Effective stiffness of reinforced thin-webbed timber beams

Transcription

1 ffective tiffne of einfoced thin-webbed timbe bem Ohndj Ayin 1 ABSTRACT Thi ppe peent two implified nlyticl method popoed fo evluting the ective tiffne of einfoced thin-webbed timbe bem ubmitted to bending moment. Method 1 ume the volume of the einfocement to be pted unifomly long the web while Method conide n integted men vlue fo the moment of ineti. The compion between theoeticl eult fom nlyticl clcultion nd expeimentl eult fom thee-bending tet cied out on lge ize pecimen.5 mete long nd 40 centimete high how tht Method 1 undevlue the ective moment of ineti while Method i tifctoy with 5% eo. 1. NTRODUCTON Mny compnie tody Joit Tut Mcmilln TM poduce -bem fo mny ue in contuction cffolding, oof, floo,. Fo lge cle poduction need, thee bem hve genelly thee component: two flnge mde of olid wood o engineeed wood poduct LVL o glulm, nd the web mde of OSB pnel. Line joint between the flnge nd the web well continuity joint in the component e glued. Deign iue e tcled in uocode 5 though method bed on the homogenition technique which i ecommended fo detemining the ective e of the ection of the compoite bem nd it ective moment of ineti well. The ditibution of tee within the co-ection i given lo. Menwhile, the height of thee bem i limited to 500mm to pevent the ltel bucling hzd. Fo highe ection bem ubmitted to high level bending moment, it i necey to einfoce the web uitbly in ode to impove ignificntly it mechnicl tbility vi-à-vi both the bending moment nd the ltel bucling phenomenon. Thi ppe im to popoe two implified method fo evluting the ective igidity of uch thin-webbed bem which web i einfoced with wood tu b on ech ide ee figue 1. n the pecil ce of developing countie whee wood induty i vey we, bolt e ued inted of glue ince even ul communitie fo thei ective economicl nd ocil development cn eily mte thei ue. Adopted fo mny poject in Cmeoon duing the pt ten ye, the bolted ytem of figue 1 i tudied in thi ppe, but the nlyticl method popoed e independent on the connecto ued. Figue 1. A einfoced thin-webbed bem. THORTCAL DVLOPMNTS Let conide the bem of figue 1. t cn be modelled n -bem embled with two chin of tu b o two tue embled with wood-bed pnel. We dopted the fit model it bic tuctue, the -Bem, i ledy peented by Solli o tht ou t conit jut in completing the C5 eqution elted to long-tem loding which follow: Senio lectue, School of ngineeing, Univeity of Youndé 1, Cmeoon

2 1 ffective e of co-ection: A ffective moment of ineti: A + A 1 def, + def, The ditibution of tee in the flnge nd web i then immedite. n eqution 1 nd, indice nd elte to the web nd the flnge epectively. A,, nd def e the e of the co-ection, the moment of ineti MO, the modulu of elticity MO nd the dution of lod pmete, epectively. qution bove e yielded by homogeniing the co-ection with epect to mteil of flnge. The ect of the dution of lod nd the ect of the moitue content e ten into ccount though the coicient def. Then, the flexul igidity i immedite. The einfocement my be poceeded with two model: Anlyticl method 1 t volume cn be pted on the ufce of the web, with depth of: v e 3 hb whee e i the depth, v nd b e epectively the volume nd the length of the bic plot of the einfocement nd h i the height of the web. Figue how the modelled co-ection. uppe flnge e / e / h web lowe flnge Figue. The compoite co-ection Then, the dditionl tem of eqution 1 fo the new ection i: A e h def, And the ective moment of ineti of eqution might be completed follow:

3 eh def, Anlyticl method The poition of the cente of gvity of the co-ection of the einfocement l vie with epect to the neutl line of the bem fom vlue 0 to vlue h/. The ubequent chnge of the Huygen tem yield to ymmetic non line vition of the moment of ineti within bic plot hown in figue 3. l x B/ B/ Figue 3. Bic plot of the einfocement Since l i the following function of x, l h x B 6 f we conide the men vlue of the Huygen tem given by: H B B 0 bh h x inα B dx 7 H b h h h 1B + B 8 whee B i the length of bic plot of the einfocement, h nd b e ectionl dimenion of the einfocement nd α, the ngle between the einfocement element unde conidetion nd the flnge. Theefoe, the contibution of the einfocement in the new moment of ineti i: bh h h + h B The coeponding poition of the einfocement ection i moment of ineti. n pctice, α vie between 30 et 60. Finlly, the ective e of the co-ection i: h 1 h nd not 4 which led to low vlue of the

