# The Influence of Vertical Ground Motion on the Design of Common R/C Frames
## 6 Conclusions  
In this article, the response of reinforced concrete frames concurrently subjected to both horizontal and vertical seismic motions was assessed. The 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, six eight-storey planar frames were designed according to the contemporary European codes for various seismic intensities and ductility classes. On the basis of the relevant code criteria, the vertical component was omitted from the initial design. Subsequently, the seismic response of the frames under simultaneous horizontal and vertical seismic loading was evaluated by applying both modal response spectrum and inelastic dynamic analyses. Thereafter, the frames were redesigned without neglecting the vertical seismic component and the changes in the members' cross-sectional dimensions and reinforcement were determined. Finally, the impact of including the vertical component in the design process on the construction cost of the frames was estimated. The most important findings obtained from this study are as follows:  
* The vertical component affects a lot of design aspects, such as the design actions, the members' resistance, the confinement requirements, etc. It may lead to the violation of several code provisions even for simple structures without irregularities or special morphologies;
* The main cause of the aforementioned violations is the fluctuation of the normalized axial forces of the columns, \(\mathrm{v_{d}}\), as well as the amplification of the bending moments of the beams. More specifically, the maximum normalized axial forces might increase by  
Figure 23: Construction cost of frames. Figure 22: Steel mass of frames. up to about 49%, while the minimum ones might decrease by up to 51%. In addition, the beam bending moments might increase by up to 45% and 114% at the ends and the mid-points, respectively, leading to many deficiencies in the flexural strength;
* The normalized axial force fluctuation might induce (i) several violations of the \(\mathrm{v_{d}}\) maximum limit, (ii) up to 12% exceedance of the column shear capacity, (iii) up to 42% exceedance of confinement demands in comparison with the available confinement in terms of \(\alpha w_{\mathrm{wd}}\), (iv) a reduction in the flexural resistance ratio at joints, even to below the minimum value permitted, and (v) up to a 42% reduction in the shear resistance and a significant increase in the reinforcement demands of joints;
* The vertical seismic component may induce non-linear deformations at unexpected locations like the mid-spans of beams and the ends of columns, potentially leading to unfavorable plastic mechanisms;
* The upper stories seem to be more vulnerable to vertical excitation;
* Vertical ground motion is more impactful for higher seismic intensities;
* The omission of the vertical component suggested by seismic codes for most structures is not justified. Further, taking it into account would not add a significant cost, since the additional expense does not exceed 4% of the initial total construction cost. This results from increases in the required concrete volume and steel mass of up to 7% and 32%, respectively. It is worth noticing that the present investigation should be viewed as preliminary since it did not take into account all factors affecting the design and the response of structures under simultaneous horizontal and vertical excitation. Thus, the generalization of the aforementioned derivations requires further research involving structures with various configurations including 3D and complex structures and comprising inelastic dynamic analyses with an adequately high number of recorded or artificial ground motions.