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Evaluation of the effect of knots on rolling shear strength of cross laminated timber (CLT)
Construction and Building Materials 222 (2019) 579–587
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Evaluation of the effect of knots on rolling shear strength of cross laminated timber (CLT) Yawei Cao a, Jason Street a, Minghao Li b, Hyungsuk Lim a,⇑ a b
Department of Sustainable Bioproducts, Mississippi State University, 201 Locksley Way, Starkville, MS 39759, USA Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
h i g h l i g h t s Knots would not decrease rolling shear strength of cross laminated timber. Knot presence affects rolling shear failure mechanisms. Two-plate shear test can be used to evaluate effects of laminations’ heterogeneity. Short-span bending test is more conservative than two-plate shear test.
a r t i c l e
i n f o
Article history: Received 13 November 2018 Received in revised form 3 May 2019 Accepted 20 June 2019 Available online 26 June 2019 Keywords: Cross laminated timber (CLT) Rolling shear Knot Shear analogy method Failure mechanism
a b s t r a c t The study experimentally and analytically investigated the effect of knots on the rolling shear (RS) strength of 3-ply southern yellow pine cross-laminated timber (CLT). Center-point bending tests and two-plate shear tests were conducted on six CLT configurations composed of different types of cross layer laminations based on knots conditions (No Knots, Sound Knots, and Decayed Knots) and pith conditions (Pith, No Pith). The shear analogy method was implemented to evaluate the RS strength values from the bending test results, which were compared against the results from the two-plate shear tests. The crosslayer laminations with either sound knots or decayed knots improved the RS strength of CLT. In general, the RS predicted by the shear analogy method was conservative. Published by Elsevier Ltd.
1. Introduction Knots are remnants of branches found in lumber. Knot determination and classification is critically important for grading lumber properly. Higher grade lumber requires a limited quantity of knots in specific sizes. Knots have widely been considered as defects in wood quality, which can adversely affect the mechanical properties. Specifically, knots significantly affect bending properties according to previous experimental and analytical studies. A theoretical model [1] revealed that knots negatively affected the bending stiffness of pine lumber. Experimental and numerical studies [2,3] also showed that knots reduce the bending strength of wood, and their presence significantly downgrades the value of the wood. Based on finite element model simulation results, Guindos and Polocoser [4] claimed that the modulus of rupture (MOR) of wooden boards could be reduced up to 50% due to the slope of grain
⇑ Corresponding author. E-mail address: [email protected] (H. Lim). https://doi.org/10.1016/j.conbuildmat.2019.06.165 0950-0618/Published by Elsevier Ltd.
caused by knots. However, when it comes to shear proper ties, knots are not considered as defects in all circumstances. Gupta et al. [5] found that knots did not affect shear parallel or perpendicular to wood grain significantly. In contrast, Cao et al. [6] reported that the effect of knots on transverse shear strength is dependent on the conditions of the knots. Cross-laminated timber (CLT) is an engineered wood product widely used in mass timber construction, which is composed of orthogonally oriented multi-layers of dimensional lumber. CLT products are assembled using chemical adhesives or mechanical fasteners, such as dowels or nails [7]. In CLT manufacturing, lower grade lumber characterized by various types of knots is typically assembled into cross layers aligned in the minor direction since they have negligible contribution to the out-of-plane and inplane mechanical properties of the full-size cross-laminated system in the major direction. Rolling shear (RS) is defined as shear stresses leading to shear strain in a plane perpendicular to the grain direction. In CLT, when it is under short-span out-of-plane
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loading cases, shear (RS) properties of the cross layers determine the flexural behavior of CLT. Several studies have been conducted to evaluate CLT RS properties. Aicher et al. [8] investigated the RS modulus and strength of beech laminations with four different sawing patterns (flat-sawn, semi-quarter-sawn, quarter-sawn, and with pith) using two-plate shear tests. The semi-quarter sawn lumber showed the highest RS strength, while the lumber with pith showed the lowest RS strength. The research was extended by evaluating the shortspan flexural performance of 3-ply CLT with outer and core layers composed of spruce and beech, respectively. Various methods of measuring and calculating RS properties were implemented and discussed [9]. Zhou et al. [10] also investigated the RS properties of CLT panels by conducting two-plate shear tests. Based on the RS measurements, the shear analogy method was utilized to predict the deflections of the panels under center-point loading conditions with different span-to-depth ratios. Lam et al. [11] conducted torsional shear tests to evaluate the RS strength properties of CLT made out of Canadian hem-fir lumber. Li [12] conducted shortspan bending tests and modified planar shear tests, and remarked that the lamination thickness significantly affected RS strength of CLT. Also, the duration of load effect on the RS strength has been examined [13]. Few studies have been conducted on the effect of knots on RS properties of CLT. Grandvuinet and Muszyn´ski [14] evaluated the effect of knots in cross layers on the rolling shear properties of CLT by conducting short-span bending tests. Since short-span flexural performance is governed by rolling shear properties in CLT, instead of directly measuring and analyzing RS properties, bending properties, modulus of elasticity (MOE) and the modulus or rupture (MOR), of the knotty-core test specimens were compared against the ones of the clear-core specimens. The conclusion was that the knots in the core laminations did not affect the RS properties. Theoretical models also have been studied in order to predict the mechanical properties of layered composite panel [15,16], specifically, for estimations in CLT, shear analogy method [17], k-method [18], and c-method [19] are commonly used. Wood is an anisotropic material which has higher shear strength along its cross-sectional (transverse) plane than ones of longitudinal (tangential and radial) planes [20]. The grain directions of knots make this natural material heterogeneous, which have inclined angles to its longitudinal axis. Thus, the knotty cross laminations subjected to short-span flexure and in-plane shear loads experience planar stresses traveling along both transverse planes of the knots and radial-tangential planes of the clear wood. Therefore, in this presented study, it has been hypothesized that the knots of cross laminations will increase RS strength of their composite systems. The RS strength of CLT composed of lumber laminations with different knot conditions were examined and compared analytically and experimentally. Shear analogy method [17] was implemented in calculating the RS strength using experimentally obtained inputs. Two-plate shear test was conducted to directly measure the RS strength of the cross layer.
2. Materials and methods 2.1. CLT specimens Three-layer CLT panels were constructed using flatsawn No.3 2 6 16ft southern yellow pine (Pinus spp.) lumber from Shuqualak, Mississippi, USA. The lumber was cut to a length of 838 mm and stored in an environmental chamber for a minimum of one week at relative humidity of 65 ± 5% and temperature of 20 ± 2 °C. Non-destructive four-point bending tests with a spanto-depth ratio of 18 were conducted to measure their modulus of
elasticity (MOE) properties. According to 1978 IGTP (In-Grade Test Program) [21], modulus of rupture (MOR) of No.3 2 4 and 2 8 southern pine lumber at MC of 15% are 49.4 MPa and 36.6 MPa, respectively. So, we assume MOR of 2 6 southern pine lumber is 43.0 MPa. Thus, the maximum load (Fest. max) of the member tested under a third-point loading setup is estimated to be 12.7 kN. Non-destructive bending test were terminated when the applied load reached 3.8 kN which is approximately 30% Fest. max. MOE was calculated using the slope of a line segment connecting 10% Fest. max and 30% Fest. max. This conservative range was chosen to ensure the tested lumber do not experience any permanent deformations. Table 1 showed the properties of 2 6 SYP lumber from thirdpoint non-destructive bending test, in which SG was calculated at the Moisture Content (MC) around 15%. The measured MOE ranged from 3.71 GPa to 13.15 GPa. The lumber specimens with MOE that ranged from 6.90 GPa to 13.15 GPa were fabricated as laminations of the face-layers which are parallel to the major direction, while the lumber specimens with an average MOE below 6.90 GPa were fabricated as laminations of the core-layers which are perpendicular to the major direction. These values were used as inputs for the shear analogy method for estimating the RS strength, which is described and discussed in depth later in this paper. The width of a CLT specimen for a flatwise shear test should be at least 305 mm (12 in.) according to ANSI/APA PRG 320 [22]. However, it is rare to find multiple knots in the same condition within this distance on a piece of lumber, and the dimensions of the knots found in 2 6 lumber are usually smaller than its width. Therefore, the CLT test specimens used in this study were made to a width of 136 mm. The face- and cross-laminations were planed to a thickness of 35 mm, and cut to lengths of 685 mm and 136 mm, respectively. Within 24 h after the planing process, the laminations were face-glued into CLT using phenol resorcinol formaldehyde (PRF) adhesive (Hexion Inc., Columbus, OH, USA). The CLT specimens with dimensions of 685 mm-length, 136 mm-width, and 105 mm-thickness were pressed using a hydraulic press at a pressure of 0.86 MPa (125 psi) for 9 h while the inner glue line temperature remained at 21–24 °C. Three conditions of knots were considered in this study and included decayed knots (DK), sound knots (SK), or no knots (NK). Six CLT configurations were constructed with cross layers composed of laminations with pith (P) or without pith (NP) as illustrated in Fig. 1; they are denoted as DK-P, SK-P, NK-P, DK-NP, SK-NP, NK-NP respectively. A sound knot is characterized as intergrown wood with solid surface and no symptoms of decay, while a decayed knot is characterized as encased wood surrounded by deteriorated fibers around the brim. Neither completely decayed knots with holes nor missing knots were included in this study. In the knotty CLT specimens, all cross laminations had knots with a minimum diameter of 34 mm. 2.2. Two-plate shear test A planar shear test (compression shear test) is an alternative method for measuring RS properties of CLT which is acknowledged Table 1 Properties of 2 6 SYP lumber from four-point non-destructive bending test.
