Chapter 5 Holes and notches Contents

Transcription

1 Chapte 5 Holes and notches Contents 5 Holes and notches End notched beams Reinocement o end notched beams Intenal einocement o end notched beams Extenal einocement o end notched beams Beams with a hole Reinocement o beams with a hole Intenal einocement o beams with a hole Extenal einocement o beams with a hole Reeences... 12

2 5 Holes and notches The intoduction o a hole o a notch in a membe constitutes a sudden change in the coss section, which signiicantly inluences the stess state and may in a timbe membe educe the stength consideably. The low o nomal stess paallel to gain and o shea stess is distubed. Instead, the local stess state will be chaacteized by concentated, pependicula to gain tensile stess and shea stess in the vicinity o the hole o the notch. This stess situation may lead to cack initiation o elatively low extenal loads and cack popagation in the ibe diection, which typically occus in a vey bittle manne. As o othe applications with simila types o loading, expeimental tests have shown a signiicant beam size dependency o the stength o both notched beams and beams with a hole. Design consideations o uneinoced beams with a notch at the beam end o a hole o ae teated in Section 5.1 and Section 5.3 espectively. Field notching on the tension side should not be allowed, unless the beam is popely einoced. Due to the lage stength eduction commonly elated to beams with a notch o a hole, some type o einocement is geneally advisable. Reinocement o end notched beams is teated in Section 5.2 and einocement o beams with a hole is teated in Section End notched beams Notches at beam ends should be handled with geat cae in design, as even a small notch constitutes a stating point o a potential cack and may hence educe the load caying capacity consideably. Fo a beam with ibe diection coinciding with the beam length diection, an end notch at the tension side intoduces concentated tensile stesses pependicula to gain and shea stesses, which accoding to linea elasticity tend to ininity at the tip o a ight angled notch. The ailue type is typically vey bittle, with cack initiation at the tip o the notch and popagation in the ibe diection. An end notch on the compession side gives a less sevee eduction o the load caying capacity compaed to an end notch on the tension side. I notches cannot be avoided they should peeably, at least i placed on the tension side, be tapeed o given a cone adius o at least 25 mm. Lage notches than 0,5h o 500 mm should not be allowed without einocement. Special cae should be taken with stuctues whee thee is a isk o majo vaiations in the moistue content. All suaces in a notch shall be suace teated. The load caying capacity o an uneinoced beam with an end notch can be checked using the ollowing method ound in Euocode 5, with notation accoding to Figue 5 1. The method is based on a actue mechanics analysis o ight angled notches pesented by Gustasson (1988). Although the design citeion omally eads as a compaison between a nominal shea stess and a educed shea stength, the action o both pependicula to gain tensile stess and shea stess is implicitly consideed. The decisive mateial popeties in the actue mechanics appoach ae the actue enegy in tension pependicula to gain, the stiness in beam length diection and the shea stiness. These paametes ente the design equation though the acto k n via assumptions o thei elations with the shea stength v. The modiication tem elated to the notch inclination i is an addition to the oiginal actue mechanics equation, based on expeimental tests o beams with tapeed notches pesented by Ribeholt et al. (1992). Fo a beam with a ectangula coss section and with ibe diection coinciding with the beam length diection, the ollowing citeion should be ulilled

3 2 3 V bh e k v v (5 1) whee o beams with the notch at the compession side k v = 1.0, while o beams with the notch at the tension side 1 1,5 1,1 i k min k 1 v n (5 2) h x 1 2 h 1 0,8 h and whee V is the shea oce b is the beam width h, h e is the total beam depth and eective beam depth espectively, in mm x is distance om suppot load line o action to notch tip, in mm i is notch inclination, see Figue 5 1 α= h e /h is the eective to total beam depth atio k n = 6,5 o glulam (4,5 o LVL and 5,0 o solid timbe) Figue 5 1. Notation o design o end notched beams accoding to Euocode Reinocement o end notched beams Beams with an end notch can be extenally o intenally einoced in ode to incease the beam capacity. Intenal einocement may consist o glued in theaded ods, glued in concete einocement bas o ully theaded scews. Extenal einocement may consist o glued on panels such as LVL o plywood, glued on lamellas o pessed in punched metal plate astenes. Design appoaches o extenal and intenal einocement o beams with a ectangula coss section and a ectangula notch (i = 0, see Figue 5 1) ae pesented below, based on the Geman National Annex to Euocode 5 (DIN EN /NA). The basic idea is that the einocement should be designed to esist the entie oce esultant o the damage elevant pependicula to gain tensile stess along the potential cack plane stating om the cone o the notch. The pependicula to gain tensile stength o the beam itsel is neglected. The pependicula to gain tensile oce esultant F t,90 is detemined om integation o the beam theoy shea stesses below the depth o the notch, as indicated in Figue 5 2. A modiication acto o 1,3 is applied to account o the discepancy

