CALCULATE EARTHQUAKE FORCES ON BUILDINGS AND STRUCTURES

Earthquake resistant design of structures have become integral part of structural design of any structure. The guide to earthquake resistant design of building and structures are given by IS1893 – 2002 in India. Here we will talk about how to calculate the earthquake forces for buildings and structures as per above mentioned code.
First step to calculate earthquake loads on structure is to identify the earthquake zone for which structure needs to be designed. This earthquake zones are displayed in a map on page – 6 of the code.
After earthquake zone has been identified, the following steps are followed:
1. Calculate design horizontal seismic coefficient, A_h, which is given by (cl. 6.4.2 of IS1893 – 2002:

Where, Z is the zone factor, given in table 2 of IS1893 – 2002.
I is the importance factor of the structure depending on the function or use. This factor can be obtained from table 6 of the code.
R is response reduction factor. This value is obtained from table 7 of the code. The value of 1/R shall not be more than one.
S_a/g is average response acceleration coefficient. This value depends on time period of structure and on soil type. This can be obtained from clause 6.4.5 of the code.
2. Calculate design seismic base shear for the structure (V_B). This is the total design lateral force along any principal direction. This is calculated as:
V_B = A_h x W
Where A_h = horizontal seismic coefficient as calculated above in step 1.
W = Total weight of the structure.
3. Now calculate the distribution of design forces on the structure. The seismic design base shear calculate in step above is distributed on the structure as design seismic forces. This is calculated as below:

Where Q_i = Design lateral force at floor i
W_i = seismic weight of the floor i
h_i = height of the floor i from the base
n = number of storeys of the building at which masses are located.
4. Distribution of horizontal seismic forces on structure: These forces are distributed on the vertical elements of the building resisting lateral forces.
Example:
Consider a two-bay two-storied building for which earthquake forces need to be calculated. Consider total weight of the building as 1000 kN. Top roof has the weight of 200 kN and both floors have weight of 400 kN as shown in figure below. The calculation of earthquake seismic forces will be as shown below:

	Total Weight of the Structure < ?xml:namespace prefix = "o" />			Wi =	1000	kN
	Zone Factor (Zone IV)			Z =	0.24
	Importance factor (Table6)			I =	1
	Response Reduction Factor			R =	3
	Average response acceleration coefficient
		Let time period		T	0.373358	(Cl. 7.6)
				Sa/g	2.5
	Design Horizontal Seismic coefficient Ah				0.10
	Base Shear				100	kN
Storey	Base Shear	Height	Wi	Wixhi2	Qi	Design Force
3	100	8.5	200	14450	57.00197	9.50
2	100	5	400	10000	39.44773	6.57
1	100	1.5	400	900	3.550296	0.59
			Total	25350		(in kN)