N Mean Max Min COVb a b
MC (%)
SG15a
MOE (GPa)
164 15.00 20.84 6.35 11.52%
164 0.44 0.64 0.21 11.68%
224 7.54 13.15 3.71 22.74%
Specific gravity measured based on MC of 15%. Coefficient of variation.
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Fig. 1. Cross layer configurations.
in the European CLT standard BS EN 16351 [23], which enables two choices of test setups. Aicher [9] experimentally investigated the two different test setups: A) compression loads on one top and one bottom of two outer layers with screw reinforcement, and B) compression loads on glued-on steel plates with a tilt angle of approximately 7°. The results showed that setup B overestimated the RS strength due to the adhesive penetration to the planned thin outer layers. In setup A, the length to depth ratio has critical influence on the RS strength due to the effect of the compression failure on outer layers. Limited to the available CLT specimen size, a revised two-plate shear test setup was used, as illustrated in Fig. 2. Two metal brackets were attached to the CLT specimens by installing ten 3/800 2–1/200 lag bolts and twelve #8 200 screws on the edge and face sides of the outer layers, respectively. These rigidly connected brackets were loaded at an angle of 18° from the vertical to induce shear along the diagonal planes of the core
layers. A compression load was applied to the face layers through the metal plates, and this load was transferred to the core layer of interest. The test specimens were cut to a length of 342 mm which were laid up as described in Table 2. The loading rate of the tests was determined to be 0.762 mm/ min based on preliminary tests, which kept the testing time within a range of 3–12 min as recommended in the ASTM D2718 standard [24]. 2.3. Short-span bending test In order to study RS strength of CLT, four-point bending and center-point bending test setups are recommended in the European BS EN 16351 standard [23] and the US ANSI/APA PRG 320 standard [22], respectively. Since there is no attempt to determine the RS stiffness in the presented study, a center-point short-span bending test was sufficient. Short-span bending tests were conducted as shown in Fig. 3a. The CLT specimens were simply supported, and a transverse load was applied across the whole width of the specimens at a constant rate of 0.250 mm/min. The midspan deflection was measured at the neutral axis (Fig. 3b). 2.4. Shear analogy method The anisotropic nature of wood and orthogonal assembly lead to incongruity in mechanical properties between the laminations parallel and perpendicular to the major direction of a CLT panel. Thus, unlike glue-laminated timber, it is not valid to assume that the cross sections of the CLT layers are perpendicular to the neutral axis under out-of-plane loads. This is especially true under shortspan bending conditions with span-to-depth ratios between 5 and 6 where the transverse shear stress governs structural failure, and the contribution of shear deformations in cross layers to the total deformation becomes significant. Considering the abovementioned attributes, Kreuzinger [17] introduced the shear analogy method which can more accurately estimate the mechanical
Table 2 Specimen layups and dimensions for two test types.
Fig. 2. Two-plate shear test setup.
Test type
N
Lamination thickness (mm)
Width (mm)
Length (mm)
Bending test Two-plate shear test
54 54
35/35/35 35/35/35
136 136
685 342
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BA ¼
n X
3
hi 12
ð2Þ
Ei Ai Z 2i
ð3Þ
Ei bi
i¼1
BB ¼
n X i¼1
where Ei is the modulus of elasticity of the ith layer; hi is the thickness of ith layer; Ai is the cross section area of ith layer; Zi is the distance between the centroid of ith layer to the neutral axis of composite system. Applied transverse forces and bending moments are proportionally distributed to the virtual beams by their flexural stiffness. As it is stated in the above content, in the virtual system of shear analogy method, each lamination in Beam A has the infinite shear stiffness, so the deflection induced by shear can be ignored. However, contribution of shear stiffness needs to be addressed in determining the apparent flexural stiffness of Beam B (BB*) which can be calculated using Eq. (4).
BB ¼ BB
1 12BB 1 þ KSl 2
ð4Þ
Therefore, the total apparent stiffness of the composite system (B*) is given by Eq. (5).
B ¼ BA þ BB
ð5Þ
Accordingly, the applied transverse shear forces are distributed to Beam A (VA) and Beam B (VB) as Eqs. (6) and (7), respectively.
VA ¼ V
BA B
ð6Þ
VB ¼ V
BB B
ð7Þ
Fig. 3. (a) Short-span bending setup (b) deflectometer setup.
properties of CLT, including the rolling shear strength when compared with other composite beam theories. This analytical method has also been adopted by German standard DIN 1052 [25], and American standard ANSI/APA PRG 320 [22]. RS strength estimation procedures of the shear analogy are concisely summarized below based on DIN 1052 and TUM reports [25,26]. The shear analogy method idealizes a layered composite product as a virtual system composed of two beams connected with infinitely rigid web members which experience the same out-ofplane deformations (shown in Fig. 4). Beam A accounts for the intrinsic flexural stiffness of each layer, which is assumed to have infinite shear stiffness along its own centroid. Beam B describes the combined bending stiffness of each layer with finite shear stiffness based on the distances from their centroids to the neutral axis of the system. Based on the assumptions that the shear stiffness of Beam A is infinite and the links between layers are perfectly rigid (ci = 1), shear stiffness of the composite system SB becomes the result of Eq. (1).
S ¼ SB ¼ Pn1
1 i¼1 ci
þ
h1 2G1 b1
a2 P hi hn þ n1 i¼2 Gi bi þ 2Gn bn
ð1Þ
where Gi is the shear modulus of the ith layer; a is the distance between the centroids of two outmost layers; bi is the width of ith layer; ci is the flexible connection between the ith and (i + 1)th layer. The flexural stiffnesses of Beam A (BA) and Beam B (BB) in the major direction are given by Eqs. (2) and (3), respectively.
When it comes to the stress, the shear stresses of each layer of Beam A (sA,i) and Beam B (sB,i) are given by Eqs. (8) and (9), respectively.
sA;i ¼
V A Ei zi hi BA 2 8
ð8Þ
sB;i ¼
VB Ei hi Z i zi þ þ s0i BB 2
ð9Þ
where zi is the location of interest within the ith layer; it sits between – hi/2 and hi/2; s0i is the shear stress of the centroid of (i-1)th layer of Beam B. For a beam under bending moment, the neutral axis is subjected to the highest shear strength. Specifically, for a 3-ply CLT specimen, the core layer (cross lamination) is subjected to the highest rolling shear strength. Since the MOE of the cross layer without edgebonding in the major direction is negligible, the shear stresses throughout the thickness of the layer in Beam A are assumed to be zero according to Eq. (8). In Beam B, the shear stresses from the outer layers are transferred to the cross layer following the Eq. (9). Thus, the RS strength (sB,2) of a 3-ply CLT can calculated using Eq. (10).
sB;2 ¼ s02 ¼
V B E1 h1 h1 Z1 þ BB 2 2
ð10Þ
3. Results 3.1. Two-plate shear test
Fig. 4. Virtual beam of shear analogy method.
