SURE: Shizuoka University REpository http://ir.lib.shizuoka.ac.jp/ Title Author(s) Citation Issue Date URL Measurement of Flexural Rigidity of Plywood-Webbed BoxBeams by Vibration Method Sobue, Nobuo; Ikeda, Kiyohiko; Arima, Takanori 木材学会誌. 34(6), p. 543-546 1988-06 http://hdl.handle.net/10297/4596 Version publisher Rights Copyright © 日本木材学会 This document is downloaded at: 2015-02-01T00:27:41Z 5 4 3 [ Mo kuEat 'Gakkal s hz - vol ・ 3 4,No・ 6 ,p・ 5 4 3 5 4 6( 1 9 8 8 ) ] Me as 弧T e me n息ofF且 e x弧T a 且温i gi 誠紙yof 鮎鮎e d迅蝿 Be ams触yVi bT a息 i omM如hod* l mywoo姐-We Nobuo SoBUE*2 ,Ki yohi koIKEDA*3andTaka nor iARI MA*4 振 動 法 に よる合板 ウェブボ ックス ビームの曲げ剛性の測定 * 1 祖 父江信 夫喪 2 ,池 田潔 彦 * 3 ,有 馬孝穏 *4 振動 試験 による合板 ウェブ ・ボ ックス ビームの曲げ剛性 ( EI )の測定法 を検討 した。 試験体 は総数 3 0体 で,同一製造マニュアルに従 って 6社 で製造 された。両端 を単純支持 した栄 を ゴム‥ ンマで打撃 し,支持点 に加 わ る振動の反力の波形か ら梁の固有振動数 を求めた。 ボ ックス ピ- ム を均質梁 とみ な して振動理論 を適用 した場合 お よびボ ックスビームの構造の不 均 一性 を考慮 して伝達 マ トリクス法 を適用 した場合 につ いて検討 したo計算結果 に両者の差は認 5%過小評価 した。 め られず, 静的 曲げ試験 に よる EIに比べ ていずれ も平均値 で約 1 振 動試験 によって,梁の重量 と固有振動数か ら静的曲げ剛性 を推定す るモデル式 を誘導 した。 Thene xur alr i g i di t y( EI)ofpl ywoo we bbe dbox be a mse s t i ma t edf r om mi ni mum i nf or ma t i on ● i nar nanuf T a c t ur l ngPr oc e s sWasi nve s t i ga t e d. Thi r t ys i mpl e s uppor t e dbox be amswe r et a ppe dwi t haha mme r ,a ndt her e s ona nc ef r e que nc i e s we r eme a s ur e df r om t hef T r e evi br a t i onsoft hebe a ms . か Theel e me nt ar y Vi br a t i ont he or yofuni f or m be a msandat r a ns f e r ma t r i xme t hodf orvi br a t i on pr obl e mswe r eus e dt oe s t i ma t et heEIoft hebe a ms .Ther e s ul t swe r ec ompa r e dw it ht hos eb ■ ly s t at i c bendi n gt e s t s .Bot hEIe s t i mat e sbyt hee l e me nt a rvi br a t i ont he or yandbyt het r a ns f e ma t r i x 5% t hant ha tbyt hes t a t i c be ndi ngt e s t s . me t hodwe r es ma l l e rbyana ve r a ge1 A pr e di c t i onf わr mul aofEIbys t a t i ct e s t sc a l c ul a t e df r om vi br a t i ont e s t swa sobt ai ne d. y ト Ke ywo r ・ ds:boxbe am,me xur a lr i idi g t y,vi br a t i onme t hod・ us eha sbe e nl a i df orbot ht e c hni c alandf unda me nt a l 1 .I NTRODUCTI ON The s hor t ageofl ar gかS i z et i mbe r sand i mpr ove as pe c t s ・Thi s dat a ha st he pot e nt i a lt os uppl y de s i gne dbe a msofl a柑eS i z e . me nt si ngl ui ngt e c hni que sha v epr omot e dde ve l op Thi swor ka i mst ode t e r mi net hef e as i bi l i t yofa mentofc ompos i t ebea msf ors t r uc t ur a lme mbe r s ・I n ibr v a t i ont e c hni quef わre s t i ma t l ngt hene xur a lr igi d- he ut i l l i z a t i on ofpl ywood・ we bbe d box J apan, t EI)ofpl ywoodweb be d box・ be a msf r om t he i t y( mi ni mum i nf or ma t i onwhi c hca nbeobt ai ne de a s i l y - - 叫 butt hebas i sf brt he i r beamsi snotpopul aratpr e s e i namanuf a c t ur i ngpr oc e s s;na me l y,r e s ona nc ef r e ・ Recei v e dNov e mbe r1 6,1 987 和 之 名 古 屋 大 学 贋 学 部 Fac ul t y of