4 A + A A + A 10 def, def, nd the ective moment of ineti i: def, def, then, the theoeticl igidity come immeditely. 3. XPRMNTS Thee-point bending tet wee cied out on.5 mete long nd 0.35 high bem. Flnge nd einfocement wee mde of Spelli when the web w in n Ayou plywood. A peliminy chcteition of the mechnicl popetie of mteil olid wood fo pelli nd plywood fo you w pefomed. The modulu of elticity nd the he modulu well the moitue content wee detemined fo wood mteil. Fom the line pt of the foce-diplcement cuve yielded by the bending tet, we could compute the expeimentl vlue of the igidity exp which w then comped with the theoeticl vlue. We noted ome diffeence which e due to the ppoximtion mde when evluting the cuent moment of ineti nd to, mybe, the type of emblge. One hould notice tht when the Foce P-Deflection f cuve i line, 3 PL 48 f exp 1 Then we defined coicient which i the tio between the expeimentl igidity nd the theoeticl igidity. t i the coection to poceed on th. exp 13 th 4. RSULTS AND DSCUSSON 4.1. Reult Bem of.5 mete long nd 0.40 mete high wee teted unde fou-point bending. Wood pecie wee: 1 Spelli fo flnge nd einfocement. Sectionl dimenion wee 8x4cm Ayou fo the double-ide einfoced web. 15 mm wide plywood pnel wee ued. Bolt φ1mm wee ued connecto. The me 15 mm wide plywood pnel w ued fo joint plte. t i vey convenient economicl olution. Figue 4 peent typicl expeimentl foce-deflection cuve fo teted bem nd tble 1 peent the mechnicl popetie of mteil while tble compe the expeimentl nd theoeticl vlue of the igidity.

5 Lod-Deflection cuve y 1959x R 0,9901 Lod N Line 1000 Non-line Linéie Line ,78 0,8 0,8 0,84 0,86 0,88 0,9 0,9 0,94 0,96 Deflection mm Figue 4. xpeimentl Foce-Deflection cuve Tble 1. Mteil popetie Moitue content of wood MC Men MP vlue Vince MP xtpolted vlue t 15% MCMP MO fo Spelli 7% MO fo Ayou plywood 14% Tble. Compion between igidity vlue Theoeticl igidity MP xpeimentl igidity b men vlue in MP Rtio b/ Method Method

6 4.. Dicuion The following obevtion hould be noticed: - t i obviou tht the tio of eqution 13 depend on the connecto bolt, nil, glue. A emi-igid ppoch hould be developed. - Alo, thee my be ize ect to te into ccount. - Method eem to be mot elitic nd ppe good ill fo pe-deign of tue ince fomul 11 bing to good etimtion of the igidity of the tu without clculting foce in it membe the tditionl method ue to do. So tht the deflection i ey to clculte. 5. CONCLUSON Two implified nlyticl method fo the etimtion of the ective tiffne of einfoced thin-webbed timbe bem wee comped to expeimentl dt. Method bought to good eult with 5% eo depite the impefection of the connection. t gve n uppe vlue of the ective moment of ineti. Alo, thi method ppe good ill fo the pe-deign of tue ince the deflection i immedite. 6. RFRNCS Solli, B. 1996: Deign of thin webbed bem. Step 1, leon B9, uofothec edition. Rche,P., Bige,J.P., Rouge,F., Sgot,G. nd Vidon,G. 1998: in Step, Chpte 3 Stuctue en Boi ux tt Limite. ntoduction à l uocode 5, Clcul de Stuctue. yolle edition. Acnowledgement: The utho thn wmfully the GS AR DÉVLOPPMNT Fnce which funded thi eech.