International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 11, November 2012)
Effect of Height and Number Floors to Natural Time Period
of a Multi- Storey Building
Nilesh v prajapati1, Prof. A.N.Desai2
1
M.E. civil(Structural engineering) from, BVM engineering college, Gujarat Technological University
Vallabh Vidyanagar, Anand,Gujarat,India.
2
Associate Professor at Structural engineering departmentt, BVM engineering college, Gujarat Technological University
Vallabh Vidyanagar, Anand,Gujarat,India.
Abstract — The design of structures subjected to natural
hazards such as earthquakes and typhoons demands safety
of structures which is governed by the natural frequencies
and the amount of damping in each mode of vibration. The
dynamic behavior of structures is governed by the
fundamental natural frequency and the amount of damping
exhibited by each mode of vibration. Fundamental
frequency of a building and its damping has a remarkable
effect on the magnitude of its response.
As per IS 1893:2002 The approximate fundamental
natural period of vibration (T), in seconds, is a function of
Height of a building and Plan dimension of a building.
In this Research work objective is to show that natural
time period is also a function of number of floors and not
only the height of the building, which is not mentioned in IS
1893:2002.
II.
SCOPE AND OBJECTIVE
The scope of this work is limited to find out change in
natural frequency with respect to variation in number of
floors as well as in height of building in R.C.C. building.
The height of the R.C.C. building varies from 60 meter to
90 meter. And number of floors varies from 20 to 30,
keeping constant storey height as 3 m of each.
The general objective of this study is to prepare
various models of R.C.C. building in STADD-Pro
software and evaluate the change in natural frequency
with respect to variation of number of floors as well as
height of building.
The specific objectives are as follows:
1) To prepare various R.C.C. models in STADD-Pro
2) To assess the change in natural frequency with
respect to variation of number of floors of R.C.C.
building.
3) To derive the expression to calculate natural time
period and natural frequency.
Keywords — Storey, Number of Storeys (n), Height of
Floor (hi), Height of Structure (h), Natural Period (T),
Fundamental Natural Period (T1), Modal Natural Period
(T~), Base Dimensions (d).
I. INTRODUCTION
III.
In this research work STADD-Pro software is used. In
it, various model of R.C.C. frame has been prepared. The
height of RCC building varies from 60m to 90m with
respect to increase in number of floors from 20 to 30
numbers. The plan dimension of all models is 70 m × 70
m. All columns are of same size and also all beams are of
same size in each model. In each model there will be a
variation in number of floors. Suppose in first model,
number of floors are 20. In next model, the number of
floors will be 21. Thus, the variation of each number of
floors would be conducted in each sub-sequent model.
The number of floor varies from 20 to 30 and height of
building varies from 60m to 90m respectively for the
constant storey height of 3m and keeping plan
dimensions as constant.
For these models the STATIC ANALYSIS has been
carried out using STAAD-Pro software.
As the number of floors increases, height of building
will be increased and due to this, variation in natural
frequency can be obtained as per the formula given in the
IS 1893:2002. This formula will be revised as a function
of not only height but also as a function of number of
storeys.
B ACK GROUND
The IS1893:2002 has more clearly defined the
irregularities (vertical and horizontal) in the
configuration of buildings than the earlier version. The
current specifications would imply that most of the RCC
buildings in the country have irregular configurations,
and have to be analyzed as three-dimensional systems.
There are a number of commercial software packages,
which have the ability to analyses three-dimensional
systems. However, the main problems are with modeling
of the structure and member section properties. The Code
provides no guidelines on these aspects leading to a wide
variation in the results of the analyses.
All objects or structures have a natural tendency to
vibrate. The rate at which it wants to vibrate is its
fundamental period (natural frequency).
Fn=
Where,
K= Stiffness
M = Mass
237
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 11, November 2012)
 Wall thickness: 230 mm (periphery wall)
115 mm (internal wall)
230 mm (parapet wall)
Fig shows one sample model shown above with plan
dimension (fig 1), front view (fig 2), and 3D view (fig 3).
As per IS 1893:2002 The approximate fundamental
natural period of vibration (T ), in seconds, of a momentresisting frame building without brick infill panels may
be estimated by the empirical expression:
Ta = 0.075 h0.75 for RC frame building
= 0.085 h0.75 for steel frame building
Where,
h = Height of building, in m. This excludes the basement
storeys, where basement walls are connected with
the ground floor deck or fitted between the building
columns. But it includes the basement storeys, when
they are not so connected.
The approximate fundamental natural period of
vibration (T), in seconds, of all other buildings, including
moment-resisting fame buildings with brick infill panels,
may be estimated by the empirical expression:
Ta = 0.09h/
Where,
h= Height of building, in m
d=Base dimension of the building at the plinth level, in
m, along the considered direction of the lateral force.
IV.
P ROBLEM FORMULATION
 Plan dimension : 70 m × 70 m
 Height of building : 90 m for sample model
(varies from 60 m to 90 m)
 Height of each storey : 3m (constant)
 Number of bays along X-direction: 14 nos.
