Figure 1.
A chart for effects of staircase on seismic behavior of structure and variables studied in defined groups
Figure 2.
Architectural plan of southern building with a width of 6 meter and staircase at corner
Figure 3.
Architectural plan of southern building with a width of 10 meter and staircase at corner
Figure 4.
Architectural plan of northern building with a width of 10 meter and staircase at the middle of length
Table 1.
Concrete and rebar properties
| Mass per unit volume kg/m3 | Modulus of Elasticity N/mm2 | Poisson’s Ratio- | f’c Concrete compressive Strength N/mm2 | fy Bending Reinforcement Yield Stress N/mm2 | fys Shear Reinforcement Yield Stress N/mm2 |
|---|---|---|---|---|---|
| 2500 | 24516 | 0.15 | 24.5 | 392 | 392 |
Table 2.
Period and mode shape of southern building with a width of 6 meter
| Mode 1 | Mode 2 | Mode 3 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | |
| Bare frame | 0.90 | X | 69.45 | 0.00 | 0.74 | Y | 0.03 | 68.82 | 0.70 | T | 1.15 | 1.04 |
| Frame with staircase slabs | 0.75 | X | 46.33 | 1.73 | 0.59 | Y | 14.37 | 47.47 | 0.52 | T | 12.26 | 24.05 |
| Frame with stringer beams | 0.93 | X | 71.58 | 0.05 | 0.72 | T | 0.29 | 14.12 | 0.62 | Y | 0.00 | 58.87 |
Figure 5.
Model of southern building with a width of 6 meter and staircase slabs
Figure 6.
Drift ratio of southern building with a width of 6 meter in X direction
Figure 7.
Drift ratio of southern building with a width of 6 meter in Y direction
Figure 8.
K-shaped bracing performance of staircase attached to the structure
Figure 9.
Southern building with a width of 10 meter; (a) All frames with the same dimension, (b) Frame with shorter length on the landing, (c) Both frames of staircase with shorter length
Figure 10.
Northern building with a width of 10 meter; (a) All frames with the same dimension, (b) Frame with shorter length on the landing, (c) Both frames of staircase with shorter length
Table 3.
Period and mode shape of southern building with a width of 10 meter and staircase at the corner
| Mode 1 | Mode 2 | Mode 3 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | |
| All frames the same | 1.01 | X | 73.76 | 0.00 | 0.97 | Y | 0.01 | 73.43 | 0.82 | T | 0.19 | 1.04 |
| One different frame | 0.97 | X | 68.80 | 3.93 | 0.95 | Y | 3.42 | 69.95 | 0.78 | T | 2.82 | 0.39 |
| Two different frames | 0.96 | X | 42.19 | 31.50 | 0.94 | Y | 30.81 | 43.05 | 0.78 | T | 2.81 | 0.00 |
Table 4.
Eccentricity of southern building with a width of 10 meter and staircase at the corner
| Story 1 | Story 2 | Story 3 | Story 4 | Story 5 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | |
| All frames the same | 4.26 | 6.61 | 2.65 | 6.50 | 2.32 | 5.58 | 1.88 | 5.01 | -1.46 | 2.28 |
| One different frame | 8.26 | 7.82 | 5.89 | 11.70 | 5.26 | 14.99 | 4.29 | 15.49 | 0.10 | 10.68 |
| Two different frames | 10.04 | 7.86 | 8.38 | 11.73 | 8.11 | 14.89 | 7.25 | 15.39 | 3.06 | 11.08 |
Table 5.
Ratio of the maximum relative story drift to the average relative story drift in story 3 of southern building with a width of 10 meter and staircase at the corner
| EQX | EQXP | EQXN | EQY | EQYP | EQYN | |
|---|---|---|---|---|---|---|
| All frames the same | 1.00 | 1.11 | 1.07 | 1.02 | 1.06 | 1.02 |
| One different frame | 1.21 | 1.12 | 1.30 | 1.00 | 1.04 | 1.02 |
| Two different frames | 1.21 | 1.12 | 1.29 | 1.02 | 1.01 | 1.05 |
Table 6.
