Shaking Table Testing. 1. Overview

Transcription

1 1. Overview (1) Introduction The seismic response of building structure depends on its dynmic properties nd chrcteristics of input ground motions. Nowdys, the dynmic properties of structures cn be esily clculted using computer softwre. However, vrious uncertin fctors disturb the exct estimtion of the dynmic properties. For exmple, influence of non-structurl elements is usully left out of ccount in the computtion. Effect of the soil-structure interction is one of the importnt yet hrd fctors. Under such sitution, it is importnt to investigte the dynmic properties of ctul structures nd discuss the vlidity of the computtion. There re some methods of investigting the dynmic properties of the building structures. Bsiclly, we need to mesure the response of the structure to externl force. Tble 1 explins some methods to exmine the dynmic properties. The method using rtificil externl force is delt with s dynmic testing hereinfter. Tble 1 Methods to investigte dynmic properties of structures Method Externl force Amplitude Micro-tremor mesurement Ambient vibrtions nd/or wind Very smll Strong motion observtion Erthquke motions Smll to lrge Dynmic testing Artificil forces Smll to lrge Dynmic testing cn be clssified into three types, i.e. shking tble test, vibrtion genertor test nd free vibrtion test, s shown in Tble. We need to use some equipment to pply externl force to the trget structure. The response of the structure is mesured s displcement, velocity nd/or ccelertion time histories. Through the nlysis of the response, the dynmic properties, represented by nturl frequencies, dmping rtios, nd vibrtion modes, cn be estimted. Tble Dynmic testing methods Shking tble Test Externl force Result 1- to 3-D hrmonic or rndom wve 1- to 3-D rndom wve (white noise, rtificil wve or observed strong motion) Elstic resonnce curve Time history of elstic or elsto-plstic response Vibrtion genertor 1-D hrmonic wve Resonnce curve Free vibrtion Initil movement Time history of free vibrtion 1

2 () Shking Tble Test The shking tble test is relistic nd cler when the response of structure during n erthquke is discussed. A specimen is set up on the tble which cn be driven by ctutors s shown in Fig. 1. Test specimens re usully mnufctured for the shking tble test; therefore destructive test cn be performed. Miniturized specimens re sometime used becuse of the cpcity limittion of the tble. BRI hs one-dimensionl middle-sized shking tble in the Structurl Testing Lbortory. Recently constructed shking tbles cn be driven in two- or three-dimensions. Consequently, those cn reproduce ctul erthquke motions more fithfully thn one-dimensionl tbles. Periodic wves, such s sine, rectngulr nd tringulr, nd rndom wves, such s white noise, rtificil erthquke motions nd observed erthquke motions, cn be chosen s the input motion. Stedy-stte shking using hrmonic wves with vrious frequencies is usully mde to grsp generl dynmic properties of the specimen. Amplitudes of the input hrmonic wves re low nd response of the specimen remins in the elstic rnge. Rndom shking using white noise is utilized to check the dynmic properties in the elstic rnge s well. Rndom shking using observed strong motions cn simulte ctul sitution during n erthquke. The mplitude of the strong motion record is djusted ccording to the seismic cpcity of the specimen nd the testing purpose. You cn dmge nd destroy the specimen by the erthquke motion. Artificil erthquke motions my be used if strong motion records with desired chrcteristics cnnot be found out. By the other hnd, shking tble test is generlly costly to execute. The construction of shking tble fcilities would be big project. Specimens must be newly built only for testing. In ddition, there re limittions of size nd weight due to the shking tble cpcity. It is not esy to reproduce n ctul sitution.

3 Hrmonic wve Rndom wve Shking Tble Actutor Figure 1 Shking tble test (3) Vibrtion Genertor Test In the cse of ctul buildings, vibrtion genertor is often used to pply hrmonic externl forces. A vibrtion genertor is usully set up on the top of the trget structure s shown in Fig.. A simple vibrtion genertor consists of two sets of weights rotting in the opposite directions mutully. Consequently, the force in the X-direction is cnceled nd the cyclic force is generted in the Y-direction. The rotting speed is chnged step by step nd stedy-stte response t ech step is mesured. Finlly the vibrtion genertor test brings the resonnce curve of the trget structure. The hrmonic force generted by the equipment shown in Fig. is given by the following eqution: i t Ft () mr R e (1) where m R is the totl mss of the rotting weight, r is the rdius of the rotting weights, nd ω is the circulr frequency (rotting speed). Hrmonic force becomes lrger s rottion speed increses. So, hevy weights re required for testing lrge structures with low nturl frequencies. 3

4 1/4m R 1/m R Shking Tble Testing Vibrtion genertor Exciting Direction Top view 1/4m R Side view Figure Vibrtion genertor test (4) Free Vibrtion Test Free vibrtion test is intuitive nd reltively esy. The free vibrtion of the trget structure is mesured by providing initil movement s shown in Fig. 3. This test will be utilized for lrge-scle buildings if enough initil movement cn be pplied. The time history of free vibrtion provides the nturl period nd the dmping rtio of the trget structure. Initil movement Dmped free vibrtion Figure 3 Free vibrtion test 4

