 N31 5 n26 54 N35 57 N N2 N29 49 n25 53 N34 N38

26 Seismic analysis of real buildings Pushover Analysis Dynamic Analysis 4 Direzione X Tbase (kn) Umedio sommità (mm) T (kn) s (mm) 4 Direzione Y Tbase (kn) T (kn) Umedio sommità (mm) s (mm)

27 Analisi di edifici reali Municipio Castelnuovo Damage simulation BelboMonferrato Earthquake 2 N N n128 n n126 n n N97 N197 5 N94222 N74 N N N96 6 N93 7 N N13 31 N95 N N N23 N98 N91 N71 N N17 n N n N16 13 N762 n7762 N62 N N761 n N N76 n N N759 n7759 N59

28 Simulazione del danno osservato Municipio Castelnuovo Damage simulation BelboMonferrato Earthquake 2 N N n128 n n126 n n N97 N197 5 N94222 N74 N N N96 6 N93 7 N N13 31 N95 N N N23 N98 N91 N71 N N17 n N n N16 13 N762 n7762 N62 N N761 n N N76 n N Observed damage N759 n7759 N59 Numerical simulation