DESIGN OF REINFORCEMENT AROUND HOLES IN LAMINATED VENEER LUMBER (LVL) BEAMS

Transcription

1 DESIGN OF REINFORCEMENT AROUND HOLES IN LAMINATED VENEER LUMBER (LVL) BEAMS Manoocheh Adalany 1, Massimo Fagiacomo, Buce Deam 3, Andew Buchanan 4 ABSTRACT: Many pactical situations equie holes in timbe beams. When the hole is lage elative to the depth, the ailue o the beam is govened by cack initiation and popagation aound the hole. Cacking o a timbe beam deceases the capacity o the beam consideably. This pape pesents a method o designing the einocement aound holes in Laminate Venee Lumbe (LVL) beams so as to ecove thei ull lexual capacity. The design pocedue is complemented by a woked example whee all veiications ae discussed with geat detail. KEYWORDS: LVL, Scew, Plywood, hole, einocement, tensile stesses 1 INTRODUCTION 13 Many pactical situations like building sevices, achitectual consideations, etc. equie the intoduction o holes in timbe beams. Cutting hole into the timbe beam causes concentation o tensile and compessive stesses aound the hole. The inheent low tensile stength o wood mateial pependicula to gain makes the beam susceptible to cack initiation and popagation at athe low load levels [1]. Figue 1 pesents a photo o a Laminated Venee Lumbe (LVL) beam with a hole that has cacked at the peimete. Aound the hole, the tensile stesses will most likely exceed the mateial low tensile stength pependicula to gain, in this way causing cack initiation. Subsequently, the cack popagation due to the coupled shea and moment in the beam section educes signiicantly the 1 Manoocheh Adalany, Depatment o Civil and Natual Resouces Engineeing, Univesity o Cantebuy, Chistchuch, New Zealand. Manoocheh.adalany@pg.cantebuy.ac.nz stength and stiness o the beam. Reinocement aound the hole is an eective option o impoving the behaviou o the timbe beam. Dieent options o einocement could be egaded. A good einocement should ecove the load caying capacity o the beam completely. Plywood and scews ae two altenatives shown to be appopiate to contol cack popagation. The choice o the einocement type is mucependent on the stesses in the section, achitectual equiements, ease o the installation, and othe actos. The mechanisms developed by plywood and scews to contol the stesses aound the holes ae dieent. Scews develop stess concentation aound the theaded pat, wheeas plywood uniomly contols the stesses aound the hole due to its lage contact aea with LVL. Fo thick membes whee plywood is not so eective, scews can povide a bette means to educe the stess concentation aound the hole. Massimo Fagiacomo, Depatment o Achitectue, Design and Uban Planning, Univesity o Sassai, Italy. agiacomo@uniss.it 3 Buce Deam,, Depatment o Civil and Natual esouces Engineeing, Univesity o Cantebuy, New Zealand. Buce.deam@cantebuy.ac.nz 4 Andy Buchanan, Depatment o Civil and Natual esouces Engineeing, Univesity o Cantebuy, New Zealand. Andy.buchanan@cantebuy.ac.nz Figue 1. Cack popagation aound the hole

2 1.1 Scew einocing Sel tapping scews ae dilled into the beam to block the path o the cack popagation, in this way inceasing the load-caying capacity o the beam (Figue ). Although the scews can handle the tensile stesses and contol those stesses vey well, it may not possibly stop popagation o the shea stesses in the section o the beam eectively. The shea stesses in the section o the beam will hence incease signiicantly. 1. Plywood einocing Anothe einocement option is the use o plywood sheet glued to the oute edges o the beam. The plywood and the beam om a unique entity, in this way deceasing the tensile stesses in the wood. Although plywood woks vey well o thin membes, it is not o much use in thick beams as plywood cannot educe the stesses at a a distance om its suace. Figue 4 shows an example o einocement using plywood in LVL beam. Figue. Reinocing with scews The design o the scews is somehow challenging because the scews should meet a numbe o design citeia. The main citeia o the design o the scews ae that the scews should cay tensile oces in the section without yielding, and without exceeding the withdawal capacity. Besides, the scew has to be inseted at a distance om the opening to pevent wood splitting. Finally, stess concentation close to the scew should not cause the edge ailue o the beam. A photo o the edge ailue in a LVL beam is pesented in Figue 3. Figue 4. Reinocing with plywood Design o the plywood also needs to be addessed caeully. Plywood should be designed o the tensile oces poduced in the section o the beam. The plywood dimensions should be lage enough to cove the stessed aea. 1.3 Finite element modelling Thee ae ew inite element models that can handle well the cack initiation and popagation, paticulaly o wood stuctues. One o the possibilities is the use o the cohesive elements. The idea o the cohesive element in cack popagation is to diminish gadually the stiness o the elements that have eached the maximum tensile stength o the mateial. In this way, numeical poblems ae educed, and cack popagation can be eectively modelled. Figue 5 shows an example o stess distibution pependicula to the gain in a beam at cack suace, which is located at the level o the most likely cack plane, namely at the point along the peimete o the hole whee the maximum tensile stess pependicula to the gain is attained in an elastic analysis. Figue 3. Edge ailue in LVL beam einoced with scew