Agr i c ul t ur e , Nagoy aUni ve r s l t y,Chi kus a ku,Na goya46 4 *3 静 岡 県林業 試験場 Shi z uoka Pr e f e c t ur al For es t r yExpe r i me ntSt a t i on,Ne ga t a Hama ki t a43 4 *4 東 京 大学農学部 Fa c ul t y or Agr i c ul t ur e ,The ku,Tokyo 11 3 Uni ve r s l t yOrTokyo,Bunkyo81 i g ht ,anddi me ns i onsorabe a m・ que nc y,we Thi swor kwaspr opos e dbe ca us et hede s i gns i z eor woode nbe amsus ual l yi sc ont r ol l edbyt he i rs t i f f ne s s - whi c hi sapr a c t i c a lde s i gnpa r a me t e ri nt hede s i g nof woode ns t r uc t ur esa ndbe c a us eavi br a t i ont e c hni que woul dpr ovi deas i mpl ede vi c et os e r v eapr a c t i c a lu s e Nobu oSoBUE,Ki y ohi koI KEDAandTak a no r iARI MA 5 44 [ Moku z aiGakk aL ' s hE . EII 4・ l3・ fr 2・ W/ 7 r 2 i nf T a c t or i e s . (I ) whe r eH sl eng t h ora be am,〟 i st her e s onanc e 2 .mATERI ALANDMETHOI ) S f r equency,and w i st hewei h toft g hebe a m・ 2 . 1 Pl ywo odwe bbe dbo xbe ams De t ai l sorbe am c ons t r u c t i ona r es howni nFi gur e 2. 3. 2 Tr ans fe r mat r i xmet hod2) I .He mFi rorSpr uc e Pi ne Fi r2"by 4" ( nomi nal l i ne arc ombi na t i onoft woki ndsore l e me nt s ,S pr l ng el e ment sandma s se l e me nt s . F l a n g e( 2 ' ' b y4F) ' * St i f f n e r ( 2 〝b y4′ ′ ) * A boxbe a m wascons i de r e dasabe am ma deora TF] andt hepoi ntma t r i xlTp ]of Thef i e l dmat r i xl e a che l e me ntar ee xpr e s s e dasf ol l ows; 1I 1 2 /( 2EI)l3 /( 6EI) [㌫ ] = 01 00 I / EI 1 00 0 / ( 2EI) / l2 ( 2) 1 1 0 0 0 3 6 4 0 and [㌫ 〕n i t: mm Fi g.1 .Cons t r uc t i on or pl ywoodwebbed box be ams . Nomi na li nc hs i z e sofme mbe r s . * 0 ] = 1 0 0 0 0 10 ( 3) Ma 7 20 0 1 ,r e s pe c t i ve l y, smas s ,a nda i sci r cul arf r e que nc y. wher eM i Thet r ans f e rma t r i xofane ir m ebe a ml N]i sgi v en bymul t i pl yi ngt hef T l e l dma t r i xandt hepoi ntma t r i x l nt ur n, i nc hs i z e )No・ 2g r a del umbe rwasus e df わrmangea nd s t i 恥e rme mbe r s ・ No.1gr adepl y wood,1 2mm t hi c k ,wa sus e df T orwe bme mbe r s . f orc ons t r uc t i onus e ● We bme mbe r swe r eJ oi ne dwi t hma ngeands t i 恥e r ● me mbe r sby an a qu e ousvl nyトpol y me rs ol ut i on - yl β l [ Tp n ][ TF n ][ Tp n _ L ][TF n _L ]・ ・ ・ [Tp l ][ TF l ] Ml ¢1 ( 4) - be t we e ns t i f f ne rme mbe r sa ndma ng eme mber swe r e ma dewi t hCN9 0nai l s . Thi r t ybox be a mswe r ef a br i c at e da ts i xf a c t or i e s; name l y,r l V ebe a msa te a c hf a c t or y,a c c or di ngt ot he s a mepr oc e s s i ngf or mul a. 2 . 