**8. Analyze building response**

Simplified analysis is used to generate median estimates of peak transient drift, peak floor accelerations and residual drifts. Associated dispersions are generated using simplified analysis. Peak total floor velocities are not generated since none of the vulnerable building components use this demand parameter. A linear building model is constructed using the modeling criteria of [8], linear static procedure.

#### **8.1 Estimate median story drift ratio**

Firstly, we determined the pseudo lateral force by the formula:

$$\mathbf{V} = \mathbf{C\_1}\mathbf{C\_2}\mathbf{S\_a}(T\_1)\mathbf{W\_1} \tag{3}$$

where C1 is an adjustment factor for inelastic displacements; C2 is an adjustment factor for cyclic degradation; Sa(T1) is the 5% damped spectral acceleration at the

*Performance-Based Design for Healthcare Facilities DOI: http://dx.doi.org/10.5772/intechopen.95320*


<sup>T</sup> <sup>¼</sup> *Tx* <sup>þ</sup> *Ty*

Firstly, we determined the pseudo lateral force by the formula:

Simplified analysis is used to generate median estimates of peak transient drift, peak floor accelerations and residual drifts. Associated dispersions are generated using simplified analysis. Peak total floor velocities are not generated since none of the vulnerable building components use this demand parameter. A linear building model is constructed using the modeling criteria of [8], linear static procedure.

where C1 is an adjustment factor for inelastic displacements; C2 is an adjustment factor for cyclic degradation; Sa(T1) is the 5% damped spectral acceleration at the

**8. Analyze building response**

*Natural Hazards - Impacts, Adjustments and Resilience*

**Figure 22.**

**244**

*SPO2IDA tool, SPO tab.*

**8.1 Estimate median story drift ratio**

<sup>2</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>96</sup> *sec* (2)

*V* ¼ *C***1***C***2***Sa*ð Þ *T***<sup>1</sup>** *W***<sup>1</sup>** (3)

fundamental period of the building, in the direction under consideration, for the selected level of ground shaking; and W1 is the first modal effective weight in the direction under consideration, taken as not less than 80% of the total weight, W.

**Figures 27** and **28** and **Table 3** show the computed lateral displacement in X (2) direction and the corresponding drift ratio.

$$
\Delta\_i^\* = H\_{\Delta i}(\mathbb{S}, T\_1, h\_i, H) \times \Delta\_i \, i = \mathbf{1} \text{to} \mathbf{N} \tag{4}
$$

where *H<sup>Δ</sup><sup>i</sup> S*, *T*1, *hi* ð Þ , *H* is the drift modification factor for story *i* computed.

$$\ln\left(H\_{\Delta i}\right) = a\_0 + a\_1 T\_1 + a\_2 \mathcal{S} + a\_3 \frac{h\_{i+1}}{H} + a\_4 \left(\frac{h\_{i+1}}{H}\right)^2 + a\_5 \left(\frac{h\_{i+1}}{H}\right)^3, \mathcal{S} \succeq 1, i = 1 \text{ to } N \tag{5}$$

With

$$T\_1 = \textbf{1.96s}, H = \textbf{24.6m}$$

Values of *a*<sup>0</sup> through *a*<sup>5</sup> for 6 stories or less in height are provided in [1] Table 5-4 by using the strength ratio given by:

**Figure 24.** *PACT collapse fragility tab.*

**Figure 25.** *Selected 11 earthquake ground motions response spectrum scaled according to the design spectra.*

$$\mathcal{S} = \frac{\mathcal{S}\_a(T)V}{V\_{y1}}\tag{6}$$

*a*∗

*hi* þ 1 *<sup>H</sup>* <sup>þ</sup> *<sup>a</sup>*<sup>4</sup>

**8.3 Estimate of dispersion for median story ratio, median peak floor**

**acceleration, and median peak floor velocity**

acceleration, *βFA*, and floor velocity, *βFV*, are needed.

*ln H*ð Þ¼ *ai a*<sup>0</sup> þ *a*1*T*<sup>1</sup> þ *a*2*S* þ *a*<sup>3</sup>

*SAP2000 lateral force applied.*

**Table 5-4**.

**247**

**Figure 27.**

**Figure 26.**

*Mean matched Spectrum.*

*Performance-Based Design for Healthcare Facilities DOI: http://dx.doi.org/10.5772/intechopen.95320*

*<sup>i</sup>* ¼ *Hai S*, *T*1, *hi* ð Þ� , *H PGA i* ¼ 2*toN* þ 1 (7)

þ *a*<sup>5</sup>

*hi* þ 1 *H* <sup>3</sup>

, *S*≥1, *i* ¼ 1*toN*

(8)

*hi* þ 1 *H* <sup>2</sup>

The coefficients of a0 through a5 for 6 stories or less in height are provided in [1]

For intensity-based, separate values of total dispersion for drift ratio, *βSD*, floor

The value of *Vy1* is taken from the pushover analysis used to estimate the collapse fragility (see SPO2IDA input, **Figure 22**, Elastic Segment end point) (**Table 4**).