4 between the beam theoy assumptions and the tue behaviou, yielding the ollowing expession o the tensile oce esultant 2 3, 90 1,3V 3(1 ) 2(1 ) F t (5 3) whee V is the shea oce and α = h e /h. Use o the modiication acto 1,3 yields suiciently accuate values o x h e /3. Fo lage values o x, the expession given in (5 3) may yield un consevative values o F t,90. The entie shea oce V may then be assigned to F t,90. σ τ F t90 h e h V x Figue 5 2. Schematic illustation o stess distibution at notch cone and illustation o tensile oce esultant F t,90. Figue 5 3. Notation o intenal (1) and extenal (2) einocement o end notched beams (DIN EN \NA) Intenal einocement o end notched beams Fo glued in ods it should be checked that the stess τ e in the glue line (cylinde), assumed to be evenly distibuted, satisies the ollowing expession e Ft,90 n d l ad k,1 (5 4) whee F t,90 is the oce esultant o the pependicula to gain tensile stess, see (5 3) n is the numbe o ods, only one ow in beam length diection may be consideed active d is the oute thead diamete o the intenal einocement, d 20 mm l ad is the eective anchoage length, see Figue 5 3 k,1 is the shea stength o the glue line, see Table 5 1 o chaacteistic values k,1,k

5 Table 5 1. Chaacteistic shea stength o glue line o glued in ods when used o einocement. These values may be used i the applicability o the glue system has been poven (DIN EN /NA). Eective glued in length l ad o steel od [mm] < l ad < l ad 1000 Chaacteistic shea stength k,1,k o glue line [MPa] 4,0 5,25 0,005l ad 3,5 0,0015l ad The tensile axial capacity o the steel ods should also be checked. Only one ow o steel ods in the beam length diection should be consideed as einocement. The minimum length o each steel od is 2l ad and the oute thead diamete is limited to d 20 mm. Edge distances and spacing o the einocement elements should be such that 3d a 2 and 2,5d a 3,c 4d and 2,5d a 4,c with notation accoding to Figue 5 3. Since the pependicula to gain tensile stess is highly concentated to the vicinity o the notch cone, the edge distance a 3,c should be kept as small as possible without violating the minimum equied edge distance. Fo membes exposed to tension paallel to gain, the eduction in net coss section aea due to the intenal einocement should be consideed. Fully theaded scews may also be used as intenal einocement and should then be designed o the tensile oce F t,90 with espect to withdawal and tensile axial capacity. In addition to veiication o the intenal einocement capacity, the shea stess o the educed coss section should also be veiied accoding to (5 1) with k v = 1,0. Attention should also be paid to the shea stess concentations at the notch cone when using intenal einocement Extenal einocement o end notched beams Fo glued on panels it should be checked that the stess τ e in the glue line, assumed to be evenly distibuted, satisies the ollowing expession e F 2( h h t,90 e ) l k,2 (5 5) whee F t,90 is the oce esultant o the pependicula to gain tensile stess, see (5 3) h, h e ae the total beam depth and eective beam depth espectively, see Figue 5 3 l is the width o the einocement panels, see Figue 5 3 k,2 is the shea stength o the glue line. DIN EN 1995:1 1 1/NA states chaacteistic value k,2,k = 0,75 MPa o glue systems which have been poven to be applicable. The tensile stess σ t in the panels should satisy the ollowing expession F t, 90 t 2 t l k t k (5 6) whee F t,90 is the oce esultant o the pependicula to gain tensile stess, see (5 3) t is the thickness o one einocement panel, see Figue 5 3 l is the width o the einocement panels, see Figue 5 3 t is the tensile stength o the einocement panel in the diection o F t,90 k k is a acto accounting o the non uniom stess distibution. DIN EN 1995:1 1 1/NA states that k k = 2,0 may be applied without uthe veiication.

