Unied Saes Deparmen of Agriculure Fores Service Fores Producs Laboraory Research Paper FPL RP 540 Modeling Prong Tes Response During Condiioning of Red Oak Lumber James Fuller W/2 L
Absrac The prong es has long been used o deermine how much condiioning is required o relieve ransverse drying sresses in lumber. Neverheless, lile research has been direced a proper inerpreaion of he prong es. The purpose of his sudy was o develop furher undersanding of how alered sresses ha occur during condiioning influence prong response. Red oak lumber was dried using a convenional kiln schedule. Informaion on sress disribuion, moisure gradien, and casehardening was obained periodically during condiioning. A residual srain release mehod, slicing, was used o obain sress disribuions. Wih he gain of moisure during condiioning, he surface sresses were found o aain a maximum value and subside o near zero. The subsurface layers aained a high level of compressive sress. The srain daa were used o predic he prong es response for various prong hickness (10, 20, 35, and 50 percen of oal board hickness). The prong es response was srongly dependen on prong hickness he hinner he prong, he more responsive o sress changes which demonsraes he effec of alered sress disribuion on prong response. Two mahemaical echniques used o predic he prong response he Elasic Beam and Surface Arc echniques yielded excellen resuls. Furher sudies are needed o deermine any recommendaions for new prong es procedures. Keywords: Prong es, drying sress, predicion Acknowledgmen Research was conduced a Norh Carolina Sae Universiy, Wood and Paper Science Deparmen, Raleigh, Norh Carolina. Conens Page Inroducion...1 Maerials and Mehods...1 Srain Release Slice Tes...2 Prong Tes...2 Resuls and Discussion...2 Moisure Conen...2 Prong Tes...2 Transverse Sress...3 Prediced Prong Response...4 Conclusion...5 References...5 Appendix Derivaion of Predicion Equaions...6 July 1995 Fuller, James J. 1995. Modeling prong es response during condiioning of red oak lumber. Res. Pap. FPL RP 540. Madison, WI: U.S. Deparmen of Agriculure, Fores Service, Fores Producs Laboraory. 7 p. Predicion of Prong Response From Sress Gradien Tes Daa...6 Predicion of Prong Response by Surface Arc Technique...6 A limied number of free copies of his publicaion are available o he public from he Fores Producs Laboraory, One Gifford Pincho Drive, Madison, WI 53705 2398. Laboraory publicaions are sen o more han 1,000 libraries in he Unied Saes and elsewhere. The Fores Producs Laboraory is mainained in cooperaion wih he Universiy of Wisconsin. The Unied Saes Deparmen of Agriculure (USDA) Fores Service is a diverse organizaion commied o equal opporuniy in employmen and program delivery. USDA prohibis discriminaion on he basis of race, color, naional origin, sex, religion, age, disabiliy, poliical affiliaion, and familial saus. Persons believing hey have been discriminaed agains should conac he Secreary, U.S. Deparmen of Agriculure, Washingon, DC 20250, or call (202) 720 7327 (voice), or (202) 720 1127 (TTY).
Modeling Prong Tes Response During Condiioning of Red Oak Lumber James J. Fuller, Research Fores Producs Technologis Fores Producs Laboraory, Madison, Wisconsin Inroducion Undersanding he developmen and relief of drying sresses in wood is he firs sep oward improving drying schedules. A he end of drying, lumber is casehardened, a phenomenon in which surface layers are in compression and he cener region is in ension. If casehardened lumber is resawn or unequally surfaced, is final shape will be disored. To avoid such disorion, lumber is condiioned afer drying. Mos sudies of drying sress have provided a deailed record of drying sress during drying and of he final sress sae afer condiioning. The developmen of inernal ransverse sress during drying was exensively described by McMillen (1963) and Youngs (1957). However, lile or no research has been conduced o invesigae sress developmen or relief during condiioning. Therefore, sress developmen during condiioning is no well undersood. The primary experimenal mehod used o deermine drying sress levels is he slice es (Fig. 1). The underlying premise of he slice es is ha sress level is relaed o released srain and he modulus of elasiciy of he slice (McMillen 1955a,b, 1963; Youngs and Norris 1959; Youngs and Bendsen 1964). Kiln operaors, however, use he prong es o deermine he sress sae of lumber (Fig. 2). There are problems in using he prong es because differen