Report - PEER - University of California, Berkeley

where the derivatives ∂ D / ∂xare calculated at the time instants where theik jcorresponding maxima occur.The demand in failure mode i can thus be rewritten accounting for its (linearised)dependence on x as:∂Di( ) = µ ( µ ) ε + ∑ ( x − )Di x Dij x jD x µi(9)∂xjand the reliability problem can be written, similarly to Eq.(7), as:Pf{ C ( ) ≤ D ( )}iiUj1Iin C = ∈ICjj= Prx x(10)where now it is understood that the vector x includes, besides the basic variables,also the capacity error terms εC's and the demands variability terms εD's.3. APPLICATIONThe method described in the previous section is applied in the fragility analysis of athree-storey 3D RC structure (Figure 1), designed solely for gravity loads accordingto the design and construction practice of the early 70’s in southern Europe, i.e.,including plan irregularity, strongly eccentric beam-column connections, overall poordetailing. The building has been designed, constructed and pseudo-dynamically testedunder bi-directional loading within the framework of the EU funded project SPEAR(Negro 2004).3000 5000C5 C1C21700Columns C1-C5 & C7-C9250x250 4ø1255006000stirrups ø8@250Column C6250x750 10ø12C9C3C450004000YC8C6C7Xstirrups ø8@250Figure 1. Photo of the test structure outside the lab (left) andplan of the framing (right).225