6 Reinocement panels should be glued onto both sides o the membe accoding to Figue 5 3 with panel width limited by 0,25 l /(h h e ) 0,5 and panel thickness t 10 mm. Suicient pessue duing gluing should be ensued, e.g. by the use o theaded nails o scews with appopiate anchoage length and spacing. Punched in metal plate astenes may also be used as extenal einocement, and should be designed in analogy with the above given ecommendations. In addition to veiication o the extenal einocement capacity, the shea stess o the educed coss section should also be veiied accoding to (5 1) with k v = 1,0. The capacity with espect to shea stess concentations at the notch cone may be assumed to be suicient when using extenal einocement designed in accodance with the above given ecommendations. 5.3 Beams with a hole Holes in membes should peeably be avoided. A hole constitutes a sudden change in the coss section which impedes the low o oces in the membe and geneally educes the beam stength consideably. Fo a beam loaded in bending with ibe diection coinciding with the beam length diection, the low o paallel to gain nomal stess and shea stess is distubed and instead thee appea concentated pependicula to gain tensile stess and shea stess in the vicinity o the hole. Such concentated stesses also appea o membes axially loaded in compession o tension. The magnitude and the distibution o the unavouable stess ields depend on many paametes such as type o loading, hole shape, hole size and hole position elative to the beam depth diection. Schematic illustations o the pependicula to gain tensile stess distibution ae shown in Figue 5 4 o a beam with a cicula hole in dieent types o loading situations. The associated ailue type, with cack initiation at the hole peiphey and cack popagation in the beam diection, is typically vey bittle Figue 5 4. Schematic illustations o pependicula to gain tensile stess distibution; hole placed in shea oce dominated egion (let), pue bending (middle) and axially loaded membe (ight). I holes cannot be avoided thee ae some basic ecommendations concening hole shape and placing. Holes should peeably be placed at the neutal axis o the beam, especially holes placed in a position o dominating bending moment action. Cicula holes ae to be peeed ove ectangula o quadatic ones. The sides o the hole should be suace teated to educe vaiation in the moistue content and thus the isk o splitting. Hot pipes and ducts passing though holes shall be insulated. Holes should not be used in outdoo stuctues o elsewhee in places whee thee is a isk o lage vaiations in the moistue content. Special cae is necessay o membes whee the geometical om itsel causes pependicula to gain tensile stess, o example in the apex egion o double tapeed beams. In cuved stuctual membes, including ame haunches and pitched cambeed beams, holes should not be pemitted at all. Fo beams with holes as o end notched beams and othe applications whee stength is limited pedominantly by pependicula to gain tensile stess expeimental tests show a signiicant beam size inluence on the stength. Hence special attention should be paid when making holes in lage membes. Since the pependicula to gain tensile stess is

7 not limited to the absolute vicinity o the hole, the case o multiple holes in a beam should be teated with geat cae. Design o uneinoced beams with a hole is a challenging task. Despite ecent eseach eots, thee is at the moment no ully accepted and eliable design method which is based on a completely sound and ational mechanical backgound. The Geman National Annex to Euocode 5 (DIN EN /NA) does, howeve, state design equations o uneinoced beams with a hole. The method is based on linea elastic stess analysis and equilibium consideations and oiginates om the wok pesented by Kolb and Epple (1985), although simpliications and empiical modiications have been added ove time. Due to the uncetainties elated to stength and design o such beams with a hole, it is ecommended to einoce the beam i holes cannot be avoided. Uneinoced beams with a hole may only be used in sevice class 1 and 2, while popely einoced beams with a hole may be used also in sevice class 3. Reinocement o beams with a hole is dealt with in Section 5.4. Regulations concening hole size and placement ae stated in Table 5 2 with notation accoding to Figue 5 5. Holes with a diamete o diagonal length d 50 mm and h d 0,15h may be teated as a educed coss section, i placed close to the neutal axis. Table 5 2. Regulations concening hole size and location o beams with cicula and ectangula holes, accoding to DIN EN /NA with the exception o minimum hole cone adius, whee DIN EN /NA states 15 mm. l v h l z 1,5h o at least 300 mm l A 0,5h h o 0,35h h u 0,35h a 0,4h h d 0,15h 25 mm l v l v h o d h d h d d h u l A a l z a b a l z a l A Figue 5 5. Notation o design o a beam with a ectangula o cicula hole. The design citeion, (5 7), eads as a compaison o pependicula to gain tensile stess with the coesponding stength, modiied by an empiically based beam depth acto. Pependicula to gain tensile stesses appea on both sides o the hole, at dieent locations depending on the type o loading and hole shape. Potential cack planes ae o cicula and ectangula holes, espectively, assumed at locations accoding to Figue 5 6. The tensile stess along these planes is uthe assumed to have a tiangula distibution. The magnitude o the pependicula to gain tensile stess is detemined by its oce esultant F t,90 which in tun is detemined based on contibutions om the shea oce and bending moment. The contibution F t,90,v om the shea oce V is assumed to be equivalent to the integal o the beam theoy shea stesses om beam mid axis to the potential cack plane o a beam with a centically placed hole, as illustated schematically in Figue 5 6. The contibution F t,90,m om the bending moment M is empiically based.

