effect of number of storeys to natyral time periode

8/21/2019 Effect of Number of Storeys to Natyral Time Periode

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Effect of Number of StoreysTo Natural Time Period of Building

Sudhir K. Patel#1, Prof. A.N.Desai*2, Prof V.B.Patel#3

#1P.G. student at Structural engineering department, BVM engineering college,

Gujarat Technological University, Vallabh Vidyanagar, Anand, Gujarat, [email protected]

*2

Associate Professor at Structural engineering department, BVM engineering college,Gujarat Technological University, Vallabh Vidyanagar, Anand, Gujarat, India.

#3Associate Professor at Structural engineering department, BVM engineering college,

Gujarat Technological University, Vallabh Vidyanagar, Anand, Gujarat, India.

ABSTRACT: Indian standard recommended that the natural time

period is a function of Height of building and the Base dimension of

the building. Here in this work, the attempt is to show that natural

time period is also a function of number of storeys.

Various R.C.C. building models are made in STAAD-Pro

software. Each R.C.C. buildings modelled to have base dimension of

70 meter 70 meter. The height of the R.C.C. buildings is

approximately 90 meters. The storey height of the R.C.C. building ischanged from model to model. The change in the storey height is of

0.25 meter. As the storey height increase the number of storeys is

decrease. In each model the storey height is kept constant for each

storey. With the use of STAAD-Pro software analysis is carried out to

find maximum axial load on the column. Mass and stiffness of each

model is calculated manually. After finding mass and stiffness, natural

time period for each model is found out by lumped mass matrix

method of structural dynamics.

INTRODUCTION

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 behaviour of structures isgoverned 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 onthe magnitude of its response.

In this research work, various R.C.C frame models have

been prepared in STAAD-Pro software. The height of each model

is kept approximately 90 meter. Plan dimension is 70 m 70 m.

All columns and beams size in each model is same. Then, variation

in storey height is made. The storey height variation is 0.25 meter.

Means in first model storey height is 3 meter. In next models,

likewise, storey height is 3.25, 3.5, 3.75 4.75, 5.0. With using

STAAD- Pro software analysis is carried out to find maximum

axial load. Mass and stiffness is manually calculated. After

calculating mass and stiffness, natural frequency and natural time

period is calculated. As the storey height increase, number ofstoreys will be decrease. As per IS-1893, there is no variation in the

frequency as the formula for the natural time period on the basis of

height of building and base dimension of the building.

BACK GROUND

The 2002 version of IS 1893 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 analysed 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 modelling 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 = MassAs per IS 1893:2002 The approximate fundamentalnatural period of vibration (T ), in seconds, of a moment-resisting

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/

13-14 May 2011 B.V.M. Engineering College, V.V.Nagar,Gujarat,India

National Conference on Recent Trends in Engineering & Technology


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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.

PROBLEM FORMULATION

Plan dimension : 70 m 70 m

Height of building : 90 m for sample

model(approximately)

Height of each storey : changes from model to model(3m,3.25m,3.5m,,4.75m,5m)

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

Column size: 450 mm 450 mm (may be changed as per

actual design)

Beam size: 300 mm 600 mm (may be changed as peractual design)

Modules of elasticity of concrete: 2 105

Grade of concrete: M-20

Grade of steel: Fe-415

Density of concrete: 25 KN/m

3

Density of brick masonry: 20 KN/m3

Live load: 3 KN/m2

Slab thickness: 120 mm

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).

Fig 1 plan of a sample model

Fig 2 Front view of a model

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 columns are 10001000 mm and all the beams

are 300600 mm.

For this revised section mass and stiffness is found out.

From this mass and stiffness natural frequency and natural time

period is calculated.

CALCULATION

Slab = 0.12257070 = 14700 KN

Beam = 0.30.6257070= 9450 KN

Live load = 70701.5 =7350 KN

Column = 11252253 =16875 KN

Ex. Wall= 0.23207042.4 = 3091.2 KN




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Int. Wall=0.1152070262.4 = 10046.4 KN

Total mass (m) = 61512.6 KN

= 6151260 kg

K = n =

= 1.666109N/mm =

= 1.6661012

N/m = 529.42Hz

h= height of column

= 529.420.05149 T =

= 26.797Hz =

= 0.234 Sec

TABLE 1

Sr.

No

Storey

height

(m)

Mass

(kg)

Stiffness,1012

(N/m)

1 3 6151260 1.667

2 3.25 6428700 1.31

3 3.5 6706100 1.05

4 3.75 6983500 0.85

5 4 7261100 0.703

6 4.25 7538500 0.586

7 4.5 7816000 0.493

8 4.75 8093500 0.419

9 5 8371000 0.36

TABLE 2

Sr.No

Naturalfrequency

n(Hz)

Constant Frequency (Hz)

Naturaltime

period

T (sec)

1 529.42 0.05149 26.797 0.234

2 451.41 0.0551 24.87 0.256

3 395.69 0.05926 23.451 0.268

4 348.877 0.0641 22.363 0.281

5 311.154 0.06979 21.71 0.289

6 278.8 0.07304 20.35 0.308

7 251.14 0.0766 19.23 0.327

8 227.53 0.08053 18.32 0.343

9 207.37 0.08488 17.6 0.357

For this building the natural time period assuming infilled brick walls is

calculated based on codal provision is approximately 0.928secs, for all themodels

.NOTE: The constant is obtained by preparing a programme in FORTRANlanguage for the lumped mass matrix method assuming that the stiffness of

each floor level and mass of each floor level are same.

CONCLUSION

The conclusion drawn from this research work is, as the number of storeys

increases natural time period increases although the height of the buildingremains same.

REFERENCE

1) Mills, R.S. Small-scale modeling of the nonlinear response of steel-framed buildings to earthquakes Design for Dynamic Loading andModal Analysis, Construction Press, pp.171-177.(1979)

2) Krawinkler, H. and Benjamin.J. Wallace., Small-scale modelexperimentation on steel assemblies Report No.75, The John A.

Blume Earthquake Engineering Centre, Department of CivilEngineering, Stanford University, Stanford.(1985)

3) Lagomarsino, S., Forecast models for damping and vibration periodsof buildings J. of Wind Eng. and Ind Aerodyn. Vol. 48, pp.221-

239,(1993)

4) Tamura, Y., Suganuma, S. , Evaluation of amplitude-dependentdamping 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 moment- resistingframe 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 andinterference 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 forpseudo dynamic test on small-scale steel modelsJ.of EarthquakeEng. Society of Korea, Vol.7, pp. 49-57. (2003)

12)Tremblay, R. and Rogers, C.A. Impact of capacity design provisionsand period limitations on the seismic design of lowrise steel

buildings Intl.J.of Steel Struct., Vol. 5, pp.1-22. (2005)

13)Technical paper by Dr V Kanwar, Dr N Kwatra, Non-memberDr PAggarwal, Dr M L Gambir, Evaluation of Dynamic Parameters of a

Three-storey RCC Building Model using Vibration Techniques , July04, (2007)



effect of number of storeys to natyral time periode

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