The MOE and MOR of 112 air-dry small, clear specimens (2 x 2 x 30 cm) of six species of hardwoods grown in Egypt were determined. Simple linear regression analysis revealed that MOR is highly correlated with MOE of Eucalyptus camaldulensis, Khaya senegalensis, Tamarix articulata and Casuarina spp. However, the "r" values for Jacaranda ovalifolia and Melia azedarach were not significant. In addition, covariance analysis showed that the six regressions equations have different slopes and Y-intercepts and therefore cannot be grouped. The only grouping was that between the regression lines of the first three species mentiones above.Introducing specific gravity in the regression equation did not result in improving the correlation coefficients, except in the case of Casuarina spp. Using specific gravity alone for predicting the MOR was found to be unreliable due to the relatively low "r" values obtained for the species except in the case of Casuarina spp

Badran, O. A.

Ei-Osta, M. L. M.

El-Wakeel, A. O. K.

English

Wood and Fiber Science (E-Journal)

PREDICTION O F  MODULUS O F  RUPTURE FROM MODULUS O F  ELASTICITY FOR SOME EGYPTIAN HARDWOODS' 44. L.  M .  El-Ostu, 0. A.  Budrctn, and A.  0 .  K .  El-Wukeel Asjistant Professor, Professor. and Graduate Student, Department of Timber Trees and Wood Technology, Faculty of Agriculture, Alexandria University, Alexandria, Egypt (Received 29 June 1978) ABSTRACT The MOE and MOR of 112 air-dry small, clear specimens (2  x 2 x 30 cm) of six species of hard- woods grown in Egypt were determined. Simple linear regression analysis revealed that MOR is highly correlated with MOE of Euc.~~!\'ptlls curnc~ltlulensi.s, Khayu srnrgulrn,si.s, Ttimurix urticulutu and Ctr.sritr~intr spp. However, the "r" values for Jnc~trrcrndu ot~trlif(11itr and Meliu uzedtrrtrc~h were not significant. In addition, covariance analysis showed that the six regression equations have different slopes and Y-intercepts and therefore cannot be grouped. The only grouping was that between the regression lines of the first three species mentioned above. Introducing specific gravity in the regression equation did not result in improving the correlation coefficients. except in the case of Crr.srccrrintr spp. Using specific gravity alone for predicting the MOR was found to be unreliable due to the relatively low "r" values obtained for the species except in the case of Ctrs~rer~~itirr app. Kr?.n,orcis: Euc~u1yptri.s c~crt?~ulclrrlc~nsis. Khuyu sc~nrjiulrtisis. Tcrtncrrix cirtic~rrlntri, Cnsucrrincr spp. ,  .In(.- crrcrtldn o~.tilifi)licr, Molitr (l~cc/crrtlt~h. stress grading, bending strength, modulus of elasticity, specific gravity. INTRODUCTION During the past two decades, a considerable effort has been spent to develop accurate nondestructive tests for predicting the strength of wood. The majority of these efforts were directed towards a single concept: statistically correlating the modulus of rupture (MOK) with the modulus of elasticity (MOE). In spite of the inadequate theoretical basis for this correlation (Hearmon 19661, research laboratories in the United States, Australia, England, and Canada have developed this functional relationship into a useful, if not perfect, stress grading system. Most of the research in this field has been conducted on softwoods (Miller- 1963; Corder 1965; Johnson 1965; Hilbrand and Miller 1966: Hoyle 1968; Orosz 1968; Kennedy 1969; O'Halloran and Bodig 1972). A little information, however, is available on hardwoods (Badran et al. 1975: Senft and Della Lucia 1975; Walter!: and Reiss 1977). Badran et al. (1975) studied the relationship between MOR and MOE of C'trsrrririirt; s t r ic t t i  Lab. They found that the best reduced regression model was one that included MOE only, with a correlation coefficient (r) of 0.63. In a current research program at the Department of Timber Trees and Wood Technology, Alexandria University, an investigation of the strength and related properties of hardwood species grown in plantations in Egypt is underway. The objective of this study was to examine the correlation between the ultimate bena- ing strength (MOK) and stiffness (MOE), for six hardwood species, namely, ,511- ' his ~reaearch as suppol-led in pat-t by PL 480 Grant No.  