# On the Modeling and Analysis of Brittle Failure in Existing R/C Structures Due to Seismic Loads
## 2 Procedures for Simulating Strength Mechanisms in Substandard R/C Buildings  
Contrary to analysis procedures used in the design of new R/C buildings that focus on the numerical simulation of ductile resistance mechanisms in structural members (under the proviso that all undesirable brittle failure modes will be capacity-designed and therefore suppressed) in the analytical seismic assessment of poorly reinforced R/C buildings, the potential prevalence of brittle-type mechanisms of resistance across the structural system must be examined. The typical layout of the structural system of R/C buildings constructed up to the early 1980s (at a time when construction details were still relatively primitive since their role in the seismic response was not yet fully understood) included poorly reinforced frames comprising columns of section sizes ranging between 250 mm and 500 mm, beams of a 150 mm to 250 mm width and 600 mm to 700 mm height (including the slab thickness), and slabs with a thickness ranging between 120 mm and 160 mm. Longitudinal reinforcement usually comprised relative low amounts of StI (\(f_{y}\) = 220 MPa, \(f_{u}\) = 340 MPa) to StIII (\(f_{y}\) = 420 MPa, \(f_{u}\) = 500 MPa) smooth bars, lap-spliced to arbitrary lengths and under poor confinement conditions. Column and beam stirrups were usually 6 mm to 8 mm, smooth, rectangular, StI bars (usually mild steel), with 90\({}^{\circ}\) hooks in the ends, spaced at 200 mm to 300 mm on center (o.c.). Beam-column joints were usually left without stirrups for the convenience of construction. Concrete quality was usually Bn150 to Bn200 as per DIN 1045 [33], corresponding to C12/15 and C16/20 concrete grades according to EN1992-1-1 [34].  
To address the need for an effective simulation of the seismic response of substandard R/C buildings, the present research introduces new procedures for modeling the mechanisms of resistance developing in old-type R/C structural elements. Based on the principles of the RSA System [30; 31; 32], emphasis is placed on numerical simulation procedures that are applicable to column lines of existing R/C buildings, non-conforming to modern standards of seismic design and detailing. These lines usually collapse in a brittle manner, forming a mechanism characterized by pronounced localization of damage in a few locations with a high shear demand before there is a chance for the development of any form of redistribution and ductility (see [PERSON] and [PERSON] [35], [PERSON] and [PERSON] [36], [PERSON] and [PERSON] [37], [PERSON] [38], [PERSON] and [PERSON] [39], and [PERSON] [40]).  
The modeling procedures introduced here include the simulation of the following mechanisms: M1: non-linear flexural response of columns and beams; M2: shear failure of the column web; M3: anchorage failure of longitudinal reinforcement of columns; M4: attainment of the development capacity in column lap splices; and M5: beam-column joint shear failure. The proposed procedures for simulating the seismic response of substandard R/C buildings are summarized in Figure 1 and discussed in detail in the following sections. Note that simulation of mechanisms [M2-M5] along column lines of existing R/C building is meaningful only if they prevail over mechanism M1. According to the RSA system, this occurs when the corresponding resistance ratios (\(r\)) that represent the shear strength associated with the examined failure mode, normalized by the shearing force required in order to support flexural yielding in the column, are equal to or greater than 1.0.