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Analysis Of Harmonic Behaviour Of Human Rhythmic Activity In A Rcc Roof Slab

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ISSN 2348 – 7968

Analysis of Harmonic Behaviour of Human Rhythmic

Activity in A RCC Roof Slab

1

G.Gajalakshmi, 2Dr.J.Abbas Mohaideen, 3Dr.A.R.Santha Kumar

1 Asst.Prof., Department of Civil Engineering,Sathyabama university.

2Principal, Maamallan Institute of Technology, Sriperumbudur.

3 Former Dean, Anna University. Chennai.

Abstract

Floor vibration is a natural phenomenon of a floor system in response to dynamic forces due to people activities like jumping, walking, dancing applied directly to the floor system. All suspended floors vibrate irrespective of the floor type whether steel or concrete or wood. The research related to vibration is not new and it is a complex phenomena. This paper is concerned with the dynamic study of a RCC floor slab of size7mx 7.5m. The analysis is done using ANSYS. The human rhythmic activity is been conducted on the slab and the modal and Harmonic analysis are done. The results are compared with IS 800 recommendations.

Key words: Vibration, rhythmic,Modal,Harmonic,Frequency,Amplitude,ANSYS

Introduction

The vibration is a general problem related to the dynamic movements of human rhythmic activities like jumping,dancing(Bachmann and Ammann 1987, Murray and Howard 1998, Silva et al. 2003). The modern construction concentrate on slender floor with high strength materials. This slender slab creates unwanted vibration. This excessive floor vibration can make people feel insecure and uncomfortable. Sometimes, the vibration can create people get afraid of a structural failure also. The fear, of course is unwarranted since the displacement and stress induced by floor vibration are generally small in view of the design criteria for structural safety.

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ISSN 2348 – 7968

Mathematical Equation from Faisca

Faisca (2003) considered the dynamic loads, based on results achieved through a long series of experimental tests made with individuals carrying out rhythmic and non-rhythmic activities. These dynamic loads, generated by human activities, are described such as jumps with and without stimulation, aerobics, soccer, rock concert audiences and dancing. The load modeling is able to simulate human activities like aerobic gymnastics, dancing and free jumps.

The mathematical representation of the human dynamic loading is described by the following equation .This expression requires some parameters like the activity period T, contact period with the structure Tc, period without contact with the model Ts, impact coefficient Kp, and phase coefficient CD.

Where:

F (t): dynamic loading, in (N);

t: time, in (s);

T: activity period (s);

Tc: activity contact period (s);

P: weight of the individual (N);

Kp: impact coefficient;

CD: phase coefficient.

STRUCTURAL FLOOR DETAILS

The composite floor system consisted of span 7mx 7.5m .

RC Beam Details: 8"x 18"

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ISSN 2348 – 7968 The concrete slab had a 25N/mm2 specified compression strength and a 2.4x104 N/mm2 Young’s Modulus (Faisca).

Fig.1 Layout of the floor plan.

Finite Element Analysis using ANSYS

The proposed computational model, developed for the RCC floor dynamic analysis, adopted the usual mesh refinement techniques present in finite element method simulations implemented in the ANSYS program (ANSYS, 11). In the present computational model, the floor beams are represented by three-dimensional beam elements (BEAM44), tension, compression, bending and torsion capabilities. The floor slab is represented by shell finite elements (SHELL63).

In this investigation, it is considered that materials (beam and slab) presented total interaction and have an elastic behaviour.

ANALYSES OF FLOOR MODEL

LOADING SCHEME

The individual person weight is equal to 70kg(0.8kN- Bachmann &Amman, 1987).The assumed Damping ratio is equal to 2%(ξ = 0.02(IS 800- 2007).

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ISSN 2348 – 7968 influence of the dynamical loads on the adjacent slab floor, as shown Fig. 2. In the current investigation, the human rhythmic dynamic loads are applied to the structural model corresponding to the effect of 2, 4, 8, 10, 12,14,16 and 18 individuals practicing aerobics. Hence 18 individual practicing is the full load condition for the numerical model.

Fig.2 Load distribution Scheme associated to fourteen individuals

METHODS OF ANALYSIS

The following analysis are performed for the numerical model,

 Model Analysis

 Harmonic analysis

MODAL ANALYSIS

The concrete floor's natural frequencies is determined with the aid of the numerical simulations. The structural system vibration mode shapes and the natural frequency values are tabulated. It is starting point for more detailed dynamic analysis, such as harmonic response analysis, transient dynamic analysis.

HARMONIC ANALYSIS

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ISSN 2348 – 7968 corresponding Amplitudes are measured. The dynamic response of FE model floor Amplitudes are compared by varying number of person’s activities.

Results and Discussions.

Modal Analysis:

The first six mode shapes are considered and the corresponding natural frequencies are tabulated.

