International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
Influence of Tie Beams in Seismic Analysis of Moment-Resisting Frames
P. Sachithanantham1, Dr. S. Elavenil2, Dr. S. Sankaran3
1-Asst. Professor, Department of Civil Engineering,
Bharath University, Selaiyur, Chennai, Tamilnadu, India.
2-Professor, Department of Civil Engineering,
SRM University, Kattankulathur, Tamilnadu, India,
3-Dean of Civil Engineering,
Arunai College of Engineering, Thiruvannamalai, Tamilnadu, India,
Abstract: Due to the frequent occurrence of earthquakes sudden failure of structures leads to maximum loss of
lives and property. Multistoryed buildings are affected severely since they are more susceptible to damage
during earthquakes. Due to the large lateral displacements, both structural and non structural distress and
damages are observed in reinforced concrete frames. The current codal provisions emphasis lateral forces
rather than lateral displacements. The maximum lateral displacements are checked at the end of the design
process to satisfy serviceability requirements. In recent times a growing interest in performance based design
procedures in which lateral displacements are emphasized than lateral forces. From the lessons learnt due to
past earthquakes is it observed that large numbers of multistoryed buildings are severely affected. This leads to
increased awareness in the analysis of multistoreyed buildings. In this study seismic analysis of five stoyred
reinforced cement concrete frames is carried with and without the horizontal bracing element at substructure
level. The analysis is carried out using standard software package. The results are compared to study the
earthquake resistant behaviour of the multistoryed building frame systems with and without horizontal brace
elements.
INTRODUCTION
Ordinary reinforced concrete moment-resisting frames (OMRF) and special reinforced concrete momentresisting frames (SMRF) with and without shear wall are very popular in construction of multistoryed buildings.
The percentage of permissible increase in allowable bearing pressure or resistance of soil given in IS 1893 (Part
I) as fifty for type I rock or hard soil for the foundation of combined or isolated RCC footing with tie beams and
twenty five for type II medium soil and type III soft soils for the foundation of RCC isolated footing without tie
beams or unreinforced strip foundations. IS 1893, also specifies isolated RCC footing without tie beams or unreinforced strip foundations shall not be permitted in soft soils with N value less than ten. In the analysis of
building frame systems this is considered and the tie beams are provided as plinth beams to distribute the
masonry loads. Much attention is given only for the provision of plinth beams connecting the footings
depending on the functional plans, rather than connecting the footings with tie beams.
In this paper the investigation on seismic analysis of building frame systems with and without tie beams
connecting isolated footings are considered. Building frame system comprising five floors with each storey with
a height of 3.5 m is adopted for the analysis. The building plan consisting six modules of 12 m x 10 m and three
modules of 12 m x 3 m as shown in figure 1 is considered for the seismic analysis.
METHODOLOGY
Structural Modelling
To investigate the influence of tie beams connecting the footings, building frame systems with and with out tie
beams are considered and designated as
1.
BFS I
- Building frame system with tie beam at plinth level
2.
BFS II - Building frame system without tie beam at plinth level
Building frame system BFS I is modelled by assigning the corresponding coordinates in x, y and z directions.
Element connectivity is carried by connecting the nodes. For BFS I at plinth level tie beams are connected with
appropriated nodes connecting all the nodes as shown in figure 2. For BFS II, at plinth level plinth beams are
connected only with nodes where ever masonry walls are to be constructed as shown in figure 3.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
4m
4m
4m
10 m
4m
4m
4m
10 m
4m
4m
4m
4m
4m
4m
3m
4m
4m
10 m
4m
4m
4m
4m
4m
4m
3m
10 m
4m
10 m
4m
4m
4m
4m
4m
4m
3m
10 m
3m
10 m
10 m
Load 1
4m
4m
4m
4m
4m
4m
4m
4m
4m
Figure 1 Functional building plan
The geometry of the building frame system is modelled by defining and assigning the member sizes and
member properties for and beams and columns as presented in table 1.