manuals sugges differen sandard prong geomery and response, and here is lile apparen agreemen on he appropriae prong geomery and prong response (Bramhill and Wellwood 1976; Cech and Pfaff 1977, 1979; Page 1973; Simpson 1991; Wenger 1990). In addiion, mos of hese sources ignore he influence of immediae change in surface moisure afer cuing. The lack of knowledge on inernal sress relief during condiioning has limied improvemens in condiioning schedules. There is a need and desire for proper procedures for deermining when o disconinue condiioning so ha lumber can be processed wih he leas casehardening and residual sress variabiliy can be more ighly conrolled. The objecive of his sudy was o deermine how he prong es response is alered during condiioning and how prong lengh and hickness influence he prong response. The approach used in his sudy was firs o record moisure conen, srain disribuion hrough he board, and prong es resuls during condiioning. Then, he prediced prong response, as dicaed by he srain disribuion, was compared o he acual prong response o gain a more horough undersanding of he influence of sress aleraions. Maerials and Mehods The es specimens were aken from 1-1/2-in. (38-mm) airdried red oak boards. The boards were grouped ino wo ses: maerial propery boards and kiln boards. The maerial propery boards were used o deermine modulus of elasiciy (MOE) as a funcion of moisure conen and specific graviy. From he kiln boards, hree of he cleares boards more han 5 in. (127 mm) wide were ripped o 5 in. (127 mm) for use in he sress evaluaion, and eigh boards represenaive of he charge were seleced for moisure conen monioring; hese eigh boards, ypically called kiln sample boards, are referred o as moisure sample blocks in his repor. All he kiln boards were planed o 1-1/4 in. (32 mm) hick o reduce boh he presence of surface checks and drying ime. The moisure sample blocks were used o monior he moisure conen of he charge during drying for he purpose of adjusing he kiln in accordance wih a modified T2 C1 schedule (Boone and ohers 1988), which is commonly used for lowland red oak. The moisure sample blocks indicaed an average moisure conen of 34 percen afer planing. Sress sample blocks were aken from he hree es boards. For each board, he blocks provided four prong samples and a slice sample for each of he eigh condiioning imes (0, 1, 2, 4, 6, 14, 22, and 35 h). A each sampling ime, he freshly cu board ends were sealed immediaely wih neoprene coaing before he boards were replaced in he sack.
1 2 3 4 5 6 7 8 9 10 Figure 1 Sample for srain release slice es. Curved, doed lines show orienaion of growh rings. W W' Srain Release Slice Tes The slice es was used o obain moisure and srain gradiens. These daa were used o predic he prong sample response and o deermine he level of sress presen. The widh of each sample was measured. Each sample was cu ino nine slices; he cener slice (slice 5,6) was wice he hickness of he oher slices, as shown in Figure 1. The individual slices were immediaely weighed and heir lenghs measured o he neares 0.001 in. (0.02 mm). All he slices were hen ovendried for 24 h and reweighed o deermine moisure conen. Released srain was calculaed as he change in slice lengh divided by he original lengh. Prong Tes Prong es samples were aken o record he response a kiln operaor would observe and o compare he prong es predicions, which uilized he slice es daa. Four prong samples were cu from each board; each sample yielded wo prongs. For each board, each se of prongs was a differen percenage of board hickness: 10, 20, 35, or 50 percen of he board hickness. The precu prong ip disance W, released prong ip disance W, and prong lengh L, as depiced in Figure 2, were recorded o he neares 0.01 in. (0.2 mm), along wih he nominal prong hickness. The prongs were cu using a plywood emplae o mainain consisen hickness. All he samples for each board were processed wihin 15 min from when he sample block was removed from he kiln. Figure 2 Linear dimensions for prong es. W is precu prong ip disance; W released prong ip disance; L, prong lengh; and, prong hickness. L Resuls and Discussion Moisure Conen Moisure conen was used o deermine he MOE values of each slice for he prong es predicions. In a previous sudy, we had deermined ha some surface moisure evaporaes from he sample during he srain release slice es (Fuller 1995). Alhough his loss in moisure conen would slighly aler srain, his effec would be he same in boh he prong es and he slice es. Therefore, he measured srain can be used o predic he resuls of he prong es. Prong Tes The prong es indicaes only he sress sae of he prong (i.e., wheher or no an unbalanced sress gradien exiss wihin he prong), no he sress sae of he whole board. Alhough he prong es has been used for decades o deermine he sress sae, here has been no sandard way o record he resuls. The following mehod is he appropriae way o record resuls for research comparaive purposes, even hough i is doubful wheher indusry would adop such a mehod. 2
