(Ethiopian Building Code Standard - 1995)

Summary of EBCS-8-95 Equivalent Static Force Procedure and Dynamic Analysis

(A)  Equivalent Static Force Analysis

This method is deemed applicable when regularity conditions stipulated in the code are met and the fundamental periods of vibration T in the two main directions are less than 2 seconds.

The seismic base shear force F_b for each main direction is determined from:

F_b = S_d(T₁) W

Where,

 S_d(T₁) - is the ordinate of the design spectrum as given in Equation 1.1 at period ‘T₁’.

T₁       - is the fundamental period of vibration of the structure for translational motion in the direction considered,

W          - is the seismic dead load computed in accordance with Clause 1.4.3(3), i.e., the total permanent load for all occupancies except for storage and warehouse. In storage and warehouses, 25% of the floor variable (live) load is added to the total permanent load.

Determining S_d(T₁)

 For linear analysis, the design spectrum S_d(T)  normalized by the acceleration of gravity g is defined by the following expression:

Sd(T) = abg                           (Equation 1.1)

Where a is the ratio of the design bedrock acceleration to the acceleration of gravity g and is given by:

a = a_oI                                                 (Equation 1.2) 

Where a_o is the bedrock acceleration ratio for the site and depends on the seismic zone as given in Table 1.1 shown below:

I is the importance factor given in Table 2.4 of EBCS-8.  For ordinary buildings, I is 1.0 whereas for such structures as hospitals, fire stations, etc, I is as high as 1.4.

The parameter b is the design response factor for the site and is given by Equation (1.3):

b = 1.2S/T^2/3 <= 2.5               (Equation 1.3)

S is the site coefficient for soil characteristics given in Table 1.2.

S = 1.0 for subsoil class A

   = 1.2 for subsoil class B, and

   = 1.3 for subsoil class C.

g is the “behavior factor” that is an approximation of the ratio of the minimum seismic forces that may be used in design with a conventional linear model (still ensuring a satisfactory response of the structure), to the seismic forces that the structure would experience if the response was completely elastic with 5% viscous damping.

As a limiting case, for the design of non-dissipative structures, g is taken as 1.0. For dissipating structures, the behavior factor is taken smaller than 1.0 accounting for the hysteretic energy dissipation. 

For concrete structures, 

g = g_o k_D k_R k_W < = 0.70                                    (Equation 3.2) 

The different constants are defined in Section 3.3 of EBCS-8.  

Typical values of the different constants are as given below:

go = 0.2 for frame systems, 0.2 for dual systems and 0.3 for core systems.

k_D = 1.00, 1.50 or 2.0,

k_R = 1.00 for regular structures, and 1.25

k_W = 1.00 for frame and frame equivalent dual systems, >= 1 for core-systems. 

For steel buildings,

EBCS-6 gives the g  values in Section 4.3.

Typical values are:

g = 0.18 (moment resisting frames)

   = 0.25 (concentric braced frames)

   = 0.20 (V-bracing, invert3d Chevron)

   = 1.00 (K-bracing)

   = 0.17 (EBF) etc.

The period T may be determined by:

a)      Methods or expressions based on structural dynamics (eigenvalue or Raleigh method). (Method A)

b)      In lieu of the above, approximate expressions given below may be used: (Method B)

 T = C H^3/4      (Equation 2.3)

Where T is the period of the building in seconds and H is the height above the base in meters. H should not exceed 80 meters and

C = 0.085 for steel MRFs

    = 0.075 for concrete MRFs and steel EBFs

    = 0.050 for all other buildings.

Alternatively, T could be determined approximately from

T = 2*Sqrt(d)       (Equation 2.5)

where d is the lateral displacement at the top of the building when subjected to gravity loads applied horizontally.

The base shear is distributed over the height of the structure as:

F_b = F_t + S Fi, i =1 to n

Where F_t = 0.07*T*Fb

F_i = (F_b – F_t) * W_ih_i / SW_jh_j

 (B)  Dynamic Response Spectra Analysis

For buildings with plan regularity, a 2-Dimensional model can be used for analysis. However, for buildings with plan and elevation irregularity, 3-Dimensional models are required. 

At least 90% modal mass participation is required. In addition, it is required to demonstrate that all modes with effective modal masses greater than 5% are considered.

In buildings with significant torsional modes where the above condition could not be met(?), the minimum number of modes, k, to be considered should satisfy the following conditions:

k >= 3*Sqrt(n)

Tk <= 0.2sec

The code allows SRSS scheme of modal combinations if

T_j <= 0.9T_i.

Otherwise, CQC has to be used.