Number of solutions | 4 | 3 | 7 | 13 | ||||
---|---|---|---|---|---|---|---|---|
Arch axis coefficient | 1.6 | 1.8 | 2 | 2.2 | ||||
Scope of solutions | lower limit | upper limit | lower limit | upper limit | lower limit | upper limit | lower limit | upper limit |
Z1/m | 22.12 | 23.68 | 19.40 | 21.05 | 17.19 | 23.48 | 17.90 | 23.48 |
Z2/m | 10.14 | 11.75 | 10.02 | 10.15 | 10.02 | 13.00 | 10.02 | 13.00 |
L1/m | 139.04 | 155.30 | 175.13 | 182.22 | 177.60 | 251.79 | 177.60 | 254.41 |
H1/m | 12.72 | 13.30 | 13.59 | 13.81 | 10.24 | 15.00 | 10.24 | 15.00 |
H2/m | 7.79 | 8.33 | 7.87 | 8.06 | 7.27 | 9.17 | 7.08 | 9.17 |
Feasible solutions | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
L1(DV)/m | 200.00 | 200.37 | 234.87 | 259.61 | 218.37 | 242.73 | 269.43 |
N(DV)/m | 0.92 | 0.99 | 1.01 | 1.15 | 1.08 | 2.57 | 2.10 |
Z1(DV)/m | 24.00 | 17.93 | 16.76 | 16.45 | 25.78 | 15.70 | 19.27 |
T1(DV)/m | 0.60 | 0.58 | 0.51 | 0.51 | 0.55 | 0.47 | 0.54 |
T2(DV)/m | 0.60 | 0.46 | 0.43 | 0.42 | 0.58 | 0.40 | 0.51 |
Z2(DV)/m | 12.00 | 13.53 | 12.92 | 12.98 | 11.08 | 14.22 | 14.24 |
H1(DV)/m | 14.00 | 12.51 | 14.51 | 14.85 | 13.47 | 11.59 | 10.02 |
H2(DV)/m | 10.00 | 8.47 | 7.71 | 7.55 | 7.53 | 8.07 | 7.35 |
VOLUME(DV) | 10.406 | 8.264 | 6.369 | 6.281 | 6.722 | 6.265 | 7.355 |
DISP(SV)/mm | −423 | −487 | −483 | −475 | −377 | −533 | −475 |
Design variable | Symbol | Optimum solution | Feasible solution range |
---|---|---|---|
Width of foot/m | Z1 | 22 | 15–22 |
Width of constant section /m | Z2 | 13 | 13–15 |
Height of foot /m | H1 | 15 | 12–15 |
Height of constant section /m | H2 | 7.5 | 6–8 |
variability index of width | N | 2.2 | 2–3 |
Length of variable section /m | L1 | 220 | 200–250 |
Thickness of roof and floor /m | T1 | 0.5 | 0.42–0.6 |
Thickness of web /m | T2 | 0.55 | 0.55–0.6 |
Arch axis coefficient | 1.6 | 1.8 | 2.0 | 2.20 |
---|---|---|---|---|
FREQN | 7.11 | 6.44 | 6.04 | 6.25 |
Vault deformation/mm | −401.67 | −398.24 | −429.90 | −463.15 |
Z1/m | 17.39 | 23.15 | 24.05 | 23.76 |
Z2/m | 10.26 | 11.13 | 11.00 | 11.07 |
H1/m | 14.90 | 12.91 | 12.86 | 12.65 |
H2/m | 8.36 | 7.60 | 7.03 | 7.40 |
Volume/m3 | 14462 | 14480 | 14014 | 14493 |
State variables | Symbol | Lower limit | Upper limit |
---|---|---|---|
Vault deformation/mm | DISP | −700 | −400 |
First order elastic stability coefficient | FREQN | 6 | |
Tensile stress of arch foot/MPa | SMAX1 | 0 | 1.7 |
Pressure stress of arch foot/MPa | SMAX2 | −27 | 0 |
Tensile stress of L/8/ MPa | SMAX3 | 0 | 1.7 |
