## 5 Multi-Scale Model  
Multi-scale modeling is a numerical modeling technique involved in FE modeling, which refers to the combined modeling of different scales. In multi-scale modeling, the important parts are modeled with relatively fine mesh while the parts which do not need attention are modeled with relatively coarse mesh. By appropriate connections at the boundaries of different element models, the force balance and deformation coordination are realized, thus more accurate results will be obtained by spending less computing resources and time. Figure 4: Power spectrum. Figure 3: Fluctuating wind time-history. In the structure, the beam-to-column connections in the ground floor are relatively easy to produce stress concentration, because the horizontal wind force and the gravity of the structure finally transmit to the ground floor through beams and columns. Since wind loading is much smaller than the gravity, under the gravity, in a beam-to-column connection the upper beam flange is easy to produce tension while the lower flange is easy to produce pressure, and as known to us all, when it comes to fatigue damage prevention, pressure is more conductive to the structure than tension. Thus, the upper flange is the position where fatigue cracks are easier to initiate and the welds connecting upper beam flange and the column is where local model is required. Thus, a multi-scale FE model is established by the commercial FE software ANSYS (ANSYS, Inc., Canonsburg, PA, USA) with a global scale model, a local connection scale model and a local weld scale model. In the global scale model, a model of the whole structure is established and beams and columns are simulated by element BEAM188 and floors are simulated by element SHELL63, as shown in Figure 5a. A typical beam-to-column connection considered to be more stress-concentrated in the first floor is chosen to establish the local connection scale model, whose beam and column are simulated by element SHELL63, as illustrated in Figure 5b. The upper flange plate on the inner beam where the tension stress concentration usually happens is chosen to establish a local weld scale model, which is simulated by eight-node element SOLID45, as shown in Figure 5c. The connections among the three different scale models are created by establishing the rigid region which can provide the desirable constraint equation. Thus, the multi-scale element model embodies the force transition from the global scale to the local connection scale then to the local weld scale and the connection between beam elements to shell elements then to solid elements. Figure 5: Multi-scale element model: (**a**) global scale; (**b**) local connection scale; and (**c**) local weld scale. The structural windward surface is divided into several pressure regions, each of which contains a beam-to-column connection, as illustrated in Figure 6. The wind pressure on each pressure region can be approximately equivalent to a concentrated force in the region center, which is the exact location where each beam-to-column connection is, as represented in Figure 6 as the black dot in the pressure region center. Therefore, the simulated wind speed time history curves are transformed into corresponding wind loading (concentrated force) time history curves by Equation (9). \[ \begin{array}{ll}P_{i}=A_{i}\upmu_{s}W_{i}(z,t)&=\frac{1}{2}A_{i}\upmu_{s} \rho V_{i}^{2}(z,t)=\frac{1}{2}A_{i}\upmu_{s}\rho[\overline{v}_{i}(z)+v_{i}(z, t)]^{2}\\ &=\frac{1}{2}A_{i}\upmu_{s}\rho\overline{v}_{i}^{2}(z)+\frac{1}{2}A_{i}\upmu_{s} \rho[\overline{v}_{i}(z,t)+{v_{i}}^{2}(z,t)]\\ &\approx\frac{1}{2}A_{i}\upmu_{s}\rho\overline{v}_{i}^{2}(z)+A_{i}\upmu_{s} \rho\overline{v}_{i}(z)v_{i}(z,t)\end{array}