DEVELOPMENT OF REAL-TIME RESIDUAL SEISMIC CAPACITY EVALUATION SYSTEM -INTEGRAL METHOD AND SHAKING TABLE TEST WITH PLAIN STEEL FRAME-

Size: px
Start display at page:

Download "DEVELOPMENT OF REAL-TIME RESIDUAL SEISMIC CAPACITY EVALUATION SYSTEM -INTEGRAL METHOD AND SHAKING TABLE TEST WITH PLAIN STEEL FRAME-"

Transcription

1 13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 24 Paper No. 69 DEVEOPENT OF REA-TIE RESIDUA SEISIC CAPACITY EVAUATION SYSTE -INTEGRA ETHOD AND SHAKING TABE TEST WITH PAIN STEE FRAE- Koch KUSUNOKI 1 and asaom TESHIGAWARA 2 SUARY In order to reduce furthermore damage of structures and the number of refugee due to an aftershock, a quck nspecton on the damaged buldngs must be carred out. However, the buldngs have to be nvestgated one by one by engneers or researchers under the present stuaton. The judgement can vary accordng to the engneers experences and t takes long tme to nvestgate all damaged buldngs. Ths research ams to develop a new automatc and quck nspecton system that has only a few cheap accelerometers. Ths system makes t possble to ndcate the safety level of a buldng aganst an aftershock to nhabtants mmedately. The judgement wll be made based on the spectrum method. In ths paper, shakng table test results wth steel frame structures are presented to confrm the valdty of the system. INTRODUCTION Once a bg earthquake occurs, many buldngs are severely damaged, and consequently t gves rse to many homeless. The damage level could ncrease due to an aftershock n some buldngs. Thus enormous harm to the nhabtants n such buldngs could occur. On the contrary, some people could get caught up n fear and would escape from even the buldngs that have enough resdual sesmc capacty from the engneerng pont of vew. Hence, the number of homeless can ncrease drastcally. In order to reduce further damage due to an aftershock and to reduce the number of homeless, a quck nspecton on the damaged buldngs must be carred out soon after a man shock. However, under the present stuaton, the buldngs have to be nvestgated one by one by engneers or researchers. For example, 5,68 engneers and 19 days were needed to nvestgate 46, buldngs on a damaged area at the Kobe earthquake (JBDP [1]). Nneteen days were too long and yet the number of nvestgated buldngs was not enough. oreover, many buldngs were judged as Cauton level, whch needs detaled nvestgaton by engneers. Cauton judgement s a gray zone and t could not take away anxetes from nhabtants. Furthermore, the current quck nvestgaton system presents a dlemma snce buldngs should be nvestgated by vsual observaton of engneers. Thus, ths judgement vares accordng to the engneers experences. 1 Senor Researcher of Buldng Research Insttute, Japan, kusunok@kenken.go.jp 2 Chef Researcher of Buldng Research Insttute, Japan, tesh@kenken.go.jp

2 On the other hand, f t s possble to calculate the performance and demand curve (JBRP [2]) from a measured acceleraton of the basement and of each floor of a structure wth cheap accelerometers, and further estmate the resdual sesmc capacty of a structure by comparng these curves, the problems mentoned above can be solved. To draw the performance curve, the absolute response acceleratons and relatve response dsplacement on each floor are needed. A certan fxture s generally needed to measure the nter-story drft or the relatve response dsplacement to the basement. Ths fxture can be obstructve for usage. On the contrary, t s easy to measure acceleratons wth accelerometers. If dsplacements can be derved from the acceleratons wth double ntegral, the performance curve of structures can be easly measured. In ths paper, a new real-tme resdual sesmc capacty evaluaton system was proposed. Furthermore, shakng table tests wth steel plane frame was carred out to confrm the valdty of the proposed evaluaton system. CONFIGURATION OF THE SYSTE AND OUTINE OF THE EVAUATION Ths system has bascally two accelerometers and one judgement machne as shown n Fg. 1. The evaluaton method s based on the performance desgn concept as shown n Fg. 2. The resdual sesmc capacty wll be judged by comparng the measured performance curve of a structure and the measured demand curve. Accelerometer Accelerometer Judgement machne Fg. 1 Confguraton of the system The performance curve s the relatonshp between the representatve deformaton D and the representatve restorng force S, whch shows the predomnant response of a structure. The method to evaluate theses representatve values s outlned below. The calculated relatve dsplacement vector to the basement { x} derved as Eq. 1 wth the modal partcpaton factor { x} s the unque vbraton mode. { x} = { u} β Eq. 1 from measured acceleratons can be β, mode vector { u}, and the assumpton that the

3 S Shear coef. and Resp. Acc. Sa (kn/ud) Yeldng dampng of 5% Redcton due to damage ax. response Ultmate dsp. Performance curve Horzontal deformaton Sd (m) Fg. 2 Outlne of the evaluaton based on the Performance desgn concept The story shear (nerta force) of the frst story Q B can be calculated usng Eq. 2 wth the measured absolute acceleraton { & x + & x } and mass m of each floor. Q ( x& & x ) m & + Eq. 2 B = The equaton of moton of a mult-degree-of-freedom system can be reduced to a sngle- degree-offreedom system as gven n Eq & C ~ + & K ~ = & : Total mass of a structure C ~ : Equvalent dampng K ~ : Equvalent stffness & x& : Ground acceleraton x The Q B can be calculated wth Eq. 4. If the frst mode s predomnant enough, the calculated angular K ~ frequency, ω =, can be the natural angular frequency of the frst mode. Eq. 3 S= Q = & B Eq. 4 Eq. 5 can be derved from Eq. 1 by devdng both sdes by. The nerta force actng on each floor can be derved as Eq. 6 by usng Eq. 1 and Eq. 5. x β u = Eq. 5 x P = m β u && = m & Eq. 6 P

4 The total mass can also be derved from Eq. 4 and Eq. 6 snce the total mass s the sum of each floor mass,.e.; x m && Q m x B = = = = m && && Therefore, the representatve dsplacement can be derved as Eq. 7. = m m x Eq. 7 The representatve acceleraton, & s appled to the representatve restorng force, S ( S = Q m = & ). If a system s elastc, the representatve dsplacement, and the representatve acceleraton, can be calculated wth Eq. 8,.e.; 2 2 & + 2 h & & ω + ω = x Eq. 8 h : Dampng coeffcent ω : Angular frequency S As a result, the maxmum representatve dsplacement max and the absolute acceleraton ( & + & x& ) max correspond to the value from the response dsplacement and acceleraton spectrum wth a dampng coeffcent of h. On the other hand, the demand curve s the relatonshp between the response acceleraton (Sa) and dsplacement (Sd) spectrum. The ntersecton pont of the demand and performance curve shows the maxmum elastc response. However, the damage of a structure can dsspate some amount of an nput energy, thus the dampng effect can be ncreased. Therefore, the demand curve can be reduced accordng to the damage (Fg. 2). The ntersecton pont of the reduced demand and performance curves shows the maxmum nelastc response. Addtonally, the followng three challengng assumptons were appled for the judgement of the resdual sesmc capacty. These assumptons need further studes. Defnton of aftershock The mechansm of an aftershock s the same as the man shock, and the aftershock s always smaller than the man shock Wth ths assumpton, the demand curve of the aftershock corresponds to the man shock. Substtute dampng rato for aftershock and judgement The dampng coeffcent for the demand curve of an aftershock s 5% In fact, f further damage occurred n a structure durng an aftershock, an addtonal dampng can be acheved, then the demand curve wll be reduced. However, t s dffcult now to estmate accurately the dampng effect due to the damage durng an aftershock. Therefore, the dampng effect due to nelastc behavor durng an aftershock s neglected and 5% vscous dampng s taken nto account for the judgement on the safe sde. The resdual sesmc capacty can be calculated wth the comparson of the demand curve wth 5% dampng and the performance curve. If the rato of the Sa(=Sa p ) at the ultmate

