DIMENSIONING MACHINE STRUCTURE FOR EARTHQUAKE RESISTANCE IN DESIGN STAGE

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1 INTERNATIONAL DESIGN CONFERENCE - DESIGN 2006 Dubrovnk - Croata, May 15-18, DIMENSIONING MACHINE STRUCTURE FOR EARQUAKE RESISTANCE IN DESIGN STAGE M. Butkovć, B. Orčć, M. Tevčć and M. Jokć Keywords: earthquake, sesmc acceleraton, frequency response 1. Introducton In the course of the desgn of power plants and large chemcal plants up to the mddle of 20th century, the equpment has been desgned and calculated takng nto account standard and predctable loads (temperature, pressure, rotatonal speed, wnd). Through the desgn of large fossl and nuclear power plants and large chemcal and petrochemcal plants, mechancal and electrcal engneers have encountered the need to evaluate the constructon regardng possble earthquake. Desgners started to perform earthquake calculatons as well, sgnfcantly mprovng knowledge about earthquakes and response of dfferent structures and machnes [Sngh 1992]. Requrements on the safe operaton of large plant equpment have became more strctdurng the last several years. The desgners are faced wth the demands of contnuous operaton or slght damages of the equpment durng excess stuatons, whch nclude earthquake. Gas turbnes and steam turbnes are mostly standardsed products, whch are nstalled n varous locatons n the world, and redesgn to accommodate to local earthquake requrements can be expensve and tme consumng. However, earthquakes are partally random events, and there s no determnstc method, whch fulfls all demands thoroughly. Natonal and nternatonal bureaus of standards n dfferent countres of the world try to overcome these problems [UBC 1977], [EUROCODE 1994]. Because earthquakes are bascally statstcal events, buldngs and plants are only statstcally (probablstcally) safe to earthquakes. Rsks of earthquake are classfed for dfferent constructons and purposes of constructon, such as: apartments, workshops and offce buldngs, publc buldngs, and nfrastructure constructons. Most of the prevously mentoned s the reason to desgn machnes whch would satsfy earthquake requrements of most locatons over the world, but at the same tme wll not be too expensve to cover all the locatons. In ths paper an optmal sesmc ntensty for calculatons s proposed, as well as the method of earthquake response calculaton of the machnery structure. 2. Methods used for calculaton of structure response to earthquake Gas and steam turbne parts are desgned to retan requred operatonal functonalty, ntegrty, to be safe to human operator and the envronment, takng nto account loads due to normal operatng condtons as well as n excess stuatons such as earthquake. Sgnfcant porton of excess stuatons s predctable and the desgner can take nto account ther nfluence and magntude durng the desgn process. Examples of such events are: exceedng the pressure, temperature, rotatonal speed, and mbalance. However, as already sad n the ntroducton, earthquake s statstcal event wth several unknown characterstcs : MEODS AND TOOLS IN DESIGN PRACTICE 199