Table1. Mode Shape and its Natural Frequency

Mode shape

1 2 3 4 5 6

Natural frequency

9.055 16.913 17.983 21.302 29.645 37.621

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ISSN 2348 – 7968

Fig.4 Mode shape 4 with natural frequency 21.302Hz.

Harmonic Analysis:

The results of 2,4,6,8,10,12,16 &18 persons rhythmic movements of Harmonic analysis are tabulated below.

Table 2.maximum amplitude values

No of Persons

Maximum.Freq Maximum Amplitude

Point A Point B Point A Point B

2 9.05 9.05 0.12 0.147

4 9.05 9.05 0.251 0.305

6 9.05 9.05 0.375 0.46

8 9.05 9.05 0.49 0.599

10 9.05 9.05 0.639 0.778

12 9.05 9.05 0.732 0.891

14 9.05 9.05 0.851 1.039

16 9.05 9.05 0.981 1.19

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ISSN 2348 – 7968

Fig.5 SIX PERSONS LOADING AT POINT A

Fig.6 TEN PERSONS LOADING AT POINT B

Discussions:

IS 800-2007 quotes that" In the frequency range of 2 to 8Hz in which people are most sensitive to vibration"

The first natural frequency which is obtained from analysis is 9.05Hz. This value is closer to the value suggested by IS 800. The floor slab may be in the critical place for dynamic activities like jumping.

Two points A & B are selected on which the response like modal analysis and Harmonic analysis are obtained.

The first six mode shapes are considered for such dynamic activities. The amplitudes are measured at point A and B. The human induced loads by jumping on the respective node points. Initially two persons are allowed to jump. Consecutively it is by 4,6,8,10,12,16,18 persons . The values are comparatively lesser in point A to Point B.

‐0.6 ‐0.4 ‐0.2 0 0.2 0.4 0.6

0 10 20 30 40 50 60

AM PLI TUDE   IN   "MM" FRQUENCY IN Hz

FREQUENCY

 

VS

 

AMPLITUDE

‐1 ‐0.5 0 0.5 1

0 20 40 60

AMPLITUD E   IN   "MM" FRQUENCY IN Hz

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ISSN 2348 – 7968

Fig. 7Harmonic Analysis-Maximum Amplitude Vs Number of Persons 

Conclusion:

The RC concrete floor slab is analysed using ANSYS. The first natural frequency is obtained as 9.05 Hz. As per IS 800, " Natural frequency of the floor vibration corresponding to the lowest mode of vibration, damping characteristics are important characteristics in floor vibration". Since the frequency value is to the value of 8Hz(IS 800-2007), it advise able to make floor with more stiffness. The designer should know the occupancy usage of floor before construction. This will make the structure under dynamic activities like human rhythmic activity more stiffener at the initial stage itself.

Reference:

1. Allen ,D.E et al(1985) Vibration criteria for assembly occupancies, Canadian journal of Civil engineering, vol.12, pp. 617 – 623.

2. Allen ,D.E (1990) Building vibration from human activities, ACI concrete International -Design and Construction.

3. Bachmann,H (1992) Case studies of structures with man induced vibration , Journal of Structural Engineering,vol-118,No:3.

4. Bruce Ellingwood,M and Andrew Tallin (1984) Structural Serviceability -Floor vibration, Journal of Structural Engineering, vol.110,No.2,ISSN 0733-9445.

0 0.5 1 1.5

0 2 4 6 8 10 12 14 16 18 20

Ma xi mu m   Amp litud e   in"mm" Number of persons

Harmonic Analysis‐Maximum Amplitude 

Vs Number of Persons

Maximum Amplitude 

Point A

Maximum Amplitude 

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ISSN 2348 – 7968

5. Da Silva, J.G.S. et al(2006) Dynamical response of composite steel deck floors, Latin American Journal of Solids and Structures, 3 .

6. Da Silva, J.G.S. et al(2008) Vibration Analysis of orthotropic composite floors for human rhythmic activities, Journal of Brazilian Society of Mechanical Sciences and Engineering, pp. 56 – 65, 2008.

7. Da Silva, J.G.S. et al(2011) Vibration Analysis of long span joist floors submitted to Human Rhythmic Activities, State University of Ride janeiro , ISBN 978-953-307-209-8, pp. 231 – 244, 2011.

8. Faisca, R.G. (2003)Caracterização de cargasdinâmicasgeradasporatividadeshumanas (Characterization of Dynamic Loads due to Human Activities), PhD Thesis (in Portuguese), COPPE/UFRJ, Rio de Janeiro, RJ, Brazil, pp. 1-240

9. IS 800:2007, Indian standard general construction in steel – code of practice- third revision

Figure

Fig.4  Mode shape 4 with natural frequency 21.302Hz.
Fig. 7Harmonic Analysis-Maximum Amplitude Vs Number of Persons

References

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