5 dsplacement on the performance curve to the Sa(=Sa d ) on the demand curve s greater than 1., the structure wll be judged as SAFE, and f t s less than 1., t wll be judged as UNSAFE. The restorng force and the vbraton mode wll be constant after the maxmum response s reached and less than the ultmate. If the maxmum response s less than the ultmate dsplacement, the performance curve to the ultmate dsplacement must be extrapolated. The restorng force and the vbraton mode are assumed as constant after the maxmum response reached to the ultmate dsplacement. If a structure s elastc durng a man shock, the performance curve calculated wth the assumpton (3) can be much underestmated snce the restorng force at the ultmate dsplacement can be less than the yeldng strength. Therefore, t must be judged separately f a structure s elastc. The elastc-nelastc judgement method s shown n Fg. 3. Frstly, the approxmated stffness of the envelope curve of the performance curve s calculated. Secondly, the error between the envelope curve and the approxmated lne, Sd ( ), s calculated. If the rato of the maxmum value of, Sd ( ), to the maxmum response, Sd max, s less than a tolerance, t s judged as elastc. In ths study, a 5% tolerance s appled. Approxmated stffness ax. response Sd () Sa (G) Sa-Sd Envelope Sd (cm) Sd max Fg. 3 Elastc-nelastc judgement The judgement flowchart s shown n Fg. 4. The responses of a buldng and an nput earthquake moton are measured by accelerometers, and the resdual sesmc capacty,.e. how large the aftershock can be sustaned by the buldng, s calculated from these measured acceleratons. The safety level aganst an aftershock can be ndcated just soon after a man shock. Ths System has a computer applcaton, whch can calculate the followng tems; Integrate the measured acceleratons twce to calculate the response dsplacements. Calculate the base-shear coeffcent and the representatve dsplacement of the buldng wth an assumed mode shape. (tems 7 & 8 n Fg. 4) Draw the performance curve of the structure. (tem 9 n Fg. 4) Draw the envelope curve of the performance curve. (tem 1 n Fg. 4) Calculate the response spectrum of the measured acceleraton on the basement, and calculate the demand curve. (14 n Fg. 4)

6 Evaluate the resdual sesmc capacty of the buldng by means of the performance and demand curves. easured acceleraton on basement 1 measurem X & j Integraton 2 relatve dsp. m X j 3 Vbraton mode of buldng 4 Calculate Interstory drft C X 5 Calculate Abs. Acc. on each & floor C X& 6 ass rato m ~ 7 Representatve Dsp. Sd m ~ C X Sd = ~ 2 m X C 8 Representatve Acc. Sa = m ~ C X& S a m~ 13 From measured acc. X & m Calculate Resp. Acc. Spectra Ra Resp. Dsp. Spectra Rd 9 Generate Performance Curve 1 Draw envelope curve of 9 11 Ultmate Dsp. Ru 14 Calculate (Ra- Rd Curve) Compare 12 Draw Performance curve untl Ultmate Dsp. 15 Judgement Elastc Safe Danger Input value 16 Indcate judgement Fg. 4 Judgement flow chart Items 3, 6, and 11 n Fg. 4 must be defned pror to makng a judgement. The tem 3 (vbraton mode shape) s to calculate the response acceleratons on the floors where there are no accelerometers. For example, a lnear or a constant dstrbuton shape between measured floors can be appled. The tem 6 (mass rato) can be calculated from floor area rato between each floor. At the moment, tem 11 (ultmate dsplacement) can be defned from the correspondng adopted buldng code.

7 INTEGRATION ETHOD TO CACUATE DISPACEENT FRO ACCEERATION The response dsplacement s derved from measured acceleraton wth double ntegral technque n the proposed evaluaton system. If dsplacement s calculated wth the trapezodal ntegral technque, t can dverge easly. There are two ways to ntegrate acceleraton record, ntegraton n frequency-doman and n tme-doman. The Iwan s method (Iwan [3]) was appled for the system, whch ntegrates n tme-doman. The outlne of Iwan s method s descrbed below. The nose level observed durng a prncpal shock s assumed to be constant. The nose level before and after a prncpal shock are also assumed to be constant but dfferent values. The nose level before a prncpal shock can be calculated as the average of measured acceleraton record untl the prncpal shock starts. At frst, the calculated nose level before the prncpal shock s subtracted from whole measured acceleraton record. Then adjusted acceleraton record s ntegrated to calculate tme hstory of velocty (Fg. 5). The velocty baselne shft after a prncpal shock s calculated wth lnearzaton technque so that the velocty can be zero at enough after the prncpal shock. The velocty baselne shft durng the prncpal shock can be calculated so that the velocty baselne shft due to the nose level can contnue from the prncpal shock doman to after the prncpal shock doman. The measured acceleraton from the shakng table test of the 3-story steel structure, and the ntegrated dsplacement wthout usng the Iwan s method are shown n Fg. 6. The calculated velocty baselne shft by usng Iwan s method mentoned above s shown n Fg. 7, and the acceleraton baselne shft s shown n Fg. 8. It s obvous from Fg. 7that the calculated velocty baselne shft s not approprate. The tmehstory of the adjusted velocty s elbowed durng the prncpal shock, and the calculated dsplacement from the elbowed velocty can nclude much error. It can be the reason why several strong pulses are observed durng the prncpal shock n Fg. 6, and the baselne shft could occur at each pulse because of the non-lnearty of the accelerometers. Because of that, the baselne shft durng the prncpal shock could not be represented by the constant acceleraton. Velocty (kne) 2 15 Velocty due to Nose Before Prncpal shock After prncpal shock Tme (sec) Fg. 5 Iwan s ntegraton method (velocty) Acceleraton (gal) Dsplacement (cm) (1) (2) Tme (sec) Fg. 6 easured acceleraton and the ntegrated dsplacement (3)