The equaion used in his sudy was seleced o indicae an exising sress gradien as displayed by he prong es and o represen he rue prong behavior. The equaion akes ino accoun ha when he prongs are released, hey do no merely shif in or ou nor do hey bend a he connecing base. The prongs bow hrough he enire lengh, following a curve ha can be described by a second-degree polynomial. Therefore, he prong response is a funcion of he prong lengh squared: 0.06 0.04 0.02 0-0.02-0.04 Prong hickness 10% 35% 20% 50% a PR = (W W )/L 2 (1) -0.06 where PR is he degree of prong response, W he precu prong ip disance, W he released prong ip disance, and L he prong lengh. The prong response is recorded as inches 1 (millimeers 1 ). When he prongs bow in, he value is posiive, and when he prongs bow ou, he value is negaive. Noe ha he released prong ip disance is negaive if he prongs cross each oher when insered ino Equaion (1), his informaion gives he correc oal prong deflecion. For example, in a prong es from a 6-in.- (152-mm-) wide board, he prongs would deflec 1 in. (25.4 mm), wih a prong response of 0.03 in 1 (0.76 mm 1 ). Figure 3a shows he prong response for he four prong hicknesses as a funcion of ime. The 10-percen prong hickness samples showed he greaes iniial prong response. The prong response quickly became negaive by he second hour of condiioning and remained negaive for he duraion of condiioning. The 20-percen prong hickness samples developed a negaive prong response a abou he 12h hour of condiioning. The magniude of negaive prong response was much lower in he 20-percen prong hickness samples compared o he 10-percen prong hickness samples. Alhough he 35- and 50-percen prong hickness samples never developed a negaive prong response, he magniude of prong response was reduced slighly over ime. There was lile variaion in resuls from prongs cu from differen boards. Figure 4 shows he resuls of a prong es consising of four prong hicknesses from one board. The resuls show he influence of prong hickness on prong response. Transverse Sress Sress is used o mainain saic equilibrium for calculaion purposes. Sress was calculaed using he MOE moisure conen curves obained from he preliminary ess. However, i is he released srain ha is measured during condiioning; herefore, srain is shown in Figure 5. The resuls from only hree board layers are shown for clariy. Prong response (in -1 ) -0.08 0 5 10 15 20 25 30 35 0.06 0.04 0.02 0-0.02-0.04-0.06 Number of slices (%) b 2 (15%) 5 (50%) 4 (35%) -0.08 0 5 10 15 20 25 30 35 0.06 0.04 0.02 0-0.02-0.04-0.06 Number of slices (%) c 2 (15%) 5 (50%) 4 (35%) -0.08 0 5 10 15 20 25 30 35 Condiioning duraion (h) Figure 3 Average prong response from prong es and predicions. (a) Prong es, (b) predicion by Elasic Beam echnique, and (c) predicion by Surface Arc echnique. Iniially, all hree boards showed high levels of compression in he surface layers (slices 1 and 10), nearly zero srain in he subsurface layers (slices 2 and 9), and moderae levels of ension in he cener layers (slice 5,6) (Fig. 5). Wihin a few hours of condiioning, he srain in he surface layers dropped o he viciniy of zero while he srain in he subsurface layers rose o high levels of compression. Throughou he duraion of condiioning, he subsurface layers coninued o show higher levels of compression han did he surface layers. This 3
