[N571] Dynamic Load Factor for Floor Vibration due to Lively Concert. Kappyo Hong. Kwang Sup Yoon ABSTRACT

Transcription

1 The 3nd International Congress and Exposition on Noise Control Engineering Jeju International Convention Center, Seogwipo, Korea, August 5-8, 003 [N571] Dynamic Load Factor for Floor Vibration due to Lively Concert Kappyo Hong Department of Architectural Engineering, Yonsei University 134 Sinchon-dong Seodaemun-gu, Seoul, Korea Kwang Sup Yoon Department of Architectural Engineering, Yonsei University ABSTRACT Modern structures are being built using high-strength and light-weight construction materials resulting in decreased structural mass and damping properties. Especially rhythmic activities such as jumping, dancing and clapping due to lively concerts can produce excessive vibration in structures. In this study, dynamic load factors for lively concerts are presented through vibration tests on force platform and existing concert halls. The vibration test includes modal analysis and jumping tests according to the forcing frequencies and the number of participants. Dynamic load factors are acquired directly from the dynamic force transducer at each harmonics. Comparing NBC 1995, 3rd harmonic must be included in the design of lively concert halls, and dynamic load factors must be increased as a result of vibration tests. INTRODUCTION Modern structures are being built using high-strength and light-weight construction materials resulting in decreased structural mass and damping properties. Rhythmic activities such as jumping, dancing and clapping during lively concerts can produce excessive vibration in structures. Generally NBC 1995, Structural Commentaries Part 4 and AISC 1997, Floor vibrations caused by human activities are used for the design of rhythmic excitation. The codes define 3 types of activities such as dancing, lively concerts and jumping exercises. The

2 code for lively concerts are mainly derived from in-situ measurement of concert halls in 1970's and 1980's. Those days, the activities of lively concerts were defined as "rhythmic hand clapping in front of one's chest or above the head while bouncing vertically by forward and backward knee movement of about 50 mm []. But recently the activities of lively concerts without fixed seating have become harder, faster and more enthusiastic, much like a jumping exercise. Therefore, D.E Allen(1990) pointed out that some people near the stage of rock concerts, jump to the music beat and the loading function for these individuals should be assumed as that for jumping exercise [5]. But there are many problems in applying the jumping code to the lively concerts. There are many differences between the two activities, for example, the weight density of participant, forcing frequency and the number of harmonics and it may lead to conservative design of lively concerts. Accordingly new design code for lively concerts is required. The purpose of this study is to present revised dynamic load factors for lively concerts in line with new circumstances. At first, we measured the acceleration of a concert hall which has no fixed seating and found out the difference from the code. Then we constructed a force platform to measure the dynamic load. Based upon these measurements, we propose new dynamic load factors for lively concerts, which are varied according to the number of people per unit area. DEFINITION OF DYNAMIC LOAD FACTOR The forcing function P(t) will be given by the sum of the static component W P, and a dynamic component, F(t) [3,6] P(t)=W P+F(t) =Wp 1+ nsin(πnft+φ n) n=1 (1) where, n : Dynamic load factors φ n : Phase angle f : Forcing frequency W P : Weight of participant The dynamic load factor, n is defined as the ratio of peak sinusoidal force to the weight of participants. It may be easily seen that n is the Fourier coefficient of the dynamic forcing function normalized by the static weight of participants.

3 The steady-state response of sinusoidal force of equation (1) assuming single degree of freedom beam model can be expressed as follows [3]. ai 1.3 iwp Wt = g f o f o 1 + β f i f i () where, a : peak acceleration due to the i th harmonic of the loading function i g : gravity acceleration f i : forcing frequency f : natural frequency o β : damping ratio W t : the total weight of floor system IN-SITU VIBRATION MEASUREMENT OF CONCERT HALL Structural system The slab system is a composite metal deck(75 mm depth) with topping concrete of 80 mm and finished with light-weight concrete of 00 mm depth. An accelerometer was placed under the metal deck at the center of span. Modal Analysis Modal analysis was performed with accelerometer, impact hammer and analyzer. As a result of the modal analysis, fundamental frequency was 8.57Hz with 5.46% of damping ratio. Dynamic Load Factor from Field Measurement