8 Velocty (kne) Acceleraton baselne shft (gal) (1) Intal baselne shft (2) (3) Baselne shft Tme (sec) Fg. 7 Velocty wthout ntal acceleraton baselne shft and velocty baselne shft Tme (sec) Fg. 8 Calculated baselne shft Fg. 9 shows the Fourer ampltude of the ntegrated dsplacement from the tme hstory of the elbowed velocty. It can be observed that t contans much low-frequency (long perod) components because of the elbowed shaped velocty. In order to remove the error components n frequency-doman, the proper lower and upper bound frequences ω and ω H must be found automatcally. The proposed method to fnd out ω and ω s descrbed below. H Frstly, the power spectrum of the adjusted velocty wth the Iwan s method s smoothed wth the Parzen s Spectral Wndow (Osak [4]) (Fg. 1). Secondly, the frequences mnω when the Fourer ampltude s a local mnmum are found. Sometmes more than one mnω can be found. Three mnω were shown n Fg. 1. Thrdly, the frequences maxω when the Fourer ampltude s a local maxmum between mnω and mnω +1, and the dfference of the Fourer ampltudes at mnω and maxω, h, can be calculated. The mnω of whch h s the maxmum s appled for the ω. Snce the h 2 was the maxmum n Fg. 1, the ω was calculated as Hz. If the Fourer ampltude at the frst natural frequency s enough greater than the Fourer ampltude at the ω (F 2 n Fg. 1), an approprate ω can be found. If t s not enough greater, a hgher degree functon must be appled to calculate baselne shft durng a prncpal shock. If a measured acceleraton contans no error, the ω s calculated as Hz snce the power spectrum shows monotone ncreasng functon from Hz to the frst natural frequency. The upper bound frequency ω H was defned as 25 Hz snce the frequency characterstc of the accelerometer (frequency bandwdth able to be measured) was from a DC up to 3Hz. Fnally, the Butterworth flter, whch s a knd of band-pass flter, wth ts parameter of 4 (Boore [5]) was appled for the Fourer spectrum of the calculated velocty wth the Iwan s method from ω to ω H. The Fourer spectra wth and wthout the Butterworth flter are shown n Fg. 11. The dsplacement can be calculated from the velocty, whch s nversely Fourer transferred from Fg. 11. The calculated dsplacement of the measured acceleraton shown n Fg. 6 and measured dsplacement durng the shakng table test are shown n Fg. 12. It can be observed that the calculated dsplacement agreed well wth the measured dsplacement. It can be thought to use the band-pass flter for the dsplacement wthout the Iwan s method shown n Fg. 6. However, f the Iwan s method was not appled, the effect of nose can be bg enough so that the

9 component of real vbraton can hde behnd the nose components n the Fourer. In other words, the Iwan s method must be appled to reduce the nose components so that the ω can be clearly observed. The proposed method to fnd out the ω s utlzng the characterstc of the structural vbraton of whch natural frequency can be clearly found n the Fourer spectrum. Therefore, the proposed method has to be used carefully n case of ntegratng a measured ground acceleraton snce t has many and random predomnant frequences Fourer ampltude 6 4 Fourer Ampltude 6 4 h 1 h F Frequency (Hz) Fg. 9 Fourer ampltude of the ntegrated dsplacement (Iwan s method) h 3 ω 2 4 6ω 1 ω 2 =ω Frequency (Hz) Fg. 1 How to fnd the ω Fourer Ampltude Velocty w/ Iwan's method Wth Butterworth Flter Between ω <->ω h Butterworth flter H (ω) H(ω) for Butterworth flter Response dsplacement (mm) Integrated dsplacement easured dsplacement. ω 2 =ω Frequency (Hz) Fg. 11 Comparson of Fourer spectra Tme (sec) Fg. 12 Integrated dsplacement wth band-pass flter and measured dsplacement APPICABIITY WITH THE SHAKING TABE TEST RESUTS Test specmens The specmens were one span plane steel frame structure of whch masses are concentrated to the nodal ponts. Steel plats, of whch wdth was 1mm and thckness was 6mm, were used for columns and beams. The number of story was 1, 2, and 3. The 3-story specmen s shown n Fg. 13. The span length was 1,mm and the story heght was 595mm for the frst story and 6mm for the second and thrd story. The weght at the nodal pont was 19 N.

10 Two dfferent falure modes of specmen, story falure n the frst story and total yeldng falure (both ends of beams and bottom of the frst story columns yeld, referred to as total falure, subsequently) were expected. In order to acheve the expected falure, the low-yeld strength steel (nomnal strength s 1 N/mm 2, referred to as Y1, subsequently) was used for the yeld members, and the ordnal strength steel (nomnal strength s 4 N/mm 2, referred to as SN4, subsequently) was appled for the not-yeld members. The materal test results are lsted n Table 1. The average yeld strength of Y1 was 72.4 N/mm 2, and N/mm 2 for SN4. The lateral strength of each specmen was calculated wth these average strengths lsted n Table 1 based on the prncple of vrtual work. The base shear coeffcent of each specmen s lsted n Table 2. Sngle story had hgh base shear coeffcent of.67. On the other hand, the value for other specmens were relatvely low as not exceedng Case Fg. 13 Test specmen (3-story) Table 1 ateral propertes Yeld stress (N/mm 2 ) Young s module (N/mm 2 ) Yeld Stran ( µ ) Fracture stress (N/mm 2 ) Y Average SN Average Table 2 Base shear coeffcent of each specmen Sngle story 2-story 3-story Story falure Total falure

11 The NS component of the El Centro earthquake record was used for the nput moton. The 5% PGA level of the record was nputted frst. Then the nput level was ncreased by 5% up to the maxmum capacty of the shakng table, 18%. The nput moton s shown n Fg. 14, and the Sa-Sd curve (demand curve) s shown n Fg. 15. The elastc response lne wth natural perod of.5 s also shown n the fgure. Ground acceleraton (m/sec 2 ) Sa (G) T=.5sec Tme (sec) Fg. 14 Input moton (1% amplfcaton) Sd (mm) Fg. 15 Sa-Sd curve for the nput moton (1% amplfcaton) easurement The measurng system s shown n Fg. 16. Each story had an accelerometer on the center of the beam to measure the response acceleraton and to be used for double ntegral to calculate dsplacement. Another accelerometer was also placed on the surface of the shakng table to measure the actually nputted moton. The response dsplacements of each floor and the shakng table were also measured by transducers to confrm the accuracy of the ntegrated dsplacement and of the performance curve wth the ntegrated dsplacement. easurng tower Transducer Specmen Transducer Accelerometer Transducer Transducer Shakng table Fg. 16 easurng system

