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

44

5

For stiff structures or artifacts, the transfer functions H AS (ω) or H SG (ω) equal unity in which case the response is identica l to theground motion. However, for just a stiff structure the floor response is identical to that of theground, while for stiff artifacts theresponse is identical to that of the floor. Note that this is true when the two transfer functions are independent, which is not thecasewhen the mass of the artifacts is very large orwhen the structure is very flexible. In such case the transfer function of the artifact in respect to theground H AG (ω) must include the interactionof structure to the artifact. The forces acting in the artifacts are proportional to the weight of the artifact W P and theaccelerationdeveloping a t floor j where the artifact is loca ted applied a t its center of gravity.

(5)

/ j p F ü W g =  p

for a rigid body, or,

(6)

( ) AS p F ü H W g    =   ( ) ( ) / p j

for a flexible body artifact (where H AS ( ω ) , the transfer function of the artifact body, containing the distribution of the weights and the dynamics of the body). It should be noted that the second equationconsiders a ll the flexibilities and the dynamics of thestructure and the artifact. For simplified static equivalent calculations it is suggested by theUS standard, ASCE 7-16, to determine the forces on an artifact, or piece of equipment, P by using: ( ) ( )   0.4 1 2 / / / * * P P DS P P P a P F a S z h R I W S W   =   = + (7) where F P is the force on the component P with a weight of W P , a P is an amplification factor spcific to either architectural components (Tbl. 13.5-1in the standard) ormechanical components (Tbl. 13.6-1in the standard), S DS is the acceleration responsespectrum on theground , z/h is the rela tivepositionof the artifact ’s floor about the height of building, R P /I P is a ra tio ofmodificationductility based factor to the importanceof component (providedbyTbls 15.5 1/2 and15.6-1 in the standard, resp.) At the same time the European standard, EC8, suggests for the responsespectrum acceleration (equivalent to [S a ] in the ASCE 7-16): where [ S a ] has same significance as in the ASCS 7-16 with the distinct difference that it includes thera tioof periods of vibra tion of the artifact and the building (when the artifact if flexible) anda local soil factor α. In summary the forces which act in the artifacts are amplifiedby both the structural system up to the floor where the artifact is loca tedand by the flexibility of the artifact itself. The standardsfor non-structural componentsrecognize these facts and offer someapproximated and simplified recommendations. However, when the structures are complex and flexible would require individual considerations based on equations (4), (6) or (8) dependingon the evaluation’s rigor. 4. Systemmodifications considering modifiedhazard Solutions of ways to strengthening and rehabilitating the structures were suggested in order to mitiga te the hazardous effects on the artifacts in particularwhenaffectedby thestructural systems, but not a lways achieving their purpose. However, such strengtheninga lthough reduce thedisplacements of structure andmovement of the artifacts, tends to increase the accelerations (and with it the inertia forces) leading to deformations and eventual crackingand collapse (of brittle artifacts).   ( ) ( ) ( ) 2 1 3 1 / / 1 1 / z h T T + + − 0.5 −  a S S  = S        (8)