## 3 Methods for Assessing the Impact of Vibrations on People in Buildings Selected for Analysis  
### The Root Mean Square (RMS) Method  
The Root Mean Square (RMS) method, introduced already in the first edition of the ISO standard, has its physical interpretation, which is the energy of vibrations. The RMS value effectively describes vibrations because it contains information about the RMS components of vibrations across the entire range of frequencies considered. The effective (RMS) value a\({}_{\text{RMS}}\) of vibration acceleration, is defined by the formula:  
\[\text{a}_{\text{RMS}}=\sqrt{\frac{1}{\text{T}}\int\limits_{0}^{\text{T}}\text {a}^{2}(\text{t})\text{dt}} \tag{2}\]  
where: T--duration time [s], a(t)--vibration acceleration [m/s\({}^{2}\)]. In practical measurements of the impact of vibrations on individuals in buildings, the RMS value of accelerations presented in 1/3 octave bands is used. This provides information not only about exceeding the threshold values of vibration perceptibility but also about the frequency band in which this exceedance occurred. This is particularly useful in building design because it then allows for \"returning\" the structure of the floor or even the building in such a way as to avoid exceedances in specific frequency bands. The RMS method, known as the fundamental method in ISO [6], stipulates that studies regarding the impact of vibrations on people in buildings should always include measurement results in RMS values. Due to the ease of interpretation of results presented using this method, many researchers employ it [19; 20; 21; 22], and it has also been incorporated into the majority of standards in various countries. In [19], for instance, the impact of the speed of passing trains on building structures as well as on the perceptibility of vibrations by people was analyzed. In [20], the influence of vibrations induced by wind was determined, while works [21] and Ref. [22] constitute a synthesis of the impact of transportation vibrations on people residing in buildings. Work [21] serves as a kind of general compendium, whereas [22] focuses on the influence of vibrations from roads and railways. In assessing the impact of vibrations on people in buildings conducted according to the RMS method, factors such as the room's purpose, the time of day when vibrations occur, the nature and repeatability, as well as the direction of vibrations and the position of the human body receiving vibrations in the room, are taken into account. In the revised Polish standard [15], a new index has been introduced to express the assessment result of the impact of vibrations on people in buildings. This index, called the Human Perception of Vibration Index (HPVI), in relation to vibrations transmitted to humans in the \"z\" direction, can be calculated using the formula:  
\[\text{HPVI}=\text{max}\bigg{(}\frac{\text{a}_{\text{RMS}}}{\text{a}_{\text{z }}}\bigg{)} \tag{3}\]where: a\({}_{\text{RMS}}\)--the root mean square value of vibration accelerations obtained from the analysis, a\({}_{\text{z}}\)--the root mean square value of vibration accelerations equal to the vibration perceptibility threshold for humans in the \"z\" direction in the same frequency band in which a\({}_{\text{RMS}}\) was determined. The numerical value of the index supplemented with information about the center frequency of the band in which it was determined serves as a complement to the information obtained using the RMS method, presented in 1/3-octave bands, in the form of a graph. The HPVI not only informs about the exceeding of the vibration perceptibility threshold but also about the value of this exceedance. It should be noted that the result of the RMS method is illustrated in a graph on a logarithmic scale, which often causes problems in interpreting the requirement for ensuring necessary comfort. However, the graph along with information about the HPVI value provides more complete information.