In the two-plate shear tests, RS strength was calculated by dividing the maximum applied load by the diagonal planar area of each specimen’s core layer with Eq. (11).
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Y. Cao et al. / Construction and Building Materials 222 (2019) 579–587 Table 3 RS strength values from two-plate shear test. NK_NP RS strength (MPa) N 9 Mean 1.95 Max 2.39 Min 1.52 COV 13.72%
NK_P
DK_NP
Table 5 T-test results of pith groups from two methods. DK_P
SK_NP
SK_P
Compared config.
9 2.53 3.01 2.12 11.07%
9 2.58 3.12 2.23 12.15%
9 2.62 3.34 2.08 13.77%
9 2.33 2.75 2.12 8.42%
NK_NP – NK_P DK_NP – DK_P SK_NP – SK_P a
c
Table 4 RS strength values estimated using shear analogy method based on short-span bending test results.
RS strength (MPa) N 9 Mean 1.72 Max 2.20 Min 1.37 COV 13.80%
s¼
NK_P
DK_NP
DK_P
SK_NP
SK_P
9 1.72 1.88 1.29 10.84%
9 1.86 2.26 1.11 20.84%
9 1.92 2.30 1.69 11.18%
9 1.88 2.40 1.36 15.37%
9 1.90 2.18 1.69 8.28%
F qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 b l þ h2
ð11Þ
where F is maximum shear force (N); b is width of specimen (mm); l is length of specimen (mm); h2 is thickness of core layer (mm). Table 3 shows the maximum shear force and RS strength for the six configurations. 3.2. Short-span bending test (shear analogy method) The shear analogy method discussed in Section 2.4 was implemented in estimating the RS strength using the short-span bending test results. In calculating flexural and shear stiffness properties as expressed in Eqs. (1)–(3), the longitudinal MOE values EL were obtained from the non-destructive four-point bending tests described in Section 2.1 (Table 1). Other modulus properties approximated and assumed according to values recorded in literature [26–28] and were used as the inputs for this analytical method. The shear modulus in the radial-tangential plane GRT was approximated to be one-tenth of the shear modulus in longitudinal-radial plane GLR [28]. The loblolly pine elastic ratios of 0.078 and 0.082 were used for ET/EL and GLR/EL, respectively [27]. However, since cross laminations were not edge bonded, ET of the cross layer was assumed to be zero [26]. Ultimately, Eq. (10) was used to estimate the RS strength for each specimen using the non-destructively measured MOE values and transverse shear forces calculated based on the recorded failure loads as summarized in Table 4.
Bending test
a
SIG
H
SIG
NSb NS NS
NS NS Sc
NS NS NS
NS NS NS
H 9 2.05 2.40 1.72 11.03%
b
NK_NP
Two-plate shear test
Homogenous test-Levene’s test (Ho: r2NP = r2P, a = 0.05). Not significantly different. Significantly different.
determines the knot types as described in [29], the effect of pith on the RS strength could not be clearly evaluated using either the SK or DK group test results. The cross laminations of the SK_P and DK_P configurations had knots grown in multiple directions from pith, while SK_NP and DK_NP had knots running across the width or thickness of the laminations. Thus, it was determined to be more appropriate to analyze the test results of the NK group to evaluate the effect that pith has on the RS strength. Regardless the test method, no significant differences were found between the NK_NP specimens and NK_P specimens in terms of RS strength. Hence, hereafter, the pith presence was not considered as an experimental factor, and the NP specimens were combined with P specimens in the same knot condition. 4.1.2. Knots In order to evaluate the effect of knots on the RS strength, a least significant difference (LSD) t-test was performed at a significance level of ɑ = 0.05 in SAS 9.4 (SAS Institute Inc., version 9.4, Cary, NC, USA). Table 6 summarizes the LSD test results on the mean RS values of the three groups obtained from the two-plate and short-bending tests. Cumulative distributions of the results from both tests are illustrated in Figs. 5 and 6. In the two-plate shear test, the DK and SK specimens had significantly higher RS strength than the NK specimens. The average RS strength of the DK specimens was slightly higher than that of the
Table 6 LSD results of knots groups from two methods. Config.
NK DK SK a
Two-plate shear test
Bending test
Mean RS strength (MPa)
T groupa
Mean RS strength (MPa)
T groupa
2.00 2.55 2.48
a b b
1.77 1.89 1.89
a a a
Groups with the same letter are not statistically different, a = 0.05.
4. Discussion 4.1. Effect of pith and knots on RS strength 4.1.1. Pith A two-sample t-test was performed at a significance level of ɑ = 0.05 in SAS 9.4 (SAS Institute Inc., version 9.4, Cary, NC) to evaluate the effect of pith on the RS strength. Table 5 shows that the homogeneity concerning the variations of NP specimens and P specimens of NK group, SK group, and DK group were equal. The difference in RS strength between NP specimens and P specimens was significant (p = 0.046) in the SK group based on the twoplate shear test results. However, since the pith location
Fig. 5. Cumulative frequencies of RS strength measured from two-plate shear tests.
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In the bending test (shear analogy method), the difference in the RS strength between any of the three groups was not statistically different, but the RS strength of the SK and DK specimens were slightly higher than that of the NK specimens. However, the failure behavior of the NK, SK, and DK bending specimens was different and is described Section 4.2. 4.2. Failure behavior
Fig. 6. Cumulative frequencies of RS strength calculated using the shear analogy method.
SK specimen, but the difference was not statistically significant. The knots in the cross lamination were under shear in the crosssectional plane which made the laminations that included knots have a higher shear resistance than the laminations that did not have knots.
4.2.1. Two-plate shear test In the two-plate shear tests, all 54 specimens had RS failures, with cracks observed in the core layer at inclined angles to the glue lines. Each NK specimen had 2 to 4 cracks which propagated almost parallel to each other across the entire core layer (Fig. 7a). In contrast, the crack growth patterns of the SK and DK specimens were affected by knot conditions and shapes. The failure patterns of the SK specimens showed that the sound knots prevented the fibers of cross laminations to roll over each other as seen in the NK specimens, which led to significant wood failure near the glue lines as shown in Fig. 7b. The decayed knots caused
Fig. 7. Failure of (a) Clear specimen (b) Sound-Knot specimen (c) Decayed-Knot specimen.
Y. Cao et al. / Construction and Building Materials 222 (2019) 579–587
irregular stress distributions throughout the cross laminations of the DK specimens and led to distorted crack formations as shown in Fig. 7c. 4.2.2. Short span bending test Under short-span out-of-plane loads, 89% of the specimens failed in RS while 11% failed in tension at their bottom face layers. Failure was defined as a load drop of over 5%. Flat-sawn cross laminations had shear cracks which formed in the early wood and propagated across or along the wood grain, while the cross laminations containing pith had cracks initiate from or propagate through the pith (Fig. 8).
585
In general, as shown in Fig. 8a, the NK specimens had shear cracks that formed in the core layers at inclined angles. As the load increased, the cracks propagated further and caused more fractures to occur in the fibers surrounding them, which caused negligible load drops in the load-deflection curve (Fig. 9a). Ultimately, wood failure occurred close to the glue lines near the edge and were shown as the main load drops in the curves. After the failure occurred, the fractured wood pieces were interlocked, and the specimens continued to resist loads which resulted in subsequent peaks which were lower than the failure loads. Similar to the failure mechanisms observed during the twoplate shear tests, the knots in the cross laminations of the SK and
Fig. 8. (a) Failure of clear specimens (b) Failure of sound knot specimens (c) Failure of decayed knot specimen.