2 Me t hods EIwasme as ur e dbybot hs t a t i candvi br a t i ont es t s . e l γユ i s oc i ana t eadhe s i veandCN50nai l s ,andt hej oi nt s -[ 〃] 叫 ( 5) Ql whe r e[ N] ,y,C ,M,a nd Q ar e( 4 × 4)mat r i x, de f わr mat i on, s l opeofbe a m, mome nt , ands he a rf or c e, ● r e s pec t i ve l y.Thes ubs c r l pt S1and〟a r et hepos i t i on numbe r sort het woe ndsort hebe am. Thef or me rwe r ema dewi t hat wopoi ntl oa di nga t The n,Equa t i on 5wa ss ol ve df ort hebounda r y one t hi r dors panl e ngt h・Thel a t t e rwe r ema debyt he c ondi t i onofas i mpl e s uppor t e dbe am , Iname l y, ynyl =OandMn-M1 -0. f r e evi b r a t i onofs i mpl e S uppor t e dbe a mswi t hs pa n l e ng t hsor36 0c m・Spe c i me nswe r et a ppe d wi t ha r ubbe rha mme ra tt he i rmi dpol nt S ,a ndt hevi br a t i onswe r ed e t e c t e dbyal oa dc e l lwhi c hwasi ns t al l e d asoneoft hes uppor tbl oc ks .Ther e s onanc ef T r e - que n c ywa sme as ur e dbyaFa s tFour i e rTr ans f わr ma - Thea c c ur a c yoft hes ol ut i onde e ndsont p henum be rore l e me nt sc ons i de r e d.I twase xa mi ne d asa - homog ene ousr e c t a ng ul a rbe am.Thedi f f e r en c eofEI be t we e n t he t r ans f e r 一 ma t r i x me t hod and t he r ・ t i onSpe c t r u m Ar l al yz e e l e ment a r y vi br at i ont he or yde c r e as edwi t hi nc r e as e s i nt henumbe rore l e me nt s .I nourwor kt henumbe r 2 ・ 3 Cal c ul at i o no fJZ e xur alr i gi di t y ofe l e me nt swe r e6 5.Thedi f f e r e nc ewasa bout5x 2 ・ 3 ・ 1 El e me nt ar yt he o r yo fv i b r at i onl) 1 0-4 %. TheEIofas i mpl e s uppor t e duni f br mbe am byt he e l e me nt a r y v i br a t i ont he or yl Sgl Ve nby vol ・3 4,No・6 ,1 98 8 ] Fl e xu r a lRi gi di t yMe a s ur e me ntorPl ywoodWe bbe dBox Be a msbyVi br a t i onMe t h od 5 4 5 Thee f f e c toft hede ns l t yOfwe bme mbe r sa l s owa s 3.RESULTSANI )DI SCUSSI ONS 3 ・ I Appl i c at l ono ft hee l e menl ay yv i br at E ' ont he or y AnEJobt ai ne dbys t at i c be ndi ngt e s t s( EI s)i snot t hepur eEIofabox be am be c aus ei nabe am whos e i nve s t i gat e dwi t hr e s pe c tt ot her ang e什om β=0 ・ 5t o 0. 7g/ cm3 .Noi nnue nc ee xi s t e de i t he r . 3 ・ 3 Theot he yc aus e sa j fe c l i n gEIe s t i mat i on Ar ot a t or yI ne r t i aofbeamsa f f e c t sar es ona nc e hei ghti sl a r gef わraboxbe am t hei nnue nc eort he f r eque nc y. 3 )Thi se f f e c t ,whe nt hes t i f f ne rme mbe r s s heardef or mat i onoft hebe am c annotbei gnor ed・ we r edi s r e gar dedi nt hec al cul at i on,wase s t i mat e dt o bea bout0 . 5%.Thi sf a c t oral s owasmi nori n EI ● es t l mat l On. Howe ve r ,t hi sappar e ntval uei sus edcur r ent l yasa pr act i cali ndi c at orort he me chani calpr ope r t y or compos i t ebeams .Ourgoali s ,t he r ef わr e,howwec an sb yvi br at i ont e c hni ques ・ es t i mat et heEI Thes he a rde f or mat i onoft hi c kbe a msa f f e c t st he i r appa r entde ne c t i on.Thet ot a lde ne c t i onorabe am Ther e l at i ons hi p be t we en EI by s t at i ct e s t sand EI v)was t hatby t heel e me nt a r yvi br a t i on t heor y( i nves t l gat ed. ● TheEI vt o EI sr a t i o ave r a g ed0. 