PSI - Issue 29

Andrei M Reinhorn et al. / Procedia Structural Integrity 29 (2020) 40–47 Reinhorn and Viti/ Structural Integrity Procedia 00 (2019) 000 – 000

43

4

Similar behavior was observed and well documented for buildings’ precious contents, such as ho spitals (Hutchinson et al., 2012), supportedby controlled experiments and analytical evaluations. Moreover, in the authors’ experience, building components such as suspended ceilings used in museums and modern exhibit halls become unstable and collapse in rangesamplifiedby the host structures endangering, or destroyingexposed artifacts (see Figs 2 and 6).

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

100 120 140 160 180 200

a)

b)

NTC08 Ground Lagomarsino, 2015 EC8

Sa (g)

0 20 40 60 80

Sd (mm)

NTC08 Ground Lagomarsino, 2015

0

1

2

3

0

1

2

3

T (s)

T (s)

Fig. 6. Fallen statues and ceilings, damaged artifacts, due to external explosions (similar to earthquakes) in Palmyra, Syria

Fig. 5. (a) Acceleration and (b) Displacement response spectra for 2 nd floor according to EC8, Lagomarsino et al. (2015) compared to ground spectrum NTC08 (from Baggio 2018).

3. Assessment of risk of consideringmodifiedhazard Specia l a ttention should be pa id to eva luate the artifacts together with the structural behavior of monumental buildings and palaces alongwith their sensitive contents; a selectionof procedures and response parameters such as those describing filtering thebase motions shouldbe definedanddeveloped toassure therequired safety to thecontent. Such tasks areusually tediousandexpensive andmost of the timecost ineffective. However, filteredmotions affecting specific or assembles of artifacts can be derived to evaluate their behavior when located in monumental structures. While this process is not usually done formuseums and artifacts, procedures and methods were developed by Merino at al. , (2019), for sensitive contents and for equipment of buildings (suchas hospitals) and for architectural and non structural components (Ryu andReinhorn, 2017). The floor accelerations can be described as a function of the groundmotion as (Ryuand Reinhorn, 2017): ̈ ( ) = ( ) ⋅ ̈ ( ) (1) where u S (ω) represents the structural response, u G (ω) the disturbance function and H SG (ω) is the structures transfer function. This frequency domain formulation includes contribution of a ll parts of structure between ground and a j loca tion in structure. For a simple storied structure experiencingbase motions the floor acceleration responsea t level j can be expressedas: ̈ ( ) = ∑ [ (2 + 2 ) (2 +( 2 − 2 )) ̈ ( )] =1 = , ⋅ ̈ ( ) (2) The maximumacceleration at level j can be approximated froma modal superpositionof spectral accelerations: ̈ , = {∑ [ ( , ) ] =1 2 } (3) where S A is the spectra l acceleration of the base motion and ξ k is the modal damping. Note that this accelerationcan be definedas the floor ’s acceleration. However, the responseof the artifact is further amplified by the transfer function H AS (ω) , of the artifact to the floor, where it is anchored: ̈ ( ) = ( ) ⋅ ̈ ( ) = ( ) ⋅ ( ) ⋅ ̈ ( ) (4)