4m
10 m
4m
10 m
4m
3m
10 m
4m
3m
4m
10 m
4m
4m
4m
4m
10 m
3m
10 m
4m
4m
4m
4m
4m
4m
4m
4m
4m
10 m
4m
3m
4m
10 m
4m
4m
10 m
3m
10 m
4m
4m
10 m
3m
10 m
4m
4m
10 m
3m
10 m
4m
4m
10 m
3m
10 m
4m
4m
4m
3m
4m
10 m
4m
10 m
3m
4m
10 m
4m
10 m
4m
Figure 2 Building frame system with tie beam at plinth level (BFS I)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
4m
4m
4m
10 m
4m
4m
4m
10 m
4m
4m
4m
3m
4m
4m
4m
10 m
4m
4m
10 m
4m
4m
3m
4m
4m
10 m
4m
4m
4m
3m
4m
4m
4m
10 m
3m
4m
4m
4m
10 m
10 m
Load 1
4m
4m
4m
4m
4m
4m
4m
4m
4m
Figure 3 Building frame system without tie beam at plinth level (BFS II)
Table 1 Geometrical Properties for BFS I and BFS II
Description
Dimension, mm
C1 – Column
300 x 300
C2 – Column
450 x 300
PB 1 – Plinth Beam
450 x 300
TB 1 – Tie Beam
450 x 300
The 3 D modelled building frame system BFS I and BFS II are shown in figure 4 and 5 respectively. Restraints
are given for the supports. Loads are assigned on all the members. The analysis is carried out for both BFS I
and BFS II with the following load combinations as per IS 1893-2002
i)
1.5 ( DL + IL )
ISSN: 2231-5381
ii)
1.2 ( DL  IL  EL )
iii)
1.5 ( DL  EL )
iv)
0.9 DL  1.5 EL.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
Figure 4 Rendered View - BFS I
Figure 5 Rendered View - BFS II
SEISMIC ANALYSIS
Seismic analysis is performed by response spectrum method with the inputs shown in table 2 and the response
quantities are arrived.
Table 2 Seismic Input parameters for BFS I and BFS II
Description
Zone factor
Value
0.16
Response reduction factor
5
Importance factor
1
Soil factor
Hard soil
Damping
5%
Number of Modes
6
RESULTS AND DISCUSSION
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
From results of dynamic analysis the story drifts in X and Z direction are calculated at each level of storey
height for both BFS I and BFS II and presented in table 3. It is inferred that the story drift in BFS II is relatively
larger than BFS I in both X and Z directions.
Table 3 Storey Drift
BFS I
BFS II
Storey Height,
m
Drift – X, mm
Drift – Z, mm
Drift – X,
mm
Drift – Z, mm
0
1.908
2.509
3.198
4.003
3.5
2.646
3.477
4.273
4.754
7
2.247
2.952
3.634
2.458
10.5
1.691
2.228
2.721
1.716
14
0.996
1.315
1.583
1.047
17.5
0.282
0.371
0.376
0.399
From the post processor results the maximum nodal displacements in X and Z directions of each storey are
calculated and presentable in table 4. A plot is made between storey height and maximum nodal displacement
as shown in figure 6. From this plot it is observed that the nodal displacement increases with storey height. The
nodal displacements of BFS II are more compared with BFS I. This behaviour indicates the influence of tie
beam in BFS I.
Table 4 Maximum Nodal Displacement
Storey Height,
m
BFS I
BFS II
DisplacementX, mm
DisplacementZ, mm
DisplacementX, mm
DisplacementZ, mm
0
2.058
3.887
3.269
6.458
3.5
4.911
9.271
7.625
13.405
7
7.322
13.877
11.317
16.556
10.5
9.121
17.422
14.062
19.635
14
10.15
19.636
15.621
21.755
17.5
10.399
20.479
15.926
22.74
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
Maximum Displacement
BFS I X
25
BFS I - Z
Maximum displacment , mm
BFS II X
BFS II Z
20
15
10
5
0
0
3.5
7
10.5
14
17.5
Storey Height, m
Figure 6 Relationship between storey height and maximum nodal displacement
The maximum shear force, positive and negative bending moments of beams in each storey of both BFS I and
BFS II are taken from the analysis results and presented in table 5. From this table it is inferred that the
maximum shear force, positive and negative bending moments of beams in each storey is appreciably more in
BFS II when compared to BSF I, which indicates the influence of tie beams in BFS I.
From the dynamic analysis frequency, period and mass participation in X, Y and Z directions are calculated and
presented in table 6 and 7 for BFS I and BFS II respectively. A plot is made between mode and frequency for
both BFS I and BFS II as shown in figure 7. From the plot it is observed that the frequency is less in case of
BFS II compared to BFS I due to the presence of tie beams at the plinth level. Figure 8 to 19 show the various
mode shapes for both BFS I and BFS II.
