*4.1. Earthquake E*ff*ect*

The base shears in the *X* and *Y* directions of the factory with and without LRBs are shown in Figure 7, where the PGA of the applied seismic load is 0.32 g, and *Ts* is 0.7 and 1.4 s for two cases, respectively. The base shear is determined from the summation of the shear forces at the top of all the piles, and it represents the total seismic loads changing with time for the superstructure of the high-tech factory. To simplify the time-dependent base shears in the *X* and *Y* directions, we first find the magnitude (*S*(*t*)) of the two-direction base shears using the following equation:

$$S(t) = \sqrt{{\mathcal{S}\_x(t)}^2 + {\mathcal{S}\_y(t)}^2} \tag{5}$$

where *Sx*(*t*) and *Sy*(*t*), as shown in Figure 7, are the time-dependent base shears in *X* and *Y* directions, respectively. Then, we obtain the maximum base shear (*Smax*) of all the time steps during the finite element analysis. Finally, we define the base shear ratio (*R* = *SmaxLRB*/ *SmaxNO-LRB*) as the maximum base shear of the structure with LRBs (*SmaxLRB*) over that without LRBs (*SmaxNO-LRB*)), and this ratio can be used to understand the efficiency of the LRB used to structures during earthquakes. Figure 8 shows this base shear ratio changing with PGA under *Ts* of 0.6 s, and Figure 9 shows that changing with *Ts* under the PGA of 0.32 g. These figures indicate the following features:

(1) Figure 8 shows that when PGA increases, the base shear ratio increases slightly. However, for the worse case, the ratio for the PGA of 0.4 g is still small, which means that the LRB can effectively reduce the seismic load regardless of the magnitude of earthquakes. Figure 9 shows that when the dominant period of the earthquake increases, the base shear ratio increases to a noted extent. For long period seismic loads, such as near fault earthquakes, this situation can lead to LRB disadvantages.

(2) Usually, the high-tech factory requires thick floor slabs, big long trusses, and dense RC columns to reduce ambient vibration, but this arrangemen<sup>t</sup> will largely increase the building mass that causes large seismic loads during earthquakes. The high-tech factory with LRBs can decrease over 50% of the seismic base shear under *Ts* ≤ 1.0, which means that the high-tech factory can resist larger earthquakes using LRBs for not very long periods of seismic loads. The comparison of base shears, shown in Figure 7a,b, between the factory with and without LRBs indicates the above conclusion, where the time-history base shears of the factory with LRBs are much smaller than those without LRB.

(3) For the earthquake with a very long dominant period, such as 1.4 s, the LRB efficiency to reduce the factory base shear may decrease a little, since the natural period of the factory, due to the full yield of the LRB, can approach the earthquake with a long dominant period. However, earthquakes with this long dominant period often occur in significantly soft soil, and the design of LRBs for the high-tech factory may avoid this condition. Nevertheless, the simulation results indicate that the LRB efficiency for the earthquake with a long dominant period is still in the acceptable range, as shown in Figure 7c,d.

**Figure 7.** Comparison of base shears between the factory with and without LRBs under the seismic load of PGA = 0.32 g and *Ts* = 0.7 s and 0.14 s.

**Figure 8.** The base shear ratio changing with PGA under *Ts* of 0.6 s.

**Figure 9.** The base shear ratio changing with *Ts* under the PGA of 0.32 g.

#### *4.2. Micro-Vibration Induced by Mobile Cranes*

Floor micro-vibration induced by moving cranes inside the high-tech factory is the major environmental source which affects the production operation in high-tech factories. As shown in Figure 4, the rail and crane system on the second level was studied, where the crane moves back and forth on the 60-m rail system with a maximum crane speed of 3 m/s. Figure 10 shows the ambient vibration in *X*, *Y*, and *Z* directions at the 10 m location from the railway centerline of the moving crane, while the factory was arranged with and without LRBs. This figure shows that the vertical (*Z*) vibration induced by moving cranes is much larger than those in the in-plane (*X* and *Y*) directions. Moreover, the major vibrations that are above 40 dB, and between 15 to 40 Hz, in these three directions for the factory with and without LRBs are almost identical, in which these major vibrations between 15 to 40 Hz are the slab natural frequencies invoked by the vibration of the moving crane, more details can be referred to in [20]. The ambient vibrations at other frequencies are small but different from the factory with and without LRBs. One can still realize that the factory without LRBs has smaller ambient vibrations than that with LRBs, because the LRBs cause a big rigid body motion of the high-tech factory. Nevertheless, the moving crane does not change the major ambient vibrations between the factory with and without LRBs.