5 . Prctice in Dynmic Testing (1) Testing Model nd Mesuring System We use smll specimen which cn be regrded s single-degree-of-freedom system. The specimen consists of hevy steel hed, two thin steel pltes, nd rigid steel bse s shown in Fig. 4. Our objective is to determine the dynmic properties, i.e. the nturl period nd dmping rtio, of this specimen. Horizontl movements of the top nd bse of the model re importnt in most cses, so two ccelerometers (ccelertion sensors) re set up t the top nd t the bse of the specimen. The cbles from the ccelerometers re connected to the mplifier, which converts ccelertion to electric signl. Outputs from the mplifier re drwn on pen recorder s time histories. Accelerometer # Accelerometer #1 Specimen Amplifier Pen recorder Figure 4 Test specimen nd mesuring system () Accelerometer Clibrtion Before strting the dynmic testing, ccelerometers must be clibrted to determine their sensitivity which is necessry to convert mesured vlues to ccelertion. Figure 5 indictes the procedure of the ccelerometer clibrtion. First, n ccelerometer is set on the flt plce. The pen recorder drws stright line representing zero of ccelertion. When you turn its positive side down, the pen of the recorder shifts nd indictes the ccelertion of grvity. Then return the ccelerometer to the neutrl position, nd turn its negtive side down. Finlly, return it to the neutrl position gin. We cn know the sensitivity from the wveform s shown in Fig. 5. 5

6 (1) Neutrl () Turn to positive side (3) Neutrl (4) Turn to negtive side (5) Neutrl (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) +1G (+980 cm/s ) () (1) (3) Lpp (mm) (5) ±0G Time (4) Pen recorder rnge: R (volt/mm) Sensitivity: /(R Lpp) (G/volt) -1G (-980 cm/s ) Figure 5 Clibrtion of ccelerometers using grvity (3) Free Vibrtion Test One of the simplest wys to determine the dynmic properties of system is free vibrtion test. A stnding system strts vibrting freely when initil movement is pplied. For instnce, pull the top of the model nd relese it. Dmped free vibrtion cn be observed (Fig. 6). The nturl period nd the dmping rtio cn be red from the wve form of free vibrtion. Tm Tm+1 Accelertion m m+1 m+ tm tm+1 tm+ Time t Figure 6 Dmped free vibrtion The eqution of motion for single-degree-of-freedom system without pplied force is s follows: 6

7 xt () h xt () xt () () where x() t, x () t nd x() t.re ccelertion, velocity nd displcement of the mss, respectively. h is the dmping rtio nd 0 is the nturl circulr frequency. The solution of Eq. becomes: xt Ce h t h t () sin( 1 ) (3) where the constnts C nd re determined from initil conditions. The dmped nturl period is represented s time intervls, T m, T m 1,, of cyclic wves s shown in Fig. 6. The verge of severl time intervls should be used to ensure ccurcy. T n T 0 T ( t ) m i m n t m n i 0 n 1 h (4) where T 0 is the dmped nturl period nd T 0 is the undmped nturl period T / ). ( 0 0 The dmping rtio h cn be estimted from rtio of mplitude to one t the next cycle. The mplitude rtio of m to m 1 is the function of the dmping rtio. log e m m 1 h 1 h (5) The mplitude cn be of displcement, velocity nd ccelertion. When dmping rtio h is low, 1 h is close to one. Consequently, h cn be estimted s follows: loge h m m 1 (6) It is recommended to use the mplitude fter severl cycles ( m n ) in order to reduce error: 7

8 loge h n m m n (7) (4) Shking Tble Test A simple test using smll shking tble will be performed to determine the dynmic properties of the specimen. The tble is driven hrmoniclly with the specified frequency. The frequency of the hrmonic wve cn be controlled step by step nd ccelertions t the bse ( B ) nd t the top ( T ) re cptured on the recording pper t ech step s shown in Fig. 7. Ti = 1/fi Tj = 1/fj Accelertion Bse Top step i B, i T, i step j B, j T, j Time t Figure 7 Accelertion record from the shking tble test An exct frequency of the hrmonic wve nd pek-to-pek mplitudes B nd T cn be red from the wveform on the pper. It is recommended to use severl cycles to get the frequency T =(t10 - t0)/10 f =1/T t0 t10 Figure 8 Reding frequency Time t A resonnce curve is obtined from the reltionship between frequencies f of hrmonic wves nd mplitude rtios ( T / B) of the top to the bse. The frequency fmx t which the resonnce curve becomes highest is pproximtely equl to the nturl frequency of the system. A dmping rtio is computed from the shpe of the resonnce curve s shown in Fig. 9. 8

9 ρ mx T B ρ / Amplitude rtio ρ mx f1 f fmx Frequency f Figure 9 Resonnce curve Dmping rtio h is roughly determined from the pek vlue using the following eqution if h is low: mx of resonnce curve 1 h mx (8) Another method determined h from frequencies (f 1 nd f in Fig. 9) t which the response mplitude is reduced to the level / mx, 1/ times of its pek vlue. The dmping rtio cn be estimted using f 1 nd f s follows. h f f f f 1 1 (9) 9

10 Exercises (1) Find out the nturl frequency nd the dmping rtio from the wveform of the free vibrtion test. Attch the wveform in the report s well. () Drw the resonnce curve from the result of the stedy-stte shking test. Find out the nturl frequency nd the dmping rtios (using eqution (8) nd (9)) from the resonnce curve. 10