FCi-E<;-132 Wood n,,d I r h ~ , .  1 I('). 1970. pp. 147-154 Fj 1979 hy S o c ~ e t y  of Wood S c ~ e n c c  .ind rrchnolugr WOOD AND FIBER, FALL 1979, V .  11(3) - v, -e - m  r4 i r  i s ic 5 L - 9 a 3  - : Y d m v i m  v, m El-Ost(r ct ir1.-MOR AND MOE IN EGYPTIAN HARDWOODS 149 (A)  E~rc,crlvptrr.\ c~t11~ltrlr1rrlet1.si.s ( B )  7'co~icrri.r trrtic.rrlutrr (C) Klictytr .sc~trrgcrlr~r.\i.\ Three species (A -t B + C) (11) C'tr.sr~iit.itio spp. ( E) Jirc~rrrrrtitl~ o~~rrl~folici (F)  Wrlirr tt:r(lrrrac~l~ Numher of measure- Kegress~on eqoatlon ment, MOK = -32.78 + 0.0097 MOE 48 MOR = -76.07 + 0.0094 MOE 8 MOR = - 118.35 + 0.0109 MOE 19 MOR - -69.39 + 0.0102 MOE 75 MOR = 321.96 + 0.0049 MOE 18 MOR = 403.25 + 0.0024 MOE 10 M O K =  218 .69 t0 .0023MOE 9 Correlation coefficient " Standard error of estimate. Kg/cm2 ' S~gnlficant at the 0.01 level of prohahillty c,til!ptrrs c~t~itlu/dir/~tl.si.s Dehn., Tuincrriu arriculrrra Vahl., Kliuyci srnegu1en.si.s Desr.. C(tsirtrrintr spp., Jtrc,nt.trnd(i ol~tilifhlitr R. ,  and Mrlitr trzrdurtrc,h Linn. and to examine the possibility of using this correlation for predicting the MOR. MATtR1AL.S A N D  METHODS Wood specimens of Euc~rlyptrls c~rrrntrld~rlensis Dehn., Ctrs~rririn~~ spp., Jcrc(ir- utltlrr o ~ ~ u l ~ f i ) l i t ~  R . ,  Tclinuri.~ ~r t i cu la to  Vahl., Khuyu s~~t~rguletz.sis Desr. and .M~lelirr u,-.eti(irtrcl~ Linn. were chosen from available stock in the Department of Timber Trees and Wood Technology. Eight air-dry pieces (nominal 8 cm x 4 cm x 80 cm) were randomly chosen for each species. Each piece was then ma- chined down to a number of standard small clear test specimens (nominal 2 cm radially, 2 cm tangentially, and 30 cm longitudinally). It was originally planned to use 50 test beams of each species, but because of the presence of natural defects such as large knots, tension wood, and grain irregularities, each species was represented by an unequal sample size (Table 1). However, the chosen species furnished satisfactory specific gravity and strength properties ranges for the purpose of this investigation (Badran and El-Osta 1967; El-Wakeel 1978). Each beam was tested in bending according to British Standard Specification No. 373 (BSI 1957) using an Amsler 4-ton wood testing machine. Each small beam was loaded to failure flatwise at its midpoint over a 28-cm span. Then. MOR and MOE were calculated. At the completion of each test, three sections were taken, one from each end and the third near the region of failure. The moisture content and specific gravity (based on oven-dry weight and volume at test) were determined for each section, the average of which was used in the statistical analyses. The volume at test was determined by mercury-immersion method using the Amsler Volume-Meter. RESUI-TS A N D  DISCUSSION Average values of MOE and MOR together with specific gravity (G)  and mois- ture content are presented in Table 1 .  It can be seen from this table that the total number of specimens furnished a wide range of specific gravity (0.273 to 0.748) and hence a wide range in MOE and MOR. The simple linear regression analysis 150 WOOD AND FIBER. FALL 1979, V .  11(3) Group 0 . F  S . S  M S .  F C'tr.