8 49w it has t anvwass mal l e rby1 5% dar dde vi at i onofO・ 0821TheEI ( y)i st hes um oft hede ne c t i onbyamome nt( yM)an d t ha tbyas he a rf or c e( yQ) . y=yM+ yQ=yM(I+C ) ( 6) They Qt Oy Mr at i o( C)i sg ive nby4) t han t he EIs・ Why doe ss uc h a di f f er enc ee xi s t be t we ent het wome t hods? ( 7) C -( i) i ・ KL ・ KF ・ ( i) 2 whe r eK Li sal oadf a c t or ,KFi sadi me ns i onl e s ss he a r Cons i der i ngt her ol eorea chel e me nti nabe am, t he f a c t or ,( E/G) ii st hee qui va lentE t oG r a t i oofa s t i nt ne rme mbe r sc ont r i but enotonl y ass t r uc t ur a l member s butal s o asa c onc ent r at ed mas swhi c h beam,and h/ Ii st hehe i g ht t ol e ng t hr at i o. di i ni m s hest her es onanc ef r e quencyofabe am.I nt he EI vand EI s be c aus et he r ei sa di f f e r e nc ei nt he el eme nt a r yvi br at i ont he or y,t hel at t ere f f e c ti sa ve r manne rorl oa di ng;na me l y,at wopol ntl oa di ngf わr - ,KL4)af f e c t st hedi f f e r enc ebe t we e n Oft he s ef a c t or s agedbydi s t r i but i ngt hema s soft hes t i f f ne rme mbe r s s t at i ct es t sa ndas i nus oi dal l ydi s t r i but e dl oa di ngf or uni 丘) r ml yove rt hee nt i r el eng t hort hebeam.Thi s vi br a t i ont e s t s .The r e f わr e ,g L= 9. 3 9f わrs t at i ct es t s , i ghtbeoneort m hec aus eoft hee r r ori n EIes t i ma - a ndだ L = 9. 87f わrvi br a t i ont e s t s .Thi sme anst ha t he f ol l owi ng t r anS f T e r mat r i x t i ons . Ther ef or e, t met hod was us e dt o de t e r mi ne t he e f hc t soft he t hev i br a t i ont e s ti nduc e sani nc r e as eorg L b ya bout cons t i t ut i onof . abe a m onEIes t i mat i ons . t .Fi na l l y,t hevi br a t i on 5渇mor et ha nt hes t a t i ct e s t es te s t i ma t e st hegJ 1 . 2渇 l e s st handoe st hes t a t i c 3. 2Appl i cat l ' ono ft het r ans fe r mat r i x me t hod t e s t . (I)The r ei snos l i pbe t we enwe bandmang eme mbe r s ・ The r es t i l lexi s t sadi f f e r e nc eofEIby1 3t o1 4渇 be t we ent hes t at i ct e s t sandvi br a t i ont e s t s .Thec aus e ( 2)Thes t i f f ne rme mber sal s owor kasaconc e nt r a t e d oft hi sdi f r e r e nc ei snotcl earatt hi st i me,andf ur t he r mas s .(3)Thedens i t yofnangeands t i f F nerme mbe r s i nve s t l ga t i oni snotpl a nne dbe c aus eourf i nalt a r g e t i s0. 5g/ cm3 .( 4)Themas soft henai l si st akeni nt o i sonl yhow t oe s t i ma t et heEIf r om t h emi ni mum cons i der at i on,butt hatort hegl uei sdi s r ega r ded・ i nf わr ma t i ononbea mswhi c hi sobt ai ne deas i l yi nt he Thef わl l owi ngas s umpt l OnSWe r ei mpos e d: Thedi f 托r enc eofEIbe t we ent her es ul t sby t he manuf ac t ur i ngPr OC eS S ・ el ement a r yvi br at i on t he or y and by t he t r a ns f e r mat r i xme t hodwasl es st han0. 1%.Thi sme anst hat 3 . 4Pr e di ct i onfor mul ao f EI sfr o mv i br at i o nt e s t s t he c onc ent r a t ed mas sofs t i f f nerme mber shasno Fi gur e2.Thes t a t i s t i c alr es ul t sha v es hownt ha tEI v / s l gni r l Cante f f e c tont hec al c ul a t i onoft heEIofa boxbeam. EI si sO・ 8 490na ve r a g eandt ha ti t ss t anda r dde v i a t i oni s0. 