Fig. 9. Typical load-deflection curves from short span bending test: (a) No-Knot specimens (b) Sound-Knot specimens (c) Decayed-Knot specimens.
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DK specimens reinforced the clear wood fibers under RS stresses and transferred the shear force to the glue lines where wood failures were found, as shown in Fig. 8b and c. The load-deflection curves involving the SK specimens were highly linear until the maximum loads were reached (Fig. 9b). The rigid linkage between the sound knots and the clear wood, as well as the discontinuities of fibers of the cross laminations due to the knots, prevented shear crack formations. DK specimens had curves similar to the NK specimens but were more ductile. As the curves highlighted in Fig. 9c show, serval specimens continued to resist higher loads after the RS failures occurred and ultimately failed in tension. The weak linkage between the decayed knots and the clear wood caused the cross laminations to experience several cracks before they failed in RS. As the specimens were loaded outof-plane and the cracks propagated, the decayed knots detached from the surrounding wood and began to act as shear keys which prevented rolling of the wood fibers. Overall, based on the loaddeformation curves and failure mechanism, SK specimens failed in a more brittle manner than the NK and DK specimens. 4.3. Effect of test setup on RS strength As shown in Fig. 10, the average RS strength derived from the shear analogy method (based on the bending test results) was smaller than the average RS values from the two-plate shear tests. The differences between the estimated RS means from the two methods were statistically analyzed by implementing the twosample t-test for each knot configuration (a = 0.05). The homogeneity of variance from the collected RS data using the two test methods was confirmed to be equal. Table 7 shows that the RS strength values obtained from the bending tests were significantly different from those obtained from the two-plate shear tests for all three configurations. On average, the RS strength of the NK, SK, and
Fig. 10. Comparison of estimated RS strength values from bending and two-plate shear tests (bars represent standard deviation).
DK specimens from bending test were lower than that from twoplate shear test by 13.0%, 34.9%, and 31.2%, respectively. During the two-plate shear tests, the load was applied at an inclination angle of 18° from the metal plates to the face layers by bolts, specifically the top-left and the bottom-right two bolts. This setup was to constrain the out-of-plane movements of the face layers by inducing normal stresses against the RS plane [30]. Since the inclination angle used in this study was relatively large compared with previous studies [8,9,10,30], the normal stresses could have prevented propagation of the shear cracks which led to a large RS strength. In addition, shear stress derived from this setup is not only from the core layer, but also influenced by the transverse shear strength of the outer layers. In the bending test, the shear analogy method was applied to predict the RS strength. This test neglected the heterogeneity (mainly knots) in the estimation of RS strength. This is because the elastic ratio applied for use in the shear analogy method was from data in the wood handbook [27] that was found from clear wood samples. Also, the MOE input into the shear analogy method equation for each lamination could not fully describe the properties of the knotty lumber. Therefore, the variation of the RS strength from the short-span bending test was lower than that of the two-plate shear test. 5. Conclusions In the present study, the RS strength of CLT specimens composed of cross laminations with three knot conditions (no knot, intergrown sound knot, and encased decayed knot) were evaluated by implementing experimental and analytical approaches. The CLT specimens with the knotty cross laminations yielded a higher RS strength than the ones without knots. Although the intense knot distributions within the CLT test specimens do not represent the ones found in commercial CLT products, the results of this study suggest that the presence of knots in cross laminations of commercial products would not negatively affect their RS strength values. Also, it was found that the CLT specimens composed of clear cross laminations with pith did not show a significant difference in RS strength compared to the CLT specimens composed of cross laminations without pith. Initial shear cracks were formed through piths or in earlywood/decayed parts (brim) of the knots. As shear stresses increased, cracks propagated along or across the wood grain and followed the border of the decayed knots. The RS strength estimated using the short-span bending test setup as proposed in the ANSI/APA PRG 320 standard along with the shear analogy method was more conservative (allows for a better safety factor) than the two-plate shear test. The shear analogy methodology is suggested for investigating the RS strength, since the results will not be affected significantly by the heterogeneity of the cross laminations. However, if the research aims to address the effects of specific features or conditions of cross laminations on the RS strength, then the two-plate shear test setup methodology would be preferred. Declaration of Competing Interest None.
Table 7 T-test of RS strength from two methods.
Levene’s test two-sample t-test a b
Not significantly different. Significantly different.
Acknowledgements
NK
DK
SK
NSa Sb
NS S
NS S
The authors would like to thank Mr. Brian Mitchell, Mr. David Butler, and Mr. Chris McGinnis from Department of Sustainable Bioproducts at Mississippi state university for providing assistance with sample preparation and experimental tests. The authors would also like to thank Shuqualak Lumber Co. for donating
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lumber, and Hexion Inc. for donating the adhesive used for this research. This material is supported by the National Institute of Food and Agriculture, U.S. Department of Agriculture, and McIntire Stennis under accession number 1009735. This report was made possible through a grant from the USDA Forest Service under FPL agreement number 16-JV-11111133-058.
References [1] X. Ping, Estimating the influence of knots on the local longitudinal stiffness in radiata pine structural timber, Wood Sci. Technol. 36 (2002) 501–509, https:// doi.org/10.1007/s00226-002-0156-2. [2] R. Dávalos-Sotelo, V.R. Ordóñez Candelaria, Effect of knots on the bending strength of pine wood for structural use, Ciencia Forestal en Mexico 2 (2011) 43–55. [3] V. Baño, F. Arriaga, M. Guaita, Determination of the influence of size and position of knots on load capacity and stress distribution in timber beams of Pinus sylvestris using finite element model, Biosyst. Eng. 114 (2013) 214–222, https://doi.org/10.1016/j.biosystemseng.2012.12.010. [4] P. Guindos, T. Polocoser, Numerical calculations of the influence of the slope of grain on the effect of knots, Eur. J. Wood Prod. 73 (2015) 271–273, https://doi. org/10.1007/s00107-014-0876-7. [5] R. Gupta, C. Basta, S.M. Kent, Effect of knots on longitudinal shear strength of Douglas-fir using shear blocks, Forest Prod. J. 54 (2004) 77–83. [6] Y. Cao, J. Street, B. Mitchell, F. To, J. DuBien, R.D. Seale, R. Shmulsky, Effect of knots on horizontal shear strength in southern yellow pine, BioResources 13 (2018) 4509–4520. https://doi.org/10.15376/biores.13.2.4509-4520. [7] FPInnovations. CLT Handbook, Vancouver. 2011. [8] S. Aicher, Z. Christian, M. Hirsch, Rolling shear modulus and strength of beech wood laminations, Holzforschung 70 (2016) 773–781, https://doi.org/10.1515/ hf-2015-0229. [9] S. Aicher, M. Hirsch, Z. Christian, Hybrid cross-laminated timber plates with beech wood cross-layers, Constr. Build. Mater. 124 (2016) 1007–1018, https:// doi.org/10.1016/j.conbuildmat.2016.08.051. [10] Q. Zhou, M. Gong, Y.H. Chui, M. Mohammad, Measurement of rolling shear modulus and strength of cross laminated timber fabricated with black spruce, Constr. Build. Mater. 64 (2014) 379–386, https://doi.org/10.1016/ j.conbuildmat.2014.04.039. [11] F. Lam, Y. Li, M. Li, Torque loading tests on the rolling shear strength of cross laminated timber, J. Wood Sci. 62 (2016) 407–415, https://doi.org/10.1007/ s10086-016-1567-2. [12] M. Li, Evaluating rolling shear strength properties of cross-laminated timber by short-span bending tests and modified planar shear tests, J. Wood Sci. 63 (2017) 331–337, https://doi.org/10.1007/s10086-017-1631-6.