\rrtrrintr spp. 16 J~r~~(ir.crrr( /~i  o~,(rI i f>)l i ( i  8 1fcliii ti,c~cltrr.t~c~lr 7 Total 100 Difference for testing slopes Sums 105 Dift'erencea for testing intercepts Combined I-egre5sion -- l lo . . S~gnllicant at thc 0 01 lcvcl of prohah~ll t)  was conducted to develop a mathematical model that best represents the func- tional relationship between MOE and MOR for each species (Freese 1964). The regression equations are given in 'Table 2. Examination of Table 2 indicates that in the case of Elrc~ilypfirs c~trtnultlrrlen.sis, 7'irtnirt.i.t- nrtic.rrlrriri. Kl~rryrr sc~nc,~~trlpn,si,s and Caslrtrrintr spp. the "r" values are highly significant. This, in fact, reflects the reliability of the regression equations for predicting MOR from MOE. On the other hand, "r" values for Jt icur~ndr i  o\.r~lifhliri and A4elitr azetitirtrc,h are considerably lower (not significant at the 5% level). This indicates that the predictive equations for the above two species are ~~nreliable. This result is not unexpected, since the species that gave high "I-" values showed much wider ranges in specific gravity, MOE and MOR than did Jirc~rir.titltiil o~~trlifhlirr and ,Melitr ir~cciuriich (Tables 1 and 2 ) .  The above results raise the question of whether a separate prediction equation should be used for each species or whether these species should be represented b y  a single regression equation. Therefore, covariance analysis (Freese 1964) was carried out to test the heterogeneity of the six equations and the results of the analysis are presented in Table 3. Examination of Table 3 revealed that the dif- ferences for testing slopes and intercepts are significant at the 1% level. Conse- quently. the six linear regressions could not be pooled. Covariance analysis was also carried out to determine whether the regression lines for the first foul- species in Table 2 could be combined: results are given in '['able 4. I t  is clear from this table that the differences for testing slopes and intel-cepts al-e significant at the 1 %  level. Therefore. theil- I-egression lines cannot be pooled. The only group of species that can be pooled in one predictive equation is that of E1rc.ci1ypt1r.s c ~ r r i t ~ r i l t l r r l o r l . s i ~ ~ ,  7irtnuri.r rrrfic~rrlrita, and Khnytr s~nrgrr lct l -  .A;.\, since their slopes and intercepts are not significantly different (Table 5 ) .  In fact. the problem of grouping all species in one common relationship or El-O\rrr rt 01.-MOR A N D  MOE IN EGYPTIAN HARDWOODS 151 TARI F 4. C'o~'(~ri(rtre.(, t ~ n c ~ I y ~ i . s  , f i r  t e~ t i t rg  the cliff<~rc~rrc.e.\ itr .slopes crrltl it~terc.ept.\ of'rhe regression c~yrrtrtion\ , f iw  Eucalyptus carnaldulensis ( A ) .  Tarnarix articulata ( B ) .  Khaya senegalensis (C) cind Casuarina s p p .  ( D ) .  Group ( A )  Errc.trlyptrr.\ c ~ c ~ t ? r c t l t l r t l c ~ t ~ . \ i . \  ( B )  7'[rt?rcrri.x crrfi(~~r/(rf(r (C)  Klrtrycr .\c~t~rgcil<~tr.ri,\ (D) Ctr.\rctrrrtrtr spp. rota1 Differences for testing slopes Sums Difference\ for te5ting intercepts Combined regression Devlatlon from regression S .S .  272,521.9 18,785.7 21,488.2 71,490.2 384.286.0 M.S.  F ' S~gi~tlicant a the 0.01 level of plohabtlit) separating them has been discussed previously (Hilbrand and Miller 1966: Hoyle 1968: Senft and Della Lucia 1975: Walters and Reiss 1977). Senft and Della Lucia (1975) in their investigation used three Brazilian hardwoods, namely banak (Virolrr spp.), tachi (Ttrchigtrlirr prrnic.rrltrtr4tn) and pequia ( C N I . ~ O ~ . N ~  spp.) and found that for any single species, the correlation between MOE and MOR was rather poor. However, combining all three species greatly improved the correlation. They attributed this improvement to the fact that the combined species represent a wide range of densities and strengths. Some investigators prefer to use a separate equation for every species (Hilbrand and Miller 1966: Kennedy 1969: Walters and Reiss 1977). This seems to be un- desirable hecau5e it will complicate structural design (Hoyle 1968). On the other 1 . 4 ~ 1  t 5. Coi,c~ri(rtr( cJ ( I I I ~ I ~ \ . J I S  , tor tr.rri17n. tile d(ffi.rc,t~c.c~.s itr  slop^,.\ rrtrtl i~rtcrc,t~pt.\ (?/'tile rrgrr,r.siorr c~ytrcrriotr.\ , / i)r Eucalyptu\ carnaldulensis ( A ) .  Tarnarix articulata ( B )  crtrd Khaya senegalensis (C'). :Iev!atlon from tcgl-e,\!on -. - (iroup U.F. S S '4 S F . -. --- -. -  .- --- - -- ( A )  Orc~ t r l~p t r r .~  c~trttrtrl(lrilrrr.ti\ 46 272,521.9 ( B )  1-tr/~lcrri.t. crrtic~riltr~~~ 6 i8.785.7 I C )  Klrtr\*cr .