Question 6.5: For the seven-story office building in Example 6.3, check th......
For the seven-story office building in Example 6.3, check the story drift limits in both the N-S and E-W directions. For illustration purposes, use the lateral deflections determined by the equivalent lateral force procedure.
1. Drift limits in N-S direction.
To check drift limits, the deflections determined by Eq. 12.8-15 must be used:
\delta_{x}=\frac{C_{d}{\delta}_{xe}}{I}The maximum story displacements δ_{xe} in the N-S direction are summarized in Table 6.12. For special steel concentrically braced frames, the deflection amplification factor C_d is equal to 5 from Table 12.2-1.
A summary of the displacements at each floor level in the N-S direction is given in Table 6.13.
The interstory drifts Δ computed from the δ_{x} are also given in the table. The drift at story level x is determined by subtracting the design earthquake displacement at the bottom of the story from the design earthquake displacement at the top of the story:
\Delta=\delta_{x}-\delta_{x-1}The design story drifts Δ shall not exceed the allowable story drift Δ_a given in Table 12.12-1. For Occupancy Category II and “all other structures,” Δ_a = 0.020h_{sx} where h_{sx} is the story height below level x.
For the 18-ft story height, Δ_a = 0.020×18×12 = 4.32 in. > 2.30 in.
For the 13-ft story heights, Δ_a = 0.020×13×12 = 3.12 in., which is greater than the values of Δ at floor levels 2 through 7.
Thus, drift limits are satisfied in the N-S direction.
2. Drift limits in the E-W direction.
The maximum story displacements δ_{xe} in the N-S direction are summarized in Table 6.12. For special steel moment frames, the deflection amplification factor C_d is equal to 5.5 from Table 12.2-1.
A summary of the displacements at each floor level in the E-W direction is given in Table 6.14. The interstory drifts Δ computed from the δ_{x} are also given in the table.
In accordance with 12.12.1.1, design story drifts Δ must not exceed Δ_a /ρ for seismic force-resisting systems comprised solely of moment frames in structures assigned to SDC D, E or F where ρ is the redundancy factor determined in accordance with 12.3.4.2.
Due to the Type 1b extreme torsional irregularity, ρ must be equal to 1.3. Therefore, for the 18-ft story height, Δ_a /ρ = 0.020×18×12/1.3 = 3.32 in. < 3.41 in.
For the 13-ft story heights, Δ_a /ρ = 0.020×13×12/1.3 = 2.40 in., which is less than the design drifts at stories 2 through 6.
Thus, drift limits are not satisfied in the N-S direction. Increasing member sizes may not be sufficient to reduce the design drift; including additional members in the seismic force-resisting system may be needed to control drift. This, in turn, may help reduce the torsional effects.
Table 6.13 Lateral Displacements and Story Drifts due to Seismic Forces in the N-S Direction
| Story | δ_{xe} (in.) |
δ_{x} (in.) |
Δ (in.) |
| 7 | 1.59 | 7.95 | 0.70 |
| 6 | 1.45 | 7.25 | 0.85 |
| 5 | 1.28 | 6.40 | 1.10 |
| 4 | 1.06 | 5.30 | 1.05 |
| 3 | 0.85 | 4.25 | 1.10 |
| 2 | 0.63 | 3.15 | 0.85 |
| 1 | 0.46 | 2.30 | 2.30 |
Table 6.14 Lateral Displacements and Story Drifts due to Seismic Forces in the E-W Direction
| Story | δ_{xe} (in.) |
δ_{x} (in.) |
Δ (in.) |
| 7 | 5.36 | 29.48 | 1.98 |
| 6 | 5.00 | 27.50 | 2.69 |
| 5 | 4.51 | 24.81 | 3.91 |
| 4 | 3.80 | 20.90 | 6.05 |
| 3 | 2.70 | 14.85 | 6.54 |
| 2 | 1.51 | 8.31 | 4.90 |
| 1 | 0.62 | 3.41 | 3.41 |
Table 6.12 Lateral Displacements and Story Drifts due to Seismic Forces
| Story | N-S Direction | E-W Direction | ||||||||||
| (δ_\mathrm{xe})_1 (in.) |
Δ_1 (in.) |
(δ_\mathrm{xe})_2 (in.) |
Δ_2 (in.) |
Δ_\mathrm{avg} (in.) |
\frac{Δ_\mathrm{max}}{Δ_\mathrm{avg}} | (δ_\mathrm{xe})_1 (in.) |
Δ_1 (in.) |
(δ_\mathrm{xe})_2 (in.) |
Δ_2 (in.) |
Δ_\mathrm{avg} (in.) |
\frac{Δ_\mathrm{max}}{Δ_\mathrm{avg}} | |
| 7 | 1.59 | 0.14 | 1.23 | 0.12 | 0.13 | 1.08 | 5.36 | 0.36 | 5.22 | 0.34 | 0.35 | 1.03 |
| 6 | 1.45 | 0.17 | 1.11 | 0.15 | 0.16 | 1.06 | 5.00 | 0.49 | 4.88 | 0.47 | 0.48 | 1.02 |
| 5 | 1.28 | 0.22 | 0.96 | 0.20 | 0.21 | 1.05 | 4.51 | 0.71 | 4.41 | 0.71 | 0.71 | 1.00 |
| 4 | 1.06 | 0.21 | 0.76 | 0.19 | 0.20 | 1.05 | 3.80 | 1.10 | 3.70 | 1.06 | 1.08 | 1.02 |
| 3 | 0.85 | 0.22 | 0.57 | 0.17 | 0.19 | 1.16 | 2.70 | 1.19 | 2.64 | 1.16 | 1.17 | 1.02 |
| 2 | 0.63 | 0.17 | 0.40 | 0.22 | 0.19 | 1.16 | 1.51 | 0.89 | 1.48 | 0.87 | 0.88 | 1.01 |
| 1 | 0.46 | 0.46 | 0.18 | 0.18 | 0.32 | 1.44 | 0.62 | 0.62 | 0.61 | 0.61 | 0.61 | 1.02 |