# Peak Net Pressure Coefficients of Elliptical Center-Open Dome Roofs

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Wind Tunnel Tests

#### 2.1. Model Details

#### 2.2. Wind Tunnel Test Conditions and Methods

#### 2.3. Experimental Flows

^{5}(green box in the legend). Therefore, we set Re = 2.4 × 10

^{5}, which is similar to the Reynolds number determined by Noguchi and Uematsu [17]. Letchford and Sarkar [18] confirmed that wind pressure distribution is stable within a Reynolds number range of 2.3 × 10

^{5}–4.6 × 10

^{5}. Figure 6b shows the power spectra of wind velocity fluctuations for the two oncoming flows at the maximum model height of 0.24 m. These spectra are consistent with the Karman spectra.

## 3. Results and Discussion

_{p}(t) = (P-P

_{pitot})/q

_{H}, where P is the pressure measured at each pressure tap; P

_{pitot}is the pressure measured in the pitot tube installed 1.2 m above the wind tunnel floor, and q

_{H}is the velocity pressure at the maximum roof height (H + f) for each model (see Figure 2). The peak pressure coefficients proposed in the Japanese wind load code (AIJ–RLB (2015)) were defined as the negative and maximum values for each 10-min sample of C

_{p}(t). Moreover, 10 ensemble-averaged values were calculated for the external peak pressure coefficients to be applied in the cladding design. Therefore, for a more accurate comparison, this study analyzed 10 ensemble-averaged values under the same conditions.

_{pe,min}), a positive external peak pressure (C

_{pe,max}), an inner surface negative internal peak pressure (C

_{pi,min}), and an inner surface positive internal peak pressure coefficients (C

_{pi,max}) (see Figure 7). The estimations of the wind pressure coefficients are achieved using Equations (2)–(5).

_{pn,i}as the negative peak net pressure coefficient (C

_{pn,min}) and positive peak net pressure coefficient (C

_{pn,max}), respectively.

#### 3.1. Peak Pressure Coefficient Characteristics of Elliptical Center-Open Dome

_{pe,min}, the comparison was made at h/D = 0.5, where the absolute values were the largest (h/D = 0.1 for C

_{pe,max}). The analysis expresses the line of the pressure taps from which the largest absolute value was derived in all the wind directions. The x-axis shows the normalized diameter, and the y-axis shows each peak pressure. A normalized diameter of 1 represents the windward side, 0.5 represents the center of the dome, and 0 represents the leeward side.

#### 3.2. External Roof Surface Peak Pressure Coefficients

#### 3.3. Peak Pressure Coefficients and Peak Net Pressure Coefficients of Internal Roof Surface

#### 3.4. Comparison of Experimental Values for Different Wind Load Codes

#### Peak Net Pressure Coefficients

#### 3.5. Comparison with Proposed Peak Pressure Coefficients for Spherical Dome with Opening

_{a}values were proposed for all the h/D in the area corresponding to 60% of the dome roof end. For Zone 2, one value of R

_{b}was proposed for all the h/D values in the area corresponding to the remaining 40% of the dome roof.

_{a}and R

_{b}zones at all the h/D values. In contrast, for the positive peak net pressure coefficients, as shown in Figure 20b, the experimental values at all the h/D exceeded the proposed values by at most 1.3 times in the central zone of the dome, R

_{b}.

#### 3.6. Proposal of Peak Net Pressure Coefficients

_{b}, and satisfy the code in the end zone of the dome, R

_{a}. Therefore, a code was proposed based on the experimental values only in the central zone of the dome, R

_{b}, and was limited to the positive peak net pressure coefficient. Additionally, in the previous study, as similar R

_{b}values were observed regardless of changes in h/D at the central zone of the dome, only one positive peak net pressure coefficient was proposed, whereas the absolute values of the experimental values in this study tended to change according to changes in h/D because the representative length (length of the open space) varying with changes in the wind direction, with the negative external peak pressure coefficient on the inner surface changing accordingly.

_{pn,max}), indicating the largest absolute value in the various wind directions. The red dotted line corresponds to h/D = 0.1, indicating the largest absolute value among all the h/D values. The proposed R

_{b}values range from 1.2 to 1.4 for each h/D in the central zone of the dome.

## 4. Conclusions

- (1)
- The trend of the external peak pressure coefficient on the inner surface of the center-open elliptical dome roof was dominated by the negative pressure, rendering the absolute values of the negative external peak pressure coefficients constant on the windward side. On the leeward side, the values and trends were similar to those of the negative external peak pressure coefficients on the outer surface of the roof owing to separation.
- (2)
- Considering the trends of the peak net pressure coefficient, the negative pressure was offset on the windward side compared with the outer side owing to the influence of the negative pressure on the inner surface, and the absolute value of the peak net pressure coefficient decreased. The positive peak net pressure coefficients were similar to the positive external peak pressure coefficients on the outer and windward sides of the roof. On the leeward side, because the negative pressure significantly increased owing to the separation that occurred on the inner side of the roof, upward pressure was generated owing to the difference in wind pressure. As a result, the positive peak net pressure coefficient was larger than the positive external peak pressure coefficient on the outer side of the roof, and the absolute value of the negative peak net pressure coefficient decreased as the large negative pressures offset each other.
- (3)
- The peak net pressure coefficients were compared with the Korean wind load code KDS 41 10 15. When h/D = 0.3, the experimental values of the positive peak net pressure coefficient exceeded the code by 1.1 times in the R
_{b}zone. - (4)
- The peak net pressure coefficients for the cladding design of center-open elliptical dome roofs were proposed based on the experimental values. For the negative peak net pressure coefficient, a proposal was unnecessary because the values were similar to the proposed values in a previous study for center-open circular dome roofs. The proposed values for the positive peak net pressure coefficient ranged from 1.2 to 1.4 according to the h/D value in the R
_{b}zone. Thus, the same proposed values in the previous study for the R_{a}region could be used. - (5)
- While the experimental values exceeded the proposed values of the previous study, they exceeded the values in specific areas rather than those in the entire area in some cases. Conversely, they occasionally satisfied the proposed values. For dome roof structures with specific shapes, such as elliptical roofs, appropriate external peak pressure coefficients should be proposed for each area to consider stability and prevent overdesigning.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Profiles of experimental flows: (