\c~trr~n.lrlc~~rsi\ 17 21.488.9 Total 69 312,795.8 4,533.3 Differences for testing slopes I>ifkrence\ for testing intercepts Combined regression 152 WOOD A N D  FIBER,  FALL 1979, V .  11(3) hand, combining all species in one common relationship leads to some sacrifice of the efficiency of predicting bending strength of those species that gave higher correlations from their specific equations (Hilbrand and Miller 1966). It must be pointed out that combining E1rc.rr1ypt1r.s c .ut r~~i l t l~r l~ t~.s is ,  Trrl~iuriY ~rrt icr i lut~r and Klzrrycr .seticgrript~.si.s in one regression equation did not result in any reduction in efficiency as is clear from 'Table 2. The "r" value required for the purpose of the prediction in this respect has been previously discussed. Pellerin (1965) considered "r" values of 0.90 or higher ro be essential for successful application. However, Hoyle (1968) provided a comprehensive summary of forty-four studies into the correlation between +trength and stiffness in structural timber. He found that the "r" values were ?I-edominantly above 0.70 with the range being 0.57 to 0.88. In addition, using multiple regression analysis to predict MOR, Orosz r 1968) improved the corre- lation coefficients but did not exceed 0.90, In the light of the above information, the "r" values calculated in this study for each of the first four species in Table 2 and the combined equation for the first three species might be sufficient for prediction purposes and can be consid- ered as a basis for further work using samples of larger dimensions and size. I n  an attempt to improve the correlation coefficients given in Table 2 ,  specific gn~vity iG) was introduced as a second independent variable in the regression equations. Multiple regression analysis was then carried out for each of the fil-st b u r  species in 'rable I .  The analysis revealed that the addtion of "6" did not significantly contribute to the variation in MOR, except in the case of Ca.vtitrritrt~ \pp. wherehy the following model was obtained: S = Standard el-1.0s of cstirnate. kgicm2, 3 = Multiple correlation coefficient, :U == Number of rneasuremcnts, and .A, partial "F" value of 17.45 with 1.15 degrees of freedom was obtained which i 4  51gnific:rnt at the 0.01 level of psobal7ility. jt is clear fi-om the pr,evious equation that the addition of "G" incl-eased R' ti-om 0.837 to 0.925. Accordingly. the addtion of G to the prediction equation of r' ~isrrti~.itlci spp. was justifiable. Interest was next directed to the possibility of using "G" alone for predicting hending stl-ength. Therefore. simple linear regression analysis t echniq~~e  was used to express MOR as a function of "G" and the fitted models are presented in .i'nble 6. It is obvious from this table that the "r" values for 7ui?lrr1.i.v nrtic.rilrrtrr, .Irrc~trt~tr~~titr o\.trljfi)litr and Mc.litr o:rtlurac,l~ are not significant, whereas those of L:ric~~rl\~ptrr.s c~trti~rrltlrilct~.\i.v and KIitrytr .sc~tirgtrlo~si.s are significant, but their val- ues are not high enough to be used for prediction purposes. These results agree well with previous findings on softwoods (Miller 1963). The only good, reliable El-O\rrr 6.1 <I/.-MOR AND MOE IN EGYPTIAN HARDWOODS 153 ~ A B L . ~  6. Litlerrr ri,,q~.t,.\.\iot~ eqrititiot~.\ .fOr p r ~ ( l i c / i t ~ g  hc~l(l i t lg .\tr(,tlgtll ( MOH) ,jrot,l .\prc,i$c grti\si/x (G) .  Number of mea5ure- Correlation Regression equation\ rnent, SE;' coefficient I I / ~  1 ~ 1 t i 1 / 1 i I t  MOR = 9 6 5 . 4 3  + 2,355.90 G 48 146.66 0.585" To~t~ori.t-  c i r ~ i ~ ~ ~ ( / ( i i ( ~  MOR = 7 6 2 . 1 5  + 2,155.01 G 8 106.06 0.659 Klrtryrr ~c,trrgti lat~.\ i \  MOR = -11.16 + 1,182.40G 19 57.69 0.665' C ~ ~ \ ~ i [ r r i r ~ ( r  spp. MOR - 8 3 . 