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[13] Y. Li, F. Lam, Low cycle fatigue tests and damage accumulation models on the rolling shear strength of cross-laminated timber, J. Wood Sci. 62 (2016) 251– 262, https://doi.org/10.1007/s10086-016-1547-6. [14] T. Grandvuinet, L. Muszyn´ski, Effect of knot and slope of grains on the rolling shear in dimensional timber used in CLT core layers, Proceeding of WCTE, 2016. [15] J. Zhou, Y.H. Chui, M. Gong, L. Hu, Elastic properties of full-size mass timber panels: characterization using modal testing and comparison with model predictions, Compos. Part B 112 (2017) 203–212, https://doi.org/10.1016/ j.compositesb.2016.12.027. [16] D.M. Moses, H.G.L. Prion, Stress and failure analysis of wood composites: a new model, Compos. Part B 35 (2004) 251–261, https://doi.org/10.1016/ j.compositesb.2003.10.002. [17] H. Kreuzinger, Flaechentragwerke – platten, scheiben und schalen – ein Berechnungsmodell fuer gaengige Staikprogramme (in German), Bauen mit Holz. S (1999) 34–39. [18] J. Bodig, B.A. Jayne, Mechanics of Wood and Wood Composites, Krieger Publishing Company, Florida, 1982. [19] EN 1995-1-1. Eurocode 5 Design of timber structures. Part 1-1: general common rules and rules for buildings. European Committee for standization: 2006. CEN/TC 250. [20] Forest Products Laboratory. Method for evaluating shear properties of wood. U. S. Forest Service Research Note. FPL-0195, June, 1968. [21] Yang Mengyu. Flexural strength reliability of visually graded southern yellow pine dimensional lumber. Thesis, Clemson University. [22] ANSI/APA PRG 320, Standard for Performance-Rated Cross-Laminated Timber, APA-The Engineered Wood Association, Tacoma, WA, 2012. [23] BS EN 16351, Timber Structures – Cross Laminated Timber – Requirements, British Standards Institution, London, 2015. [24] American Society for Testing and Materials. ASTM D2718 Standard test methods for structural panels in planar shear (rolling shear), 2011. [25] DIN 1052, Design of Timber Structures – General Rules and Rules for Buildings, German Institute for Standardisation, 2008. [26] Winter Stefan, Kreuzinger Heinrich, Mestek Peter, Teilprojekt 15 Flächen aus Brettstapeln, Brettsperrholz und Verbundkonstruktionen, Fraunhofer IRB Verlag, 2009. [27] Forest Products Laboratory, Wood Handbook – Wood as an Engineering Material. General Technical Report FPL-GTR-190, U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, WI, 2010. [28] Mestek Peter, Kreuzinger Heinrich, Winter Stefan, Design of cross lamination timber (CLT), Proceeding of WCTE, 2008. [29] American Society for Testing and Materials. ASTM D4761 Standard Test Methods for Mechanical Properties of Lumber and Wood-Base Structural Material. 2013. [30] P. Mestek, Punktgestützte Flächentragwerke aus Brettsperrholz (BSP) – Schubbemessung unter Berücksichtigung von Schubverstärkungen PhD thesis, Technische Universität München, 2011.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Evaluation of the effect of knots on rolling shear strength of cross laminated timber (CLT) Yawei Cao a, Jason Street a, Minghao Li b, Hyungsuk Lim a,⇑ a b
Department of Sustainable Bioproducts, Mississippi State University, 201 Locksley Way, Starkville, MS 39759, USA Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
h i g h l i g h t s Knots would not decrease rolling shear strength of cross laminated timber. Knot presence affects rolling shear failure mechanisms. Two-plate shear test can be used to evaluate effects of laminations’ heterogeneity. Short-span bending test is more conservative than two-plate shear test.
a r t i c l e
i n f o
Article history: Received 13 November 2018 Received in revised form 3 May 2019 Accepted 20 June 2019 Available online 26 June 2019 Keywords: Cross laminated timber (CLT) Rolling shear Knot Shear analogy method Failure mechanism
a b s t r a c t The study experimentally and analytically investigated the effect of knots on the rolling shear (RS) strength of 3-ply southern yellow pine cross-laminated timber (CLT). Center-point bending tests and two-plate shear tests were conducted on six CLT configurations composed of different types of cross layer laminations based on knots conditions (No Knots, Sound Knots, and Decayed Knots) and pith conditions (Pith, No Pith). The shear analogy method was implemented to evaluate the RS strength values from the bending test results, which were compared against the results from the two-plate shear tests. The crosslayer laminations with either sound knots or decayed knots improved the RS strength of CLT. In general, the RS predicted by the shear analogy method was conservative. Published by Elsevier Ltd.
1. Introduction Knots are remnants of branches found in lumber. Knot determination and classification is critically important for grading lumber properly. Higher grade lumber requires a limited quantity of knots in specific sizes. Knots have widely been considered as defects in wood quality, which can adversely affect the mechanical properties. Specifically, knots significantly affect bending properties according to previous experimental and analytical studies. A theoretical model [1] revealed that knots negatively affected the bending stiffness of pine lumber. Experimental and numerical studies [2,3] also showed that knots reduce the bending strength of wood, and their presence significantly downgrades the value of the wood. Based on finite element model simulation results, Guindos and Polocoser [4] claimed that the modulus of rupture (MOR) of wooden boards could be reduced up to 50% due to the slope of grain
⇑ Corresponding author. E-mail address: [email protected] (H. Lim). https://doi.org/10.1016/j.conbuildmat.2019.06.165 0950-0618/Published by Elsevier Ltd.
caused by knots. However, when it comes to shear proper ties, knots are not considered as defects in all circumstances. Gupta et al. [5] found that knots did not affect shear parallel or perpendicular to wood grain significantly. In contrast, Cao et al. [6] reported that the effect of knots on transverse shear strength is dependent on the conditions of the knots. Cross-laminated timber (CLT) is an engineered wood product widely used in mass timber construction, which is composed of orthogonally oriented multi-layers of dimensional lumber. CLT products are assembled using chemical adhesives or mechanical fasteners, such as dowels or nails [7]. In CLT manufacturing, lower grade lumber characterized by various types of knots is typically assembled into cross layers aligned in the minor direction since they have negligible contribution to the out-of-plane and inplane mechanical properties of the full-size cross-laminated system in the major direction. Rolling shear (RS) is defined as shear stresses leading to shear strain in a plane perpendicular to the grain direction. In CLT, when it is under short-span out-of-plane
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loading cases, shear (RS) properties of the cross layers determine the flexural behavior of CLT. Several studies have been conducted to evaluate CLT RS properties. Aicher et al. [8] investigated the RS modulus and strength of beech laminations with four different sawing patterns (flat-sawn, semi-quarter-sawn, quarter-sawn, and with pith) using two-plate shear tests. The semi-quarter sawn lumber showed the highest RS strength, while the lumber with pith showed the lowest RS strength. The research was extended by evaluating the shortspan flexural performance of 3-ply CLT with outer and core layers composed of spruce and beech, respectively. Various methods of measuring and calculating RS properties were implemented and discussed [9]. Zhou et al. [10] also investigated the RS properties of CLT panels by conducting two-plate shear tests. Based on the RS measurements, the shear analogy method was utilized to predict the deflections of the panels under center-point loading conditions with different span-to-depth ratios. Lam et al. [11] conducted torsional shear tests to evaluate the RS strength properties of CLT made out of Canadian hem-fir lumber. Li [12] conducted shortspan bending tests and modified planar shear tests, and remarked that the lamination thickness significantly affected RS strength of CLT. Also, the duration of load effect on the RS strength has been examined [13]. Few studies have been conducted on the effect of knots on RS properties of CLT. Grandvuinet and Muszyn´ski [14] evaluated the effect of knots in cross layers on the rolling shear properties of CLT by conducting short-span bending tests. Since short-span flexural performance is governed by rolling shear properties in CLT, instead of directly measuring and analyzing RS properties, bending properties, modulus of elasticity (MOE) and the modulus or rupture (MOR), of the knotty-core test specimens were compared against the ones of the clear-core specimens. The conclusion was that the knots in the core laminations did not affect the RS properties. Theoretical models also have been studied in order to predict the mechanical properties of layered composite panel [15,16], specifically, for estimations in CLT, shear analogy method [17], k-method [18], and c-method [19] are commonly used. Wood is an anisotropic material which has higher shear strength along its cross-sectional (transverse) plane than ones of longitudinal (tangential and radial) planes [20]. The grain directions of knots make this natural material heterogeneous, which have inclined angles to its longitudinal axis. Thus, the knotty cross laminations subjected to short-span flexure and in-plane shear loads experience planar stresses traveling along both transverse planes of the knots and radial-tangential planes of the clear wood. Therefore, in this presented study, it has been hypothesized that the knots of cross laminations will increase RS strength of their composite systems. The RS strength of CLT composed of lumber laminations with different knot conditions were examined and compared analytically and experimentally. Shear analogy method [17] was implemented in calculating the RS strength using experimentally obtained inputs. Two-plate shear test was conducted to directly measure the RS strength of the cross layer.