Table 5 Maximum Shear Force and Bending Moment - Beams
BFS I
Storey
Height, m
Shear Force
(Max), kN
BFS II
Bending Moment, kNm
Positive
Negative
Shear Force
(Max), kN
Bending Moment, kNm
Positive
Negative
0
39.901
66.533
-66.126
101.052
151.578
-151.578
3.5
32.764
53.846
-53.517
67.202
100.804
-100.804
7
24.796
41.932
-41.679
42.564
63.847
-63.847
10.5
15.581
26.582
-27.171
23.56
35.341
-35.934
14
5.955
12.886
-14.785
6.951
19.999
-21.293
17.5
5.919
9.235
-9.416
5.299
11.492
-9.627
Table 6 Frequencies and Mass Participation - BFS I
Mode
Frequency,
Hz
Period, s
Participation
X, %
Participation
Y, %
Participation
Z, %
1
0.435
2.3
0
0
67.786
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
2
0.62
1.612
0
0
16.038
3
0.714
1.4
83.293
0
0
4
0.936
1.069
0
0
0.157
5
0.996
1.004
0
0
0.062
6
1.045
0.957
0.868
0
0
Table 7 Frequencies and Mass Participation - BFS II
Mode
Frequency,
Hz
Period, s
Participation
X, %
Participation
Y, %
Participation
Z, %
1
0.438
2.281
0
0
71.023
2
0.537
1.862
84.837
0
0
3
0.597
1.674
0
0
17.58
4
0.813
1.23
0
0
0.85
5
0.917
1.091
0.282
0
0
6
1.008
0.992
0
0
0.238
Mode vs Frequency
BFS I
1.1
1
BFS II
Frequency, Hz
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0
1
2
3
4
5
6
Mode
Figure 7 Relationship between mode and frequency
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
Figure 8 Mode shape 1 – BFS I
Load 3 : Mode Shape 1 :
Figure 9 Mode shape 1 – BFS II
Figure 10 Mode shape 2 – BFS I
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
Load 3 : Mode Shape 2 : Displacement
Figure 11 Mode shape 2 – BFS II
Figure 12 Mode shape 3 – BFS I
Load 3 : Mode Shape 3 : Displacement
Figure 13 Mode shape 3 – BFS II
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
Figure 14 Mode shape 4 – BFS I
Load 3 : Mode Shape 4 :
Figure 15 Mode shape 4 – BFS II
Figure 16 Mode shape 5 – BFS I
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
Load 3 : Mode Shape 5 : D isplacement
Figure 17 Mode shape 5 – BFS II
Figure 18 Mode shape 6 – BFS I
Load 3 : Mode Shape 6 : Displacement
Figure 19 Mode shape 6 – BFS II
CONCLUSIONS
1.
From the seismic analysis of building frame systems the following conclusions are drawn.
The storey drift of building frame system without tie beams increases from a minimum of 33% to a
maximum of 68% to that of building frame system with tie beam at plinth level.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 3 Issue 2 No3 – March 2012
2.
3.
The nodal displacement of building frame system without tie beam is increased up to 66% when
compared to building frame system with tie beam.
It is also concluded that the shear force and bending moment increase appreciably in the absence of tie
beams at plinth level which results in un-economy in the design of reinforced concrete building frame
systems.
Acknowledgements
The authors would like to acknowledge Bharath University for funding the research reported in this paper.
References
[1]
Bing Li, Hai-Cheng Rong, Tso-Chien Pan, “Drift-controlled design of reinforced concrete frame
structures under distant blast conditions – Part I: Theoretical basis”, Int. Jr. of Impact of Engineering,
Vol.34, pp 743 – 754, 2007.
[2}
IS: 1893-2002 (Part I) “Criteria for Earthquake Resistant Design of Structures”, Bureau of Indian
Standards, 2002.
[3]
IS: 13920 – 1993, “Ductile detailing of Reinforced Concrete Structures subjected to Seismic forces –
Code of Practice”, Bureau of Indian Standards, 2002.
[4]
Kalyanaraman V, K. Mahadevan and Vikram Thairani, “Core Loaded Earthquake Resistant Bracing
System”, Jr. Construct. Steel Res. Vol. 46, pp 437 – 439, 1998.
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