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

For intensity-based, separate values of total dispersion for drift ratio, *βSD*, floor acceleration, *βFA*, and floor velocity, *βFV*, are needed.

*<sup>S</sup>* <sup>¼</sup> *Sa*ð Þ *<sup>T</sup> <sup>V</sup> Vy*<sup>1</sup>

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

**8.2 Estimate peak floor acceleration**

ground acceleration using:

**Figure 24.**

**Figure 25.**

**246**

*PACT collapse fragility tab.*

*Natural Hazards - Impacts, Adjustments and Resilience*

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**).

At the base of the building, peak floor acceleration is taken as equal to the peak ground acceleration. At other floor levels, *i*, the estimated median peak floor acceleration, *a*\*(**Table 5**) relative to a fixed point in space, is derived from the peak

(6)

These are calculated based on [1] Table 5-6 values for analysis record- to-record

Since the requirements for direct simulation of residual drift are computationally complex and not practical for general implementation in design, the following equations were developed to estimate the median residual drift ratio, response of

**Δ<sup>r</sup>** ¼ **0 for Δ** ≤ **Δ<sup>y</sup>**

where Δ is the median story drift ratio calculated by analysis, and Δ *y* is the

The peak transient drift ratios were estimated. The yield drift ratio is obtained from the capacity curve derived from the pushover analysis used to generate the

At yield, the peak transient acceleration is determined by the equation for the

From the capacity curve, the corresponding roof displacement for the peak transient acceleration at yield then is 0.0045 m. Thus, the yield drift ratio is:

The maximum transient drift ratio for the building occurs at the first story

*Δ<sup>r</sup>* ¼ ð0*:*0090–3 ∗ 0*:*0002Þ ¼ 0*:*0084

for <sup>Δ</sup> <sup>≥</sup>4Δy<sup>Þ</sup>

for <sup>Δ</sup><sup>y</sup> <sup>&</sup>lt; <sup>Δ</sup> <sup>&</sup>lt;4ΔyÞg (12)

*<sup>T</sup>* <sup>¼</sup> **<sup>0</sup>***:***755g** (13)

<sup>24</sup>*:*<sup>6</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>0002</sup> (14)

dispersion for drift, *βaΔ*, acceleration, *βaa*, and velocity, *βav*, respectively, by

**9. Estimate median residual story drift ratio and dispersion**

fΔ<sup>r</sup> ¼ 0*:*3 Δ � Δ<sup>y</sup>

median story drift ratio calculated at yield.

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

story shear at yield (**Figure 29**).

(*Δ*= 0.0090).

**Figure 29.**

**249**

*Capacity curve from pushover analysis.*

Δ<sup>r</sup> ¼ Δ � 3Δ<sup>y</sup>

building fundamental period between the range of 0.7 sec to 2 sec:

*Sa*ð Þ¼ *<sup>T</sup> Sa*ð Þ**<sup>1</sup>**

*<sup>Δ</sup><sup>y</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>0045</sup>

interpolation approach.

the structure:

**Figure 28.** *X-X deformed shape.*


#### **Table 4.**

*Median story drift ratio estimates.*


#### **Table 5.** *Median floor acceleration estimates.*

*βSD* ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *βa<sup>Δ</sup>* <sup>2</sup> <sup>þ</sup> *<sup>β</sup><sup>m</sup>* 2 q (9)

$$
\beta\_{\rm FA} = \sqrt{\beta\_{aa}^{'}^{2} + \beta\_{m}^{'}^{2}} \tag{10}
$$

$$
\beta\_{\rm FV} = \sqrt{\beta\_{a\Delta}^{\prime}^{2} + \beta\_{m}^{\prime}^{\prime}^{2}} \tag{11}
$$

These are calculated based on [1] Table 5-6 values for analysis record- to-record dispersion for drift, *βaΔ*, acceleration, *βaa*, and velocity, *βav*, respectively, by interpolation approach.
