This paper focuses on the first-mode natural period and damping ratio in the vertical direction for the purpose of grasping the actual characteristics of the vertical vibration of buildings. The identifications of period and damping ratio based on earthquake observation records of multiple buildings are carried out. The targets of the identifications are a total of 18 buildings consisting of reinforced concrete (RC), steel and reinforced concrete (SRC), and steel (S) structures. Auto regression and exogenous (ARX) model is used to identify the first-mode vertical natural period and damping ratio. The identified values are summarized for each structural type, and its characteristics are discussed in view of the input amplitude and the height of buildings and in comparison with its natural period and damping ratio in the horizontal direction as well.
The main findings obtained here are summarized as follows:
1) The 1st-mode vertical natural periods of 18 buildings show relatively small dependence on the input acceleration amplitude. On the other hand, the 1st-mode vertical damping ratios are found to be dependent on the amplitude especially in RC buildings. No significant change is found in 1st-mode vertical natural periods and damping ratios of 18 buildings between before and after The 2011 off the Pacific coast of Tohoku Earthquake.
2) When the effective value (root-mean-square value) of vertical acceleration at the lower point of the building is 2.0 Gal, the 1st-mode vertical damping ratios are about 2~5% in RC and SRC buildings and about 0.5~2% in Steel building.
3) The gradient of vertical natural period of a building tends to be smaller as the height increases, in contrast to the horizontal period, which is generally proportional to the height of a building.
4) The above tendency is examined based on the natural period of equivalent single-degree-of-freedom (SDOF) system, and the estimation equation of the 1st-mode vertical natural period which is proportional to the square root of building height is proposed. The coefficient C of the estimation equation is proportional to the square root of the material strength f and the axial force ratio β of the first story, and inversely proportional to the square root of the Young's modulus E of vertical structural members such as columns. The estimation equation shows good correspondence to the identified values in this paper and the data from the past references.
5) The simple equation of relation between the 1st-mode vertical natural period vT1 and the horizontal 1st-mode natural period hT1 is proposed.
6) The 1st-mode vertical damping ratios of 18 buildings are similar to the horizontal 1st-mode damping ratios of the same buildings in the RC and SRC building, and those tend to be small in the Steel buildings.