**Figure 10.** Velocity vibration dB at 10 m from the centerline of the crane railway on the first steel level for the factory with or without LRBs.

#### *4.3. Micro-Vibration Simulation Under Wind Loads*

In addition to vibration generated by moving cranes, wind-induced floor vibration in high-tech buildings is another major source of environmental loads affecting production operations. Therefore, we followed the reference [23] to study the wind induced vibration, and the LRB effect was investigated in this paper, where the analysis only included dead and wind loads and the seismic load was not used in this section. Since wind forces applied to the factory are space- and time-dependent, we used the wind speed simulation software TurbSim [27] to generate the space- and time-dependent wind speed field in the *Y* direction on the whole *X*-direction outer plane to compare the floor vibration of the factory with and without LRBs. Since the building is much longer in the *X* direction than that in the *Y* and Z directions, the *Y-*direction wind-induced vibration should be the largest, and we will thus only focus on this direction vibration. The normal turbulence model is used in the analysis with the average wind speed at the height of 30 m (*V30m*) during 10 min, while *V30m* is set to 5, 10, 15, 20, and 25 m/s for the five cases, and the turbulence standard deviation is set according to IEC-61400-1 in 2019 [28], as follows:

$$
\sigma\_1(m/s) = 0.16(0.75Vy\_{90m} + 5.6) \tag{6}
$$

In the setting of this program, an area of 500 m wide by 60 m high was arranged with 41 by 41 girders to find the turbulent wind speeds. The average wind speed in the vertical direction is according to the normal wind profile as below:

$$VZ = V\_{30m} \left(\frac{Z}{30}\right)^a \tag{7}$$

where *Z* (m) is the vertical height above the ground, and α equal to 0.14 is the power law exponent. Figure 11 shows the turbulent wind velocity at the height of 30 m on the building center, and it is noted that the wind velocity is time- and location-dependent. The wind pressure is determined as below:

$$P(\mathbf{X}, \mathbf{Y}, \mathbf{Z}, \mathbf{t}) = \mathbb{C}\_P \rho V(\mathbf{X}, \mathbf{Y}, \mathbf{Z}, \mathbf{t})^2 / 2 \tag{8}$$

where *P*(*X,Y,Z*,*<sup>t</sup>*) is the time- and space-dependent wind pressure, *V*(*X,Y,Z*,*<sup>t</sup>*) is the time-and space-dependent wind speed from the TurbSim result, *Cp* (0.8) is the shape coefficient, and ρ (0.00128 <sup>t</sup>/m3) is the air density. Finally, the time-history finite element analysis is performed to find the wind-induced vibrations on the three floors, which are shown in Figure 12 for the case of the average wind speed *V30m* equal to 15 m/s. These figures indicate that the high-tech factory with LRBs will have much larger wind-induced vibration than that without LRBs, especially for the RC level that is located at the first level. The increased velocity vibration dBs for the RC level, the first steel level, and the second steel level are about 19, 6, and 4 dB, respectively. Therefore, this situation will bring grea<sup>t</sup> disadvantage to the use of LRB in high-tech factories. The reason for largely increasing the floor vibration induced by wind loads is that the initial stiffness of the LRB is considerably soft, so that the rigid body motion of the factory superstructure cannot be avoided due to the wind load. Even for a small wind load, which is still much larger than the load of moving cranes, the wind induced rigid body motion still causes problems for the factory with LRBs. We further analyzed the factory under different average wind speeds (*V30m*) and then only selected the maximum dB from all the frequencies, as shown in Figure 13. This figure indicates a very similar conclusion as that of the average wind speed equal to 15 m/s not only for the steel levels but also for the RC level, while the average wind speed was set to a board range from 5 to 25 m/s. An interpolation scheme was used to find the requirement of micro vibration according to the guidelines for high-tech factories, and the result is shown in Table 3. The table can be used to estimate the wind-induced vibration for a high-tech factory approximately, although the result is dependent on the structure dimensions and member sizes. This table also indicates that using LRBs for the high-tech factory will highly increase the wind-induced vibration, especially for the vibration on the RC level. For the high-tech without LRBs, the RC level at the first floor can resistant vibration under a moderate wind field, but the steel levels above the RC level may not be qualified for such a wind field. To overcome this problem, the shade of adjacent buildings for the high-tech factory was proposed to resistant the wind induced vibration [23], where the height of the shading building should be more than 60% of the factory height. This shade method is still useful for the high-tech factory with LRBs.

