Equivalent Lateral Force Method (ELF) per ASCE 7-16 §12.8

Symbols

C_s = The seismic response coefficient
W = The effective seismic weight
S_DS = The design spectral response acceleration parameter in the short period range
R = The response modification factor in Table 12.2-1
I_e = The Importance Factor
S_D1 = the design spectral response acceleration parameter at a period of 1.0 s
T = The fundamental period of the structure(s)
T_L = The long-period transition period(s)
S₁ = The mapped maximum considered earthquake spectral response acceleration parameter
N = Number of stories above the base
C_q =0.0019 ft (0.00058 m)
A_B = area of base of structure [ft² (m²)];
A_i = web area of shear wall i [ft² (m²)];
D_i = length of shear-wall i [ft (m)]; and
x = number of shear walls in the building effective in resisting lateral forces in the direction under consideration.
F_i = The portion of the seismic base shear (V) [kip (kN)] induced at level i
C_vx = vertical distribution factor
V = total design lateral force or shear at the base of the structure [kip (kN)];
w_i and w_x = portion of the total effective seismic weight of the structure (W) located or assigned to level i or x;
h_i and h_x = height [ft (m)] from the base to level i or x; and
k = an exponent related to the structure period

The equivalent Lateral Force Method is based on the principle that the dynamic behavior of the building in the direction of the earthquake considered in buildings with low height is represented by the behavior of the structural system in the dominant vibration mode, and the shape of this mode is considered as an approximately inverted triangle. The Equivalent Lateral Force Method is only used to determine structural irregularities.

Seismic Base Shear

The seismic base shear, V, in the earthquake direction considered, is determined by the following equation.

Seismic Response Coefficient

The seismic response coefficient, C_s, is determined by the following equation.

The value of C_s computed with Eq. (12.8-2) need not exceed the following:

for T ≤ T_L

for T > T_L

C_s should not be less than

Period Determination

The fundamental period, T, does not exceed the product of the coefficient for the upper limit on the calculated period (C_u) from Table 12.8-1, and the approximate fundamental period, T_a, is determined in accordance with ASCE 7-16 Section 12.8.2.1.

Approximate Fundamental Period

The approximate fundamental period (T_a), in seconds, is determined by the following equation.

Vertical Distribution of Seismic Forces

The lateral seismic force (F_x) (kip or kN) induced at any level is determined from eq 12.8-11 and 12.8-12:

k = an exponent related to the structure period as follows:
• for structures that have a period of 0.5 s or less, k = 1;
• for structures that have a period of 2.5 s or more, k = 2; and
• for structures that have a period between 0.5 and 2.5 s, k shall be 2 or shall be determined by linear
interpolation between 1 and 2.