Shear Stress and Interlaminar Shear Strength Tests of Cross-laminated Timber Beams

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1 Shear Stress and nterlaminar Shear Strength Tests of Cross-laminated Timber Beams Yao Lu, Wenbo Xie, Zheng Wang,* and Zizhen Gao The interlaminar shear stresses of the three-laer, five-laer, and sevenlaer cross laminated timber (CLT and those of the oriented laminated beams were calculated according to Hooke's law and the differential relationship between the beam bending moment and shear force. The interlaminar and maimum shear stresses of the CLT beam are related to the number of CLT laers and to the elastic modulus ratio EL/ET (or EL/ER of the parallel and perpendicular laers. The interlaminar shear strength of the Hemlock CLT was positivel correlated with the elastic modulus of its parallel laer. The results showed that the CLT short-span beams had three failure modes when subjected to a three-point bending test, namel perpendicular laer rolling shear failure, CLT interlaminar shear failure, and parallel laer bending failure. The shear stress of the oriented laminated beam followed a parabolic distribution along the height of the section, while the shear stress of the orthogonall laminated beams tended to be balanced, rather than parabolicall distributed along the height of section. The short beam three-point bending method was able to effectivel test the interlaminar shear strength of CLT due to its stable and readable load. Kewords: Cross-laminated timber; nterlaminar shear stress; nterlaminar shear strength; Test Contact information: College of Materials Science and Engineering, Nanjing Forestr Universit, Nanjing, Jiangsu 0037, China;*Corresponding author: wangzheng6358@63.com NTRODUCTON Cross-laminated timber (CLT is the basic unit of production for heav wood structures used in mid- to high-rise buildings. The advantages of CLT as a building material include factor prefabrication, simple installation, light weight, high strength, good structural integrit, high thermal insulation performance, and durabilit (Que et al. 07; Wang et al. 07. As a new solid wood composite building material, it is particularl important to control the design, processing technolog, and processing parameters of CLT (Wang et al. 0; Gagnon et al. 0; Cao et al. 06; Sikora et al. 06. The interlaminar shear strength of CLT, which is widel used to evaluate the interlaminar mechanical properties of CLT, refers to the strength limit under shear stress between the laminates. At present, the shear strength of CLT is commonl measured using the short beam bending method. n other words, to ensure shear failure rather than bending damage, CLT short beams are subjected to load measurement during the three-point bending test. According to the ANS/APA PRG 30-0 standard (ANS/APA PRG 30-0, the span should be 5 to 6 times the thickness of the specimen when the interlaminar shear strength of the CLT is tested. The ASTM D98 standard (ASTM D shows that Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

the short beam three-point bending method is suitable for testing the interlaminar shear strength of engineered wood products with irregular sections, including those with rectangular sectional wood

2 the short beam three-point bending method is suitable for testing the interlaminar shear strength of engineered wood products with irregular sections, including those with rectangular sectional wood materials, wooden joists, and circular columns. Moreover, the interlaminar shear strength of the rectangular section wood specimen is.5 times the average shear stress of the section, namel 3P/4bh, where P is the interlaminar shear failure load of specimen, b is the width, and h is the thickness. t is uncertain whether the calculation formula of interlaminar shear strength based on the ASTM D98 standard is suitable for CLT. t is necessar to find a wa to estimate the accurac of the test. One of the purposes of this work is to solve these two problems. n the current work, the formula describing the normal stress of the CLT beam along the height of the rectangular section was obtained first according to the orthogonal anisotrop of CLT. Then, the calculation formula for the shear stress of the CLT beam was derived according to the differential relationship between the bending moment and the shear on the beam section. After that, the interlaminar and maimum shear stresses of the three-laer, five-laer, and seven-laer CLT beams were calculated. The interlaminar shear strength of the CLT hemlock was measured using a short-span three-point bending method with a span-to-depth ratio of 6 (ANS/APA PRG 30-0, ASTM D EXPERMENTAL nterlaminar Shear Strength Test of Three-laer CLT According to the ANS APA PRG30-0 standard, the interlaminar shear strength of CLT was tested b means of short span three-point bending method. The designed CLT boards had dimensions of 5,500 mm,00 mm 05 mm. Figure shows the unit structure of the boards. Fig.. CLT unit structure The full-scale CLT boards (Fig. were made on the CLT production line of the Ningbo Sino-Canada Low-Carbon Technolog Research nstitute Co., Ltd. according to the CLT manual (Wang et al. 0 and conventional Canadian CLT production technolog. Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