2. Materials and methods 2.1. CLT specimens Three-layer CLT panels were constructed using flatsawn No.3 2 6 16ft southern yellow pine (Pinus spp.) lumber from Shuqualak, Mississippi, USA. The lumber was cut to a length of 838 mm and stored in an environmental chamber for a minimum of one week at relative humidity of 65 ± 5% and temperature of 20 ± 2 °C. Non-destructive four-point bending tests with a spanto-depth ratio of 18 were conducted to measure their modulus of
elasticity (MOE) properties. According to 1978 IGTP (In-Grade Test Program) [21], modulus of rupture (MOR) of No.3 2 4 and 2 8 southern pine lumber at MC of 15% are 49.4 MPa and 36.6 MPa, respectively. So, we assume MOR of 2 6 southern pine lumber is 43.0 MPa. Thus, the maximum load (Fest. max) of the member tested under a third-point loading setup is estimated to be 12.7 kN. Non-destructive bending test were terminated when the applied load reached 3.8 kN which is approximately 30% Fest. max. MOE was calculated using the slope of a line segment connecting 10% Fest. max and 30% Fest. max. This conservative range was chosen to ensure the tested lumber do not experience any permanent deformations. Table 1 showed the properties of 2 6 SYP lumber from thirdpoint non-destructive bending test, in which SG was calculated at the Moisture Content (MC) around 15%. The measured MOE ranged from 3.71 GPa to 13.15 GPa. The lumber specimens with MOE that ranged from 6.90 GPa to 13.15 GPa were fabricated as laminations of the face-layers which are parallel to the major direction, while the lumber specimens with an average MOE below 6.90 GPa were fabricated as laminations of the core-layers which are perpendicular to the major direction. These values were used as inputs for the shear analogy method for estimating the RS strength, which is described and discussed in depth later in this paper. The width of a CLT specimen for a flatwise shear test should be at least 305 mm (12 in.) according to ANSI/APA PRG 320 [22]. However, it is rare to find multiple knots in the same condition within this distance on a piece of lumber, and the dimensions of the knots found in 2 6 lumber are usually smaller than its width. Therefore, the CLT test specimens used in this study were made to a width of 136 mm. The face- and cross-laminations were planed to a thickness of 35 mm, and cut to lengths of 685 mm and 136 mm, respectively. Within 24 h after the planing process, the laminations were face-glued into CLT using phenol resorcinol formaldehyde (PRF) adhesive (Hexion Inc., Columbus, OH, USA). The CLT specimens with dimensions of 685 mm-length, 136 mm-width, and 105 mm-thickness were pressed using a hydraulic press at a pressure of 0.86 MPa (125 psi) for 9 h while the inner glue line temperature remained at 21–24 °C. Three conditions of knots were considered in this study and included decayed knots (DK), sound knots (SK), or no knots (NK). Six CLT configurations were constructed with cross layers composed of laminations with pith (P) or without pith (NP) as illustrated in Fig. 1; they are denoted as DK-P, SK-P, NK-P, DK-NP, SK-NP, NK-NP respectively. A sound knot is characterized as intergrown wood with solid surface and no symptoms of decay, while a decayed knot is characterized as encased wood surrounded by deteriorated fibers around the brim. Neither completely decayed knots with holes nor missing knots were included in this study. In the knotty CLT specimens, all cross laminations had knots with a minimum diameter of 34 mm. 2.2. Two-plate shear test A planar shear test (compression shear test) is an alternative method for measuring RS properties of CLT which is acknowledged Table 1 Properties of 2 6 SYP lumber from four-point non-destructive bending test.
N Mean Max Min COVb a b
MC (%)
SG15a
MOE (GPa)
164 15.00 20.84 6.35 11.52%
164 0.44 0.64 0.21 11.68%
224 7.54 13.15 3.71 22.74%
Specific gravity measured based on MC of 15%. Coefficient of variation.
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Fig. 1. Cross layer configurations.
in the European CLT standard BS EN 16351 [23], which enables two choices of test setups. Aicher [9] experimentally investigated the two different test setups: A) compression loads on one top and one bottom of two outer layers with screw reinforcement, and B) compression loads on glued-on steel plates with a tilt angle of approximately 7°. The results showed that setup B overestimated the RS strength due to the adhesive penetration to the planned thin outer layers. In setup A, the length to depth ratio has critical influence on the RS strength due to the effect of the compression failure on outer layers. Limited to the available CLT specimen size, a revised two-plate shear test setup was used, as illustrated in Fig. 2. Two metal brackets were attached to the CLT specimens by installing ten 3/800 2–1/200 lag bolts and twelve #8 200 screws on the edge and face sides of the outer layers, respectively. These rigidly connected brackets were loaded at an angle of 18° from the vertical to induce shear along the diagonal planes of the core
layers. A compression load was applied to the face layers through the metal plates, and this load was transferred to the core layer of interest. The test specimens were cut to a length of 342 mm which were laid up as described in Table 2. The loading rate of the tests was determined to be 0.762 mm/ min based on preliminary tests, which kept the testing time within a range of 3–12 min as recommended in the ASTM D2718 standard [24]. 2.3. Short-span bending test In order to study RS strength of CLT, four-point bending and center-point bending test setups are recommended in the European BS EN 16351 standard [23] and the US ANSI/APA PRG 320 standard [22], respectively. Since there is no attempt to determine the RS stiffness in the presented study, a center-point short-span bending test was sufficient. Short-span bending tests were conducted as shown in Fig. 3a. The CLT specimens were simply supported, and a transverse load was applied across the whole width of the specimens at a constant rate of 0.250 mm/min. The midspan deflection was measured at the neutral axis (Fig. 3b). 2.4. Shear analogy method The anisotropic nature of wood and orthogonal assembly lead to incongruity in mechanical properties between the laminations parallel and perpendicular to the major direction of a CLT panel. Thus, unlike glue-laminated timber, it is not valid to assume that the cross sections of the CLT layers are perpendicular to the neutral axis under out-of-plane loads. This is especially true under shortspan bending conditions with span-to-depth ratios between 5 and 6 where the transverse shear stress governs structural failure, and the contribution of shear deformations in cross layers to the total deformation becomes significant. Considering the abovementioned attributes, Kreuzinger [17] introduced the shear analogy method which can more accurately estimate the mechanical
Table 2 Specimen layups and dimensions for two test types.
Fig. 2. Two-plate shear test setup.
Test type
N
Lamination thickness (mm)
Width (mm)
Length (mm)
Bending test Two-plate shear test
54 54
35/35/35 35/35/35
136 136
685 342
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BA ¼
n X
3
hi 12
ð2Þ
Ei Ai Z 2i
ð3Þ
Ei bi
i¼1
BB ¼
n X i¼1
where Ei is the modulus of elasticity of the ith layer; hi is the thickness of ith layer; Ai is the cross section area of ith layer; Zi is the distance between the centroid of ith layer to the neutral axis of composite system. Applied transverse forces and bending moments are proportionally distributed to the virtual beams by their flexural stiffness. As it is stated in the above content, in the virtual system of shear analogy method, each lamination in Beam A has the infinite shear stiffness, so the deflection induced by shear can be ignored. However, contribution of shear stiffness needs to be addressed in determining the apparent flexural stiffness of Beam B (BB*) which can be calculated using Eq. (4).