 Number of bays along Y-direction: 14 nos.
 Length of each bay(in X-direction): 5m
 Length of each bay(in Y-direction): 5m
 Number
of
floors
varies
as
:20,21,22,23,24,25,26,27,28,29,30.
 Column size: 450 mm × 450 mm (may be
changed as per actual design)
 Beam size: 300 mm × 600 mm (may be changed
as per actual design)







Fig 1 Plan of a sample model
Modules of elasticity of concrete: 2 ×
Grade of concrete: M-20
Grade of steel: Fe-415
Density of concrete: 25 KN/m3
Density of brick masonary: 20 KN/m3
Live load: 3 KN/m2
Slab thickness: 120 mm
Fig 2 Front view of a model
238
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 11, November 2012)
V.
CONCLUSION
Derivation for the expressions to calculate natural time
period and natural frequency will be carried out to compare
with these natural frequencies from STAAD.Pro. Analysis (as
per IS1893:2002).
REFERENCES
[1 ] Mills, R.S. “Small-scale modeling of the nonlinear response of
steel-framed buildings to earthquakes” Design for Dynamic
Loading and Modal Analysis, Construction Press, pp.171177.(1979)
[2 ] Krawinkler, H. and Benjamin.J. Wallace., “Small-scale model
experimentation on steel assemblies” Report No.75, The John A.
Blume Earthquake Engineering Centre, Department of Civil
Engineering, Stanford University, Stanford.(1985)
[3 ] Lagomarsino, S., “Forecast models for damping and vibration
periods of buildings” J. of Wind Eng. and Ind Aerodyn. Vol. 48,
pp.221-239,(1993)
[4 ] Tamura, Y., Suganuma, S. , “Evaluation of amplitude-dependent
damping and natural frequency of buildings during strong winds.”
J. of Wind Eng. and Ind. Aerodyn., Vol. 59, pp. 115-130.(1996)
[5 ] Goel, K.R.and Chopra, K.A. “Period formulas for momentresisting
frame
Buildings”,
J.of
Struct.Eng.,
ASCE,Vol.123,pp.1454-1461. (1997),
[6 ] D.E. Allen and G. Pernica, Control of Floor Vibration,dec (1998)
[7 ] Bhandari, N. and Sharma, B. K., Damage pattern due to
January,2001 Bhuj earthquake, India: Importance of site
amplification and interference of shear waves, Abstracts of
International Conference on Seismic Hazard with particular
reference to Bhuj Earthquake of 26 January 200I,
NewDelhi,(2001),.
[8 ] IITK, KANPUR, INDIA (EARTHQUAKE TIPS-10) (2002).
[9 ] IS 1893:2002 indian standard code of practice for earthquale
resistant design.
[10 ] L. Govinda Rajul, G. V. Ramana, C. HanumanthaRao and T. G.
Sitharaml ,site specific ground response analysis,(2003)
[11 ] Kim, N.S., Kwak, Y.H.and Chang, S.P, “Modified similitude law
for pseudo dynamic test on small-scale steel models”J.of
Earthquake Eng. Society of Korea, Vol.7, pp. 49-57. (2003)
[12 ] Tremblay, R. and Rogers, C.A. “Impact of capacity design
provisions and period limitations on the seismic design of lowrise
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[13 ] Technical paper by Dr V Kanwar, Dr N Kwatra, Non-memberDr
P Aggarwal, Dr M L Gambir, Evaluation of Dynamic Parameters
of a Three-storey RCC Building Model using Vibration
Techniques , July 04, (2007)
Fig 3 3-D view of a model
As per the analysis carried out for all the load cases
manual concrete design is done for the maximum axial
force for column and maximum bending moment for
beams considering all load cases including earthquake in
direction X. As per this revised design, sizes for all
column as 1000*1000 mm and all the beams as 300*600
mm.
With this revised sizes further STATIC ANALYSIS
has been carried out for the variation of each number of
floors and height for sub-sequent model.
As the number of floors increases, height of building
will be increased and due to this, variation in natural
frequency will be obtained. The results obtained for
variation in number of floors and height of building is as
shown in table 1.
Table 1
Results for Natural Time period for Different models.
Sr
no
No.
of
floors
storey
height
(m)
Height
of
building
(m)
1
2
2
4
5
6
7
8
9
10
11
20
21
22
23
24
25
26
27
28
29
30
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
60.00
63.00
66.00
69.00
72.00
75.00
78.00
81.00
84.00
87.00
90.00
Natural time
period
T(second) (as
per STAAD
analysis)
0.6454
0.6777
0.7100
0.7422
0.7745
0.8068
0.8391
0.8713
0.9036
0.9359
0.9681
Natural
frequency
(ω=2π/T)
9.7301
9.2668
8.8454
8.4609
8.1084
7.7840
7.4847
7.2075
6.9501
6.7104
6.4867
239