*4.1. Seismic Arrays Input*

The degree of seismic fortification intensity of the gymnasium is seven, and falls into the third seismic group. In light of the rules of seismic grouping, the Imperial Valley-06 far-field seismic wave files, DLT-352 and DLT-DWN, were collected from Pacific Earthquake Engineering Research Center (PEERC). The seismic acceleration curve and response spectrum curve are showed in Figure 6a–d. The horizontal seismic waves (X or Y direction) of DLT-352 were combined with the vertical seismic waves (Z direction) of DLT-DWN, and the seismic excitation effect partial coefficients, *γEh* and *γEv*, were, respectively, set as 1.3 and 0.5 under two components, and set as 1.0, 0.85 and 0.65 under three components [27]. The combination formulas are as follows.

$$\text{No. 1 Seismic Array: K1} = 1.3 \times \text{X} + 0.5 \times Z\_{\text{\textquotesingle}} \tag{1}$$

$$\text{No. 2 Seismic Array: K2} = 1.3 \times \text{Y} + 0.5 \times Z\_2 \tag{2}$$

$$\text{No. 3 Seismic Array: K3} = 1.0 \times \text{X} + 0.85 \times \text{Y} + 0.65 \times Z\_t \tag{3}$$

To better analyze the response of the structure under seismic excitation, the peak ground acceleration (PGA) was adjusted to 0.22 g in consideration of the impact of earthquakes that rarely occur. Meanwhile, when analyzing the elastoplasticity of dome structure in the context of rarely occurring earthquakes, the damping ratio was set as 0.05 and the nonlinear time history analysis method based on "self-weight" was used to analyze the seismic response.

**Figure 6.** *Cont*.

**Figure 6.** Acceleration curve and response spectrum curve of seismic wave. (**a**) DLT-352 acceleration time history; (**b**) DLT-DWN acceleration time history; (**c**) DLT-352 acceleration response spectrum; (**d**) DLT-DWN acceleration response spectrum.

### *4.2. Dynamic Response under the Excitation of No. 1 Seismic Array* 4.2.1.AnalysisoftheInternalForce ResponseofRoofSquareRingCables

As the stay cables and square ring cables unite to mainly transfer tensions, and the struts units transfer compressions, the internal force response of cables and struts of the ring-cable structure under No. 1 seismic array excitation is shown in Figure 7, where the structural dynamics remain relatively small due to the equal altitudes at both ends of the EW (X) direction, as well as grea<sup>t</sup> rigidity. It can be seen from the figure that struts (SC1 to SC16) tend to be more average in force and smaller in internal force response with comparable values, and the smallest internal force response occurs in the additional struts (SC1 to SC16) at the north and south sides of the outer ring. The inner ring and middle ring stay cables (SX1 to SX8) and ring cables (SH1 to SH8) share a relatively small internal force response within 90 kN, while the outer ring stay cables (SX9 to SX12) and ring cables (SH9 to SH12) experience a significantly increased internal force response, almost double that of the inner ring and middle ring. String cables are long in span and unilaterally connected, and the cables (SH13 to SH14) and struts (SC17 to SC24) have the largest internal force response.
