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EFFECT OF HEIGHT AND NUMBER FLOORS TO NATURAL TIME PERIOD OF A MULTI-

STOREY BUILDINGNilesh v prajapati#1, Prof. A.N.Desai*2

#1 P.G. student at Structural engineering department, BVM engineering college, Gujarat Technological UniversityVallabh Vidyanagar, Anand,Gujarat,India.

1nileshprj@gmail.com,nileshprj@rediffmail.com

*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.

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).

1. INTRODUCTION

In this research work STADD-Pro software is used. In it, variousmodel 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 plandimension 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 outusing 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.

2. Scope and objectiveThe 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.3. Back groundThe 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= StiffnessM = Mass

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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/

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.

4. PROBLEM 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)

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 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

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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 reviseddesign, sizes for all column as 1000*1000 mm and all the beams as 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 for the variation of each number of floors and height for 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. 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 and 2.

4.1 SAMPLE CALCULATION

Slab = 0.12×25×70×70 = 14700 KN

Beam = 0.3×0.6×25×70×70= 9450 KN

Live load = 70×70×1.5 =7350 KN

Column = 1×1×25×225×3 =16875 KN

Ex. Wall= 0.23×20×70×4×2.4 = 3091.2 KN

Int. Wall=0.115×20×70×26×2.4 = 10046.4 KN

Total mass (m) = 61512.6 KN

= 6151260 kg

K = ∑ ωn =

= 1.666×109 N/mm =

= 1.666×1012 N/m = 529.42Hz

h= height of column

ω = 529.42×0.05149 T =

= 26.797Hz =

= 0.234 Sec4.2 Results for Natural Time period for Different models.

Table 1.

Stiffness,*1012Sr.

NoNo of floors

Storey height

(m)

Height of building

Mass (kg)

(N/m)

1 20 3 60 6151260 1.666

2 21 3 63 6151260 1.666

3 22 3 66 6151260 1.666

4 23 3 69 6151260 1.666

5 24 3 72 6151260 1.666

6 25 3 75 6151260 1.666

7 26 3 78 6151260 1.666

8 27 3 81 6151260 1.666

9 28 3 84 6151260 1.666

10 29 3 87 6151260 1.666

11 30 3 90 6151260 1.666

Table 2.

Sr. No

Natural frequency ωn (Hz)

ConstantFrequency ω (Hz)

Natural time period T (sec)

1 520.422 0.077 39.867 0.1582 520.422 0.073 38.014 0.1653 520.422 0.070 36.325 0.1734 520.422 0.067 34.780 0.1815 520.422 0.064 33.361 0.1886 520.422 0.062 32.053 0.1967 520.422 0.059 30.844 0.2048 520.422 0.057 29.722 0.2119 520.422 0.055 28.680 0.219

10 520.422 0.053 27.708 0.22711 520.422 0.051 26.800 0.234

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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).

Reference

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National Conference on Recent Trends in Engineering & Technology

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