A 15-story building was analyzed for different seismic zones and architectural complexities. Mathematical models showed: 1) Moment values of columns in Zone II were 5-15% lower than Zone III, 10-20% lower than Zone IV, and 15-45% lower than Zone V. 2) Models accurately estimated column moment values (R2 > 0.986) for different zones and architectural complexities. 3) Moment values varied up to 15% between different architectural complexities within the same zone.

1. International Journal of Engineering Research and Development
e-ISSN: 2278-067X, p-ISSN : 2278-800X, www.ijerd.com
Volume 5, Issue 2 (December 2012), PP. 55-59
Inter-Relationship between Moment Values of Columns in
a Building with Different Architectural Complexities and
Different Seismic Zones
Onkar V. Sapate
J.L.C.C.E., Civil Engg. Dept.., Nagpur
Abstract:- Many high rise buildings are planned and constructed with architectural complexities. The
complexities includes soft storey at lower level or at any intermediate level, floating column at various levels and
shear wall provided in basements, etc. High rise buildings are critically analyzed for the effect of earthquake.
Earthquake loads as specified in IS 1893 (part 1): 2002 are considered in the analysis of building.
A G+15 storeyed high rise building with different architectural complexities is analyzed for various earthquake
zones. In over all study of seismic analysis, critical load combinations are found out. For these critical load
combinations, zone wise variation in moments on columns at ground floor level are compared and significant co-
relationship between these moment values are established. Mathematical models developed can be used with
reasonable accuracy.
Keywords:- Architectural Complexities, Seismic Zones, Seismic Analysis, Critical Load Combinations,
Mathematical Models
I. INTRODUCTION
A G+15 storeyed high rise building with different architectural complexities such as soft storey at lower level or at
any intermediate level, floating column at various levels and providing shear wall is analyzed for various earthquake zones.
Details of the structure are given in table 1.
Table I
Type of Structure R.C.C framed, G+15 with Basement for Parking
Area of individual floor 41677.54 Sq. ft.
Storey Height 3.5 m
Earthquake Zone II, III, IV, V
Type of soil Medium
Lateral Load Resisting System Ordinary RC moment-resisting frame (OMRF)
Response Reduction Factor, R 3.0
Live Load 4 KN/m2
Number of Footings 121
1. Self Wt. of whole Structure
Dead load 2. Wt .of Brickwork = 13.34 KN/m
3. Slab Load = 4.125 KN/m2
II. ANALYSIS
The Commercial Complex with architectural complexities is analyzed for all the conditions including Earthquake
load by STAAD Pro. The building chosen was 52.5 m in height above ground level. To study the effect of various loads in
various Earthquake zone the building was modeled as per plan and the plan was remodified in two different ways so that
total number of cases are three namely:
Case 1 : Commercial Complex with 7m Height Shear Wall at Basement.
Case 2 : Commercial Complex with Soft Storey at Basement & at every fourth floor
Case 3 : Commercial Complex with Floating Column at Various Levels.
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2. Inter-Relationship between Moment Values of Columns in a Building with…
Fig. 1 Typical Plan of Commercial Complex (Columns Refer to All Floors)
III. LOAD COMBINATION
Following load combinations are considered in analysis of the building.
1. 1.5DL +1.5LL
2. 1.5DL +1.5EQX
3. 1.5DL -1.5EQX
4. 1.5DL +1.5EQZ
5. 1.5DL -1.5EQZ
6. 1.2DL +1.2LL+ 1.2EQX
7. 1.2DL +1.2LL -1.2EQX
8. 1.2DL +1.2LL+ 1.2EQZ
9. 1.2DL +1.2LL -1.2EQZ
10. 0.9DL +1.5EQX
11. 0.9DL -1.5EQX
12. 0.9DL +1.5EQZ
13. 0.9DL -1.5EQZ
Critical load combinations for Mx & Mz Values are found to be
1. 1.5DL -1.5EQZ
2. 1.5DL -1.5EQX
IV. ANALYSIS OF DATA GENERATED
The STAAD output generated is analyzed to determine relations between various parameters and develop mathematical
models. Relations developed are given below.
1 Relation between Mx Values of Zone II with other Zone values for all Cases
2 Relation between Mz Values of Zone II with other Zone values for all Cases
3 Relation between Mx values of case1 with Mx values of other cases
4 Relation between Mz values of case1 with Mz values of other cases
V. OBSERVATIONS
The following observations are made from the mathematical models developed.