8 σ t,90 h o +0.15h d F t,90 τ 3) 1) 0,7h d 2) h u +0.15h d F t,90 3) σ t,90 l t,90 1) h o h d F t,90 τ 2) h u F t,90 Figue 5 6. Location o citical planes concening cacking o ectangula and cicula holes; planes 1) and 2) elevant o holes placed in shea oce dominated egion and planes 1) and 3) elevant when action is dominated by (positive) bending moment. With a slight modiication o notation compaed to DIN EN /NA, the design citeion is omulated as a compaison o pependicula to gain tensile stess σ t,90 and the coesponding stength t,90 accoding to t,90 F 0,5l t,90 t,90 k b t,90 t,90 (5 7) whee Vh h M 4h h (5 8) h 2 d d Ft, 90 Ft,90, V Ft,90, M 3 0, and whee o cicula holes h d may be eplaced by 0,7h d in (5 8) and h h h min h h min h u o u o 0,15h d 0,15h d o ectangula holes (5 9) o cicula holes (5 10) The length l t,90 o the assumed tiangula pependicula to gain tensile stess distibution is given by lt, 90 0, 5 hd h o ectangula holes (5 11) lt, 90 0,35hd 0, 5h o cicula holes (5 12) and the stength eduction elated to beam depth is given by 1 5 k t,90 min 0, 450 / h with h in mm (5 13)

9 In addition to the pependicula to gain tensile stesses, in geneal being most elevant in design, also shea stess concentations appea in the vicinity o a hole, especially o ectangula holes. The Geman National Annex to Euocode 5 does not give explicit ecommendations egading this design issue. Fo ectangula holes, howeve, the maximum value o the shea stess at a hole cone may accoding to Blaß & Bejtka (2003) be appoximated with 3V cone cone whee 2bh 0,2 1 a / h hd cone 1,84 (5 14) 1 h / h h d whee κ cone expesses the incease o the maximum shea stess om the one in the conventional beam theoy (o a beam without a hole). The exact shea stess is closely elated to the hole cone adius and a smalle cone adius yields highe maximum shea stess. The appoximation accoding to (5 14) may yield un consevative values o cetain geomety and load coniguations. The capacity with espect to nomal stess paallel to the gain, σ 0, due to bending moment M (and possibly also nomal oce N), should uthe be veiied o the educed coss section. Fo ectangula holes, the additional bending stess in the uppe and lowe pats o the net coss section with espect to thei shea oces V o and V u and the leve am a/2 should be taken into account, see Figue 5 7. h o h d V o V M N h u V u σ 0 (N) σ 0 (M) a/2 Figue 5 7. Nomal stess paallel to the gain o a beam with a hole. 5.4 Reinocement o beams with a hole Beams with a hole should in geneal be einoced, since intoduction o a hole commonly deceases the beam capacity signiicantly and also since the design ecommendations o uneinoced beams with a hole ae elated to uncetainties. Design ecommendations o einocement o beams with a hole ae given below, based on the appoach in the Geman National Annex to Euocode 5 (DIN EN /NA). The design philosophy is equal to that o einocement o end notched beams given in Section 5.2 above; the einocement is designed to esist the oce esultant o the pependicula to gain tensile stess at a potential cack plane, while the pependicula to gain stength o the beam itsel is neglected. The pependicula to gain tensile oce F t,90 may be appoximated accoding to (5 8) and the potential cack planes ae assumed to be located accoding to Figue 5 6.Regulations concening hole size and placing o a einoced beam with a hole ae given in Table 5 3, with notation accoding to Figue 5 5.

