###### Abstract  
Damping reduction factors (DRFs) play a vital role in the seismic design of structures. DRFs have been widely studied due to their primary importance to the lateral resistance of structures subjected to earthquakes. On the other hand, devastating earthquakes have occurred all over the world, and recently, the Kahramanmaras earthquakes in Turkey revealed the import of the vertical component of earthquakes and their impact on structures and infrastructures. Considering the importance of this parameter, this paper aims to develop new damping reduction factor (DRF) equations for the acceleration (DRFa), velocity (DRFv), and displacement spectra (DRFd) of the vertical components of earthquakes. For this purpose, 775 real ground motion records were selected from the Pacific Earthquake Engineering Research (PEER) strong motion database, and the vertical elastic response spectra of selected records were computed according to linear dynamic analysis. Taking the 5%-damped vertical response spectra as the target, the vertical spectral damping reduction factors (DRFa, DRFv, and DRFd) were computed for 1%, 3%, 10%, 15%, 20%, 30%, and 40% damping ratios. The effect of the earthquake magnitude, distance, and soil types on the DRFs was investigated. The results indicated that magnitude, distance, and soil type had no particular effect on the trend in the DRFs. Based on the evaluations, extensive statistical analyses were carried out, and new prediction equations were developed according to the nonlinear regression method. The developed equations were then compared to those found in the literature and seismic design codes. The comparisons proved that the proposed DRFa, DRFd, and DRFv models are strongly compatible with real DRFs and show strong robustness compared to existing models. d 2024 1 4 438  
levels is required to assess the impacts of vertical ground motions on structures and to determine an acceptable structural design. On this subject, significant advancement has been achieved in recent decades. According to studies conducted by various researchers [8; 9; 10; 11] on the characteristics of the vertical response spectra using recorded ground motions, the vertical-to-horizontal response spectral ratio may surpass 2/3 for short periods. Currently, the vertical response spectra provided by many seismic design codes [12; 13; 14; 15] and research publications [16] mainly consider a 5% damping ratio. However, a considerable number of structures with damping ratios different from 5% are vulnerable to vertical ground motion effects. Some long-cantilevered trusses [17], large-span spatial trusses [18], cold-formed steel floors [19], and composite floor decks [20] have damping ratios lower than 5%. On the other hand, structures with additional damping devices [21; 22] and some types of steel structures with vertical hysteretic behavior [23; 24] can exhibit a damping ratio greater than 5%. To seismically design these structures to withstand vertical seismic actions at different damping ratios, the damping reduction factor (DRF) of the vertical response spectrum is required. In recent decades, few studies have been performed for the calculation of DRFs. [PERSON] [25] used 54 recordings from 16 earthquakes to study the vertical response spectrum at five damping ratios, namely 0%, 2%, 5%, 10%, and 20%. [PERSON] and [PERSON] [26] used 438 ground motions from 104 earthquakes, mostly from California, to develop GMPEs using vertical pseudo-velocity response spectra at 0%, 2%, 5%, 10%, and 20% damping ratios. Other than California earthquakes, [PERSON] [27] adopted European vertical ground motions in their study and provided vertical pseudo-acceleration response spectra at damping ratios of 5%, 7%, 10%, and 20%. Later on, [PERSON] [28] developed the acceleration constant, velocity constant, and displacement constant DRF functions for smooth vertical spectra.