BB ¼ BB
1 12BB 1 þ KSl 2
ð4Þ
Therefore, the total apparent stiffness of the composite system (B*) is given by Eq. (5).
B ¼ BA þ BB
ð5Þ
Accordingly, the applied transverse shear forces are distributed to Beam A (VA) and Beam B (VB) as Eqs. (6) and (7), respectively.
VA ¼ V
BA B
ð6Þ
VB ¼ V
BB B
ð7Þ
Fig. 3. (a) Short-span bending setup (b) deflectometer setup.
properties of CLT, including the rolling shear strength when compared with other composite beam theories. This analytical method has also been adopted by German standard DIN 1052 [25], and American standard ANSI/APA PRG 320 [22]. RS strength estimation procedures of the shear analogy are concisely summarized below based on DIN 1052 and TUM reports [25,26]. The shear analogy method idealizes a layered composite product as a virtual system composed of two beams connected with infinitely rigid web members which experience the same out-ofplane deformations (shown in Fig. 4). Beam A accounts for the intrinsic flexural stiffness of each layer, which is assumed to have infinite shear stiffness along its own centroid. Beam B describes the combined bending stiffness of each layer with finite shear stiffness based on the distances from their centroids to the neutral axis of the system. Based on the assumptions that the shear stiffness of Beam A is infinite and the links between layers are perfectly rigid (ci = 1), shear stiffness of the composite system SB becomes the result of Eq. (1).
S ¼ SB ¼ Pn1
1 i¼1 ci
þ
h1 2G1 b1
a2 P hi hn þ n1 i¼2 Gi bi þ 2Gn bn
ð1Þ
where Gi is the shear modulus of the ith layer; a is the distance between the centroids of two outmost layers; bi is the width of ith layer; ci is the flexible connection between the ith and (i + 1)th layer. The flexural stiffnesses of Beam A (BA) and Beam B (BB) in the major direction are given by Eqs. (2) and (3), respectively.
When it comes to the stress, the shear stresses of each layer of Beam A (sA,i) and Beam B (sB,i) are given by Eqs. (8) and (9), respectively.
sA;i ¼
V A Ei zi hi BA 2 8
ð8Þ
sB;i ¼
VB Ei hi Z i zi þ þ s0i BB 2
ð9Þ
where zi is the location of interest within the ith layer; it sits between – hi/2 and hi/2; s0i is the shear stress of the centroid of (i-1)th layer of Beam B. For a beam under bending moment, the neutral axis is subjected to the highest shear strength. Specifically, for a 3-ply CLT specimen, the core layer (cross lamination) is subjected to the highest rolling shear strength. Since the MOE of the cross layer without edgebonding in the major direction is negligible, the shear stresses throughout the thickness of the layer in Beam A are assumed to be zero according to Eq. (8). In Beam B, the shear stresses from the outer layers are transferred to the cross layer following the Eq. (9). Thus, the RS strength (sB,2) of a 3-ply CLT can calculated using Eq. (10).
sB;2 ¼ s02 ¼
V B E1 h1 h1 Z1 þ BB 2 2
ð10Þ
3. Results 3.1. Two-plate shear test
Fig. 4. Virtual beam of shear analogy method.
In the two-plate shear tests, RS strength was calculated by dividing the maximum applied load by the diagonal planar area of each specimen’s core layer with Eq. (11).
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Y. Cao et al. / Construction and Building Materials 222 (2019) 579–587 Table 3 RS strength values from two-plate shear test. NK_NP RS strength (MPa) N 9 Mean 1.95 Max 2.39 Min 1.52 COV 13.72%
NK_P
DK_NP
Table 5 T-test results of pith groups from two methods. DK_P
SK_NP
SK_P
Compared config.
9 2.53 3.01 2.12 11.07%
9 2.58 3.12 2.23 12.15%
9 2.62 3.34 2.08 13.77%
9 2.33 2.75 2.12 8.42%
NK_NP – NK_P DK_NP – DK_P SK_NP – SK_P a
c
Table 4 RS strength values estimated using shear analogy method based on short-span bending test results.
RS strength (MPa) N 9 Mean 1.72 Max 2.20 Min 1.37 COV 13.80%
s¼
NK_P
DK_NP
DK_P
SK_NP
SK_P
9 1.72 1.88 1.29 10.84%
9 1.86 2.26 1.11 20.84%
9 1.92 2.30 1.69 11.18%
9 1.88 2.40 1.36 15.37%
9 1.90 2.18 1.69 8.28%
F qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 b l þ h2
ð11Þ
where F is maximum shear force (N); b is width of specimen (mm); l is length of specimen (mm); h2 is thickness of core layer (mm). Table 3 shows the maximum shear force and RS strength for the six configurations. 3.2. Short-span bending test (shear analogy method) The shear analogy method discussed in Section 2.4 was implemented in estimating the RS strength using the short-span bending test results. In calculating flexural and shear stiffness properties as expressed in Eqs. (1)–(3), the longitudinal MOE values EL were obtained from the non-destructive four-point bending tests described in Section 2.1 (Table 1). Other modulus properties approximated and assumed according to values recorded in literature [26–28] and were used as the inputs for this analytical method. The shear modulus in the radial-tangential plane GRT was approximated to be one-tenth of the shear modulus in longitudinal-radial plane GLR [28]. The loblolly pine elastic ratios of 0.078 and 0.082 were used for ET/EL and GLR/EL, respectively [27]. However, since cross laminations were not edge bonded, ET of the cross layer was assumed to be zero [26]. Ultimately, Eq. (10) was used to estimate the RS strength for each specimen using the non-destructively measured MOE values and transverse shear forces calculated based on the recorded failure loads as summarized in Table 4.
Bending test
a
SIG
H
SIG
NSb NS NS
NS NS Sc
NS NS NS
NS NS NS
H 9 2.05 2.40 1.72 11.03%
b
NK_NP
Two-plate shear test
Homogenous test-Levene’s test (Ho: r2NP = r2P, a = 0.05). Not significantly different. Significantly different.
determines the knot types as described in [29], the effect of pith on the RS strength could not be clearly evaluated using either the SK or DK group test results. The cross laminations of the SK_P and DK_P configurations had knots grown in multiple directions from pith, while SK_NP and DK_NP had knots running across the width or thickness of the laminations. Thus, it was determined to be more appropriate to analyze the test results of the NK group to evaluate the effect that pith has on the RS strength. Regardless the test method, no significant differences were found between the NK_NP specimens and NK_P specimens in terms of RS strength. Hence, hereafter, the pith presence was not considered as an experimental factor, and the NP specimens were combined with P specimens in the same knot condition. 4.1.2. Knots In order to evaluate the effect of knots on the RS strength, a least significant difference (LSD) t-test was performed at a significance level of ɑ = 0.05 in SAS 9.4 (SAS Institute Inc., version 9.4, Cary, NC, USA). Table 6 summarizes the LSD test results on the mean RS values of the three groups obtained from the two-plate and short-bending tests. Cumulative distributions of the results from both tests are illustrated in Figs. 5 and 6. In the two-plate shear test, the DK and SK specimens had significantly higher RS strength than the NK specimens. The average RS strength of the DK specimens was slightly higher than that of the
Table 6 LSD results of knots groups from two methods. Config.
NK DK SK a
Two-plate shear test
Bending test
Mean RS strength (MPa)
T groupa
Mean RS strength (MPa)
T groupa
2.00 2.55 2.48
a b b
1.77 1.89 1.89
a a a
Groups with the same letter are not statistically different, a = 0.05.
