Assessment of the Effect of Wind Load on the Load Capacity of a Single-Layer Bar Dome
Abstract
:1. Introduction
2. Materials and Methods
2.1. Truss Element Description
2.2. Frame Element Description
3. Results
3.1. Example 1
3.1.1. Von Mises Truss Analysis
3.1.2. Discussion of Example 1
3.2. Example 2
3.2.1. Geometry and Loads
3.2.2. Case 1. Load Combination: 1.15G + 1.5S
3.2.3. Case 2. Load Combination 1.15 × G +1.5 × S+0.9 × W
3.2.4. Discussion of Example 2
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Force/Displacement/Analysis | LA | GNA |
---|---|---|
Axial force | 20.616 kN | 20.660 kN |
Nodal displacement of node No. 2 | 0.236 cm | 0.237 cm |
Force/Displacement/Analysis | LA | GNA |
---|---|---|
Axial force | 100.125 kN | 116.6 kN |
Nodal displacement of node No. 2 | 2.236 cm | 2.795 cm |
Group Name | Numbers of Nodes |
---|---|
R1 | 6, 16, 26, 36, 46, 56, 66, 76, 7, 17, 27, 37, 47, 57, 67, 77 |
R2 | 5, 15, 25, 35, 45, 55, 65, 75, 8, 18, 28, 38, 48, 58, 68, 78 |
R3 | 4, 14, 24, 34, 44, 54, 64, 74, 9, 19, 29, 39, 49, 59, 69, 79 |
R4 | 3, 13, 23, 33, 43, 53, 63, 73, 10, 20, 30, 40, 50, 60, 70, 80 |
R5 | 2, 12, 22, 32, 42, 52, 62, 72, 11, 21, 31, 41, 51, 61, 71, 81 |
Nodes Group | Own Weight Load Value—G (kN) |
---|---|
R1 | 3.564 |
R2 | 7.129 |
R3 | 10.683 |
R4 | 14.229 |
R5 | 8.878 |
Node No. 1 | 7.180 |
Nodes Group | Snow Load Value—S (kN) |
---|---|
R1 | 4.059 |
R2 | 8.118 |
R3 | 12.165 |
R4 | 16.203 |
R5 | 10.110 |
Node No. 1 | 8.176 |
Pressure Coefficients | xA | x1 | x2 | x3 | xB | x4 | x5 | x6 | xC |
---|---|---|---|---|---|---|---|---|---|
x | 0.00 | 3.125 | 6.25 | 9.375 | 12.50 | 15.625 | 18.75 | 21.875 | 25.00 |
Cpe | −1.14 | −1.00 | −0.85 | −0.71 | −0.56 | −0.47 | −0.38 | −0.29 | −0.20 |
Node Number | Wind Load Value (kN) | Node Number | Wind Load Value (kN) | Node Number | Wind Load Value (kN) | Node Number | Wind Load Value (kN) |
---|---|---|---|---|---|---|---|
1 | −2.588 | 21 | −1.385 | 41 | −2.245 | 61 | −3.391 |
2 | −5.445 | 22 | −4.06 | 42 | −2.675 | 62 | −1.815 |
3 | −8.726 | 23 | −6.506 | 43 | −4.286 | 63 | −2.909 |
4 | −6.551 | 24 | −4.885 | 44 | −3.218 | 64 | −2.184 |
5 | −4.372 | 25 | −3.26 | 45 | −2.148 | 65 | −1.457 |
6 | −2.186 | 26 | −1.63 | 46 | −1.074 | 66 | −0.729 |
7 | −0.383 | 27 | −0.729 | 47 | −1.074 | 67 | −1.63 |
8 | −0.767 | 28 | −1.457 | 48 | −2.148 | 68 | −3.26 |
9 | −1.149 | 29 | −2.184 | 49 | −3.218 | 69 | −4.885 |
10 | −1.5311 | 30 | −2.909 | 50 | −4.286 | 70 | −6.506 |
11 | −0.955 | 31 | −1.815 | 51 | −2.675 | 71 | −4.06 |
12 | −4.7766 | 32 | −3.391 | 52 | −2.245 | 72 | −1.385 |
13 | −7.654 | 33 | −5.434 | 53 | −3.597 | 73 | −2.22 |
14 | −5.746 | 34 | −4.08 | 54 | −2.701 | 74 | −1.666 |
15 | −3.835 | 35 | −2.723 | 55 | −1.802 | 75 | −1.112 |
16 | −1.917 | 36 | −1.361 | 56 | −0.901 | 76 | −0.556 |
17 | −0.556 | 37 | −0.901 | 57 | −1.361 | 77 | −1.917 |
18 | −1.112 | 38 | −1.802 | 58 | −2.723 | 78 | −3.835 |
19 | −1.666 | 39 | −2.701 | 59 | −4.08 | 79 | −5.746 |
20 | −2.22 | 40 | −3.597 | 60 | −5.434 | 80 | −7.654 |
- | 81 | −4.776 |
Internal Forces/Displacement | LA | ||
---|---|---|---|
Meridian Bar no 30 | Parallel Bar no 114 | Diagonal Bar no 193 | |
NEd (kN)—axial force | 563.694 | 162.79 | 1.977 |
Nc,Rd (kN)—design capacity of the section under uniform compression | 1543.95 | 552.250 | 212.910 |
Nb,Rd (kN)—design buckling resistance of the compressed element | 1486.389 | 275.405 | 60.072 |
My,Ed,Max (kNm)—design bending moment with respect to y-y axis | 28.537 | 0.569 | 0.316 |
My,c,Rd (kNm)—design bending resistance with respect to y-y axis | 102.827 | 16.511 | 4.892 |