Table 1 Predicion resuls by prong hickness and echnique a Regression (R 2 ) for various prong hicknesses Predicion echnique 16% 35% 50% Elasic Beam 0.7942 0.6858 0.5837 Surface Arc 0.7923 0.6727 0.5418 a For all resuls, p < 0.00005. Figure 4 Prong response of four prong hicknesses from a single board wih 6 h condiioning. (M94 0106-0) Srain (in./in.) 0.004 0.003 0.002 0.001 0-0.001-0.002 0 5 10 15 20 25 30 35 Condiioning duraion (h) Figure 5 Srain magniude wihin hree layers across hickness of hree red oak boards during condiioning. reversal of he srain gradien means ha a hin prong ha included only wo layers in each prong would urn ouward raher han inward. Afer 14 h of condiioning, lile change in srain occurred in he subsurface and surface layers. Prediced Prong Response Surface 1,10 Subsurface 2,9 Cener 5,6 The effec of prong hickness on prong response should be predicable if he sresses wihin he board are known. To perform hese predicions, residual sress analysis was conduced. The sampling procedure involved slicing he sample ino nine layers and measuring he released srain of each layer. Since he wo predicion echniques (Elasic Beam and Surface Arc) required a leas wo measuremens and he srain values obained from he slices did no precisely correspond o he prong es sample surfaces, he response was prediced for 16-percen prong hickness raher han 10- and 20-percen prong hicknesses. For boh predicion echniques, he following number of slices and corresponding prong hicknesses were used: wo slices, 16 percen hickness; four slices, 36 percen hickness; and five slices, 50 percen hickness. The Elasic Beam echnique is based on bending an elasic canilever beam. This mehod assumes ha he sress curve is linear wihin he slices. I uses an equaion based on Equaion (1) for prong response [see Appendix, Equaion (A1)]. The prong response prediced by he Elasic Beam echnique is shown in Figure 3b. The Elasic Beam echnique was able o predic he iniial degree of prong response for daa from four and five slices (36 and 50 percen of he board hickness, respecively). Towards he end of condiioning, he predicions were slighly lower han he es resuls; he predicion for he 36-percen prong hickness was slighly negaive. Using daa from wo slices (16-percen board hickness), he predicions were beween he resuls for he 20- and 10-percen prong hickness samples, approximaely where he 16-percen prong hickness daa would be expeced. Regression analysis of he prong es and prediced resuls yielded excellen resuls: he predicions were srongly correlaed wih he es resuls (Table 1). Any deviaions could be accouned for by he assumpion of a linear curve wihin he slices and by he knowledge ha elasic release may be greaer han iniial elasic srain (Gibson 1965; Mohager 1987, as repored in Hoffmeyer and Davidson 1989). The Surface Arc echnique is based on deermining an arc of a curved objec given he hickness and he inside and ouside surface lenghs, as obained from he srain release slice es. The derivaion of he equaion for he Surface Arc echnique is shown in he Appendix [Eq. (A2)]. This analysis assumes ha he srains produced by he slices are represenaive of a linear srain curve across he hickness of he prongs. The resuls are shown in Figure 3c. 4
Like he Elasic Beam echnique, he Surface Arc echnique was able o predic he iniial degree of prong response for daa from four and five slices (36 and 50 percen of he board hickness, respecively). Towards he end of condiioning, he Surface Arc echnique prediced a slighly negaive prong response compared wih he slighly posiive prong response showed by he prong es. Using daa from wo slices (16-percen board hickness), he predicions were beween he resuls for he 20- and 10-percen prong hickness samples. The resuls of he regression analysis showed good correlaion beween he prediced and es resuls (Table 1). Conclusion The goal of his sudy was o gain some undersanding of how alered sresses during condiioning influence he prong response. The resuls showed ha he prong es response is srongly dependen on prong hickness: he hinner he prong, he more responsive o sress changes. Thus, wo persons can obain very differen resuls while performing he same es. Furhermore, use of recorded nonlinear sress gradiens o predic he prong response showed ha proper inerpreaion of he prong es depends on knowledge abou how sresses are alered in condiioning. Recommendaions for an appropriae prong geomery and response will depend on furher research on he influence of differen drying schedules and sorage condiions on drying sresses in condiioning. References Boone, S.; Kozlik, C.; Bois, P.; Wenger, E. 1988. Dry kiln schedules for commercial woods: emperae and ropical. Gen. Tech. Rep. FPL GTR 57. Madison, WI: U.S. Deparmen of Agriculure, Fores Service, Fores Producs Laboraory. Bramhill, G.; Wellwood, R. 1976. Kiln drying of wesern Canadian lumber. Info Rep. VP X 159. Vancouver, BC, Canada: Canadian Foresry Service, Wesern Fores Producs Laboraory. Cech, M.; Pfaff, F. 1977. Kiln operaor's manual for easern Canada. Rep. OPX192E. Oawa, ON, Canada: Easern Fores Producs Laboraory. Cech, M.; Pfaff, F. 1979. A quick guide for he dry kiln operaor. Rep. OPX217E. Oawa, ON, Canada: Easern Fores Producs Laboraory. Gibson, E.J. 1965. Creep of wood: Role of waer and effec of a changing moisure conen. Naure. 