# The Influence of Vertical Ground Motion on the Design of Common R/C Frames
## 1 Introduction  
It is considered that most of the damage during strong earthquakes is induced by the horizontal seismic components. However, observations made after recent catastrophic earthquakes (e.g., Refs. [1, 2]) indicate that the vertical component might contribute to the severe damage of buildings too. This is more pronounced for near-field ground motions (recorded at a few kilometers from the epicenter), which cause considerable vertical accelerations. Unfortunately, the importance of this issue is not acknowledged by modern codes worldwide. Apart from for some special structures (e.g., frames with very large span lengths), the vertical vibrations' contribution to the overall response is neglected. In contrast with seismic codes, the fact that vertical ground shaking may significantly influence the response quantities of common buildings is recognized by many researchers in the literature [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. The main derivations of the relevant studies are the following:* The vertical component significantly affects the column axial forces [3; 4; 10; 13; 14]. On the one hand, it increases the maximum compressive axial load, and on the other hand, it may produce even tension [4; 13; 14]. Obviously, the fluctuation of axial stress may impact the efficiency of the structural design of columns, including their shear resistance [10];
* The vulnerability of beams subjected to vertical excitation does not depend on their length [3; 8; 13; 14];
* The vertical seismic component amplifies the vertical displacements and the nonlinear deformations of beams, especially on the upper stories [3; 4; 8; 13; 14], potentially inducing non-linear behavior at unexpected locations and altering the anticipated collapse mechanism [8; 13; 14];
* Many other similar publications dealing with various types of structures are presented in the literature (e.g., Refs. [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]). In this article, the response of reinforced concrete frames concurrently subjected to both horizontal and vertical seismic motions is assessed. In the framework of this study, the term \"conventionally designed frames\" designates frames designed against the horizontal component only. The whole investigation was not limited to the variation in response quantities but aimed to identify which specific design parameters were affected and how, as well as which specific code provisions could be violated due to the omission of vertical oscillations during the design process. Furthermore, the consequences that a design against vertical ground motion would cause in both technical and economic terms were investigated. For this purpose, the methodology presented in the flowchart in Figure 1 was applied. As a first step, six eight-storey planar frames were designed according to the contemporary European codes [29; 30] for three seismic intensity levels corresponding to the three seismicity zones of the Greek territory and for two ductility classes prescribed by Eurocode 8 (medium and high). On the basis of the relevant code criteria, vertical excitation was omitted during the initial design. Subsequently, in the second step of the procedure, the seismic response of the frames concurrently subjected to horizontal and vertical motions was determined using modal response spectrum and inelastic dynamic analyses. Based on the results of the spectral analysis, the Eurocode provisions related to member design were verified. In addition, with the aid of time history analysis for properly scaled accelerograms, the acceptance criteria of the three damage limit states of Eurocode 8 were checked in terms of inelastic deformations. Thereafter, the frames were redesigned without neglecting the vertical seismic component, and the changes in the members' cross-sectional dimensions and reinforcement were determined (step 3).