) of any finger joint. 22 Table 3.5 Grade outturn corresponding to T r i a l II MOE G range, Pa a> Number of boards jth, m Grade yield, m Less than Greater than or equal Grac Batch 1 Batch 2 Batch 3 Batch 4 Total lenc T1 T2 B Cc C D R 11.0 -D 33 72 46 81 1051 1051 R 0 0 12.4 11.0 C 30 63 48 42 819 819 D 1 1 0 0 7 7 R 3 0 1 0 12 12 13.1 12.4 B 12 18 21 16 297 297 Cc 0 0 0 0 0 0 C 3 2 6 3 61 61 D 1 0 0 0 2 2 R 1 0 0 0 2 2 13.8 13.1 T1 10 7 6 6 117 117 T2 1 0 1 0 7 7 B 3 0 3 0 22 22 Cc 6 7 3 0 63 63 C 0 0 0 0 0 0 D 1 0 0 0 2 2 R 1 0 0 1 7 7 13.8 T1 52 16 10 10 302 302 T2 3 0 1 0 12 12 B 6 1 9 0 63 63 C 2 0 0 0 5 5 Cc 7 2 5 1 56 56 D 2 0 0 0 5 5 R 11 0 0 0 27 27 Total length, m 189 189 160 160 2943 419 20 383 119 885 1068 49 23 The laminae graded with the above guidelines were inspected and verified by M r . A l l an Rosek (Executive Director, N L G A ) Again the resource distribution was assessed and very low yield for grade T2 observed. A t this point tensile strength tests on the new grades were carried out to assess the strength characteristics of the new grades. It was observed that some of the weakest T l grade boards which failed with lower load (~ 25 MPa) were caused by a combination of edge knot and local slope of grain deviation. Therefore, following changes were further proposed to improve the strength values at the lower tail o f the distribution. 1. Clear wood (board with no edge distortion, no edge defect such as knot, knot hole, local slope of grain deviation etc.): Each lamina shall have at least 2/3 (67%) clear wood free o f strength reducing characteristics with a slope of grain no steeper than 1:16. 2. Clear Wood (boards with edge distortion) : A n y cross section (200 mm) which has any edge defect (knot, knot hole, local slope of grain deviation, etc. ) shall have at least 75% clear wood free of strength-reducing characteristics with a slope of grain no steeper than 1:16. The typical change in the strength distribution due to the changes in the grade specifications are illustrated in Figure 3.1. It is clear that changes to the grade have minimal impact on the overall tensile strength distribution eventhough some o f the lower strength pieces are eliminated by the new grading rules. 24 Figure 3.1 Tensile strength distribution of Tl grade (Batch 5) ro - O O 1.0 0.9 0.8 0.7 0.6 0.5 g> 0.4 ro E =5 o 0.3 0.2 0.1 0.0 TENSILE STRENGTH DISTRIBUTION (Batch 5, Grade T1, 38 x 140 mm Douglas fir lamina) \u00C2\u00AE\u00C2\u00AE \u00C2\u00AE < Tensile Strengt > Tensile Strengt h Destribution According to Trial i Destribution According to Trial 1 i C II a \u00C2\u00AE / jg_ f f J 7 sr ? 10 20 30 40 50 Tensile Strength, MPa 60 70 During the subsequent re-grading and assessments following observations were made: 1. The bending T l grade has acceptable strength distribution. 2. The material resource has been fairly distributed between the grades T l , Cc, B, C andD. 3. The grade T2 has a very small (a total of 20 m length) yield. Based on these outcomes the grade T2 was dropped from the grade set. The finalized grade set consists of five potential grades : T l , Cc, B, C and D. The details of the final grade yield for these grades are given in Table 3.6. 25 Table 3.6 Grade outturn corresponding to T r i a l III Grade Number of boards Total Batch 1 Batch 2 Batch 3 Batch 4 Total length, m T1 62 23 16 16 117 419 B 25 19 35 16 95 403 Cc 13 9 8 1 31 119 C 35 65 54 45 199 885 D 38 73 46 81 238 1,068 Rejected (R) 16 0 1 1 18 49 Total 189 189 160 160 698 2,943 26 Chapter 4 Lamina Strength Assessment 4.1 INTRODUCTION The strength of laminae plays a major role in determining the load carrying capacity of glulam beams. Here the strengths of interest are the tensile strength and M O E of the laminae which are considered to be critical in common beam loading conditions. The magnitudes of these parameters are mainly controlled by the lamina grade specifications. Therefore, it is a necessity to determine these parameters each time when the grade specifications changes. The M O E of the boards can be determined using non-destructive test methods. Destructive tensile strength test is the only accurate means to measure the lamina tensile strength. Tensile strength tests were carried out in this study to determine the strengths of the laminae and the fingerjoints. A s mentioned in Chapter 2, strength of the laminating boards, strength of the fingerjoints and the distribution of the fingerjoints determine the overall strength of the laminae. The distribution of the finger joints is controlled