12 The measurng frequency of 1Hz was appled. The measurement was automatcally started wth the system start trgger of 5 mm/sec 2 (5 gal). If an accelerometer senses acceleraton of more than 5 gal, the measurement system was started. Snce the accelerometer system has a memory, the record from 5 seconds pror to the trggered tme was also stored. Then when the measured acceleraton dd not exceed 5 gal for 1 seconds, the measurement was automatcally stopped and the resdual sesmc capacty evaluaton program was executed. For the evaluaton, the ultmate deformaton angle was assumed as.1%. For the double ntegral, the prncpal nput moton ((2) porton n Fg. 6) was assumed to start when the measured acceleraton exceeds 5 gal, and to end when the measured acceleraton dd not exceeds 5 gal subsequently. Test results and dscussons The performance curve of the 2-story total falure specmen calculated wth ntegrated dsplacement from measured acceleraton and the curve wth measured dsplacement are shown n Fg. 17. The nput level was 5% of the orgnal record. The demand curve calculated from the measured acceleraton on the surface of the shakng table s also supermposed n the fgure. The specmen was judged EASTIC. The strength of the 2-story total falure specmen was calculated as.3 (Table 2). The measured maxmum base shear coeffcent exceeded.3 a lttle bt, however from Fg. 17, t can be seen the specmen s stll elastc or just yelded. The performance curve wth the dsplacement from the measured acceleraton agreed very well wth the curve wth the measured dsplacement Sa (G) Integrated -.4 easured Sd (mm) Fg. 17 Envelope of the Sa-Sd curve (2-story, total falure, 5% nput amplfcaton) Fg. 18 shows the both performance curves of the 3-story story falure specmen. The nput level was the 11% of the orgnal record. The ntegrated maxmum dsplacement was 57mm n the postve drecton. The performance curve wth the ntegrated dsplacement was extended horzontally from the recorded maxmum dsplacement pont to the assumed ultmate dsplacement. The specmen was judged UNSAFE, snce t was evaluated nelastc and the expected ultmate pont was less than the demand curve wth 5% dampng. The rato of the ultmate pont to the demand curve (resdual sesmc capacty rato) was calculated as.836. Ths value shows that the specmen wll survve after the aftershock of whch level s 83.6% of the man shock. Even the specmen was nelastc and response dsplacement was relatvely bg, the performance curve wth dsplacement from measured acceleraton agreed acceptably wth the curve wth measured dsplacement. Fg. 19 shows the response and ntegrated response dsplacement on the top of the specmen. The ntegrated dsplacement from the measured acceleraton agreed very well wth the measured dsplacement.

13 Sa (G) Integrated -.8 easured Sd (mm) Fg. 18 Envelope of the Sa-Sd curve (3-story, story falure, 11% nput amplfcaton) 14 Relatve dsplacement (mm) F Integrated easured Tme (sec) Fg. 19 Relatve dsplacement hstory on the 3 rd floor (3-story, story falure, 11% nput amplfcaton) In order to make a severe damage to the 2-story story falure specmen, the sectonal area of the column was reduced. Fg. 2 shows Sa-Sd curves wth ntegrated and measured dsplacements. The Sa-Sd curve wth ntegrated dsplacement s less than the curve wth measured dsplacement n the negatve drecton. Fg. 21 shows the ntegrated and measured relatve dsplacements to the shakng table on the top of the specmen. It can be seen that large resdual dsplacement occurred n the negatve drecton because of the yeldng. However, the resdual dsplacement could not be seen n the ntegrated dsplacement, snce the band-pass flter s appled durng the ntegraton and the long perod porton s cut off. Although the Sa-Sd curves shown n Fg. 2 are dfferent, the envelope curve of the Sa-Sd curve agreed well as shown n Fg. 22. Snce the evaluaton s carred out wth the performance curve (envelope curve of the Sa-Sd curve), f the yeldng dsplacement and strength are predcted well from the measurement, the accuracy of the evaluaton can be acceptable. Thus, the dfference of the resdual dsplacement can be not effectve to the evaluaton result.

14 Sa (G) Integrated easured Sd (mm) Fg. 2 Sa-Sd curve (2-story, story falure, 18% nput amplfcaton, column secton was reduced) Relatve dsplacement (mm) F Integrated easured Tme (sec) Fg. 21 Relatve dsplacement hstory on the 2 nd floor (2-story, story falure, 18% nput amplfcaton, column secton was reduced) 1..5 Sa (G) Integrated easured Sd (mm) Fg. 22 Envelope of the Sa-Sd curve (2-story, story falure, 18% nput amplfcaton, column secton was reduced)

15 CONCUDING REARKS In order to develop the real-tme resdual sesmc capacty evaluaton system for mprovng the safety aganst an aftershock, the outlne of the evaluaton system, the evaluaton results wth exstng shakng table results. Results obtaned from the nvestgaton can be summarzed as follows; 1. The new resdual sesmc capacty evaluaton method was proposed. 2. The Iwan s ntegraton method cannot remove errors enough for some acceleraton record. However, the band-pass flter can remove the errors, whch cannot be removed wth the Iwan s method. 3. The new ntegraton method wth the algorthm to fnd out the lowermost frequency for the band-pass flter s proposed. 4. Snce the proposed ntegraton method utlzng the characterstc of the structural vbraton n whch predomnant frequences can be found obvously, more attenton must be pad n case of usng the proposed method to ntegrate ground acceleraton. 5. The ntegrated dsplacements from the measured acceleraton at the shakng table test agreed very well wth the measured dsplacements. However, the resdual dsplacement on the shakng table dd not agree well wth the measured dsplacement. 6. The dfference of the resdual dsplacement cannot affect the resdual sesmc capacty evaluaton result done by the proposed system. 7. The envelope of the performance curve calculated wth the ntegrated dsplacement agreed very well wth the measured envelope curve. 8. The valdty of the proposed evaluaton system was demonstrated wth shakng table test results of 1 bay 1 to 3 story steel frame specmens. REFERENCES 1. Buldng Center of Japan (BCJ), Report on the reconnassance commttee on the buldng damages due to the Hanshn-Awaj Great Earthquake Dsaster, Summerzaton -, (n Japanese) 2. Japan Buldng Research Promoton Assocaton (BRPA), Gudelnes for performance evaluaton of renforced concrete buldngs, Ghodo, 2.7 (n Japanese) 3. Iwan, W. D., et al.:some Observatons on Strong-moton Earthquake easurement usng a Dgtal Accelerograph, Bulletn of the Sesmologcal Socety of Amerca, Vol. 75, pp , Osak, Revsed manual for the spectral analyss for eathquake, Kashma-Syuppanka, 1994 (n Japanese) 5. Davd. Boore, Chrstopher D. Stephens, and Wllam B. Joyner, Comments on baselne correcton of dgtal strong-moton data: Examples from the 1999 Hector ne, Calforna, earthquake, BSSA, Vol. 1.3, Koch KUSUNOKI and asaom TESHIGAWARA, A new acceleraton ntegraton method to develop a real-tme resdual sesmc capacty evaluaton system, Journal of structural and constructon engneerng, Archtectural Insttute of Japan, No. 569, pp , 23.7 (n Japanese)

Assessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion

Assessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,

More information

Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading

Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading xpermental Study on Ultmate Strength of Flexural-Falure-Type RC Beams under Impact Loadng N. Ksh 1), O. Nakano 2~, K. G. Matsuoka 1), and T. Ando 1~ 1) Dept. of Cvl ngneerng, Muroran Insttute of Technology,