Pressure stress of L/8 / MPa | SMAX4 | −27 | 0 |
Tensile stress of L/4/ MPa | SMAX5 | 0 | 1.7 |
Pressure stress of L/4/ MPa | SMAX6 | −27 | 0 |
Tensile stress of L3/8/ MPa | SMAX7 | 0 | 1.7 |
Pressure stress of L3/8/ MPa | SMAX8 | −27 | 0 |
Tensile stress of vault/MPa | SMAX9 | 0 | 1.7 |
Pressure stress of vault/MPa | SMAX10 | −27 | 0 |
Feasible solution | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
L1(DV)/m | 269.43 | 164.06 | 242.73 | 255.04 | 280.17 | 218.37 | 286.29 | 277.66 |
Z1(DV)/m | 23.47 | 19.57 | 18.88 | 21.92 | 20.38 | 21.18 | 23.48 | 15.03 |
Z2(DV)/m | 14.24 | 13.46 | 13.09 | 14.24 | 13.96 | 12.91 | 13.48 | 14.95 |
N1(DV) | 3.96 | 2.10 | 1.86 | 2.92 | 2.38 | 2.66 | 3.47 | 0.51 |
H1(DV)/m | 14.24 | 12.29 | 11.94 | 13.46 | 13.09 | 13.96 | 10.02 | 11.60 |
H2(DV)/m | 9.24 | 7.29 | 6.94 | 8.46 | 7.69 | 8.09 | 9.24 | 8.96 |
T1(DV)/m | 0.57 | 0.49 | 0.48 | 0.54 | 0.51 | 0.52 | 0.57 | 0.40 |
T2(DV)/m | 0.57 | 0.54 | 0.49 | 0.57 | 0.56 | 0.54 | 0.42 | 0.60 |
feasible solution | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
L1(DV)/m | 245.32 | 241.76 | 285.64 | 211.01 | 254.46 | 293.25 | 199.18 | 200.37 |
Z1(DV)/m | 19.69 | 18.20 | 22.93 | 20.82 | 21.95 | 15.70 | 24.90 | 23.04 |
Z2(DV)/m | 13.16 | 13.86 | 14.02 | 14.18 | 13.80 | 13.57 | 12.95 | 12.39 |
N1(DV) | 2.14 | 1.62 | 2.54 | 3.27 | 0.75 | 0.89 | 1.03 | 3.00 |
H1(DV)/m | 10.56 | 14.95 | 12.65 | 13.16 | 14.02 | 13.80 | 13.57 | 14.18 |
H2(DV)/m | 9.24 | 7.29 | 6.94 | 8.46 | 7.69 | 8.09 | 9.24 | 8.96 |
T1(DV)/m | 0.49 | 0.46 | 0.56 | 0.54 | 0.47 | 0.43 | 0.42 | 0.52 |
T2(DV)/m | 0.55 | 0.56 | 0.57 | 0.54 | 0.55 | 0.41 | 0.52 | 0.42 |
Material | Modulus of elasticity/(N/ | Mass density (kg/ | Coefficient of linear expansion | Poisson ratio |
---|---|---|---|---|
C80 | 3.80E10 | 2600 | 1.0E-5 | 0.2 |
C40 | 3.25E10 | 2500 | 1.0E-5 | 0.2 |
Design variables | Symbol | Lower limit | Upper limit |
---|---|---|---|
Width of foot/m | Z1 | 15 | 25 |
Width of constant section/m | Z2 | 10 | 15 |
Height of foot/m | H1 | 8 | 15 |
Height of constant section/m | H2 | 6 | 10 |
variability index of width | N | 0.5 | 5 |
Length of variable section/m | L1 | 100 | 300 |
Thickness of roof and floor/m | T1 | 0.4 | 0.6 |
Thickness of web/m | T2 | 0.4 | 0.6 |
Arch axis coefficient | 1.6 | 1.8 | 2 | 2.2 |
---|---|---|---|---|
L1/m | 137.84 | 163.33 | 180.98 | 217.00 |
N | 3.39 | 3.60 | 3.83 | 4.80 |
Volume/m3 | 14259 | 14698 | 14978 | 15622 |
FREQN | 6.58 | 6.60 | 6.60 | 6.79 |
Vault deformation/mm | −398 | −400 | −417 | −420 |