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

Introduction 

In this project a 2D frame to be modeled using SAP2000 software. It’s a four story with a 3-bay building which is to be built in an area of clay soil with soft rock within a seismic zone 3.

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

Gravity loads acting on the building are:

DL = 20 kN/m

LL = 15 kN/m

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.

Fig-2 : Function graph of response spectrum

Time history

Data was obtained from el-Centro earthquake

Fig-3 : Function graph of time history

Analysis results and calculation

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

II. Mode 2 (T = 0.472 | f = 2.120)

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

Fig-12 : Moment envelope of Time history

Node 1:

Fig-13

Fig-14 : Time history of node 1