More information

9.2 Seismic Loads Using ASCE Standard 7-93

9.2 Seismic Loads Using ASCE Standard 7-93 CHAPER 9: Wnd and Sesmc Loads on Buldngs 9.2 Sesmc Loads Usng ASCE Standard 7-93 Descrpton A major porton of the Unted States s beleved to be subject to sesmc actvty suffcent to cause sgnfcant structural

More information

Structural Dynamics and Earthquake Engineering

Structural Dynamics and Earthquake Engineering Structural Dynamcs and Earthuake Engneerng Course 9 Sesmc-resstant desgn of structures (1) Sesmc acton Methods of elastc analyss Course notes are avalable for download at http://www.ct.upt.ro/users/aurelstratan/

More information

NON LINEAR ANALYSIS OF STRUCTURES ACCORDING TO NEW EUROPEAN DESIGN CODE

NON LINEAR ANALYSIS OF STRUCTURES ACCORDING TO NEW EUROPEAN DESIGN CODE October 1-17, 008, Bejng, Chna NON LINEAR ANALYSIS OF SRUCURES ACCORDING O NEW EUROPEAN DESIGN CODE D. Mestrovc 1, D. Czmar and M. Pende 3 1 Professor, Dept. of Structural Engneerng, Faculty of Cvl Engneerng,

More information

November 5, 2002 SE 180: Earthquake Engineering SE 180. Final Project

November 5, 2002 SE 180: Earthquake Engineering SE 180. Final Project SE 8 Fnal Project Story Shear Frame u m Gven: u m L L m L L EI ω ω Solve for m Story Bendng Beam u u m L m L Gven: m L L EI ω ω Solve for m 3 3 Story Shear Frame u 3 m 3 Gven: L 3 m m L L L 3 EI ω ω ω

More information

CHAPTER 9 CONCLUSIONS

CHAPTER 9 CONCLUSIONS 78 CHAPTER 9 CONCLUSIONS uctlty and structural ntegrty are essentally requred for structures subjected to suddenly appled dynamc loads such as shock loads. Renforced Concrete (RC), the most wdely used

More information

SIMPLIFIED PREDICTION METHOD FOR SEISMIC RESPONSE OF ROCKING STRUCTURAL SYSTEMS WITH YIELDING BASE PLATES

SIMPLIFIED PREDICTION METHOD FOR SEISMIC RESPONSE OF ROCKING STRUCTURAL SYSTEMS WITH YIELDING BASE PLATES 13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 4 Paper No. 371 SIMPLIFIED PREDICTION METHOD FOR SEISMIC RESPONSE OF ROCKING STRUCTURAL SYSTEMS WITH YIELDING BASE PLATES

More information

Effect of loading frequency on the settlement of granular layer

Effect of loading frequency on the settlement of granular layer Effect of loadng frequency on the settlement of granular layer Akko KONO Ralway Techncal Research Insttute, Japan Takash Matsushma Tsukuba Unversty, Japan ABSTRACT: Cyclc loadng tests were performed both

More information

Identification of Instantaneous Modal Parameters of A Nonlinear Structure Via Amplitude-Dependent ARX Model

Identification of Instantaneous Modal Parameters of A Nonlinear Structure Via Amplitude-Dependent ARX Model Identfcaton of Instantaneous Modal Parameters of A Nonlnear Structure Va Ampltude-Dependent ARX Model We Chh Su(NCHC), Chung Shann Huang(NCU), Chng Yu Lu(NCU) Outlne INRODUCION MEHODOLOGY NUMERICAL VERIFICAION

More information

Second Order Analysis

Second Order Analysis Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to

More information

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng

More information

SEISMIC ANALYSIS AND DESIGN OF BUILDING STRUCTURES WITH SUPPLEMENTAL LEAD DAMPERS

SEISMIC ANALYSIS AND DESIGN OF BUILDING STRUCTURES WITH SUPPLEMENTAL LEAD DAMPERS SEISMIC ANALYSIS AND DESIGN OF BUILDING STUCTUES WITH SUPPLEMENTAL LEAD DAMPES X LIN 1, Peter J MOSS And Athol J CA 3 SUMMAY The response behavour of buldng structures ncorporatng a new type of dampng

More information

Optimum Design of Steel Frames Considering Uncertainty of Parameters

Optimum Design of Steel Frames Considering Uncertainty of Parameters 9 th World Congress on Structural and Multdscplnary Optmzaton June 13-17, 211, Shzuoka, Japan Optmum Desgn of Steel Frames Consderng ncertanty of Parameters Masahko Katsura 1, Makoto Ohsak 2 1 Hroshma

More information

ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM

ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look

More information

NEAR-FIELD PULSE-TYPE MOTION OF SMALL EVENTS IN DEEP GOLD MINES: OBSERVATIONS, RESPONSE SPECTRA AND DRIFT SPECTRA.

NEAR-FIELD PULSE-TYPE MOTION OF SMALL EVENTS IN DEEP GOLD MINES: OBSERVATIONS, RESPONSE SPECTRA AND DRIFT SPECTRA. The 4 th October 2-7, 28, Bejng, Chna NEAR-FIELD PULSE-TYPE MOTION OF SMALL EVENTS IN DEEP GOLD MINES: OBSERVATIONS, RESPONSE SPECTRA AND DRIFT SPECTRA ABSTRACT: Artur Cchowcz Dr, Sesmology Unt, Councl

More information

Chapter 3. Estimation of Earthquake Load Effects

Chapter 3. Estimation of Earthquake Load Effects Chapter 3. Estmaton of Earthquake Load Effects 3.1 Introducton Sesmc acton on chmneys forms an addtonal source of natural loads on the chmney. Sesmc acton or the earthquake s a short and strong upheaval

More information

DUE: WEDS FEB 21ST 2018

DUE: WEDS FEB 21ST 2018 HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant

More information

Chapter Newton s Method

Chapter Newton s Method Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve

More information

PRATICAL STATIC CALCULATION METHOD FOR ESTIMATING ELASTO-PLASTIC DYNAMIC RESPONSES OF SPACE FRAMES

PRATICAL STATIC CALCULATION METHOD FOR ESTIMATING ELASTO-PLASTIC DYNAMIC RESPONSES OF SPACE FRAMES th World Congress on Computatonal Mechancs (WCCM XI) 5th European Conference on Computatonal Mechancs (ECCM V) 6th European Conference on Computatonal lud ynamcs (EC VI) E. Oñate, J. Olver and A. Huerta

More information

( ) = ( ) + ( 0) ) ( )

( ) = ( ) + ( 0) ) ( ) EETOMAGNETI OMPATIBIITY HANDBOOK 1 hapter 9: Transent Behavor n the Tme Doman 9.1 Desgn a crcut usng reasonable values for the components that s capable of provdng a tme delay of 100 ms to a dgtal sgnal.

