# Comparative Assessment of Shear Demand for RC Beam-Column Joints under Earthquake Loading
## 3 Numerical Study
### Details of SPEAR Frame  
The frame was a three storey frame with two bays in both plan directions. The details of the structures are represented in Figure 7.  
Figure 6: Results for parametrical analysis on beam–column joint strength (normalized shear strength \(v_{f}\) [IMP\({}^{0.5}\)]) predicted by different building codes: (**a**) Equation (6); (**b**) Equation (7); (**c**) Equation (8); (**d**) Equation (9). All the plots includes the constant values of the prediction given by ASCE41-17 [14].  
The structure was conceived by Prof. [PERSON] [17] as a typical RC structure designed for gravity load only. Beams had a 250 \(\times\) 500 mm cross-section, column had 250 \(\times\) 250 mm cross-section, 250 \(\times\) 750 mm cross-section was used for one column. Flat slab had 150 mm thickness with reinforcement mesh grid of 8 mm diameter bar spaced at 20 cm or 40 cm. Beam-column joints were characterized by the absence of stirrups and straight anchorage for the beam longitudinal reinforcement both at the bottom (two bars with diameter 12 mm) and the beam-column joints were characterized by the absence of stirrups and straight anchorage for the beam longitudinal reinforcement both at the bottom (two bars with diameter 12 mm) and at the bottom (two bars with diameter 12 mm). The same structure was observed for the beam longitudinal reinforcement both at the bottom (two bars with diameter 12 mm) and at the bottom (two bars with diameter 12 mm).  
Figure 7: SPEAR frame layout.  
and top layers (four bars with diameter 12 mm). The estimated seismic masses were 65.5 tons for the first and second floors and 64.1 for the third floor.  
The structure was tested both in the as-built condition and retrofitted using different techniques for column strengthening, i.e., fiber-reinforced polymer (FRP) or jacketing [17; 18]. PsD tests were carried out with bi-axial seismic input. Montenegro 1979 Herceg-Novi ground motion record was selected. The recordings of the two orthogonal components of horizontal accelerations were modified from natural records to be compatible with the Eurocode 8 [10], Type 1 design spectrum, soil type C and 5% damping [19]. Time histories were scaled to conventional values of peak-ground-acceleration (PGA) equal to 0.15 g and 0.20 g.  
During the strongest test (0.20 g of PGA), the obtained displacements at the third floor were in the order of 100 mm in both directions and 20 mrad of floor rotation. Columns were the most damaged members of the structure, especially at the second story; significant inclined cracks were observed on their compressive sides and on the tensile side at the beam-column interface [20]. The damage on the rectangular column C6 was less important, even though the crushing of concrete and cracks at the interface with beams were observed [18].  
Through the years many researchers [7] addressed the SPEAR frame to validate numerical models; a survey of the most relevant studies is summarized in Table 1. NLTH analysis in conjunction with frame modeling was often adopted. In one case [21] brick finite elements were used. The validation chain usually adopted: (i) experimental results of the PsD test against NLTH; and (ii) NLTH against either NLSA or MRSA. To facilitate the validation, the modeling criteria used in this study, which are summarized in the following, were generally compliant with those assumed by the surveyed literature.