Mz,Ed,max (kNm)—design bending moment with respect to z-z axis | −2.300 | 0.572 | −0.090 |
Mz,c,Rd (kNm)—design bending resistance with respect to z-z axis | 102.827 | 16.511 | 4.892 |
Utilization (%) | 67 | 65 | 8 |
Maximum vertical displacement (mm)—for node 79 | 42.52 | ||
Allowable vertical displacement (mm)—D/300 | 83.33 | ||
Maximum horizontal displacement (mm)—for node 79 | 3.93 | ||
Allowable horizontal displacement (mm)—H/150 | 6.67 |
Group Name | Nodes Nos | Cross Section |
---|---|---|
Parallel | 2 to 81 | RO 219.1 × 10 |
Meridian | 82 to 161 | RO 101.6 × 8 |
Diagonal | 162 to 224 | RO 76.1 × 4 |
Internal Forces/Displacement | GNA | ||
---|---|---|---|
Meridian Bar no 20 | Parallel Bar no 107 | Diagonal Bar no 180 | |
NEd (kN)—axial force | 596.243 | 208.020 | 1.61 |
My,Ed,Max (kNm)—design bending moment with respect to y-y axis | 39.097 | 0.825 | 0.431 |
Mz,Ed,max (kNm)—design bending moment with respect to z-z axis | −2.774 | −0.628 | −0.119 |
Utilization (%) | 81 | 85 | 9 |
Maximum vertical displacement (mm)—for node 54 | 53.54 | ||
Allowable vertical displacement (mm)—D/300 | 83.33 | ||
Maximum horizontal displacement (mm)—for node 54 | 5.51 | ||
Allowable horizontal displacement (mm)—H/150 | 6.67 |
Internal Forces/Displacement | LA | ||
---|---|---|---|
Meridian Bar no 10 | Parallel Bar no 106 | Diagonal Bar no 165 | |
NEd (kN)—axial force | 518.05 | 164.801 | 19.766 |
Nc,Rd (kN)—design capacity of the section under uniform compression | 1543.95 | 552.25 | 212.910 |
Nb,Rd (kN)—design buckling resistance of the compressed element | 1486.389 | 275.405 | 43.369 |
My,Ed,Max (kNm)—design bending moment with respect to y-y axis | 29.862 | 0.693 | 0.122 |
My,c,Rd (kNm)—design bending resistance with respect to y-y axis | 102.827 | 16.511 | 4.892 |
Mz,Ed,max (kNm)—design bending moment with respect to z-z axis | −2.235 | −0.617 | −0.019 |
Mz,c,Rd (kNm)—design bending resistance with respect to z-z axis | 102.827 | 16.511 | 4.892 |
Utilization (%) | 65 | 67 | 49 |
Maximum vertical displacement (mm)—for node 9 | 48.42 | ||
Allowable vertical displacement (mm)—D/300 | 83.33 | ||
Maximum horizontal displacement (mm)—for node 9 | 4.52 | ||
Allowable horizontal displacement (mm)—H/150 | 6.67 |
Internal Forces/Displacement | GNA | ||
---|---|---|---|
Meridian Bar no 10 | Parallel Bar no 106 | Diagonal Bar no 165 | |
NEd (kN)—axial force | 555.081 | 214.545 | 36.408 |
My,Ed,Max (kNm)—design bending moment with respect to y-y axis | 43.965 | 1.210 | 0.173 |
Mz,Ed,max (kNm)—design bending moment with respect to z-z axis | −2.704 | −0.720 | −0.008 |
Utilization (%) | 83 | 92 | 90 |
Maximum vertical displacement (mm)—for node 9 | 68.72 | ||
Allowable vertical displacement (mm)—D/300 | 83.33 | ||
Maximum horizontal displacement (mm)—for node 9 | 6.52 | ||
Allowable horizontal displacement (mm)—H/150 | 6.67 |
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Opatowicz, D.; Radoń, U.; Zabojszcza, P. Assessment of the Effect of Wind Load on the Load Capacity of a Single-Layer Bar Dome. Buildings 2020, 10, 179. https://doi.org/10.3390/buildings10100179
Opatowicz D, Radoń U, Zabojszcza P. Assessment of the Effect of Wind Load on the Load Capacity of a Single-Layer Bar Dome. Buildings. 2020; 10(10):179. https://doi.org/10.3390/buildings10100179
Chicago/Turabian StyleOpatowicz, Dominika, Urszula Radoń, and Paweł Zabojszcza. 2020. "Assessment of the Effect of Wind Load on the Load Capacity of a Single-Layer Bar Dome" Buildings 10, no. 10: 179. https://doi.org/10.3390/buildings10100179