There are two tpes of full-scale CLT boards: those consisting of three parallel laers of Hemlock Grade (E=3.8 GPa, and those consisting of three parallel laers of Hemlock Grade (E=0.3 GPa.

3 There are two tpes of full-scale CLT boards: those consisting of three parallel laers of Hemlock Grade (E=3.8 GPa, and those consisting of three parallel laers of Hemlock Grade (E=0.3 GPa. These laers were numbered,, 3, 4, 6, and 8. The perpendicular laers of the CLT boards of Grades and were comprised of the hemlock with an average elastic modulus of 7.4 GPa. From one full-size CLT board, four specimens (735 mm 305 mm 05 mm were obtained to achieve three-point bending with the span of 630 mm, i.e., a span-to-depth ratio is 6. The test instruments consisted of one universal mechanical testing machine with a maimum load of 0T (including one set of load displacement analsis software produced b Jinan Tianchen Testing Machine Manufacturing Co., Ltd. and one self-made vacuumpressurized circulation sstem, including a vacuum pressure tank (60 m 3, vacuum pump, air compressor, and tubes. The interlaminar shear strength of the three-laer CLT was tested using the threepoint bending method. The loading point was located in the middle of span, while the loading direction was perpendicular to the specimen surface (Fig.. During the test, to record the load-displacement curve the loading rate was set as 4 mm/min. The failure location and failure mode of the specimen were represented b the point at which the load-displacement curve deviated from the characteristic of loaddisplacement curve. During the test, with the load-displacement curve was automaticall recorded. The failure position, failure tpe, and the corresponding characteristics of loaddisplacement curve were observed until the specimen was destroed. The load values were recorded when the interlaminar shear failure occurred in the specimens. t was found that interlaminar shear failure load was the maimum load in the load-displacement curve, from which the interlaminar shear strength of CLT could be calculated. Fig.. nterlaminar shear strength test of CLT Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

Load-displacement Curve and Corresponding Failure Mode of CLT Three- Point Bending Test n the three-point bending loading process, the load-displacement curve was recorded in order to be able to

4 Load-displacement Curve and Corresponding Failure Mode of CLT Three- Point Bending Test n the three-point bending loading process, the load-displacement curve was recorded in order to be able to snchronousl observe the failure mode of the specimen. When the first load peak appeared in load-displacement curve, the cross grain of the perpendicular laer of the specimen showed cracks and a sloping failure surface. Fig. 3. Load-displacement curve of CLT three-point bending test Fig. 4. Destruction surface of three-laer CLT short-span beam under three-point bending load Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