3 Figue 5. Use o the cohesive elements o cack modelling In this pape, the design o both einocement methods, scews and plywood, is discussed and two woked examples ae pesented. The tensile oces due to the hole ae calculated using an analytical omulation deived o LVL beams. The poposed design method ensues that the load-caying capacity o the entie beam section is obtained by using the minimum amount o einocement calculated. BEAM WITH HOLES AND NOstudied though a REINFORCEMENT Design o LVL beams with holes was compehensive expeimental pogamme. The expeimental pogamme indicated that o beam 00 mm, 300 mmm and 400 mm deep with span length to depth atio smalle than 10, a 50 mm hole diamete did not cause any eduction in load-caying capacity. Howeve, with the aim to povide a consevative design ecommendation, the limitation to 50 mm diamete is poposed o beams with length to depth atios o moe than 10. Based on APA ecommendations [], a 5 mm diamete hole may be used o beam o length to depth atios smalle than 10 without the need to educee the load-caying capacity to allow o the hole. 3 TENSILE LOAD Figue 6(a) and Figue 6(b) shows a dawing o a beam with a hole with notations o geometical paametes. Figue 6. Dawing o a beam with cicula and ectangula holes The tensile load due to the shea oce and bending moment in each section o a beam was calculated using the so-called Tuss model. This model assumes that the moment and shea that could not be tanseed in the section o the beam due to the hole ae tanseed though tuss action aound the hole. The model yieldedd Equation (1) o tensile load pedictions o LVL beams with cicula holes: F, V h 3h h 8 h 3 M h h h 4 h h. h h h In Equation (1) F, is the design tensile load, V is the shea oce in the section o a beam, diamete as shown in Figue 6, and M is the moment in the section o the beam. Equation (1) has two contibutions: (i) the ist contibution due to the shea; and (ii) the second contibutionn due to the moment. Fo the squae holes the omulation was evised in the tem o the moment (second tem in Equation (1))) because the poposed omulation was ove-estimating the tensile load consideably. Equation () pesents the tensile load due to the shea and moment in the section o a beam o a squae hole. h d (1) is the hole F, V h 3h h h 0.7M 8h Finally, ectangula holes wee investigated, and some omulations wee deived o tensile load pedictions. Equation (3) povides the tensile load poduced due a ectangula hole in a section o beam. F, β 4h V V h 3h h 0.7M h (3) h h ()

4 whee β signiies a paamete deined as below: b βmax and h b h b (4) It should be pointed out that only equation (1) was deived om the Tuss model, wheeas Equations (), (3), and (4) wee obtained though numeical analyses on LVL beams with holes. The aoementioned omulations weee used o beams up to 400 mmm depth. A seies o inite element analyses on beams with cicula holes showed that the pedicted tensile load though Equation (1) undeestimates the tensile load in the einocement o depth geate than 400 mm. A coection acto is equied to take into account size eect. A modiication acto o h/ /400 applied to the inal tensile load pedicted though equation (1) is poposed to take into account the lage depth. Also, o small eccenticity o the hole along the beam depth (10% o beam depth), the numeical analyses showed thatt the tensilee load in the einocement inceases consideably. Again numeical analyses showed that a magniyingg acto o ( 1+ h d/h) can be applied to incease the inal tensile load in the scew. h 5 b h < 3 REINFORCEMENT 5.1 SCREW REINFORCEMENT DESIGN Design o ully theaded SPAX scew should meet some citeia, viz.: (i) Distance o scew om edges o beam should be enough to avoid splitting o wood, (ii) scew should not yield due to the tensile stesses, and inally (iii) scew should not withdaww due to the tensile oces MINIMUM DISTANCE OF SCREW FROM EDGES OF BEAM Figue 7 shows a dawing o a beam with hole einoced with two vetical scews with edge distances o a, a, c and a mutual distance o a. The ollowing limitations wee adopted om the Geman design code DIN 105 o the distances o the scew om edges o the beam. The distances ensue that no splitting in the LVL beam can occu. (9) 1, c 4 LIMITATION OF HOLE SIZES Expeimental tests on einoced LVL beams with holes yielded the ollowing limitations, in good ageement with the Swedish glulam handbook [3], o cicula holes einoced with ully theaded scew: 0. 4h (5) In the case o plywood einocement o cicula holes, the limit in Equation (5) can be eleased because plywood inceases the shea capacity o the beam locally in the section: h (6) Limitation om Equation (5) was deceased slightly o ectangula holes due to the cones o scew einocement as below: Figue 7 Reinocement o scew.5 d a 1,c 4 d a 3d (10) (11) h Limitation om Equation (7) can be eleased when using plywood einocement: (8) 0. 4h (7) whee d is the oute diamete o the scew. a.5, c d (1) Finally, o ectangula holes, the dimension limitation suggested by the Swedish glulam handbook was adopted [4].