206: 213 215. Hoffmeyer, P.; Davidson, R.W. 1989. Mechanosorpive creep mechanism of wood in compression and bending. Wood Science and Technology. 23: 215 227. McMillen, J. 1955a. Drying sresses in red oak. Fores Producs Journal. 5: 71 76. McMillen, J. 1955b. Drying sresses in red oak: effec of emperaure. Fores Producs Journal. 5: 230 241. McMillen, J. 1963. Sresses in wood during drying. Res. Rep. 1652. U.S. Deparmen of Agriculure, Fores Service, Fores Producs Laboraory. Mohager, S. 1987. Sudier av krypning hos rä. Docoral disseraion. Sockholm, Sweden: Kungliga ekniska Högskolan. Page, R. 1973. High-emperaure versus convenional mehods of drying Souhern Pine lumber. Res. Pap. 73. Macon, GA: Fores Research Council. Simpson, W. 1991. Dry kiln operaor's manual. Agric. Handb. 188. Washingon, DC: U.S. Deparmen of Agriculure. Wenger, E. 1990. Drying oak lumber. Madison, WI: Deparmen of Foresry, Universiy of Wisconsin: 124 125. Youngs, R. 1957. The perpendicular-o-grain mechanical properies of red oak as relaed o emperaure, moisure conen, and ime. Res. Rep. 2079. Madison, WI: U.S. Deparmen of Agriculure, Fores Service, Fores Producs Laboraory. Youngs, R.; Bendsen, B.A. 1964. Tensile, compressive, and shearing sresses develop in red oak as i dries. Fores Producs Journal. 14: 113 118. Youngs, R.; Norris, C. 1959. New mehod of calculaing inernal sresses in wood. Fores Producs Journal. 9: 367 371. Fuller, J. 1995. Condiioning sress developmen and facors ha influence he prong es. Res. Pap. FPL RP 537. Madison, WI: U.S. Deparmen of Agriculure, Fores Service, Fores Producs Laboraory. 5
Appendix Derivaion of Predicion Equaions Predicion of Prong Response From Sress Gradien Tes Daa The residual sress analysis sress curve from he srain release daa can be used o obain he prong response (PR). Referring o Figure 2 (see ex) and Figure A1, W W d M PR r1 r1 = = = 2 2 L L 2EI where M is momen creaed by eccenric forces and subscrips r and l denoe righ and lef indexes. Composie flexural rigidiy can be found by (Gere and Timoshenko 1982) EI = EiIi where 3 2 Ii = b[ i /12 + i( yc yi) ] To deermine y c, i is assumed ha if an axial load is applied a y c no bending occurs and he axial srain is consan. Wih his, he sum of he forces applied a y c is equivalen o he sum of forces applied a heir respecive posiions. Then, yc Fi = Fy i i yc σiai = σyiai yc εeibi = εeiyibi ycεeb nii = εeb yinii yn y ii i c = n i i The momen creaed by he eccenric forces is M = Mi = Fe i i = σieiai = b σie i i where e= yc yc To deermine y c, i is assumed ha he sum of he individual momens is equivalen o he sum of he forces muliplied by a momen arm. Therefore, yc Fi = yifi yc σiai = y i σia i yc σibi = yiσibi yiσii y c = σii subsiuing ino e By subsiuion ino PR y e=y i i i c σ σii b σ PR = ie i i rl 3 2 2 Eb i [ i / 12 + i( yc yi) ] 05. σ e = i i i rl Ei[ i 3 2 / 12 + i( yc yi) ] (A1) The assumpions of his model are ha sresses are linear wihin incremens, annual growh rings are uniform and fla, sress axis coincides wih he maerial inheren geomeric axis, plain sress applies, and srain is elasic. Therefore, he model is a uniaxial ension model. Predicion of Prong Response by Surface Arc Technique Predicion of PR by he slice srain gradien curve requires a relaionship involving only surface lengh and hickness (Har 1983). Saring wih he definiion of surface difference, where S= ( S S) S=Rθ S=R ( )θ Subsiuing for S and S ino he equaion for S hen solving for θ S = Rθ ( R ) θ = θ[ R ( R )] = θ Subsiuing θ ino θ= S/ R = S/ θ = S/ S By use of similar riangles in Figure A1 and wih he subsiuion for R, d C Solving for d, C/ 2 C/ 2 C S = = = R S/ S 2S d= C 2 S 2S Also from Figure A1 and subsiuion of θ L=C cos( θ/ 2) = Ccos( S/ 2 ) 6
By definiion of PR and subsiuing for d and L, PR 2 2( 2 = d C S/ 2 S = ) 2 2 2 L C cos ( S/2) (A2) S = 2 S cos ( S/ 2 ) This model assumes ha he sress gradien is linear. L d S C R y S' y d Prong displacemen C Chord lengh L Prong beam lengh R Radius of curvaure S,S' Arc lenghs Prong hickness θ Angle of curvaure y Heigh posiion Figure A1 Curvaure and linear dimensions of a single prong in he prong es used o deermine he degree of prong response in lumber or of a slice in he srain release slice es. θ/2 7