4 (a) concert #8, f =.3Hz 1 (b) concert #9, f =3.0Hz 1 Figure 1. The Measurement of Lively Concert Figure 1 shows a summary of the measurement results. One is the acceleration time history and the other is the magnitude spectrum. Figure 1 shows three or four peaks. Obviously, these mean 1st, nd, 3rd harmonics respectively and have a difference in comparison with the codes that considered 1st or nd harmonic only. The range of forcing frequency measured is 1.9~3.1Hz which is similar with the codes(1.5~3.0hz). Table 1 shows dynamic load factors as a result of in-situ measurement of lively concert. The codes for lively concert was underestimated in dynamic load factors and weight of participants. Table 1. Dynamic Load Factors from In-situ Measurement No. Forcing Dynamic load factor Weight of participant frequency 1 3 (kpa) (Hz) # # # # #

5 VIBRATION TESTS USING FORCE PLATFORM Force Platform and Measurement Procedure 4000 F F H-00X00X8X1 L-100X100 H-50X15X6X9 PLYWOOD 16 T F1, F : Dynamic Force Transducer, Units are mm Figure. Force Platform Figure shows the plan of force platform. Dynamic force transducers were placed at mid span of beams, F1 and F. Dynamic loads were measured directly from two transducers, and were added at the time-domain. The combined signal was obtained using a FFT analyzer. Test Procedure Experiments for a lively concert were performed to music. Seven songs were collected according to music beat which was forcing frequency. Group sizes were 5 types (8,1,16,0,4 person), Groups of 8~4 people corresponded to density of people/ m ~ 6 people/ m. Experiments were repeated 3 times at each group sizes. 17 men and 7 women participated in the experiment program. The average weight of participants was 646N, standard deviation was 93N. This is similar to 618N(average), 100N(standard deviation), representing the adult population in Korea(1998). Table shows a summary of experiments. Table. Summary of Tests Type Number of participants Density of participant Forcing frequency 1.6Hz, 1.7Hz, 1.9Hz, Lively 8,1,16,0,4 ~6person per unit area.0hz,.3hz,.7hz, Concert.8Hz

6 Estimation of Dynamic Load Factor for Lively Concert The vibration of a lively concert has the tendency to distribute the value widely, but to decrease with a density. Table 3 shows the maximum, minimum and average of the estimated dynamic load factor for a lively concert. Table 3. The Result for Lively Concert Density of Dynamic load factor participants 1st harmonic nd harmonic 3rd harmonic Type (No. of person Max Min Avrg. Max Min Avrg. Max Min Avrg. per unit area) Lively Concert SUMMARY AND CONCLUSIONS The purpose of this study is to present revised dynamic load factors for lively concerts which have no fixed seating according to new circumstances. Tests were made to use a force platform to consider the change of dynamic load factor according to the number of participants per unit area, which is the density of participant. The dynamic loads were measured directly from the dynamic force transducers and dynamic load factor were analyzed by Fast Fourier Transform. The summarized results are as follows ; The activities of lively concerts have changed, and it is the jumping activity that governs the vibration of concert halls without fixed seating. Therefore, 3rd harmonic must be included in the design of concert hall. Dynamic load factors are reduced according to the number of participants and the density of participants. We propose new values for the dynamic load factors which varies according to the density of participants. REFERENCES 1. H. Bachman and W. Ammann, "Vibrations in Structures Induced by Man and Machines", (IABSE, 1987). H. Bachman, Vibration Problems in Structures, (Birkhauser, 1995)

7 3. D. E. Allen, J. H. Rainer and G. Pernica, "Vibration Criteria for Assembly Occupancies", Can. J. Civ. Eng. 1(3), (1985) 4. D. E. Allen, "Floor vibrations from Aerobics", Can. J. Civ. Eng., 17, (1990) 5. D. E. Allen, "Building vibrations from Human Activities", Concrete International, June, (1990) 6. G. Pernica, "Dynamic Load Factors for Pedestrian Movements and Rhythmic Exercises", Canadian Acoustics 18(), 3-18 (1990) 7. A. Ebrahimpour, R. L. Sack and W. N. Patten, "Measuring and Modeling Dynamic Loads Imposed by Moving Crowds", ASCE J. of Str. Eng. Vol.1, No.1, (1996) 8. User's Guide-Structural Commentaries to Part 4 of the National Building Code of Canada, National Research Council of Canada, Ottawa (1995) 9. Steel Design Guide Series 11, Floor Vibrations Due to Human Activity, American Institute of Steel Construction, Chicago (1997) 10. Minimizing Floor Vibration, Applied Technology Council, California (1999)