# How to Calculate Seismic Design Category

How to Calculate Seismic Design Category
Engr. Ubaid Ahmad Mughal

Calculation of seismic design category for Lahore, Peshawar, Quetta, Karachi and Azad Kashmir and comparing the accelerations with UBC-97 Code.

Step 1
Determine the Coordinates of All cities by using the following website
http://www.worldatlas.com/aatlas/latitude_and_longitude_finder.htm

 Lahore Quetta Peshawar Karachi Azad Kashmir Latitude 31° 32′ 59″ N 30° 12′ 0″ N 34° 0′ 29″ N 24° 52′ 0″ N 33° 53′ N Longitude 74° 20′ 37″ E 67° 0′ 0″ E 71° 34′ 22″ E 67° 3′ 0″ E 73° 56′ E

Step 2

Convert DMS coordinates to Decimal coordinates By using the website
http://transition.fcc.gov/mb/audio/bickel/DDDMMSS-decimal.html

 Lahore Quetta Peshawar Karachi Azad Kashmir Latitude 31.549722 N 30.2 N 34.008056  N 24.866667 N 33.883333 N Longitude 74.343611 E 67 E 71.572778  E 67.05 E 73.933333 E

Step 3

Determine the Values of Ss and S1 by entering the coordinates on the following link
https://geohazards.usgs.gov/secure/designmaps/ww/application.php

 Lahore Quetta Peshawar Karachi Azad Kashmir Latitude 31.549722 N 30.2 N 34.008056  N 24.866667 N 33.883333 N Longitude 74.343611 E 67 E 71.572778  E 67.05 E 73.933333 E Ss 0.57 1.02 0.66 0.74 0.65 S1 0.15 0.32 0.21 0.29 0.19

We have not been given the nature of occupancy so let’s assume it’s a minor storage facility (Occupancy = 1) and similarly any detail of soil type or any geotechnical report has not been given so the Site class we take is D.

Step # 4
Determine Site Class Coefficients Fa and Fv

 Lahore Quetta Peshawar Karachi Azad Kashmir Ss 0.57 1.02 0.66 0.74 0.65 Fa 1.344 1.092 1.272 1.208 1.279 S1 0.15 0.32 0.21 0.29 0.19 Fv 2.2 1.76 1.98 1.82 2.04

Note:  The Values of Fa and Fv are calculated from the Table 1613.5.3(1) & 1613.5.3(2) by using the method of linear interpolation. The formula of which is given as under.
Y = ( ( X – X1 )( Y2 – Y1) / ( X2 – X1) ) + Y1
Where,
X1,Y1 = First co-ordinates,
X2,Y2 = Second co-ordinates,
X = Target X co-ordinate,
Y = Interpolated Y co-ordinate.
Source : http://easycalculation.com/analytical/linear-interpolation.php

Step # 5

Calculate maximum considered earthquake spectral response acceleration for short period SMS and for 1-second period SM1
SMS = FA * SS
SM1 = FV * S1

 Ss Fa SMS S1 FV SM1 Lahore 0.57 1.344 0.766 0.15 2.2 0.330 Quetta 1.02 1.092 1.114 0.32 1.76 0.563 Peshawar 0.66 1.272 0.840 0.21 1.98 0.416 Karachi 0.74 1.208 0.894 0.29 1.82 0.528 Azad Kashmir 0.65 1.279 0.831 0.19 2.04 0.388

Step # 6
Calculate Design spectral response acceleration parameters at short period SDS and 1-sec period SD1 from the following Equations.
SDS = (2/3)*(SMS)
SD1 = (2/3)*(SM1)

 Ss Fa SMS S1 FV SM1 SDS SD1 Lahore 0.57 1.344 0.766 0.15 2.2 0.330 0.511 0.220 Quetta 1.02 1.092 1.114 0.32 1.76 0.563 0.743 0.375 Peshawar 0.66 1.272 0.840 0.21 1.98 0.416 0.560 0.277 Karachi 0.74 1.208 0.894 0.29 1.82 0.528 0.596 0.352 Azad Kashmir 0.65 1.279 0.831 0.19 2.04 0.388 0.554 0.259

Step # 7
Determination of seismic design category SDC from 1613.5.6(1)&(2)

Comparison with UBC-97 and Building Code of Pakistan

 SDS SD1 SDC UBC-97 Building Code of Pakistan Zone Value Zone Value Lahore 0.511 0.220 D 2A 0.15 2B 0.2 Quetta 0.743 0.375 D 4 0.4 4 0.4 Peshawar 0.560 0.277 D 4 0.4 2B 0.2 Karachi 0.596 0.352 D 4 0.4 2B 0.2 Azad Kashmir 0.554 0.259 D 4 0.4 4 0.4

Details:

According to UBC-97 seismic zone for Islamabad, Karachi, Azad kashmir & Peshawar is 4 where as for Lahore it is 2A. But according to IBC we have calculated Lahore, Karachi & Peshawar in Zone 2B Azad Kashmir is coming in zone 3 it should be in zone 4 due to the fact that some parts of it can experience zone 4 ground accelerations similarly Quetta lies in Zone 4. Whereas if we compare our values with Pakistan building code then Lahore, Karachi and Peshawar comes in Zone 2B where Azad Kashmir and Quetta comes in zone 4. This matches our calculation. As the Zone increases the danger is also increased similarly as the value of ground acceleration increases the more devastation it may cause.

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