5 5.1. YIELDING OF SCREW Tensile stesses due to holes should not cause yielding in the scew einocement. Contolling o einocement could be ensuing accoding to: Ft,90,d < y,d, scew π d (13) ( ) 4 whee y,d, scew is the design yielding stength o scew deined as: y,k y,d, scew = k mod (14) γ Note: y, k is the chaacteistic yielding stength o scew, γ m is a patial saety acto o scew o 1.3 accoding to Euocode 5 [5]. k mod signiies the patial modiication acto o load duation and moistue. Such a paamete should be assumed equal to 1 because scew design is not aected by the change o the moistue content in the wood no by the load duation SCREW WITHDRAWAL The scew should not withdaw. Scew withdawal could be pevented by using enough embedment length at both sides o the cack suace. t,90, d ax,d m F R (15) withdawal stength o scew with oute diamete o 8 mm could be obtained though the Equation (18). 6 1,k = whee ρ is the density o LVL in 3 kg / m density o LVL, 1,k is 4.5 MPa. Contolling o withdawal. L ad and L ρ (18) 3 kg / m. Fo 550 Lbd is necessay to avoid scew max(1d,l bd ad (19) Lbd ae pesented in Figue 8. Figue 8. Withdawal length 5. PLYWOOD DESIGN Design o plywood should meet the ollowing citeia, viz.: (i) plywood should cay the tensile load due to the hole; and (ii) plywood should cove the potion o beam whee tensile stesses exceed the tensile stength o LVL. ) R ax, d R ax,k k mod / γ (16) Note: R ax, d signiies the design tensile stength o scew einocement, R ax, k the chaacteistic tensile stength o the scew, γ m patial saety acto that o LVL is assumed equal to 1. and inally k mod is a modiication acto o LVL taking into account load duation and moistue content that o pemanent loading is equal to 0.6. Accoding to Aiche et al [6] R be calculated as : m ax, d could 5..1 CONTROL OF DIMENSIONS Plywood as einocement should be glued and nailed/scewed to both sides o the holes. Nailing/scewing with gluing o plywood to both sides o the hole povides ull bond between LVL and plywood. Figue 9 povides a dawing o a hole einoced with two plywood sheets witimension shown in the Figue. R ax,k = min(r t,u,k,1,k L bdd ) (17) Note: R t,u, k signiies the chaacteistic tensile stength o scew, 1, k the withdawal stength o LVL, and L bd the embedment length o scew. Accoding to the expeiments on LVL specimens, the chaacteistic Figue 9. Plywood on both sides o a hole The limitation below may be used o beams with holes. 0.5h d a 0.3(h + h d )