4. Discussion 4.1. Effect of pith and knots on RS strength 4.1.1. Pith A two-sample t-test was performed at a significance level of ɑ = 0.05 in SAS 9.4 (SAS Institute Inc., version 9.4, Cary, NC) to evaluate the effect of pith on the RS strength. Table 5 shows that the homogeneity concerning the variations of NP specimens and P specimens of NK group, SK group, and DK group were equal. The difference in RS strength between NP specimens and P specimens was significant (p = 0.046) in the SK group based on the twoplate shear test results. However, since the pith location
Fig. 5. Cumulative frequencies of RS strength measured from two-plate shear tests.
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In the bending test (shear analogy method), the difference in the RS strength between any of the three groups was not statistically different, but the RS strength of the SK and DK specimens were slightly higher than that of the NK specimens. However, the failure behavior of the NK, SK, and DK bending specimens was different and is described Section 4.2. 4.2. Failure behavior
Fig. 6. Cumulative frequencies of RS strength calculated using the shear analogy method.
SK specimen, but the difference was not statistically significant. The knots in the cross lamination were under shear in the crosssectional plane which made the laminations that included knots have a higher shear resistance than the laminations that did not have knots.
4.2.1. Two-plate shear test In the two-plate shear tests, all 54 specimens had RS failures, with cracks observed in the core layer at inclined angles to the glue lines. Each NK specimen had 2 to 4 cracks which propagated almost parallel to each other across the entire core layer (Fig. 7a). In contrast, the crack growth patterns of the SK and DK specimens were affected by knot conditions and shapes. The failure patterns of the SK specimens showed that the sound knots prevented the fibers of cross laminations to roll over each other as seen in the NK specimens, which led to significant wood failure near the glue lines as shown in Fig. 7b. The decayed knots caused
Fig. 7. Failure of (a) Clear specimen (b) Sound-Knot specimen (c) Decayed-Knot specimen.
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irregular stress distributions throughout the cross laminations of the DK specimens and led to distorted crack formations as shown in Fig. 7c. 4.2.2. Short span bending test Under short-span out-of-plane loads, 89% of the specimens failed in RS while 11% failed in tension at their bottom face layers. Failure was defined as a load drop of over 5%. Flat-sawn cross laminations had shear cracks which formed in the early wood and propagated across or along the wood grain, while the cross laminations containing pith had cracks initiate from or propagate through the pith (Fig. 8).
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In general, as shown in Fig. 8a, the NK specimens had shear cracks that formed in the core layers at inclined angles. As the load increased, the cracks propagated further and caused more fractures to occur in the fibers surrounding them, which caused negligible load drops in the load-deflection curve (Fig. 9a). Ultimately, wood failure occurred close to the glue lines near the edge and were shown as the main load drops in the curves. After the failure occurred, the fractured wood pieces were interlocked, and the specimens continued to resist loads which resulted in subsequent peaks which were lower than the failure loads. Similar to the failure mechanisms observed during the twoplate shear tests, the knots in the cross laminations of the SK and
Fig. 8. (a) Failure of clear specimens (b) Failure of sound knot specimens (c) Failure of decayed knot specimen.
Fig. 9. Typical load-deflection curves from short span bending test: (a) No-Knot specimens (b) Sound-Knot specimens (c) Decayed-Knot specimens.
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DK specimens reinforced the clear wood fibers under RS stresses and transferred the shear force to the glue lines where wood failures were found, as shown in Fig. 8b and c. The load-deflection curves involving the SK specimens were highly linear until the maximum loads were reached (Fig. 9b). The rigid linkage between the sound knots and the clear wood, as well as the discontinuities of fibers of the cross laminations due to the knots, prevented shear crack formations. DK specimens had curves similar to the NK specimens but were more ductile. As the curves highlighted in Fig. 9c show, serval specimens continued to resist higher loads after the RS failures occurred and ultimately failed in tension. The weak linkage between the decayed knots and the clear wood caused the cross laminations to experience several cracks before they failed in RS. As the specimens were loaded outof-plane and the cracks propagated, the decayed knots detached from the surrounding wood and began to act as shear keys which prevented rolling of the wood fibers. Overall, based on the loaddeformation curves and failure mechanism, SK specimens failed in a more brittle manner than the NK and DK specimens. 4.3. Effect of test setup on RS strength As shown in Fig. 10, the average RS strength derived from the shear analogy method (based on the bending test results) was smaller than the average RS values from the two-plate shear tests. The differences between the estimated RS means from the two methods were statistically analyzed by implementing the twosample t-test for each knot configuration (a = 0.05). The homogeneity of variance from the collected RS data using the two test methods was confirmed to be equal. Table 7 shows that the RS strength values obtained from the bending tests were significantly different from those obtained from the two-plate shear tests for all three configurations. On average, the RS strength of the NK, SK, and
Fig. 10. Comparison of estimated RS strength values from bending and two-plate shear tests (bars represent standard deviation).
DK specimens from bending test were lower than that from twoplate shear test by 13.0%, 34.9%, and 31.2%, respectively. During the two-plate shear tests, the load was applied at an inclination angle of 18° from the metal plates to the face layers by bolts, specifically the top-left and the bottom-right two bolts. This setup was to constrain the out-of-plane movements of the face layers by inducing normal stresses against the RS plane [30]. Since the inclination angle used in this study was relatively large compared with previous studies [8,9,10,30], the normal stresses could have prevented propagation of the shear cracks which led to a large RS strength. In addition, shear stress derived from this setup is not only from the core layer, but also influenced by the transverse shear strength of the outer layers. In the bending test, the shear analogy method was applied to predict the RS strength. This test neglected the heterogeneity (mainly knots) in the estimation of RS strength. This is because the elastic ratio applied for use in the shear analogy method was from data in the wood handbook [27] that was found from clear wood samples. Also, the MOE input into the shear analogy method equation for each lamination could not fully describe the properties of the knotty lumber. Therefore, the variation of the RS strength from the short-span bending test was lower than that of the two-plate shear test. 5. Conclusions In the present study, the RS strength of CLT specimens composed of cross laminations with three knot conditions (no knot, intergrown sound knot, and encased decayed knot) were evaluated by implementing experimental and analytical approaches. The CLT specimens with the knotty cross laminations yielded a higher RS strength than the ones without knots. Although the intense knot distributions within the CLT test specimens do not represent the ones found in commercial CLT products, the results of this study suggest that the presence of knots in cross laminations of commercial products would not negatively affect their RS strength values. Also, it was found that the CLT specimens composed of clear cross laminations with pith did not show a significant difference in RS strength compared to the CLT specimens composed of cross laminations without pith. Initial shear cracks were formed through piths or in earlywood/decayed parts (brim) of the knots. As shear stresses increased, cracks propagated along or across the wood grain and followed the border of the decayed knots. The RS strength estimated using the short-span bending test setup as proposed in the ANSI/APA PRG 320 standard along with the shear analogy method was more conservative (allows for a better safety factor) than the two-plate shear test. The shear analogy methodology is suggested for investigating the RS strength, since the results will not be affected significantly by the heterogeneity of the cross laminations. However, if the research aims to address the effects of specific features or conditions of cross laminations on the RS strength, then the two-plate shear test setup methodology would be preferred. Declaration of Competing Interest None.
Table 7 T-test of RS strength from two methods.
Levene’s test two-sample t-test a b
Not significantly different. Significantly different.
Acknowledgements
NK
DK
SK
NSa Sb
NS S
NS S
The authors would like to thank Mr. Brian Mitchell, Mr. David Butler, and Mr. Chris McGinnis from Department of Sustainable Bioproducts at Mississippi state university for providing assistance with sample preparation and experimental tests. The authors would also like to thank Shuqualak Lumber Co. for donating
Y. Cao et al. / Construction and Building Materials 222 (2019) 579–587
lumber, and Hexion Inc. for donating the adhesive used for this research. This material is supported by the National Institute of Food and Agriculture, U.S. Department of Agriculture, and McIntire Stennis under accession number 1009735. This report was made possible through a grant from the USDA Forest Service under FPL agreement number 16-JV-11111133-058.
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