Question 6.6: For the seven-story office building in Example 6.3, determin......

1. P-delta effects in the N-S direction.

In lieu of automatically considering P-delta effects in a computer analysis, the following procedure can be used to determine whether P-delta effects need to be considered in accordance with 12.8.7.

P-delta effects need not be considered when the stability coefficient θ determined by Eq. 12.8-16 is less than or equal to 0.10:

where P_x = total unfactored vertical design load at and above level x
\qquad\quad Δ = design story drift occurring simultaneously with V_x
\qquad\quad V_x = seismic shear force acting between level x and x–1
\qquad\quad h_{sx} = story height below level x
\qquad\quad C_d = deflection amplification factor in Table 12.2-1

The stability coefficient θ must not exceed \theta_{\mathrm{max}} determined by Eq. 12.8-17:

Where β is the ratio of shear demand to shear capacity between level x and x–1, which may be taken equal to 1.0 when it is not calculated.

The P-delta calculations for the N-S direction are shown in Table 6.15. It is clear that P-delta effects need not be considered at any of the floor levels. Note that \theta_{\mathrm{max}} is equal to 0.1000 in the N-S direction using β = 1.0.

2. P-delta effects in the E-W direction.

The P-delta calculations for the E-W direction are shown in Table 6.16. Note that \theta_{\mathrm{max}} is equal to 0.0909 in the E-W direction using β = 1.0, and, since θ is greater than \theta_{\mathrm{max}} at levels 2 through 4, the structure is potentially unstable and needs to be redesigned. It was determined in Example 6.4 that the shear capacity of the second floor is equal to 780 kips. Thus, β = 474 / 780 = 0.61, and \theta_{\mathrm{max}} = 0.5 /(0.61×5.5) = 0.15 . Assuming the same shear capacities at levels 3 and 4, \theta_{\mathrm{max}} = 0.16 at level 3 and \theta_{\mathrm{max}} = 0.18 at level 4. Therefore, the structure is still potentially unstable.