“Effect of Number of StoreysTo Natural Time Period of Building”

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

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

Gujarat Technological University, Vallabh Vidyanagar, Anand, Gujarat, India.1sudhirpatel_me@yahoo.com

*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 is changed from model to model. The change in the storey height is of 0.25 meter. As the storey height increase the number of storeys isdecrease. 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 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.

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 maximumaxial 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 of storeys 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= StiffnessM = Mass

As per IS 1893:2002 The approximate fundamental natural 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

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 per

actual design) Modules of elasticity of concrete: 2 ×105

Grade of concrete: M-20 Grade of steel: Fe-415 Density of concrete: 25 KN/m3

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 1000×1000 mm and all the beams are 300×600 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 = 0.12×25×70×70 = 14700 KNBeam = 0.3×0.6×25×70×70= 9450 KNLive load = 70×70×1.5 =7350 KNColumn = 1×1×25×225×3 =16875 KNEx. Wall= 0.23×20×70×4×2.4 = 3091.2 KN

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

National Conference on Recent Trends in Engineering & Technology

Int. Wall=0.115×20×70×26×2.4 = 10046.4 KNTotal mass (m) = 61512.6 KN = 6151260 kg

K = ∑ ωn =

= 1.666×109 N/mm =

= 1.666×1012 N/m = 529.42Hzh= height of column

ω = 529.42×0.05149 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

Natural frequency ωn (Hz)

Constant Frequency ω (Hz)

Natural time 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 0.928 secs, for all the models.NOTE: The constant is obtained by preparing a programme in FORTRAN language 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 storeysincreases natural time period increases although the height of the building remains same.

REFERENCE

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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)

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5) Goel, K.R.and Chopra, K.A. “Period formulas for moment- resisting 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).

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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 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 P Aggarwal, Dr M L Gambir, Evaluation of Dynamic Parameters of a Three-storey RCC Building Model using Vibration Techniques , July 04, (2007)

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

National Conference on Recent Trends in Engineering & Technology