# Nonlinear Dynamic Response of a Precast Concrete Building to Sudden Column Removal
## 2 Case Study and Modelling Technique
### Description of the Case Study  
The reference building is a three-story RC structure intended for commercial use. The structural layout is composed by primary and secondary beams as well as floor slabs. The precast units of the floor are oriented along the longest side of the frame, as reported in Figure 1a. The building dimensions in plan are equal to 43.2 and 28.8 m along the X and Y directions, respectively. The inter-story height is 3.3 m for the first floor and 3.6 m for the upper floors, as shown in Figure 1b. Different column loss scenarios at the ground floor are supposed to occur at interior (B4), edge (B1) and corner (A1) locations, as shown in Figure 1a.  
In this study, two structural typologies are analyzed: moment resisting frame (MRF) and precast concrete frame (PCF) systems. Detailing of MRF and PCF systems is reported in Figure 1b,c. In the MRF system, beams and columns are monolithically connected to each other. Columns have 600 \(\times\) 600 mm\({}^{2}\) square cross section, whereas beams have 500 \(\times\) 700 mm\({}^{2}\) at the first and second floor levels. Beams with 500 \(\times\) 500 mm\({}^{2}\) square cross section are used at the roof level and along the X direction at each floor level. All beams and columns have \(\mathcal{O}\)22 longitudinal bars and \(\mathcal{O}\)12 stirrup with 60 mm spacing. In the PCF system, beams and columns have similar cross section compared to MRF system and are connected through threaded dowels, whereas joints are completed with in-situ infills, Figure 1c. Moreover, tying reinforcements are provided in the PCF system to meet the fib Bulletin 63 [34] requirements. Indeed, to improve the progressive performance of precast RC structures subject to progressive collapse scenarios, tying systems should be placed in the transverse, longitudinal and vertical directions to provide additional integrity, redundancy and alternate load paths [34].  
Note that corbel and beam end recess detailing are assumed to be properly designed [35]. Referring to Figure 1c, two 28-mm diameter rebars are used as tying reinforcement, whereas a \(\mathcal{O}\)18 threaded dowel is used to connect precast beam and column members. Holes are provided into the precast columns to allow the passage of tying reinforcement. Moreover, beam seats are provided to allow the positioning of hollow-core slab. Design gravity loads follow the Unified Facilities Criteria [44] combination, which is more conservative than that of Eurocode 0 [45] as follows:  
\[Q_{b}=1.2D_{L}+0.5L_{L} \tag{1}\]  
Figure 1: Building layout: (**a**) Plan view of the case-study building with column removal locations; (**b**) Elevation view and MRF detailing; (**c**) PCF detailing and beam-to-column joint. (Dimensions in mm).  
where \(D_{L}\) and \(L_{L}\) are dead and live loads, respectively. Dead loads consider the self-weight of resisting-members and 22-mm-thick hollow-core slab (3.2 kN/m\({}^{2}\)), partition walls and equipment (3.2 kN/m\({}^{2}\)) and exterior panels (3.5 kN/m\({}^{2}\)), whereas live loads are assumed equal to 4 kN/m\({}^{2}\). Table 1 outlines the line loads at different floor levels and column removal locations.  
The following properties of concrete and reinforcing steel were assumed: compressive cylinder strength of concrete \(f_{c}\) = 50 MPa and elastic modulus \(E_{c}\) = 32.5 GPa; steel for longitudinal and transverse reinforcement as well as for threaded dowels with yield strength \(f_{y}\) = 500 MPa and elastic modulus \(E_{s}\) = 200 GPa; steel strain at fracture \(\varepsilon_{sat}\) = 20% and strain hardening ratio \(k\) = 0.01.