by the length of the glulam beam and the length distribution of the laminae used for its construction. These factors have been taken in to account during the beam modeling process. Shear capacity is another important parameter considered in the glulam beam design. Here the main concern is the shear strength of the D grade material which is generally placed at the middle shear core of the beam. A S T M small clear block shear test and the short span beam bending tests are the two standard test methods available to 27 assess the shear strength of the core material. On the other hand, it is recognized that the capacity of a beam in shear is influenced by its stressed volume. Therefore, A S T M small clear shear block tests are considered to be not appropriate to determine generalized shear strength of the laminae (Foschi and Barrett 1976, Lam et al. 1997). Therefore, the use of a numerical model is needed to assess the shear capacity of the glulam beam. Verification/fine-tuning of the model can be performed using full scale shear beam testing. The details of these assessments are discussed in Chapters 5 and 6. Compressive strength of the laminae is another important factor in glulam beam design. However, this is not considered to be critical within the scope of the current study and is ignored in the modelling and analysis. A S T M D3737 specifies the glulam design procedures based on the knot distribution of the laminating boards to determine the allowable properties of the structural glued laminated timber. A s part of the study a detailed knot survey was carried out to assess the performance of the new lamina grades based on A S T M D3737. 4.2 MODULUS OF ELASTICITY The M O E of the boards was measured during the grade development process using the Metriguard Model 340 E-Computer system. Summary statistics of the M O E test results are given in Table 4.1. 28 Table 4.1 Summary statistics of the M O E test results Grade T1 C c B C D Mean, M P a 15,226 14,155 13,683 11,774 9,992 Standard deviat ion (SD), M P a 1,753 941 1,224 664 1,684 C O V , % 12 7 9 6 17 Total number of boards tested 184 44 223 201 138 4.3 TENSILE S T R E N G T H TESTS I - LAMINA Approximately 750 lamina specimens of the four tension laminating grades, T l , B , C and D were tested in tension parallel to grain. A Metriguard tension testing machine with full resistant grips and a capacity of about 450 k N was used for the testing. The tests were carried out at two gauge lengths 3.66 m and 1.22 m with a 0.61 m grip length at each end. For each grade the speed of loading was adjusted to maintain an average failure time of 10 minutes. The mean tensile strength values corresponding to the T l grade tested at 3.66 m and 1.22 m gauge length are 42.9 M P a and 52.6 M P a , respectively. Based on this values a length effect factor k of 5.4 was established for the material tested. The relationship between the strength values and the corresponding material volume (Lam 2000) used in the assessment of k factor is given in equation 4.1. 29 In the equation 4.1 x and V corresponds to the tensile strength and the volume of the material, respectively. The subscripts 1 and 2 refer to the samples corresponding to the two different volumes considered. Then all the lamina strength values were size adjusted to a 2.44 m gauge length in order to establish a unique set of reference strength data. This database was used as input for the U L A G analysis. The summary statistics of the lamina tensile strength test are given in Table 4.2 and the corresponding tensile strength distributions are given in Figure 4.1. Table 4.2 Summary statistics of the tensile strength test results at 2.44 m gauge length Grade T1 B C D Mean, M P a 49.8 34.8 29.4 24.0 S D , M P a 12.2 8.0 9.4 6.5 C O V , % 24 23 32 27 Total number of boards 184 223 201 138 30 Figure 4.1 Tensile strength distributions of the new lamina grades Variation of Tensile Strength (38 mm x 140 mm Douglas fir lamina, at 3.66 m gauge length) 0 10 20 30 40 50 60 70 Tensile Strength, MPa Images of some o f the T l grade material failed at low strength level is given in Figure 4.2 31 Figure 4.2 Images of some of the T l grade material failed at low strength level 3 2 4.4 TENSILE S T R E N G T H TESTS II - FINGER JOINT Approximately four hundred finger joined lamina specimens of the four grades, T l , B , C and D were tested in tension to determine the finger joint strength. Here the gauge length and the grip lengths were kept at 0.66 m and 1.22 m, respectively. Again the speed of loading was kept to achieve a time to failure of approximately 10 minutes. A s expected, both lamina and finger joint failures were observed during the tests. This resulted in two set of strength data: one corresponding to the finger joint failure cases and the other corresponding to the lamina failure cases where the finger joint strength is higher than that of the failure load of the specimen. This issue of mixed failure modes was sorted out using the Maximum Likelihood Evaluation ( M L E ) theory to isolate the strength of fingerjoints from a censored database. A computer program based on this theory was developed to carry out the assessments. 