Period and mode shape of northern building with a width of 10 meter and staircase at the middle of length
| Mode 1 | Mode 2 | Mode 3 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | |
| All frames the same | 1.00 | X | 73.01 | 0.14 | 0.90 | Y | 0.37 | 68.61 | 0.79 | T | 1.03 | 3.39 |
| One different frame | 0.96 | X | 69.28 | 2.24 | 0.91 | Y | 2.56 | 72.60 | 0.77 | T | 1.37 | 0.90 |
| Two different frames | 0.95 | X | 72.61 | 0.63 | 0.93 | Y | 0.68 | 75.46 | 0.77 | T | 0.98 | 0.14 |
Table 7.
Eccentricity of northern building with a width of 10 meter and staircase at the middle of length
| Story 1 | Story 2 | Story 3 | Story 4 | Story 5 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | |
| All frames the same | 2.12 | 1.23 | 0.96 | 3.99 | 2.54 | 2.81 | 3.49 | 2.02 | 5.62 | 2.50 |
| One different frame | 2.07 | 1.28 | 0.43 | 4.25 | 1.79 | 3.13 | 2.65 | 2.36 | 4.43 | 2.87 |
| Two different frames | 1.74 | 2.29 | -0.80 | 4.14 | 0.23 | 2.57 | 0.83 | 1.55 | 2.31 | 1.70 |
Table 8.
Ratio of the maximum relative story drift to the average relative story drift in story 2 of northern building with a width of 10 meter and staircase at the middle of length
| EQX | EQXP | EQXN | EQY | EQYP | EQYN | |
|---|---|---|---|---|---|---|
| All frames the same | 1.07 | 1.04 | 1.19 | 1.03 | 1.02 | 1.08 |
| One different frame | 1.08 | 1.21 | 1.03 | 1.01 | 1.01 | 1.06 |
| Two different frames | 1.07 | 1.03 | 1.19 | 1.00 | 1.04 | 1.04 |
Figure 11.
Southern building with a width of 6 meter; (a) Main moment frame, (b) Hinge connections on the side of staircase, (c) Extra column on the opposite side of the staircase, (d) Columns with larger cross section on the opposite side of the staircase
Table 9.
Period and mode shape of southern building with a width of 6 meter and staircase at the corner
| Mode 1 | Mode 2 | Mode 3 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | |
| (a) Main structure | 0.79 | X | 60.41 | 0.30 | 0.74 | Y | 0.33 | 69.75 | 0.61 | T | 10.69 | 0.02 |
| (b) Structure with Hinge connections | 0.90 | X | 69.45 | 0.00 | 0.74 | Y | 0.03 | 68.82 | 0.70 | T | 1.15 | 1.04 |
| (c) Structure with extra column | 0.74 | Y | 0.07 | 69.32 | 0.71 | X | 69.09 | 0.07 | 0.59 | T | 1.44 | 0.01 |
| (d) Structure with stronger columns | 0.74 | X | 63.85 | 2.70 | 0.73 | Y | 2.72 | 67.26 | 0.59 | T | 4.00 | 0.03 |
Table 10.
Eccentricity of southern building with a width of 6 meter and staircase at the corner
| Story 1 | Story 2 | Story 3 | Story 4 | Story 5 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | |
| (a) Main structure | -0.33 | 9.29 | -0.48 | 12.37 | -0.18 | 14.08 | -0.42 | 12.65 | 0.61 | 10.53 |
| (b) Structure with Hinge connections | -0.33 | 4.11 | -0.48 | 3.42 | -0.15 | 2.65 | -0.33 | 0.69 | 0.68 | -2.56 |
| (c) Structure with extra column | -0.26 | 7.42 | -0.51 | 6.89 | -0.26 | 6.55 | -1.05 | 5.98 | 0.06 | 5.37 |
| (d) Structure with stronger columns | -0.22 | -3.25 | -0.42 | 3.71 | -0.15 | 8.34 | -0.20 | 8.78 | 0.75 | 7.22 |
Table 11.
Ratio of the maximum relative story drift to the average relative story drift in story 3 of southern building with a width of 6 meter and staircase at the corner
| EQX | EQXP | EQXN | EQY | EQYP | EQYN | |
|---|---|---|---|---|---|---|
| (a) Main structure | 1.26 | 1.17 | 1.33 | 1.01 | 1.01 | 1.04 |
| (b) Structure with Hinge connections | 1.03 | 1.12 | 1.05 | 1.01 | 1.02 | 1.04 |
| (c) Structure with extra column | 1.06 | 1.04 | 1.13 | 1.01 | 1.02 | 1.03 |
| (d) Structure with stronger columns | 1.20 | 1.09 | 1.26 | 1.01 | 1.01 | 1.03 |
Table 12.