**Figure 11.** Turbulent wind velocity at the height of 30 m on the building center.

**Table 3.** The minimax average wind speed (m/s) during 10 min for the criteria of the micro-vibration for the studied high-tech factory.


**Figure 12.** *Cont.*

(**c**) At the third floor (the second steel level)

**Figure 12.** Velocity vibration dB at the first to third floors under the wind load with the average wind speed of 15 m/s for the factory with or without LRBs.

**Figure 13.** Maximum velocity vibration dB at the first to third floors under the wind load with the average wind speed from 5 to 25 m/s for the factory with or without LRBs.

#### **5. Design of LRBs Concerning the Micro Vibration**

The LRBs should possess large stiffness for frequent small or moderate earthquakes but small stiffness for extreme earthquakes. If the micro vibration is the major concern for the high-tech factory, the investigation of Section 4 indicates that the selection of LRBs should first consider the problem of the large micro vibration induced by the wind load. Thus, the LRB with a large initial stiffness (*Ke*) and a small ratio of the final stiffness over the initial stiffness (α) should be used, where the large *Ke* can resist wind loads and the small α can reduce seismic loads. However, this situation may cause difficulties in finding a suitable LRB, so we will first select LRBs with large *Ke*, where 5E5 kN/m (*Fy* = 300 kN and *Kv* = 8E7 kN/m) and 3E5 kN/m (*Fy* = 200 kN and *Kv* = 5E7 kN/m) are used at the bottom of the big and small columns, respectively. Then, α is set to 1%, 2.5%, 5%, and 7% for three cases. The artificial earthquake is set using the PGA of 0.32 g and *Ts* of 0.9 s (Figure 5), and the average speed of the turbulent wind load is set to 25 m/s. The finite element results are shown in Figures 14 and 15, where Figure 14 shows the velocity dB changing with frequencies for the wind load, in which the results are not dependent on α because the yield of LRBs is not obvious under the average wind speed of 25 m/s, and Figure 15 shows the base shear ratio (*R* = *SmaxLRB*/ *SmaxNO-LRB*) changing with α. The two figures indicate the following features:

(1) Figure 14 shows that the slab vibrations induced by the wind load are similar between the factories with and without LRBs, where the vibrations of the LRB factory are slightly large about 2 to 3 dB greater than those without LRBs. This improvement is significant compared to the result in Figure 11, because the large initial stiffness of the LRB resists the wind loads. Moreover, most of the LRBs are still not yielded, so the slab vibrations are independent of the LRB parameter α.

(2) Figure 15 shows that the α should be smaller at higher LRB initial stiffness to reduce the seismic load of high-tech factories. This situation may make it difficult to obtain a suitable LRB, for example, α in Figure 15 is less than 2%. Nevertheless, using the large initial stiffness and small α may reduce seismic responses but not increase the micro vibration for high-tech factories

**Figure 14.** Velocity vibration dB changing with frequencies at the first to third floors under the wind load with the average speed of 25 m/s for the factory with or without LRBs (The dB values with LRBs due to α from 0.01 to 0.07 are almost identical.).

**Figure 15.** The base shear ratio changing with α (Equation (1)) under the PGA of 0.32 g and Ts of 0.9 s.