More information

829. An adaptive method for inertia force identification in cantilever under moving mass

829. An adaptive method for inertia force identification in cantilever under moving mass 89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,

More information

Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Section 1-5 Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

More information

JAB Chain. Long-tail claims development. ASTIN - September 2005 B.Verdier A. Klinger

JAB Chain. Long-tail claims development. ASTIN - September 2005 B.Verdier A. Klinger JAB Chan Long-tal clams development ASTIN - September 2005 B.Verder A. Klnger Outlne Chan Ladder : comments A frst soluton: Munch Chan Ladder JAB Chan Chan Ladder: Comments Black lne: average pad to ncurred

More information

EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES

EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES Manuel J. C. Mnhoto Polytechnc Insttute of Bragança, Bragança, Portugal E-mal: mnhoto@pb.pt Paulo A. A. Perera and Jorge

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

DESIGN SPECTRUM-BASED SCALING OF STRENGTH REDUCTION FACTORS

DESIGN SPECTRUM-BASED SCALING OF STRENGTH REDUCTION FACTORS 13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 2004 Paper No. 539 DESIGN SPECTRUM-BASED SCALING OF STRENGTH REDUCTION FACTORS Arndam CHAKRABORTI 1 and Vnay K. GUPTA

More information

A Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls

A Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls A Mechancs-Based Approach for Determnng Deflectons of Stacked Mult-Storey Wood-Based Shear Walls FPINNOVATIONS Acknowledgements Ths publcaton was developed by FPInnovatons and the Canadan Wood Councl based

More information

Chapter 11: Simple Linear Regression and Correlation

Chapter 11: Simple Linear Regression and Correlation Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests

More information

Chapter 13: Multiple Regression

Chapter 13: Multiple Regression Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to

More information

STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION

STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION CAO Wanln 1, CHANG Wehua 2, ZHANG Janwe 1 1 College of archtecture and Cvl Engneerng, Bejng

More information

Lecture 8 Modal Analysis

Lecture 8 Modal Analysis Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal 1 2015 ANSYS, Inc. February 27, 2015 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal

More information

In this section is given an overview of the common elasticity models.

In this section is given an overview of the common elasticity models. Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp

More information

Frequency dependence of the permittivity

Frequency dependence of the permittivity Frequency dependence of the permttvty February 7, 016 In materals, the delectrc constant and permeablty are actually frequency dependent. Ths does not affect our results for sngle frequency modes, but

More information

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15 NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound

More information

SIMPLE LINEAR REGRESSION

SIMPLE LINEAR REGRESSION Smple Lnear Regresson and Correlaton Introducton Prevousl, our attenton has been focused on one varable whch we desgnated b x. Frequentl, t s desrable to learn somethng about the relatonshp between two

More information

Finite Element Modelling of truss/cable structures

Finite Element Modelling of truss/cable structures Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures

More information

2016 Wiley. Study Session 2: Ethical and Professional Standards Application

2016 Wiley. Study Session 2: Ethical and Professional Standards Application 6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton

More information

Turbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH

Turbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH Turbulence classfcaton of load data by the frequency and severty of wnd gusts Introducton Oscar Moñux, DEWI GmbH Kevn Blebler, DEWI GmbH Durng the wnd turbne developng process, one of the most mportant

More information

ONE DIMENSIONAL TRIANGULAR FIN EXPERIMENT. Technical Advisor: Dr. D.C. Look, Jr. Version: 11/03/00

ONE DIMENSIONAL TRIANGULAR FIN EXPERIMENT. Technical Advisor: Dr. D.C. Look, Jr. Version: 11/03/00 ONE IMENSIONAL TRIANGULAR FIN EXPERIMENT Techncal Advsor: r..c. Look, Jr. Verson: /3/ 7. GENERAL OJECTIVES a) To understand a one-dmensonal epermental appromaton. b) To understand the art of epermental

More information

REINFORCED CONCRETE STRUCTURE DESIGN ANALYSIS UNDER EARTHQUAKE LOADING (LATERAL LOAD)

REINFORCED CONCRETE STRUCTURE DESIGN ANALYSIS UNDER EARTHQUAKE LOADING (LATERAL LOAD) REINFORCE CONCRETE STRUCTURE ESIGN ANALYSIS UNER EARTHQUAKE LOAING (LATERAL LOA) r. Muzaffer BÖREKÇİ SUMMARY FOR ANALYSIS UNER EARTQUAKE etermne the buldng parameters gven n Turksh Sesmc Code for Buldngs

More information

APPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam

APPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam APPENDIX F A DISPACEMENT-BASED BEAM EEMENT WITH SHEAR DEFORMATIONS Never use a Cubc Functon Approxmaton for a Non-Prsmatc Beam F. INTRODUCTION { XE "Shearng Deformatons" }In ths appendx a unque development

More information

Please initial the statement below to show that you have read it

Please initial the statement below to show that you have read it EN40: Dynamcs and Vbratons Mdterm Examnaton Thursday March 5 009 Dvson of Engneerng rown Unversty NME: Isaac Newton General Instructons No collaboraton of any knd s permtted on ths examnaton. You may brng

More information

Experiment 1 Mass, volume and density

Experiment 1 Mass, volume and density Experment 1 Mass, volume and densty Purpose 1. Famlarze wth basc measurement tools such as verner calper, mcrometer, and laboratory balance. 2. Learn how to use the concepts of sgnfcant fgures, expermental

More information

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,

More information

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient 58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),

More information

ON THE GENERATION OF THE DESIGN EARTHQUAKE GROUND MOTION TIME HISTORY

ON THE GENERATION OF THE DESIGN EARTHQUAKE GROUND MOTION TIME HISTORY ON THE GENERATION OF THE DESIGN EARTHQUAKE GROUND MOTION TIME HISTORY by Izuru Okawa 1), Toshhde Kashma 1), Haruyuk Ktamura 2), Masanobu Tohdo 3), Shgek Saka 4), Masaharu Tangak ), Kunak Yamagsh ), Kohj

More information

Design and Optimization of Fuzzy Controller for Inverse Pendulum System Using Genetic Algorithm

Design and Optimization of Fuzzy Controller for Inverse Pendulum System Using Genetic Algorithm Desgn and Optmzaton of Fuzzy Controller for Inverse Pendulum System Usng Genetc Algorthm H. Mehraban A. Ashoor Unversty of Tehran Unversty of Tehran h.mehraban@ece.ut.ac.r a.ashoor@ece.ut.ac.r Abstract:

More information

Study on Non-Linear Dynamic Characteristic of Vehicle. Suspension Rubber Component

Study on Non-Linear Dynamic Characteristic of Vehicle. Suspension Rubber Component Study on Non-Lnear Dynamc Characterstc of Vehcle Suspenson Rubber Component Zhan Wenzhang Ln Y Sh GuobaoJln Unversty of TechnologyChangchun, Chna Wang Lgong (MDI, Chna [Abstract] The dynamc characterstc

More information

COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS

COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS

More information

Class: Life-Science Subject: Physics

Class: Life-Science Subject: Physics Class: Lfe-Scence Subject: Physcs Frst year (6 pts): Graphc desgn of an energy exchange A partcle (B) of ass =g oves on an nclned plane of an nclned angle α = 3 relatve to the horzontal. We want to study