4.4.1 M L E A S S E S S M E N T S A s mentioned earlier the M L E assessments were performed to establish the un censored data for the finger joint strength. This procedure w i l l be later used for the assessment o f glulam beam shear capacity as well . The theoretical formulation of this program is discussed below: Consider two continuous random variables x, s and the corresponding statistical parameters 0. X j - primary data Sj - suspended data 0i - statistical parameters. 33 Then the likelihood functions L i and L 2 corresponding to the primary and suspended data can be written as, L\ (primary) = J J / ( * , 10,) L2 (suspended) = ]J [(1 - F(s, 10,)] (4.2) (4.3) where f(x/ 0) and F(s/0) are probability density function and cumulative distribution function, respectively. N o w for the likelihood of obtaining primary and secondary data, the total likelihood function can be written as, Z = Z , Z 2 For a 2p-Weibull distribution, the probability density functionf(x/ 0) and cumulative distribution function F(s/0) can be written as fallows. f(x,/0) = -m kfx >* F(sl/0) = l-e Then the logarithmic likelihood function can be written as, (4.4) (4.5) l n ( l ) = 5> 1=1 k-\ N ( Y \ Xj_ Xj_ Kmy (=1 V 7 W , (4.6) The maximum likelihood estimators of 0j were obtained by maximizing ln(L). The parameters m and k corresponding to the maximum value of equation 4.6 have been obtained by a trial and er ror-MLE program written in F O R T R A N . 34 4.4.2 F I N G E R J O I N T T E S T R E S U L T S The summary statistics of the finger joint test results are given in Tables 4.3 and 4.4. The distribution of the finger joint strength with a comparison of test specimen's strength is given in Figures 4.3 to 4.6. Table 4.3 Details of the finger joint failures Grade T1 B C D Total number of specimen tested 126 100 104 100 Number of finger joint failures 110 67 46 31 Table 4.4 Details of the finger joint strength values predicted by M L E program Grade T1 B C D 2P Weibull strength parameters m, MPa 45.1 43.8 35.5 30.7 k 5.4 5.6 6.1 5.3 Mean, MPa 41.59 40.48 32.96 28.28 COV, % 21 21 19 22 35 F i g u r e 4.3 T e n s i l e s t reng th d i s t r i b u t i o n o f the T l g r a d e 38 m m x 140 m m D o u g l a s f i r f i nge r jo in ts 1.0 \u00E2\u0080\u00A2 0.8 1 0.6 o cu I 0.4 E 5 0.2 0.0 15 25 \u00C2\u00B0 T1 grade- FJ and lamina (gauge length 0.66 m) tested * T1 grade - FJ failure cases (gauge length 0.66 m) tested A T1 grade - FJ strength predicted (MLE) 35 45 55 Tensile Strength, MPa 6 5 F i g u r e 4.4 T e n s i l e s t reng th d i s t r i b u t i o n o f the B g r a d e 38 m m x 140 m m D o u g l a s f i r f i nge r j o in t s 1.0 0.8 -Q O a> > IS 0.4 E 0.2 0.0 I '~: r ; | If & i w \u00E2\u0080\u0094 -n t ,6 \u00E2\u0080\u0094 I i jn i f \u00E2\u0080\u00A2 / J / -4\u00E2\u0080\u0094 \u00E2\u0080\u00A2 B-FJ&Lamina (Gauae Lfinoth n Rfi / Tested A B -FJ predicted (MLE) J T *AT^ A \u00E2\u0080\u009453 / A 1 A = 1 1 1 I 1 1 1 | i 1 T 15 25 35 45 Tensile Strength, MPa 55 65 36 Figure 4.5 Tensile strength distribution of the C grade 38 mm x 140 mm Douglas fir finger joints Figure 4.6 Tensile strength distribution of the D grade 38 mm x 140 mm Douglas fir finger joints E 0.0 4 ......... p.. ...... ft J -- J f \u00C2\u00A3 _ *\u00E2\u0080\u0094 IT r f ... : IT - p i \u00E2\u0080\u0094 \u00E2\u0080\u00A2 u-f-J&Lamma(Gauge Length 0.66 m) Tested \u00E2\u0080\u0094 a D-FJ predicted (MLE) / \u00E2\u0080\u0094 ? I -z IF \u00E2\u0080\u0094 <** \u00E2\u0080\u00A2 4* _ ill 111 15 25 35 45 55 65 Tensile Strength, MPa 37 A s expected, in T l grade's case, the lamina strength is much higher than that of the finger joint's. In B grade's case, both strength values come closer and in C grade's and D grade's cases, the finger joint's strength is higher than that of the lamina. Some of the typical finger joint failure images observed during the laboratory testing is shown in Figure 4.7. 