Period and mode shape of southern building with a width of 6 meter and staircase at the corner
| Mode 1 | Mode 2 | Mode 3 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | |
| (a) Bare frame | 0.90 | X | 69.45 | 0.00 | 0.74 | Y | 0.03 | 68.82 | 0.70 | T | 1.15 | 1.04 |
| (b) Bare frame with slabs of stair | 0.75 | X | 46.33 | 1.73 | 0.59 | Y | 14.37 | 47.47 | 0.52 | T | 12.26 | 24.05 |
| (c) Infilled frame | 0.75 | X | 72.73 | 0.00 | 0.48 | T | 0.84 | 0.72 | 0.42 | Y | 0.00 | 78.42 |
| (d) Infilled frame with slabs of stair | 0.60 | X | 69.86 | 0.01 | 0.43 | T | 4.44 | 5.72 | 0.38 | Y | 0.32 | 72.76 |
Table 13.
Eccentricity of southern building with a width of 6 meter and staircase at the corner
| Story 1 | Story 2 | Story 3 | Story 4 | Story 5 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | |
| (a) Bare frame | -0.33 | 4.11 | -0.48 | 3.42 | -0.15 | 2.65 | -0.33 | 0.69 | 0.68 | -2.56 |
| (b) Bare frame with slabs of stair | -7.05 | 13.96 | -12.17 | 18.51 | -13.03 | 19.89 | -13.98 | 19.94 | -14.09 | 18.70 |
| (c) Infilled frame | -0.37 | -0.08 | -0.44 | -0.04 | -0.07 | -1.22 | 0.51 | -2.87 | 2.17 | -5.76 |
| (d) Infilled frame with slabs of stair | -4.35 | 9.58 | -6.84 | 13.87 | -6.57 | 14.71 | -5.78 | 14.18 | -3.89 | 12.24 |
Table 14.
Ratio of the maximum relative story drift to the average relative story drift in story 3 of southern building with a width of 6 meter and staircase at the corner
| EQX | EQXP | EQXN | EQY | EQYP | EQYN | |
|---|---|---|---|---|---|---|
| (a) Bare frame | 1.03 | 1.12 | 1.05 | 1.01 | 1.02 | 1.04 |
| (b) Bare frame with slabs of stair | 1.43 | 1.33 | 1.52 | 1.12 | 1.20 | 1.10 |
| (c) Infilled frame | 1.07 | 1.12 | 1.01 | 1.04 | 1.04 | 1.08 |
| (d) Infilled frame with slabs of stair | 1.20 | 1.14 | 1.25 | 1.05 | 1.15 | 1.00 |
Table 15.
Period and mode shape of southern building with a width of 10 meter and staircase at the corner
| Mode 1 | Mode 2 | Mode 3 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | |
| (a) Bare frame | 1.01 | X | 73.76 | 0.00 | 0.97 | Y | 0.01 | 73.43 | 0.82 | T | 0.19 | 1.04 |
| (b) Bare frame with slabs of stair | 0.92 | X | 61.95 | 3.17 | 0.83 | Y | 8.78 | 57.92 | 0.69 | T | 4.47 | 15.91 |
| (c) Infilled frame | 0.89 | X | 74.93 | 0.00 | 0.62 | T | 1.36 | 3.37 | 0.59 | Y | 0.05 | 77.04 |
| (d) Infilled frame with slabs of stair | 0.84 | X | 71.22 | 0.08 | 0.59 | T | 4.24 | 26.98 | 0.53 | Y | 1.22 | 53.69 |
Table 16.
Eccentricity of southern building with a width of 10 meter and staircase at the corner
| Story 1 | Story 2 | Story 3 | Story 4 | Story 5 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | |
| (a) Bare frame | 4.26 | 6.61 | 2.65 | 6.50 | 2.32 | 5.58 | 1.88 | 5.01 | -1.46 | 2.28 |
| (b) Bare frame with slabs of stair | 10.70 | 11.64 | 13.24 | 12.40 | 15.63 | 12.62 | 17.38 | 12.92 | 17.27 | 11.12 |
| (c) Infilled frame | 4.03 | 9.49 | 2.51 | 11.47 | 4.52 | 12.57 | 6.19 | 13.48 | 6.02 | 12.48 |
| (d) Infilled frame with slabs of stair | 7.52 | 13.47 | 7.41 | 15.65 | 9.66 | 16.93 | 11.37 | 17.83 | 11.19 | 16.67 |
Table 17.
