**(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}(T_{1})
W

Where,

_{d}(T_{1}) -
is the ordinate of the design spectrum as given in Equation 1.1 at period ‘T_{1}’.

T_{1} - 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.

_{d}(T_{1})

_{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_{o}I
(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:

Zone |
4 |
3 |
2 |
1 |

a |
0.1 |
0.07 |
0.05 |
0.03 |

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)

^{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.

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

_{t} = 0.07*T*Fb

F_{i} = (F_{b} – F_{t})
* W_{i}h_{i} / SW_{j}h_{j}

** (B) Dynamic Response Spectra
Analysis**

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

_{j} <= 0.9T_{i}.