2 tme of duraton s unknown frequency content of earthquake movements s unknown drecton of earthquake movements s unknown Because of statstcal nature of earthquake gatherng the earthquake data mproves qualty of values but t s mpossble to have determnstc earthquake data. Regardng the requred operatonal safety and functonalty of the drvng engne durng the earthquake, desgn of structure has to satsfy ncreased load due to earthquake. There are three basc methods for calculaton of earthquake response: statstcal, determnstc and methods mxed of the two. Mxed methods are ncluded n natonal and nternatonal earthquake standards. Because no method s exact there s varety of methods whch are approxmate wth some advantages and some dsadvantages. The choce of the metod depends on the mportance of the constructon and avalable data. 2.1 Statc methods Ths s a farly smple method. Structures can be consdered as stff f natural frequences are above 33 Hz [Butkovć 2000]. Earthquake load can be consdered as an addtonal statc load ( D a ) W FES = CS W = 0 (1) where : F ES = addtonal earthquake force n horzontal or vertcal drecton, (N) C S = sesmc coeffcent, (-) W = weght of constructon, (N) D = rsk factor ( mportance factor, safety factor etc. ) for the structure, dependng on the purpose and mportance of the structure, (-) a 0 = basc sesmc acceleraton ( effectve peak ground acceleraton ) for sesmc regon and ste, n porton of gravty acceleraton g, for horzontal or vertcal drecton, ( - ) Wth addtonal sesmc force strength of the structure s assessed as by usual statc calculatons. 2.2 Quas statc methods (QSM) Ths method apples for structures wth natural frequences under 100 Hz [UBC 1977] ( D M a ) W FEQS = CQS W = 0 (2) where : F EQS = addtonal statc force on the structure foundaton or on the floors of the structure, (N) C QS = quas statc sesmc coeffcent, ( - ) W = weght of constructon, ( N ) M = magnfcaton factor whch ncludes natural frequency of structure, ts dampng behavour, ground characterstcs and duraton, ( - ) Fgure1. shows the magnfcaton factors for elastc response of structure as a functon of ts natural frequences accordng to preposton of Eurocode 8 [EUROCODE 1994]. There are other prepostons as well [ISO ]. Strength of the constructon s calculated on the bass of equaton (2) the same as f t would be statcally loaded. Addtonal earthquake forces are calculated n one horzontal drecton and one vertcal drecton wth or wthout addng of forces as vectors. 200 MEODS AND TOOLS IN DESIGN PRACTICE

3 Fgure 1. Equvalent magnfcaton factor for lnear response spectrum of structure for subsol class A as a functon of natural frequency and dampng [EUROCODE 1994] 2.3 Dynamc methods Two methods are commonly used. One s determnstc, where response s calculated and stresses and deformatons are obtaned from the exact tme doman (tme hstory) of one partcular earthquake. Calculatons can be lnear or nonlnear [EUROCODE 1994]. Second approach s statstcal where characterstcs of the earthquake are random and response s beng calculated. The problem wth determnstc approach s that one partcular osclogram wll never be exactly repeated n realty and one can not wat durng the desgn process to obtan the hstogram that wll not repeat tself. Ths can be partally overcome usng at least three to fve dfferent osclograms [EUROCODE 1994] and applyng the worst response. There s development of syntheszed earthquakes n tme doman [Bachmann 1995] whch, for the same maxmum acceleraton, are much closer to worst earthquakes. 2.4 Quas dynamc methods () Quas dynamc methods () are utlzng calculatons of response to statonary (steady state) exctatons. Quas statc methods have erroneous results manly n postons of maxmal stresses. s usng two approaches to acheve correct response values: Increase of dampng values to the equvalent ones whch wll gve, n steady state condtons, the same response as transent exctaton Decrease of acceleraton exctatons to the equvalent ones, whch wll gve the same response as transent exctaton for statonary state exctatons An advantage of n comparson to dynamc method (DM) s smplcty of calculatons and exstance of vast quantty of data on spectral dynamc coeffcent of magnfcatons of structures (response spectrum [Newmark 1976]). Thrd advantage of these methods s that the desgner can desgn the structure, early n the desgn stage, that wll satsfy earthquake requrements n over 90% of stuatons. Proposed uses the reducton of the response spectrum to calculate equvalent acceleraton coeffcents for calculaton of statonary exctaton of the structure. Method can be explaned on the system wth one degree of freedom based on EUROCODE 8 [EUROCODE 1994]. MEODS AND TOOLS IN DESIGN PRACTICE 201