38 Figure 4.7 Some of the typical finger joint and lamina failures 4.5 MOISTURE CONTENT Prior to the tensile strength test, all the boards were subjected to moisture content assessment to confirm the acceptable moisture content level of less than 15%. Moisture measurements were taken at three random locations using a moisture meter. A t this stage weight and the dimensions of the specimens were measured to determine the specific gravity of the specimens kept at room temperature. The specific gravity values corresponding to the lamina grades are given in Table 4.5. Table 4.5 Specific gravity of the new Douglas fir lamina grades measured at test moisture content Lamina grade T1 Cc B C D Mean 0.58 0.56 0.55 0.52 0.50 SD 0.05 0.04 0.04 0.04 0.03 4.6 KNOT SURVEY The knots present in a wood member are one of the key factors that influence the strength of the member. The size of the knot is measured in terms of the diameter of an equivalent cylinder placed at that section. The size of a knot varies from a tiny pin hole to a size occupying up to 70-80% of the cross-section of the wood. Generally the knots are in conical shape originating from the pith of the wood. 40 As discussed earlier ASTM D 3737 provides guidelines for knot measurement and the use of knot data to determine the allowable properties of the glue laminated timber beams. Glulam beam analysis using the GAP program and the knot data were carried out by Dr. Borjen Yeh (APA). In general the GAP program results indicated a satisfactory performance of the proposed grades. 4.6.1 KNOT SURVEY: PROCEDURE ASTM D3737 requires physical measurements (mapping) of all the knots in individual pieces of lumber. A set of nine types of knots and their measurement procedures are outlined in this standard. Based on the standards, all knots greater than 6 mm of equivalent cylindrical cross-section were measured. A sample consisting of a minimum of 100 pieces or 300 m of lumber randomly chosen from a representative group was considered for the assessment of each grade. The details of the lamina samples used for the knot survey assessments are given in Table 4.6. Table 4.6 Details of the lamina samples used for the knot survey Lamina grade T1 B Cc C D Total Total length of lamina, m 419 383 119 885 1,068 2,875 The types of the knots were determined based on the location and the shape of the knot. The measurements of the Types 7 and 8 knots were associated with the location of the pith center (Figure 4.8). Most of the cases, it was inside the lamina and its location 41 was determined based on the locations /exposures of the pith outcrops. Therefore, generally the values corresponding to the parameters PI and P2 were estimated based on judgments. Figure 4.8 Illustration of the pith center of a knot in a cross section of a lamina A s the standard requires, the scope of the knot survey was to measure all the knots greater than 6 mm. The dimensions of Types 1 and 2 knots were measured quickly; whereas Types 3 and 6 knots took little bit more time to determine some of the dimensions. Therefore, in order to ensure that all the knots greater than 6 mm were measured and expedite the knot survey process, most of the knots having an exposure larger than 6 mm across the lamina were measured with reasonable judgment. 4.6.2 KNOT SIZE CALCULATION The knot size corresponds to the diameter of the cylindrical section equivalent to the area displaced by the knot. Each of the considered nine basic knot types needs different sets of formulation to calculate their knot sizes. Furthermore within a knot type group, this formulation was slightly different based on the knot's orientation with the reference side of the board. Calculating large number of knot-sizes using simple Knot outcrop Section of the volume 'displaced by the knot Pith center of the board 42 manual/measures was practically impossible. Therefore a spread sheet program was developed to track the knot orientation from the knot data and automatically calculate the knot sizes. 4.6.3 R E S U L T S Table 4.7 shows the typical distribution of the knot sizes with the lamina grades T l , B , Cc , C and D and Figures 4.9 and 4.10 show the corresponding knot size distributions. The values given in Table 4.8 were normalized corresponding to a lamina length o f 300 m per grade for comparison purposes. Table 4.7 Knot survey summary, details of the knot distribution corresponding to knot size Number of knots Lamina grades T l B Cc C D Knot size, K*, cm K < 6 292 267 456 603 0.6 < K < 1.5 569 826 152 1788 2720 1.5