Model 1: Mx Values of column for Zone II with other zone values for case 1
Zone Model R2 value Observation
5-10%
III y = -3E-05x2 + 1.627x - 3.027 0.989 10-15%
From >15%
258 Results
2
IV y = -6E-05x + 2.464x + 23.25 0.992
20
60
V y = 3.716x + 44.29 0.988
20
0
15
Model 2: Mx Values of column for Zone II with other zone values for case 2
40
Zone Model R2 value Observation
35
III y = -3E-05x2 + 1.628x + 9.510 0.997 10
5-10%
From 258 Results
IV y = -6E-05x2 + 2.464x + 23.25 0.992 10-15%
>15%
V y = 3.716x + 44.29 0.988 0
0
20
60
56 20
0
15
40
35
10

3. Inter-Relationship between Moment Values of Columns in a Building with…
Model 3: Mx Values of column for Zone II with other zone values for case 3
Zone Model R2 value Observation
III 2
y = -5E-05x + 1.657x - 15.51 0.986 5-10%
IV 2
y = -6E-05x + 2.464x + 23.25 0.992 From10-15%
258 Results
>15%
V y = -0.000x2 + 3.716x + 44.29 0.988 20
5
Model 4: Mz Values of column for Zone II with other zone values for case 1
30
Zone Model R2 value 20 Observation
III 2
y = -3E-05x + 1.636x - 4.795 0.997 45
IV 2
y = -6E-05x + 2.464x + 23.25 0.992
5 From 5-10%
258 Results
10 10-15%
V y = 3.716x + 44.29 0.988 35
25 >15%
50
30
10
Model 5: Mz Values of column for Zone II with other zone values for case 2
Zone Model R2 value 15 Observation
2 45
III y = -2E-05x + 1.625x - 1.494 0.997 30
IV y = -6E-05x2 + 2.464x + 23.25 0.992 5 From 5-10%
258 Results
10-15%
V y = 3.716x + 44.29 0.988 20 >15%
45 15
20
25
Model 6: Mz Values of column for Zone II with other zone values for case 3
Zone Model R2 value 40
Observation
2 5
III y = -3E-05x + 1.643x - 8.990 0.997 15
5-10%
From 258 Results
IV y = -6E-05x2 + 2.464x + 23.25 0.992 35
10-15%
V y = 3.716x + 44.29 0.988 45
>15%
20
25
Model 7: Mx values of case 1 with Mx values of case 3 5
Case Model 2
R value 30
Observation
10
Case 3 y = -9E-06x2 + 0.998x + 9.697 0.992 From 1032 Results
55
5-10%
0
10-15%
Model 8: Mz values of case 1 with Mz values of case 3 30
>15%
Case Model R2 value 10
Observation
2 60
Case 3 y = 1E-05x + 0.943x - 7.975 0.995 From 1032 Results
5-10%
10-15%
Mx Values for Zone II Vs other Zone values- Case 1 >15%
7000.00 y = -3E-05x 2 + 1.627x - 3.027
R² = 0.989
6000.00
y = -6E-05x 2 + 2.464x + 23.25
R² = 0.992
5000.00
y = -0.000x 2 + 3.716x + 44.29
other Zone values
4000.00 R² = 0.988
3000.00
2000.00
1000.00
0.00
0.00 200.00 400.00 600.00 800.00 1000.00 1200.00 1400.00 1600.00 1800.00
-1000.00
Mx for Zone II
Zone 3 Zone 4 Zone 5 Poly. (Zone 3) Poly. (Zone 4) Poly. (Zone 5)
Fig. 2
Mx Values for Zone II Vs other Zone values- Case 2
10000 y = -3E-05x 2 + 1.628x + 9.510
9000 R² = 0.997
y = -6E-05x 2 + 2.464x + 23.25
8000 R² = 0.992
7000 y = -0.000x 2 + 3.716x + 44.29
other Zone values
R² = 0.988
6000
5000
4000
3000
2000
1000
0
0 500 1000 1500 2000 2500 3000
Mx for Zone II
Zone 3 Zone 4 Zone 5 Poly. (Zone 3) Poly. (Zone 4) Poly. (Zone 5)
Fig. 3
57

4. Inter-Relationship between Moment Values of Columns in a Building with…
Mx Values for Zone II Vs other Zone values- Case 3
6000 y = -5E-05x 2 + 1.657x - 15.51
R² = 0.986
5000 y = -6E-05x2 + 2.464x + 23.25
R² = 0.992
4000 y = -0.000x 2 + 3.716x + 44.29
R² = 0.988
other Zone values
3000
2000
1000
0
0 200 400 600 800 1000 1200 1400 1600 1800
-1000
Mx for Zone II
Zone 3 Zone 4 Zone 5 Poly. (Zone 3) Poly. (Zone 4) Poly. (Zone 5)