6 (0) h (1) 5.. TENSILE STRESS CONTROL The plywood should be contolled o the incease in stesses due to the hole. Contolling o the tensile stesses can be peomed thoughh the ollowing equations: σ t,90,d d,ply () Note: σ t, 90 = k d,ply mod γ t,90,k K.Ft,90,d σ t,90,d =.a.t, d signiies the tensile plywood pependicula to ace gain, d,ply the design tensile stength o plywood pependicula to ace gain, and K is a acto taking into account non-uniom stess distibution aound the holes in LVL beams. Ft,90, d is the design tensile oce in plywood due to the hole. K accoding to Aiche et al [6] may be taken as. a and t ae paametes intoduced in Figue 9. Accoding to New Zealand standadd [7], the tensile stength o plywood o dieent classes o plywood could be obtained om Table 1. Table 1. Chaacteistic tensile stength o plywood pependicula to ace gain [7] Chaacteistics tensile Class o plywood stength o plywood F 34.6 F17 30 F14 F F m (3) (4) design stesss o Figue 10. Gain diection layout 5.3 INSTALLATION OF PIPES Installation o pipes is an impotant issue in design. The weight o the pipes should not be applied to the tensilee edge o the beam. Figue 11 shows tensile stess ield obtained om inite element analysis o LVL beams with holes. The beam dimension was mmm loaded at mid-span by 50 kn concentated load. The Figue shows that two opposite ight sides ae in tensionn and two othe sides ae in compession. Figue 11. Stesss ield aound holes Avoiding exta tensile stess pependicula to gain equies that the pipe weight be applied to the uppe edgee o the beam to have a positive eect on cack (closing cack) as displayed in Figue ROLLING SHEAR Rolling shea between plywood and LVL was consideed but it did not seem to be a citical issue. A ecommendation o mitigating the eect o olling shea is pesented in Figue 10. The ist venee o plywood is glued and nailed to the LVL beam so that its gain diection is pependicula to the gain diection o the beam. Figue 1 Detail o beam penetation with pipe hangingg om the top pat o the beam

7 5.4 STRESS CONCENTRATION At squae/ectangula hole cones stess concentations occu and shea stesses ise consideably. Accoding to Bejtka et al [8], o ectangula holes with shap edges the maximum shea stess to aveage shea stess atios vay signiicantly with inceasing hole diamete to beam depth atios, as pesented in Figue 13 o squae holes. 8 Ratio o maximim shea to aveage shea Ratio o hole size to beam depth Figue 13. Ratio o the maximum shea to aveage shea o dieent hole sizes to beam depths Figue 13 shows that o / 0. the maximum shea stess poduced is 3.3 times the aveage value and o / 0.5 the atio is 6.4. Contolling o the shea stesses at the edges o the ectangle is necessay. Following omulations may be used o calculation o the maximum shea stess [9] V τ κ 1.5 bh h (5) goven the ailue mechanism. Inteaction o the holes was investigated o a set o numeical analyses on einoced beams. Figue 14 Inteaction o the holes Numeical analyses showed that o distances between scews geate than 1.5h the scews have no inteaction to each othe. This distance is ecommended as a minimum clea distance between the scews that should always be ensued. WORKED EXAMPLE OF SCREW REINFORCEMENT DESIGN A beam o dimensions has been loaded at mid-span. A hole o diamete 90 mm is intoduced into the beam at a distance o 600 mm om the end section. The beam is used within a oo o a house subjected to pemanent loads. The design o the einocement using ully theaded SPAX scews o 6 mm coe diamete with the thead o mm (see Figue 15) is equied. κ b h h h. (6) whee τ is maximum shea poduced due to the hole. The above limitation apply o 0.1 b /h 1 and 0.1 h /h 0.4. τ, (7), is design shea stess capacity o the LVL deined as:, k, γ (8), is chaacteistic shea oce capacity o LVL. Contolling o the shea capacity o scew einocement in ectangula holes is necessay. 5.5 INTERACTION OF THE HOLES Inteaction o two o moe holes (Figue 14) consideably deceases the capacity o the beam with holes. Cacks aound the holes joining each othe can Figue 15. Beam with hole einoced with scews Contolling hole diamete: The atio o the hole diamete (h ) to beam dept (h) is 0.3, which is smalle than the limitation o ully theaded SPAX scew o 0.4. The einocement by scew needs theeoe to be designed. Tensile load pependicula to gain in scew: The design hee is being peomed o maximum shea oce in the section o the beam. The chaacteistics shea capacity o LVL in the gain diection is [10]:, 6.0MPa