08 2. ● Ac c or di ngl y,t hef bl l owl nge qua t i onwi l lpr edi c - Thee f f e ctoft hedens i t i e soft hemang eands t i f f ne r membe r swasi nv e s t l gat eWi t hr es pec tt ot her ange f r om p-0. 40t oO・ 60g/c m3c ons i de r i ngt hec as eof HemFi rand S pFl umbe r .Dens l t yhadnoi nnuenCe. Ther e l at i ons hi pbe t we e nEI san dEI vi ss howni n - EI sf r om Et v: 1 . 1 8EI v EI s- ( 8 、 Howe ve r ,t hi se qua t i onove r e s t i ma t e st heEIv; oft hepl ot sbe l ow t hi spr e di c t i onl i ne・Thi so ve l [ Mo ku z alGakkaI ' s hE ' NobuoS oB UE,Ki y ohi k oI KEDA a ndTa ka no r iARI MA 546 l S i nnue nc eont hec a l c ul a t i onofEI . Ot he rf a c t or s af f e c t l ng EI c al c ul a t i ons wer e ) ⊥\ ns i t i e s ofs t i r F ne r and web e xami ne d;na me l y,de I me mbe r s ,ar ot a t or yI ne r t i a,andas he ardef わr mat i on, 山 X a ^q ^ 1! P! B! Lf eJn t hos ebys t a t i cbe ndi ngt e s t s ・ Ther e s ul toft het r ans f e r 一 ma t r i xme t hod pr oved t hatt hec onc e nt r a t e dma s sofs t i f f ne rme mbe r shadno ( . ・ L uU・ 61. , OtX Ie ■ 1Sa}U! ga ves mal l e rval ue sOFEIb y1 5% Ona ve r ag et han に 0. 4 0. 4 0 . 6 0. 8 1 . 0 1 . 2 ,E/ V( xlO9k g・ c m1-) F I e x u r a l r i g i d i t yb yv i b r a t i o nt e s t Fi g. 2 .Pr e di c t i on f or mul a ofEI f r om vi br a t i on t e s t s . p i s9 5%l owe rc onf i de nc el i mi tofEI svs Not e: EI EIvl i ne . butt he ywe r emi norf a c t or s ・ A pr e di c t i onf or mul a( EI ,) o fEI sf r om EI v was a r r i ve dati nEquat i on9 ・ I nc onc l us i on,t hepr opos e dvi br a t i onme t hodi sa f e a s i bl e pr a c t i c alway f or pr e di c t i ng t he EI of I pl ywoodwe bbe dbox be a ms . Ac knowl e d ge me nt t i ma t i on i snota c c e pt a bl ef r om t hevi e wpoi ntOf s t r u c t u r a lde s i gnbe c aus ei te s t i ma t e st hede ne c t i onof abe a ma sbe i ngl e s st ha nt hea c t ua lde ne c t i on. The n,t hel owe rc onf i de nc el i mi tof9 5渇 wa sus ed a sa ppr opr i a t et Or e du c et hea c c e pt a bl er i s kl e ve l , EIp-I . 0 2EIv ( 9) Thi spr e di c t i onl i neal s oi ss howni nFi g ur e2. 4 . CONCLUS I ON A vi br a t i on me t hod f orme a s ur i ng t he EI of pl y woodwe bbe dbox be amswa si nv e s t i g a t e d. Thee l e me nt a rvi br a t i ont he or yofuni f or m be a ms y Wet hankt heJapan2"by 4′ ′HomeBui l de r sAs s oc i a t i on f わrpr omot i ng t hi s r e s e a r c h. REFERENCES 1 )Ti mi s he nko, S∴ "Vi br at i on Pr obl ems in ● Engl ne e r l ng" ,TokyoTos ho,1 978,p. 297. ,D. J ∴" Mat r i xComput e rMe t hodsor 2)Ha t t e r Vi br a t i on Anal ys i s " ,Br a i n Tos ho Shuppan, 1 97 7,p.Ill-1 22. 3)Ti mos he nko, S∴ "Vi br a t i on Pr obl ems i n. Engl ne e r l ng" ,Tok yoTos ho,1 978,p.3 06. .・ .Ho b Roj z .We r ks E . ,27( 7) ,25 3 4)Ehl be c k,J - 26日 1 96 9) .
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