4 a M = (3) 0 red a 0 = K a 0 Q where : a = maxmum value of ground acceleraton, for locaton and drecton?? and "" natural frequency 0 - nonstatonary, (ms -2 ) a = reduced ground acceleraton, for "" natural frequency of structure statonary, (ms -2 ) red 0 M = magnfcaton factor of spectral response of structure, for "" natural frequency - nonstatonary, (-) Q = magnfcaton factor, for "" natural frequency statonary, (-) K = correcton factor, for "" natural frequency, (-) Fgure 2. shows the correcton factors for earthquake exctaton as a functon of natural frequency of structure, dampng and qualty of ground (class A). Correcton dagrams are shown n frequency range from 0.1 to 100 Hz for whch can be appled. For resonance response values are calculated usng equaton (3) and equatons (1) and (2) are not needed. Fgure 2. Correcton factor for lnear earthquake spectrum, for statonary response calculaton, subsol class A, for dfferent natural frequences and dampng [Butkovć 2000] If the structure has more than one natural frequency under 100 Hz, calculaton (3) s performed for each natural frequency. Stresses for partcular ponts are summerzed usng the method of effectve stress 2 ef = Σ (4) Ths s vald for horzontal and vertcal drecton. For vertcal drecton 2/3 of horzontal exctaton s used as a value. 202 MEODS AND TOOLS IN DESIGN PRACTICE

5 3. Procedure for desgners When machne structure s desgned by usng desgn tools such as CATIA, PROENGINEER, Sold Works, AUTOCAD etc. natural frequences of a structure have to be calculated upon some of codes n the range of frequences from 0 to 100 Hz. If a structure has the frst natural frequency under 5 or 10 Hz t s not necessary to calculate natural frequences over 30 Hz. (response of a structure to the frst natural frequency s most severe). The next step s calculaton of forced response calculaton of structure usng quas dynamc method () of calculaton (steady state response). Ground acceleraton a 0 depends on ste of nstallaton, but ths s not known n the desgn stage and t s recommended to use values of sesmc zone 4 of UBC [UBC 1977] whch gves a 0 = 0.4 g n horzontal drecton and 0.27 g n vertcal drecton. Correcton of acceleraton (factor K ), equaton (3), has to be found based on EUROCODE 8 [EUROCODE 1994] for known dampng factor of structure ζ and for ground qualty A on Fgure 2. For overvew of dampng factors for varous structures see Table 1. If values of ζ are not known, use ζ = 5%. Table 1. Dampng values for varous structures and stresses Dampng rate ζ ( ) Nr. Type and condton of structure Stresses n the range of 0.5R y Stresses n the range of yeldng stress (R y ) 1 Vtal ppelnes Welded steel structure Renforced concrete wthout cracks wth cracks normal Prestressed concrete wth partal loss of prestress 5 10 wth loss of prestress Steel structure connected wth screws and rvets Wooden screw connected constructon nal connected Steady state forced vbratons are calculated for each natural frequency and stresses (Von Mses) and deformatons are calculated usng lnear method. Sumaton of earthquake stress for each exctaton drecton s performed accordng to (4). Ths addtonal stresses have to be added to the operatonal stresses and redesgn of structure has to be perfomed, f necessary. 4. Examples 4.1 Redesgn of gas turbne ntake manfold due to the nfluence of an earthquake Fgure 3. shows a gas turbne ar ntake manfold desgned wth CAD software and calculated by fnte element method package. Natural frequences are: f 1 = 3.07 Hz, f 2 = 10.5 Hz, f 3 = 14.6 Hz, etc. method of forced vbraton calculaton s used. The only calculatons performed are those n horzontal x drecton and for the frst three natural frequences. MEODS AND TOOLS IN DESIGN PRACTICE 203

6 Fgure 3. Gas turbne ar ntake manfold FEM mesh Ground acceleraton s 0.4g. Dampng factor s ζ = 5%. Correcton factors are: K 1 = 0.25, K 2 = 0.245, K 3 = 0.2 (see Fgure 2.). Results of the calculaton are shown n Table 2. Hghest stress s at node 8260, = MPa. For comparson of the results obtaned usng wth tme doman hstory calculaton, a tme doman dagram of the earthquake Taranak [A 1997] has been analyzed usng the same dampng and maxmum acceleraton of = 0.4 g. Results are shown n the Table 2. a 0 Table 2. Comparson of stresses n gas turbne ar ntake manfold excted wth normed earthquake of 0.4g and calculated wth quas dynamc and tme hstory methods Node Frst natural frequency Hz Second natural frequency Hz Thrd natural frequency 14.6 Hz (-) (-) (-) Summ of stresses1 2 Node 2 (-) MEODS AND TOOLS IN DESIGN PRACTICE

