# The Influence of Vertical Ground Motion on the Design of Common R/C Frames
## 2 Conventional Design of Planar Frames  
Herein, we describe how six eight-storey reinforced concrete frames were designed for various seismic intensities and ductility classes. Each frame is symbolized by a string symbol that consists of a capital letter and a Latin number. The letter (M or H) designates the ductility class (medium or high) according to Eurocode 8, while the number (I, II or III) indicates the corresponding seismicity zone of Greece. For example, the symbol MI denotes a frame designed for ductility class medium (DCM) and for the design acceleration for seismicity zone I. The configuration of the frames under consideration is shown in Figure 2. It should be stressed that the present study focused on regular planar frames because its main intention was to highlight that the vertical seismic component might be important even for quite simple structures without irregularities or any special configurations. In addition, according to Eurocode 8, such frames constitute a realistic model for a large proportion of real buildings, namely those which are regular in plan. The materials (C25/30, B500C) complied with the relevant European standards. The vertical loads (G = 40.5 kN/m  
Figure 1: Sequence of steps of the applied methodology. and Q = 12 kN/m) were assigned to the beams, which constituted rigid diaphragms. The total horizontal mass of each floor (80.92 t) was concentrated at one node. The design earthquake loading ('H' excitation) was represented by the Eurocode 8 horizontal design spectrum for \(Y_{\mathrm{I}}\) = 1 and S = 1. The design acceleration (a\({}_{\mathrm{gr}}\)) in units of gravity acceleration, g, and the behavior factor q used for each frame are tabulated in Table 1, whereas the horizontal design spectra are illustrated in Figure 3. In accordance with the Eurocodes and given the span lengths of the frames, vertical earthquake loading was not considered. The well-known SAP2000v23 software was utilized for the structural analysis. The design actions were calculated for both gravity and seismic load combinations. For the latter, the modal response spectrum analysis procedure was applied. The cross-sectional dimensions of columns and beams are tabulated for all frames in Tables 2 and 3, respectively. In addition, the natural periods and the modal participating mass ratios of the predominant modes of the frames are given in Table 4. Concerning the design, it is worth reporting the following remarks:  
* Given that the frames fulfilled the relevant code criterion, second-order (P-\(\Delta\)) effects were not considered; \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Frames**} \\ \cline{2-7}  & **MI** & **MII** & **MIII** & **HI** & **HIII** & **HIII** \\ \hline a\({}_{\mathrm{gr}}\) (g) & 0.16 & 0.24 & 0.36 & 0.16 & 0.24 & 0.36 \\ \hline q & 3.90 & 3.90 & 3.90 & 5.85 & 5.85 & 5.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design acceleration, a\({}_{\mathrm{gr}}\), and behavior factor, q, of frames. Figure 2: Configuration of 8-storey reinforced concrete frames. * Given the behavior factors applied for the design (Table 1), one would expect larger member dimensions to result for DCM frames in relation to DCH ones. However, as shown in Tables 2 and 3, this was not the case. This fact is reasonably explained due to other design parameters. On the one hand, the design seismic loads for the two ductility classes did not differ so much since the fundamental period of all frames lay at the final constant branch of the design spectra (see Figure 3 and Table 4). On the other hand, Eurocode 8 prescribes more strict compliance criteria for DCH structures in a series of provisions which are critical for the dimensioning of members. Such provisions are, for example, the limitation of columns' normalized axial forces, the requirements for beam-column joints and the limitations aiming to preclude the bond failure of beam reinforcing bars.