**a**) mean wind speed and turbulence intensity and (

**b**) turbulence length scale.

**Figure 6.**Reynolds number and power spectra: (

**a**) mean pressure coefficients at different Reynolds numbers. (

**b**) Power spectra of velocity fluctuations.

**Figure 8.**Comparison between 10 ensemble-averaged and BLUE values at the largest value derived taps: (

**a**) C

_{pe,min}and (

**b**) C

_{pe,max}.

**Figure 9.**Comparison of opening roof and closed roof: (

**a**) C

_{pe,min}(h/D = 0.5) and (

**b**) C

_{pe,max}(h/D = 0.1).

**Figure 10.**Plots of largest absolute values as a function of wind direction: (

**a**) C

_{pe,min}and (

**b**) C

_{pe,min}.

**Figure 19.**Comparison of positive peak net pressure coefficients according to AIJ–RLB (2015): (

**a**) 0° and (

**b**) 90°.

**Figure 20.**Comparison of negative peak net pressure coefficients with AIJ–RLB (2015): (

**a**) 0° and (

**b**) 90°.

**Figure 21.**Comparison of peak net pressure coefficients with previous research: (

**a**) C

_{pn,min}and (

**b**) C

_{pn,max}.

**Figure 22.**Proposed positive peak net pressure coefficients for elliptical dome with an opening ratio of 30%.

Pressure Taps | |||
---|---|---|---|

Line | External Tap | Internal Tap | Total |

1 | 10 | 10 | 20 |

2 | 10 | 10 | 20 |

3 | 10 | 10 | 20 |

4 | 10 | 10 | 20 |

80 |

**Table 2.**Internal peak pressure coefficients for cladding design prescribed in AIJ–RLB (2015) [6].

AIJ–RLB (2015) [6] | ||
---|---|---|

partially open buildings | without dominant openings | 0 or −0.5 |

**Table 3.**Internal peak pressure coefficients for cladding design prescribed in KDS 41 10 15 [12].

KDS 41 10 15 [12] | ||
---|---|---|

Closed | 0.00 or −0.52 | |

partially open buildings | without dominant openings | +0.83 or −0.83 |

dominant openings | +1.40 or −1.40 | |

open | 0 |

**Table 4.**Proposed peak net pressure coefficient for cladding design for dome with an opening ratio of 50% (Cheon et al. [7]).

Negative Peak Net Pressure Coefficients | ||||

f/D | $\alpha $ | h/D | Zone 1 (d × 0.6) | Zone 2 (d × 0.4) |

0.1 | 0.21 | 0.1 | $-$2.0 | $-$1.8 |

0.2 | $-$2.3 | |||

0.3 | $-$2.3 | |||

0.4 | $-$2.4 | |||

0.5 | $-$2.1 | |||

Positive peak net pressure coefficients | ||||

f/D | $\alpha $ | h/D | zone 1 (d × 0.6) | zone 2 (d × 0.4) |

0.1 | 0.21 | 0.1 | 1.4 | 1.1 |

0.2 | 1.2 | |||

0.3 | 1.0 | |||

0.4 | 1.0 | |||

0.5 | 1.0 | |||

r: Opened area d: Roof diameter h: Wall height D: Building diameter f: Roof rise |

**Table 5.**Proposed peak net pressure coefficient for cladding design for elliptical dome with opening ratio of 30%.

Positive Peak Net Pressure Coefficients | |||
---|---|---|---|

f/D | $\mathit{\alpha}$ | h/D | Zone 1 (d × 0.6) |

r/D = 0.3 | |||

0.1 | 0.21 | 0.1 | 1.4 |

0.2 | 1.4 | ||

0.3 | 1.3 | ||

0.4 | 1.2 | ||

0.5 | 1.2 | ||

d: Roof diameter h: Wall height D: Building diameter f: Roof rise |

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**MDPI and ACS Style**

Lee, J.H.; Cheon, D.J.; Kim, Y.C.; Yoon, S.W.
Peak Net Pressure Coefficients of Elliptical Center-Open Dome Roofs. *Materials* **2022**, *15*, 5497.
https://doi.org/10.3390/ma15165497

**AMA Style**

Lee JH, Cheon DJ, Kim YC, Yoon SW.
Peak Net Pressure Coefficients of Elliptical Center-Open Dome Roofs. *Materials*. 2022; 15(16):5497.
https://doi.org/10.3390/ma15165497

**Chicago/Turabian Style**

Lee, Jong Ho, Dong Jin Cheon, Yong Chul Kim, and Sung Won Yoon.
2022. "Peak Net Pressure Coefficients of Elliptical Center-Open Dome Roofs" *Materials* 15, no. 16: 5497.
https://doi.org/10.3390/ma15165497