10 Table 5 3. Regulations concening hole size and location o a beam with a einoced cicula o ectangula hole, accoding to DIN EN /NA with the exception o minimum hole cone adius, whee DIN EN /NA states 15 mm. l v h l z 1,0h o at least 300 mm l A 0,5h h o 0,25h h u 0,25h a 1,0h a 2,5h d h d 0,30h a) h d 0,40h b) 25 mm a) = o intenal einocement, b) = o extenal einocement Intenal einocement o beams with a hole Intenal einocement may consist o glued in theaded ods, glued in concete einocement bas o ully theaded scews. The beam should be einoced with espect to the potential cack planes elevant o the speciic loading condition accoding to Figue 5 6. It should o the intenal einocement on both sides o the hole be veiied that the stess τ e in the glue line, assumed to be evenly distibuted, satisies the ollowing expession e Ft,90 nd l ad k,1 (5 15) whee F t,90 is the oce esultant o the pependicula to gain tensile stess, see (5 8) n is the numbe o ods, only one ow in beam length diection may be consideed active d is the oute thead diamete, d 20 mm k,1 is the shea stength o the glue line, see Table 5 1 o chaacteistic values k,1,k l ad = h u o h o o ectangula holes, see Figue 5 8 l ad = h u +0,15h d o h o +0,15h d o cicula holes, see Figue 5 8 The tensile axial capacity o the ods should also be checked. Only one ow o steel ods in the beam length diection should be consideed as einocement. The minimum length o each steel od is 2l ad and the oute thead diamete is limited to d 20 mm. Edge distances and spacing o the intenal einocement elements should be such that 3d a 2 and 2,5d a 3,c 4d and also 2,5d a 4,c with notation accoding to Figue 5 8. Since the pependicula to gain tensile stess is highly concentated to the vicinity o the hole, the edge distance a 3,c should be kept as small as possible without violating the minimum equied edge distance. Fully theaded scews may also be used as intenal einocement and should then be designed o the tensile oce F t,90 with espect to withdawal capacity and tensile axial capacity. In addition, the shea stess concentations at the hole cones should also be consideed o beams with intenal einocement and ectangula holes, see Section 5.3. The capacity with espect to nomal stess along gain should be also veiied o the educed coss section at hole cente, see Section 5.3.

11 Figue 5 8. Notation o intenal einocement o a beam with a hole, cack planes elevant o shea oce dominated loading Extenal einocement o beams with a hole Extenal einocement may consist o LVL o plywood. It should be veiied that the stess τ e in the glue line, assumed to be evenly distibuted, satisies the ollowing expession e Ft,90 2a h ad k,2 (5 16) whee F t,90 is the oce esultant o the pependicula to gain tensile stess, see (5 8) a is eective length o einocement panels, see Figue 5 9 h ad = h 1 o ectangula holes, with h 1 accoding to Figue 5 9 h ad = h 1 +0,15h d o cicula holes, with h 1 and h d accoding to Figue 5 9 k,2 is the shea stength o the glue line. DIN EN 1995:1 1 1/NA states chaacteistic value k,2,k = 0,75 MPa o glue systems which have been poven to be applicable. The tensile stess σ t in the panels, glued onto the membe, should satisy the ollowing expession F t, 90 t 2 t a k t k (5 17) whee F t,90 is the oce esultant o the pependicula to gain tensile stess, see (5 8) t is the thickness o one einocement panel, see Figue 5 9 a is eective length o einocement panels, see Figue 5 9 t is the tensile stength o the einocement panel in the diection o F t,90 k k is a acto accounting o the non uniom stess distibution. DIN EN 1995:1 1 1/NA states that k k = 2,0 may be applied without uthe veiication. The einocement panels should be glued onto the membe accoding to Figue 5 9 with panel size limited by 0,25a a 0,3(h d + h) and h 1 0,25a. The thickness t o the panels should be at least 10 mm. Suicient pessue duing gluing should be ensued, i.e. by the use o theaded nails o scews with appopiate anchoage length and spacing.

12 The capacity with espect to nomal stess along gain should also be veiied o the educed coss section at hole cente, see Section 5.3. The capacity with espect to shea stess concentations at hole cone may howeve be assumed to be suicient when using extenal einocement designed in accodance with the above given ecommendations. Figue 5 9. Notation o extenal einocement o a beam with a hole. 5.5 Reeences Blaß H.J., and Bejtka I. (2003). Quezugvestäkungen in geähdeten Beeichen mit selbstbohenden Holzschauben, Foschungsbeicht, Vesuchanstalt ü Stahl, Holz und Steine, Univesität Kalsuhe. Gustasson P. J. (1988). A study o stength o notched beams. CIB W18/ , Poceedings o the intenational council o eseach and innovation on building and constuction, Woking commission W18 timbe stuctues, Meeting 21, Paksville, Vancouve Island, Canada. Kolb H., and Epple A. (1985). Vestäkung von duchbochenen Bettschichtholzbinden. Voschungsvohaben I , Foschungs und Mateialpüungsanstalt Baden Wüttembeg, Stuttgat, Gemany. Ribeholt H., Enquist B., Gustasson P.J., and Jensen R.B. (1992). Timbe beams notched at the suppot. Rep. TVSM 7071, Div. o Stuct. Mech., Lund Institute o Technology, Lund, Sweden. DIN EN /NA: , Geman National Annex to Euocode 5 : Design o timbe stuctues Pat 1 1: Geneal Common ules and ules o buildings. SS EN : 2004, Euocode 5: Design o timbe stuctues Pat 1 1: Geneal Common ules and ules o buildings.