7 Maxmum stress s also at the node 8260, = MPa, whch s 10% hgher than usng of calculaton. Strength of the structure has been calculated takng nto account loads due to structure's own weght, operatng underpressure and earthquake. Total stress accordng to the more conservatve method s algebrac sum of the stresses due to structure's weght, underpressure and earthquake, whch s MPa ( ) at the node # Allowable stress, dependng on the safety of calculaton varables, s close to the yeld strength of the materal. In our case that s, due to the weldng, 160 MPa. The calculaton has shown that the redesgn of the gas turbne ar ntake manfold s not needed. In ths case, however, forces actng on anchor screws were 450 kn whch requred an ncrease n the prestress of the screws n order to prevent detachment of the AIM foot from the ground, as well as changng the materal of the anchor screws. Ths changes were ncorporated nto standard desgn of the gas turbne ar ntake manfold. 4.2 Redesgn of Auxlary Block Fgure 4.shows the part of the FEM model of an auxlary block. Strength verfcaton has been done by.the model s subjected to the own dead weght of the block flled wth ol and the earthquake condtons as n the chapter 4.1. The maxmum stress value s at the node #14 s = 212 MPa..Ths calculated stress s hgher than alowable all = 160 MPa and the supports have been strenghted by ncreasng the thckness of plates from 8 up to 10 mm. Ths changes were ncorporated nto standard desgn of the auxlary block. Fgure 4. Auxlary block FEM model 5. Concluson Takng nto account more strct regulatons regardng the operatonal safety of power plants, as well as shorter deadlnes and reduced expenses of desgn and manufacturng, a method for calculatng the load due to the earthquake actng on mechancal constructons have been proposed. Also the optmal earthquake level.,. The advantages of such approach for the desgn are the followng: The accuracy of the method s satsfactory, devaton from more accurate methods s below 10% Propopsed earthquake level of 0.4 g satsfes 95% of ste equpment over the world. Snce the year 2000, when ths method was frst appled, none of ste redesgn n over 20 delveres was requred. MEODS AND TOOLS IN DESIGN PRACTICE 205

8 Total expenses of desgn, manufacturng and assembly of machnery are lower then before the applcaton of ths method Applcaton of s smple for desngners, as t s shown n the flow chart n Fgure 5. Fgure 5. Flow chart of applcaton References Artfcal Tme Hstory MDE Taranak (A), AC Power Group Ltd.,Consultng Engneers, Wellngton, New Zealand, Bachmann, H., Erdbebenscherung von Bauwerken, Brkhauser Verlag, Basel, Bases for Desgn of Structures-Sesmc Actons of Structures, ISO 3010, Geneve,1988. Bose,P.R.., Dubey, R., Yazd,M.,A., Comparrson of Codal Provsons sugested by varous countres, Procedngs of the Tenth World Conference on Earthquake Engneerng, Madrd July, 1992, pp Butkovć, M., Orčć, B.,,New Quas-Dynamc Method of Earthquake Response Calculaton for Structure, Strojarstvo, 42, 2000, pp EUROCODE 8, Desgn Provsons for Earthquake Resstance of Structures, ENV ,CEN, Brussels, Newmark, N.,M., Hall, W., Vbraton of Structures nduced by ground moton, Part 29,from, Harrs, C.,M., Crede, Ch., E., Shock and Vbraton Handbook, McGraw-Hll, New York, Sngh, M., P., Chang, T., S., Suarez, L., E., Sezmc Desgn Response of rotatng machnes, Proceedngs of the tenth Wored Conference on Earthquake Engneerng, Madrd July,1992, Page Unform Buldng Code (UBC), Vol.2,Ch.16, Dv.III,Internatonal Conference of Buldng Offcals, Mrko Butkovć, Prof.dr.sc. Veleučlšte u Karlovcu, Meštrovća 10, Karlovac, Croata Tel.: +385 (0) Fax.: +385 (0) Emal: mrko.butkovc@vuka.hr 206 MEODS AND TOOLS IN DESIGN PRACTICE