8 8  + 1,428.05 G 18 79.95 0.876' ~ I ~ ~ ~ ~ ~ r r - t r t ~ ~ l ( t  o ~ ~ I ; f i ) / i [ r MOK = - 152.33 + 1,590.61 G 10 94.20 0.285 Mclrtr ci:rtltrrtrc./~ MOR = 214.50 + 360.17 G 9 34.42 0.145 ,' Slandard error of estlniate. Kg!crn2. ' S~gnlficatit a1 the IJ 01 level of prubah~l~ty.  correlation between MOR and G is that of C t i ~ u a r i n ~  spp. (r = 0.876). This might explain the significant contribution of "G" to the variation in MOR when it was included in addition to MOE in the multiple regression equation of Ca.\uurinu SPP. S U M M A R Y  A N D  CONCLUSIONS The MOE and MOR were determined for 112 small, clear specimens (2 x 2 x 30 cm) representing six hardwood species. From the results of this study the following conclu\~ons are warranted: 1 .  Four of the species used, namely Errc.ci!\'ptrr.s c~rri~~n/d~ilc~n.sis, Tu nmri.~ urti- c~rilrrtrr. Khrryu .scnrg(rlcnsi,s, and Crrsriririnci spp., exhibited highly significant correlation coefficients btween MOE and MOR. On the other hand, .luc~arundu o\,a/iJi)lici and .1/Ie/iu tr:~rI(~ruc.h gave a very poor correlation between MOE and MOR. 2. The differences for testing slopes and intercepts of the six regression lines were significant, and therefore they cannot be represented by one regression equation. The only possible grouping is that of Errca1yptrr.s ca~nrrldrrlcn~sis, 7irinrrri.r u r t i ( . r i / ~ t ~ ,  and Klzayu .sc~r7~gcrlensis. 3. The addition of specific gravity as a second parameter in the regression equa- tions did not improve the R2 values. except in the case of Ctr.srirrrinci spp. whereby it became 0.925 instead of 0.837. 4. Specific gravity, as an independent variable, cannot be used for predicting MOR because of the low or insignificant correlation coefficients obtained, except in the case of Crrsritrrinrr spp. 5 .  The high correlation obtained between bending strength and stiffness for the first four species indicated above is encouraging and can be considered as a basis for further work for obtaining higher "r" values. B A D R A N ,  O.,  A N  11 M. L. EL-0s I A .  1967. A study on the mechanical and physical properties of some timber tree species grown in U.A.R. Proc. 2nd Arab Horticulture Congr. Cairo, 25 March-6 April 1967. 154 WOOD AND FIBER, FALL 1979, V .  I I ( ? )  B A I I R A ~ ,  0.. S .  A. E .  K A N D E ~ I  , A N D  S .  A. T A W F I K .  1975. Regression analysis of moduli of rupture and elasticity (MOR and MOE) relationship in some Egyptian grown hardwoods. Proc. 11th Conf. on  Statistics and Computational Science. Cairo, 14-17 April 1975. B K I  I ISH S I ANDAKIIS INSTITU [-[ON (BSI) 1957. British standard methods for testing small clear spec- imens of timber. British Standards Institution Bull. No. 373, London. CORDEK. S. E.  1965. Localized deflection related to  bending strength of tirnbel-. Second Symposium on  the Nondestructive Testing of Wood.  Wash. State Univ.. Pullman, Washington. Pp. 461-473. El - W A K ~ F I .  A . 0. K.  1978. Vibrational characteristics of some hardwoods directed towards the development of nondestructive test.  Unpubl. M.Sc. thesis, Faculty of Agriculture, Alexandria University. 71 pp. F R ~ ~ s E ,  F.  1964. Linear regression methods for  forest research. USDA For.  Serv.  Res. Pap. F P L  17. 136 pp. H~.ARMOP.I .  R. F. S .  1966. Theory of the vibration testing of wood. For .  Prod. 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A vibrational approach to  nondestructive testing of structural lumber. For. Prod. J .  15(3):93-101. S F N F I .  J .  F . ,  A N D  R. M. D t 1 . k ~  L,UCIA. 1975. Increased utilization of tropical hardwoods through species-independent structural grading. For .  Prod. J .  29(6):22-28. W s [  I t ~ s ,  C .  S . ,  A N D  W. L. REISS. 1977. Predicting modulus of rupture from modulus of elasticity for small clear specimens of oak and cottonwood. For. Prod. J .  27(6):51-53. 

Prediction of Modulus of Rupture from Modulus of Elasticity for Some Egyptian Hardwoods

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Prediction of Modulus of Rupture from Modulus of Elasticity for Some Egyptian Hardwoods

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