Ratio of the maximum relative story drift to the average relative story drift in story 3 of southern building with a width of 10 meter and staircase at the corner
| EQX | EQXP | EQXN | EQY | EQYP | EQYN | |
|---|---|---|---|---|---|---|
| (a) Bare frame | 1.00 | 1.11 | 1.07 | 1.02 | 1.06 | 1.02 |
| (b) Bare frame with slabs of stair | 1.14 | 1.06 | 1.24 | 1.15 | 1.09 | 1.18 |
| (c) Infilled frame | 1.12 | 1.06 | 1.18 | 1.00 | 1.02 | 1.10 |
| (d) Infilled frame with slabs of stair | 1.19 | 1.12 | 1.25 | 1.12 | 1.05 | 1.21 |
Table 18.
Period and mode shape of northern building with a width of 10 meter and staircase at the middle of length
| Mode 1 | Mode 2 | Mode 3 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | Period (s) | Dir. | UX | UY | |
| (a) Bare frame | 1.00 | X | 73.01 | 0.14 | 0.90 | Y | 0.37 | 68.61 | 0.79 | T | 1.03 | 3.39 |
| (b) Bare frame with slabs of stair | 0.87 | X | 73.39 | 0.03 | 0.81 | Y | 0.83 | 50.39 | 0.74 | T | 1.04 | 23.82 |
| (c) Infilled frame | 0.76 | X | 72.82 | 0.05 | 0.57 | Y | 1.29 | 63.40 | 0.53 | T | 3.28 | 15.78 |
| (d) Infilled frame with slabs of stair | 0.71 | X | 72.25 | 0.00 | 0.53 | Y | 0.30 | 74.46 | 0.52 | T | 4.53 | 5.22 |
Table 19.
Eccentricity of northern building with a width of 10 meter and staircase at the middle of length
| Story 1 | Story 2 | Story 3 | Story 4 | Story 5 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | %ex | %ey | |
| (a) Bare frame | 2.12 | 1.23 | 0.96 | 3.99 | 2.54 | 2.81 | 3.49 | 2.02 | 5.62 | 2.50 |
| (b) Bare frame with slabs of stair | -1.86 | -0.21 | -6.00 | 2.87 | -6.97 | 1.83 | -7.82 | 1.09 | -8.07 | 1.43 |
| (c) Infilled frame | 2.36 | 3.28 | 1.59 | 7.73 | 2.95 | 8.11 | 3.67 | 8.47 | 5.71 | 10.22 |
| (d) Infilled frame with slabs of stair | 0.15 | 2.01 | -1.87 | 6.67 | -1.06 | 7.08 | -0.59 | 7.45 | 1.21 | 9.14 |
Table 20.
Ratio of the maximum relative story drift to the average relative story drift in story 3 of northern building with a width of 10 meter and staircase at the middle of length
| EQX | EQXP | EQXN | EQY | EQYP | EQYN | |
|---|---|---|---|---|---|---|
| (a) Bare frame | 1.05 | 1.08 | 1.18 | 1.05 | 1.00 | 1.09 |
| (b) Bare frame with slabs of stair | 1.03 | 1.12 | 1.18 | 1.09 | 1.13 | 1.03 |
| (c) Infilled frame | 1.17 | 1.08 | 1.29 | 1.07 | 0.98 | 1.16 |
| (d) Infilled frame with slabs of stair | 1.18 | 1.08 | 1.27 | 0.98 | 1.05 | 1.07 |
Figure 12.
Shear distribution under seismic force along Y direction (ton): (Left side) Model without stair case, (Right side) Model with staircase
Figure 13.
Moment distribution under seismic force along Y direction (ton.m): (Left side) Model without stair case, (Right side) Model with staircase
Figure 14.
Shear distribution under seismic force along X direction (ton): (Left side) Model without stair case, (Right side) Model with staircase
Figure 15.
Moment distribution under seismic force along X direction (ton.m): (Left side) Model without stair case, (Right side) Model with staircase
Figure 16.
Staircase isolated from master structure