Fig. 4
Mz Values for Zone II Vs other Zone values- Case 1
9000 y = -3E-05x 2 + 1.636x - 4.795
8000 R² = 0.997
y = -6E-05x 2 + 2.464x + 23.25
7000 R² = 0.992
6000 y = -0.000x 2 + 3.716x + 44.29
other Zone values
R² = 0.988
5000
4000
3000
2000
1000
0
-1000 0 500 1000 1500 2000 2500
Mx for Zone II
Zone 3 Zone 4 Zone 5 Poly. (Zone 3) Poly. (Zone 4) Poly. (Zone 5)
Fig. 5
Mz Values for Zone II Vs other Zone values- Case 2
9000 y = -2E-05x 2 + 1.625x - 1.494
R² = 0.997
8000
y = -6E-05x 2 + 2.464x + 23.25
7000 R² = 0.992
6000 y = -0.000x2 + 3.716x + 44.29
other Zone values
R² = 0.988
5000
4000
3000
2000
1000
0
-1000 0 500 1000 1500 2000 2500
Mx for Zone II
Zone 3 Zone 4 Zone 5 Poly. (Zone 3) Poly. (Zone 4) Poly. (Zone 5)
Fig. 6
Mz Values for Zone II Vs other Zone values- Case 3
9000 y = -3E-05x2 + 1.643x - 8.990
R² = 0.997
8000
y = -6E-05x2 + 2.464x + 23.25
7000 R² = 0.992
6000 y = -0.000x 2 + 3.716x + 44.29
other Zone values
R² = 0.988
5000
4000
3000
2000
1000
0
-1000 0 500 1000 1500 2000 2500 3000
Mx for Zone II
Zone 3 Zone 4 Zone 5 Poly. (Zone 3) Poly. (Zone 4) Poly. (Zone 5)
Fig. 7
58

5. Inter-Relationship between Moment Values of Columns in a Building with…
Comparison of Mx Values of Case 1 With Case 3
6000
5000
y = -9E-06x 2 + 0.998x + 9.697
R² = 0.992
4000
Mx Values of case 3
3000
2000
1000
0
0 1000 2000 3000 4000 5000 6000
Mx Values of Case 1
Case 3 Poly. (Case 3)
Fig. 8
Comparison of Mz Values of Case 1 With Case 3
9000
8000
7000 y = 1E-05x 2 + 0.943x - 7.975
R² = 0.995
6000
Mx Values of case 3
5000
4000
3000
2000
1000
0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
-1000
Mx Values of Case 1
Case 3 Poly. (Case 3)
Fig. 9
VI. CONCLUSION
1. In all cases considered values of Mx and Mz is found to be increase significantly in higher earthquake zones as
compared to lower zones.
2. The values of Mx increases more than twice in case 2 as compared to case 1. But in case 3 Mx and Mz values are found
to be reducing as compared to case 1.
3. In case 2, Mx & Mz values are increasing or decreasing significantly depending upon position and orientation of
column.
4. Significant co relationship is observed in between Mx & Mz values of zone II with other zone values for respective
cases.
5. Significant co relationship is observed in between Mx & Mz values of Case1 with other cases value.
6. The mathematical models developed can be used for rough estimation of Mx or Mz values, if values for one zone with
one of the cases are known.
REFERENCES
[1]. Jaswant N. Arlekar, Sudhir K. Jain and C.V.R. Murty, (1997), Seismic Response of RC Frame Buildings with Soft
First Storey, Proceedings of the CBRI Golden Jubilee Conference on Natural Hazards in Urban Habitat, New
Delhi.
[2]. Devesh P. Soni and Bharat B. Mistry , (December 2006),Qualitative Review of Seismic Response of Vertically
Irregular Building Frames, ISET Journal of Earthquake Technology, Technical Note, Vol. 43, No. 4, pp. 121-132.
[3]. P Mukhopadhyay, (April 2007), Performance of Buildings during Earthquake Configurational Aspects, IE(I)
Journal, Volume 88,pp. 13-17.
[4]. Sudhir K. Jain and C.V.R. Murty, (2000), Beneficial Influence of masonry Infill Walls on Seismic Performance of
RC Frame Buildings, 12 WCEE
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