5 The failure mode during the loading process in the three-point bending test and the corresponding load in the load-displacement curve showed that the interlaminar shear failure load was the maimum load in the three-point bending load-displacement curve. After local unloading, the displacement slowl increased with the reduction in the load. After that, the displacement could be increased onl b increasing the load. The specimen suffered interlaminar shear failure when the second peak was reached, namel at the maimum load in the load-displacement curve. Then, the load decreased, first slowl, then sharpl, with the increase in displacement. When the third peak occurred in the loaddisplacement curve, the parallel laer of the specimen was damaged b tensile fracture, resulting in the complete failure of the specimen (Figs. 3 and 4. RESULTS AND DSCUSSON Failure Mode of CLT Beam during Three-point Bending When the span-to-depth ratio of the three-point bending specimen is less than 7, the effect of shear stress on beam deformation will rapidl increase with the decrease in spanto-depth ratio. For instance, when the span-to-depth ratios are 6, 5, and 4 for simple beams with concentrated force across the center, the percentages of bending deformation of the shear stress and bending moment were 7.9,.4, and 7.8%, respectivel (Shao and Ma 988. Therefore, the specimens with small span-to-depth ratios (6, 5, or 4 were applied to improve shear strength accurac. n this work, the span-to-depth ratio of specimen in the test was 6. When the CLT beam was loaded b short-span three-point bending, the failure location was close to the lower support. The failure surface was near the interface between the parallel and perpendicular laers, closer to the parallel laer. Wood chips could be found on the interlaminar shear failure surface, indicating that the failure was not due to insufficient cementing strength at the adhesive laer. The failure location near the lower support led to a small bending moment (namel normal stress on the adjacent section. As there is a large shear stress at the interface between parallel and perpendicular laers, it is considered to be a virtuall pure shear state. The interlaer bore most of the shear deformation, and the failure surface was the interlaer. Thus, the interlaminar shear strength of the CLT was the shear stress as determined b the interlaminar failure load. Shear Stress Analsis of CLT beam Normal stress of three-laer CLT beam CLT beams with a parallel laer/perpendicular laer/parallel laer structure are orthotropic. The material propert is smmetrical in the middle of the beam ( = 0, see Fig. 5(a. When the beam bends, the longitudinal strain is represented b for the neutral ais = 0. The longitudinal strain of the beam changes linearl with ( =, where is the curvature of beam. n other words, had linear variation along the section depth. The strain at the junction of the parallel and perpendicular laers was continuous (Timoshenko and Gere 978. The parallel and perpendicular laers had different elastic moduli E and E (Wang et al. 06. Therefore, the normal stress of the CLT beams was discontinuous at the junction of the parallel and perpendicular laers, and there was a hop (Fig. 5 (b. Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

6 Fig. 5. Three -laer CLT coordinate sstem and normal stress distribution According to Hooke's law, the normal stress of the CLT beam on Section could be epressed as, E E, h / 6 h / E E,0 h / 6 where is the neutral laer curvature of beam, E is the elastic modulus of the parallel laer; E represents the elastic modulus of the perpendicular laer, and h is the height of the rectangular section of beam. The composite bending moment of M da A Formula ( was substituted to derive h / h /6 M [ E bd E bd h /6 6 E M E (, 7 7E M 6 E E ( 7 7E 0 on Section could be epressed as 3 where bh, and b is the width of rectangular section of beam. Then, the normal stresses of the three-laer CLT beam on Section could be epressed as E E, h / 6 h / 6 E 7 7E E E 6 E 7 7E E,0 h / 6 E ( ( Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

7 Shear stress of three-laer CLT beam On the transverse section of the bending beam, the bending moment M and shear stress Q satisfied the following differential relationship (see Fig. 5 (c, dm Q (3 d Fig. 6. Force diagram of an element in the CLT beam When h / 6 h /, given the equilibrium condition of the micro-segment separators ( and + d in the -direction Fig. 6, the following was true: bd h / According to Formula (A-,A-3, h / h / ( d bd bd d bd d d d h / h / dm Q h d ( d 6 E 6 E 4 7 7E 7 7E ( 4 / h (4 6 E A( 7 7E From Formula (4, when = h/6, the shear stress could be epressed as ( E A 0.5 ( E 0 A Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