8 The maximum shea oce capacity o the beam section accoding to Euocode 5 could be calculated as below: V,bd kn M V L knm So the tensile oce in the scew can be evaluated as: F,, F,V, F,M, = V h 3h h M. F,, , kn Design o scew einocement: With the assumption o using ully theaded SPAX scews o the einocement, the withdawal stength could be calculated as below:, 8110 ρ N/mm The embedment length o the scew could be calculated as below: L 0.5h 0.354h mm The aoementioned embedment length can cay the ollowing load: R, kn R, R,K kn γ 1. The embedment length o 118 mm povides 11.6 kn esistance to withdawal. The above oce is highe than the design oce o 10.4 kn in the scew. So that embedment length will be suicient. The scew also should not yield. Since the yielding stength o the SPAX scew is about 800 MPa, the yielding oce o the scew is: 800 π 6.0 kn 4 Since the oce o kn is geate than the design axial oce o 10.7 kn in the scew, the design is satisactoy. Contolling o distance o scew om edges: Distance o scew om the edges o the beam.5d a, 4d The oute diamete o the scew is 8 mm, theeoe we have: a, 38 0 mm The distance o the scew om the othe suace o the beam is: a,.5d The distance o the scew om the edge o the beam is: a,.5d.580 mm The distance o the hole om the suppot is contolled though the ollowing equation: sl c h h s mm The design is now complete o einocement with sel tapping scews. Contolling o citical sections also should be peomed that is not included in the woked example. WORKED EXAMPLE OF PLYWOOD REINFORCEMENT DESIGN A beam o dimension has been loaded at mid-span. A 90 mm diamete hole o dimension is intoduced into the beam at a distance o 600 mm om the end section. The beam has been used in the oo o a house and is subjected to pemanent loads (see Figue 16). Figue 16. Beam with hole einoced with plywood Contolling hole diamete: The atio o the hole diamete to beam depth is 0.3, which is smalle than the limitation o 0.45 o plywood einocement. Reinocing by plywood needs theeoe to be used. Tensile load pependicula to gain in plywood: The maximum shea oce capacity o the section accoding to Euocode 5 is: V,bd kn M V L knm The tensile oce due to the hole is calculated as:

9 F,, F,V, F,M. 8h V h 3h h 3 M h h h 4 h. h h h F,, kn Plywood Dimensions: The hoizontal dimension o the plywood should be limited with the ollowing equations: 0.5h a 0.3hh.5 a 117 The plywood should cay tensile oces due to the hole in the section o the beam. σ,, R, k, MPa γ 1. Assuming the use o 15 mm thick plywood, the length o the coveage aea is deined as below: σ,, KF,, a t mm then the value 100 mm is chosen should be: h 0.5h mm, then the value h 30 mm is chosen. The actual dimension o the plywood sheet will be mm. Contolling o the othe citical sections should be peomed that is not included. 6 CONCLUSIONS Expeiments on LVL beams show that scews and plywood can be used o einocement aound holes. The pape includes a design method o LVL beams with holes based on contolling tensile stesses at the edges o the hole. Woked examples ae pesented o designing o scews and plywood einocement. REFERENCES 1. Adalany, M., B. Deam, M. Fagiacomo, and K. Cews, Tension pependicula to gain stength o wood, Laminated Venee Lumbe (LVL) and Coss banded LVL (LVL-C), in 1 st Austalasian coneence on the mechanics o Stuctues and mateials, S. Fagomeni, et al., Editos. 010: Melboune, Victoia, Austalia. p APA, Allowable holes in LVL Repot numbe T009L , The Enigineeed Wood Association (EWA). 3. Caling, O., Swedish glulam handbook 001, Stockholm: Svenskt Limtä. 4. Aiche, S. and L. Holin, A contibution to the analysis o glulam beams with ound holes. Jounal o Otto-Ga, : p Euocode-5, Eupoean Committee o Standadization CEN, EN Design o timbe stuctues-pat 1-1: Geneal-common ules o buildings 004: Buxelles, Belgium. 6. Aiche, S., Glulam beams with intenally and extenally einoced holes- tests, detailing and design, in CIB-W18/ : Algheo, Italy. p NZS3603, Timbe stuctues standad. 1993, Standad New Zeland, Wellington: New Zealand. 8. Bejtka, I. and H.J. Blass, Sel-tapping scews as einocements in beam suppots, in Intenational council o eseach and innovation in building and constuction woking commission w18 - timbe stuctues. 006: Floence. p Blass, H. and B. Ieneusz, Reinocements pependicula to the gain using sel-tapping scews, in Poceedings o the 8th Wold Coneence on Timbe Engineeing. 004: Lahti, Finland. 10. Buchanan, A., Timbe Design Guide. 3 ed. 007: New Zealand Timbe Industy Inc. 33 pages. Acknowledgements The authos would like to extend thei gatitude to the Univesity o Cantebuy and Stuctual Timbe Innovation Company (STIC) o unding this eseach poject.