Analysis of 2D frame using equivalent lateral forces and time history analysis

Introduction 

This building can be classified as a moment resisting frame. First and second floors have (30x35) cm beams and (50x50) cm columns, third and fourth floors have same previous beams dimensions and (40x50) cm columns. 

Numerical Model 

In our numerical model equivalent lateral forces, spectral analysis and time history analysis have been used according to UBC-97 provisions.

Fig-1 : Numerical model of the frame

Equivalent lateral force

In order to use this method of analysis using SAP2000 software these factors were inserted:

- Seismic dead load (W)
W = DL + 0.25LL

- Seismic importance factor (I)
I = 1 for special occupancy structures.

- Seismic zone factor (Z)
Z = 0.3 for zone 3.

- Structural system coefficient (R)
R = 8.5 for concrete moment resisting frame.

- Soil profile type (S)
SC for very dense soil (clay) and soft rock.

- Seismic coefficients:
Ct : 0.03 for concrete moment frames.

Response spectrum analysis

Damping ratio (ξ) = 0.05

- Seismic coefficients:
Ca : 0.33 based on Z = 0.3 and soil profile SC .
Cv : 0.45 based on Z = 0.3 and soil profile SC .

period and acceleration we obtained from el-Centro earthquake data.

Time history

Data was obtained from el-Centro earthquake

Fig-3 : Function graph of time history

Modal analysis

Modal analysis has been applied (for five modes) on the frame. Deformed shape, Natural frequency and period for each mode were as follows:

I. Mode 1 (T = 1.663 | f = 0.601)

Fig-4 : Deformed shape of mode 1

Fig-5 : Deformed shape of mode 2

III. Mode 3 (T = 0.220 | f = 4.549)

Fig-6 : Deformed shape of mode 3

IV. Mode 4 (T = 0.126 | f = 7.948)

Fig-7 : Deformed shape of mode 4

V. Mode 5 (T = 0.061 | f = 16.278)

Fig-8 : Deformed shape of mode 5

Equivalent lateral force (Static analysis)

Fig-9 : Shear envelope of equivalent lateral forces

Fig-10 : Moment envelope of equivalent lateral forces

Time history analysis

Fig-11 : Shear envelope of Time history