More information

Gravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11)

Gravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11) Gravtatonal Acceleraton: A case of constant acceleraton (approx. hr.) (6/7/11) Introducton The gravtatonal force s one of the fundamental forces of nature. Under the nfluence of ths force all objects havng

More information

EVALUATION OF PERFORMANCE OF MULTI-SUSPENDED PENDULUM ISOLATION (MPI) SYSTEM WITH SPATIAL TRUSS STRUCTURE

EVALUATION OF PERFORMANCE OF MULTI-SUSPENDED PENDULUM ISOLATION (MPI) SYSTEM WITH SPATIAL TRUSS STRUCTURE EVALUATION OF PERFORMANCE OF MULTI-SUSPENDED PENDULUM ISOLATION (MPI) SYSTEM WITH SPATIAL TRUSS STRUCTURE Ryosuke NARITA 1, Tej KOJIMA 2, Haruo KURAMOCHI 3, Takash TORIYA 4, Naom KITAYAMA 5, Mcho KURAMOCHI

More information

Physics 5153 Classical Mechanics. Principle of Virtual Work-1

Physics 5153 Classical Mechanics. Principle of Virtual Work-1 P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal

More information

Analysis of the Magnetomotive Force of a Three-Phase Winding with Concentrated Coils and Different Symmetry Features

Analysis of the Magnetomotive Force of a Three-Phase Winding with Concentrated Coils and Different Symmetry Features Analyss of the Magnetomotve Force of a Three-Phase Wndng wth Concentrated Cols and Dfferent Symmetry Features Deter Gerlng Unversty of Federal Defense Munch, Neubberg, 85579, Germany Emal: Deter.Gerlng@unbw.de

More information

Lifetime prediction of EP and NBR rubber seal by thermos-viscoelastic model

Lifetime prediction of EP and NBR rubber seal by thermos-viscoelastic model ECCMR, Prague, Czech Republc; September 3 th, 2015 Lfetme predcton of EP and NBR rubber seal by thermos-vscoelastc model Kotaro KOBAYASHI, Takahro ISOZAKI, Akhro MATSUDA Unversty of Tsukuba, Japan Yoshnobu

More information

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force. Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act

More information

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable

More information

χ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body

χ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown

More information

MEEM 3700 Mechanical Vibrations

MEEM 3700 Mechanical Vibrations MEEM 700 Mechancal Vbratons Mohan D. Rao Chuck Van Karsen Mechancal Engneerng-Engneerng Mechancs Mchgan echnologcal Unversty Copyrght 00 Lecture & MEEM 700 Multple Degree of Freedom Systems (ext: S.S.

More information

Lecture 12: Discrete Laplacian

Lecture 12: Discrete Laplacian Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly

More information

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 30 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 2 Remedes for multcollnearty Varous technques have

More information

FUZZY FINITE ELEMENT METHOD

FUZZY FINITE ELEMENT METHOD FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments

More information

Constitutive Modelling of Superplastic AA-5083

Constitutive Modelling of Superplastic AA-5083 TECHNISCHE MECHANIK, 3, -5, (01, 1-6 submtted: September 19, 011 Consttutve Modellng of Superplastc AA-5083 G. Gulano In ths study a fast procedure for determnng the constants of superplastc 5083 Al alloy

More information

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers Psychology 282 Lecture #24 Outlne Regresson Dagnostcs: Outlers In an earler lecture we studed the statstcal assumptons underlyng the regresson model, ncludng the followng ponts: Formal statement of assumptons.

More information

Module 9. Lecture 6. Duality in Assignment Problems

Module 9. Lecture 6. Duality in Assignment Problems Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept

More information

= 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W]

= 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W] Secton 1.3: Acceleraton Tutoral 1 Practce, page 24 1. Gven: 0 m/s; 15.0 m/s [S]; t 12.5 s Requred: Analyss: a av v t v f v t a v av f v t 15.0 m/s [S] 0 m/s 12.5 s 15.0 m/s [S] 12.5 s 1.20 m/s 2 [S] Statement:

More information

Modeling of Dynamic Systems

Modeling of Dynamic Systems Modelng of Dynamc Systems Ref: Control System Engneerng Norman Nse : Chapters & 3 Chapter objectves : Revew the Laplace transform Learn how to fnd a mathematcal model, called a transfer functon Learn how

More information

FREQUENCY DISTRIBUTIONS Page 1 of The idea of a frequency distribution for sets of observations will be introduced,

FREQUENCY DISTRIBUTIONS Page 1 of The idea of a frequency distribution for sets of observations will be introduced, FREQUENCY DISTRIBUTIONS Page 1 of 6 I. Introducton 1. The dea of a frequency dstrbuton for sets of observatons wll be ntroduced, together wth some of the mechancs for constructng dstrbutons of data. Then

More information

THE CURRENT BALANCE Physics 258/259

THE CURRENT BALANCE Physics 258/259 DSH 1988, 005 THE CURRENT BALANCE Physcs 58/59 The tme average force between two parallel conductors carryng an alternatng current s measured by balancng ths force aganst the gravtatonal force on a set

More information

Available online at Kazuhiro Tsuboi a, * Received 31 January 2010; revised 7 March 2010; accepted 21 March 2010

Available online at  Kazuhiro Tsuboi a, * Received 31 January 2010; revised 7 March 2010; accepted 21 March 2010 Avalable onlne at www.scencedrect.com Proceda Proceda Engneerng 00 (010) (009) 000 000 305 310 Proceda Engneerng www.elsever.com/locate/proceda 8 th Conference of the Internatonal Sports Engneerng Assocaton

More information

Indeterminate pin-jointed frames (trusses)

Indeterminate pin-jointed frames (trusses) Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all

More information

Statistics for Economics & Business

Statistics for Economics & Business Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable

More information

A NEW PROPOSAL FOR LIQUEFACTION POTENTIAL BASED ON ENERGY BALANCE METHOD

A NEW PROPOSAL FOR LIQUEFACTION POTENTIAL BASED ON ENERGY BALANCE METHOD 3 th orld Conference on Earthquake Engneerng Vancouver, B.C., Canada August 6, 4 Paper No. A NE PROPOSAL FOR LIQUEFACTION POTENTIAL BASED ON ENERGY BALANCE METHOD Shuch SHIMOMURA, Norak SAKO, Tosho ADACHI

More information

arxiv:cs.cv/ Jun 2000

arxiv:cs.cv/ Jun 2000 Correlaton over Decomposed Sgnals: A Non-Lnear Approach to Fast and Effectve Sequences Comparson Lucano da Fontoura Costa arxv:cs.cv/0006040 28 Jun 2000 Cybernetc Vson Research Group IFSC Unversty of São

More information

Over-Temperature protection for IGBT modules

Over-Temperature protection for IGBT modules Over-Temperature protecton for IGBT modules Ke Wang 1, Yongjun Lao 2, Gaosheng Song 1, Xanku Ma 1 1 Mtsubsh Electrc & Electroncs (Shangha) Co., Ltd., Chna Room2202, Tower 3, Kerry Plaza, No.1-1 Zhongxns

More information

Lecture 3 Stat102, Spring 2007

Lecture 3 Stat102, Spring 2007 Lecture 3 Stat0, Sprng 007 Chapter 3. 3.: Introducton to regresson analyss Lnear regresson as a descrptve technque The least-squares equatons Chapter 3.3 Samplng dstrbuton of b 0, b. Contnued n net lecture

More information

Chapter 9: Statistical Inference and the Relationship between Two Variables

Chapter 9: Statistical Inference and the Relationship between Two Variables Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,

More information

ORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp.

ORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp. Clck to Vew Mathcad Document 2011 Knovel Corp. Buldng Structural Desgn. homas P. Magner, P.E. 2011 Parametrc echnology Corp. Chapter 3: Renforced Concrete Slabs and Beams 3.2 Renforced Concrete Beams -

More information

Professor Terje Haukaas University of British Columbia, Vancouver The Q4 Element

Professor Terje Haukaas University of British Columbia, Vancouver  The Q4 Element Professor Terje Haukaas Unversty of Brtsh Columba, ancouver www.nrsk.ubc.ca The Q Element Ths document consders fnte elements that carry load only n ther plane. These elements are sometmes referred to

More information

CONTRAST ENHANCEMENT FOR MIMIMUM MEAN BRIGHTNESS ERROR FROM HISTOGRAM PARTITIONING INTRODUCTION

CONTRAST ENHANCEMENT FOR MIMIMUM MEAN BRIGHTNESS ERROR FROM HISTOGRAM PARTITIONING INTRODUCTION CONTRAST ENHANCEMENT FOR MIMIMUM MEAN BRIGHTNESS ERROR FROM HISTOGRAM PARTITIONING N. Phanthuna 1,2, F. Cheevasuvt 2 and S. Chtwong 2 1 Department of Electrcal Engneerng, Faculty of Engneerng Rajamangala

More information

Fundamental loop-current method using virtual voltage sources technique for special cases

Fundamental loop-current method using virtual voltage sources technique for special cases Fundamental loop-current method usng vrtual voltage sources technque for specal cases George E. Chatzaraks, 1 Marna D. Tortorel 1 and Anastasos D. Tzolas 1 Electrcal and Electroncs Engneerng Departments,

More information

Irregular vibrations in multi-mass discrete-continuous systems torsionally deformed

Irregular vibrations in multi-mass discrete-continuous systems torsionally deformed (2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected

More information

Physics 2A Chapter 3 HW Solutions

Physics 2A Chapter 3 HW Solutions Phscs A Chapter 3 HW Solutons Chapter 3 Conceptual Queston: 4, 6, 8, Problems: 5,, 8, 7, 3, 44, 46, 69, 70, 73 Q3.4. Reason: (a) C = A+ B onl A and B are n the same drecton. Sze does not matter. (b) C

More information

1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations

1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations Physcs 171/271 -Davd Klenfeld - Fall 2005 (revsed Wnter 2011) 1 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys

More information

Preliminary Design of Moment-Resisting Frames

Preliminary Design of Moment-Resisting Frames Prelmnary Desgn of Moment-Resstng Frames Preprnt Aamer Haque Abstract A smple method s developed for prelmnary desgn of moment-resstng frames. Preprnt submtted to Elsever August 27, 2017 1. Introducton

More information

/ n ) are compared. The logic is: if the two

/ n ) are compared. The logic is: if the two STAT C141, Sprng 2005 Lecture 13 Two sample tests One sample tests: examples of goodness of ft tests, where we are testng whether our data supports predctons. Two sample tests: called as tests of ndependence

More information

STATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION

STATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros

More information

The optimal delay of the second test is therefore approximately 210 hours earlier than =2.

The optimal delay of the second test is therefore approximately 210 hours earlier than =2. THE IEC 61508 FORMULAS 223 The optmal delay of the second test s therefore approxmately 210 hours earler than =2. 8.4 The IEC 61508 Formulas IEC 61508-6 provdes approxmaton formulas for the PF for smple

More information

, + &. / / 0 # 1) (5

, + &. / / 0 # 1) (5 ! # % # & & + + +, + &. / / 0 # 23 4 55 006 2 54223 7 / / 2 8 Hajrasoulha I & Doostan A 200 A smplfed model for sesmc response predcton of concentrcally braced frames. Advances n Engneerng Software, 43,

More information

Polynomial Regression Models

Polynomial Regression Models LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance

More information

6.3.7 Example with Runga Kutta 4 th order method

6.3.7 Example with Runga Kutta 4 th order method 6.3.7 Example wth Runga Kutta 4 th order method Agan, as an example, 3 machne, 9 bus system shown n Fg. 6.4 s agan consdered. Intally, the dampng of the generators are neglected (.e. d = 0 for = 1, 2,

More information

System in Weibull Distribution

System in Weibull Distribution Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co

More information

APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS

APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS 6th ICPT, Sapporo, Japan, July 008 APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS James MAINA Prncpal Researcher, Transport and Infrastructure Engneerng, CSIR Bult Envronment

More information

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment

More information

Torsion Stiffness of Thin-walled Steel Beams with Web Holes

Torsion Stiffness of Thin-walled Steel Beams with Web Holes Torson Stffness of Thn-walled Steel Beams wth Web Holes MARTN HORÁČEK, JNDŘCH MELCHER Department of Metal and Tmber Structures Brno Unversty of Technology, Faculty of Cvl Engneerng Veveří 331/95, 62 Brno

More information

Pulse Coded Modulation

Pulse Coded Modulation Pulse Coded Modulaton PCM (Pulse Coded Modulaton) s a voce codng technque defned by the ITU-T G.711 standard and t s used n dgtal telephony to encode the voce sgnal. The frst step n the analog to dgtal

More information

Study on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI

Study on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI 2017 2nd Internatonal Conference on Electrcal and Electroncs: echnques and Applcatons (EEA 2017) ISBN: 978-1-60595-416-5 Study on Actve Mcro-vbraton Isolaton System wth Lnear Motor Actuator Gong-yu PAN,

More information

OPTIMUM STRENGTH RATIO OF BUCKLING-RESTRAINED BRACES AS HYSTERETIC ENERGY DISSIPATION DEVICES INSTALLED IN R/C FRAMES

OPTIMUM STRENGTH RATIO OF BUCKLING-RESTRAINED BRACES AS HYSTERETIC ENERGY DISSIPATION DEVICES INSTALLED IN R/C FRAMES The th World Conference on arthquake ngneerng October -,, Bejng, Chna OPTIMUM STRNGTH RATIO OF BUCKLING-RSTRAIND BRACS AS HYSTRTIC NRGY DISSIPATION DVICS INSTALLD IN R/C FRAMS Juan Andrés Ovedo A., Mtsumasa

More information

Statistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA

Statistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA 14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton

More information