8 0.93 ( E 0 A 0. ( E 30 A The CLT beam eperienced continuous shear stress at the junction of its parallel and perpendicular laers. However, the normal stress in the section was discontinuous at the junction of the parallel and perpendicular laers (with a jump. When 0 h / 6, Q h / 6 h / h / 6 Q d 6 E ( 7 7E 6 A( 7 Ed 6 E ( E 7 7E 8 E E 7E [ 9 9E ( 36 / h From Formula (A-5, when = 0, the shear stress could be epressed as ] (5 ( E, ( E 0 A A 0.97 ( E 0, ( E A A 30 Stress of Five-laer CLT Beam Normal stress of five-laer CLT beam The five-laer CLT had a normal stress calculation similar to that of the three-laer laminated wood beam. First, the normal stresses of the parallel and the perpendicular laers were epressed as the elastic moduli and beam bending curvatures. After that, the normal stresses snthesized the bending moment of the section to derive the normal stress of the five-laer CLT as follows: E 5E 6E 5E 6E 5E,3h /0 h / E E,0, h /0 3h /0 h /0 (6 Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

9 Shear stress of five-laer CLT beam When 3h /0 h /, h / dm Qb h bd ( (7 d 6E 6E 4 5 5E 5 5E From Formula (8, when = 3h/0, the shear stress was 6, 6E A( 5 5 5E ( E, ( E ( E 0.80 ( E When h / 0 3h / 0, Q h / 3h /0 ( Q bd 6E 5E 6 6E A( 5 5 5E A ( 5 3h /0 ( 5 E 6E E 5E E bd 6E E 5E 4(9 /00 From Formula (8, when = h/0, the shear stress was 6 E 6E 5 A 6E A( ( E 5 5E 5 5E 0.96 ( E ( E ( E ( E / h (8 Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

10 Q [ [ A When 0 h / 0, h / 3h /0 ( 5 bd 6E 5E 6 6E 5( 5 5E 5( 5 3h /0 h /0 ( 5 E 6E E 5E 8 E 6E E 5E 5( 5 bd From Formula (9, when = 0, the shear stress was ( E ( E ( E ( E 30 h /0 ( 5 ( 00 6E 5E E bd] 6E E 5E / h ] (9 Stress of Seven-laer CLT Beam Normal stress of seven-laer CLT beam The seven-laer CLT had normal stress calculations similar to those of the threelaer laminated wood beam. First, the normal stresses of the parallel and perpendicular laers were epressed as elastic moduli and beam bending curvatures. After that, the normal stresses snthesized the bending moment to obtain the normal stress of the sevenlaer CLT. 44 E E 44 E E 44 E E 44 E E,5h /4 h / E,3h /4 5h /4 E, h /4 3h /4 E,0 h /0 E (0 Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

11 Shear stress of seven-laer CLT beam The interlaer shear stress calculation process for the three-laer and five-laer CLT showed that the following four integrals needed to be calculated to obtain the interlaminar shear stress of seven-laer CLT. When 5h /4 h / : Q h / bd ( 4 / h ( 44 E 44 E ( A ( E E When 3h /4 5h /4 : Q 5h /4 E E bd 4(5/96 / h ( 44 E 44 E ( E A ( E E E When h / 4 3h /4 : Q 3h /4 bd 4(9 /96 / h (3 44 E A 44 E ( ( E E When 0 h / 4 : Q h /4 E E bd 4(/96 / h (4 44 E E A 44 E ( ( E E E f = 5h/4, then the shear stress could be epressed as ( E A ( E ( E ( E 30 f = 3h/4, then the shear stress was ( E ( E ( E ( E 30 Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

12 f = h/4, then the shear stress was ( E ( E ( E ( E 30 f = 0, then the shear stress was ( E ( E ( E ( E 30 Based on the shear stress analsis and results of CLT beam, the ratios of the interlaminar shear stresses (three-laered, five-laered, and the seven-laered CLT and the maimum shear stress of the equidirectional laminated wood (.5Q/A were obtained (Table. Table. nterlaminar Shear Stress ( /.5 of CLT, Q / A,A bh av av CLT Three laers Five laers Seven laers Y-coordinate E/E h/ h/ h/ h/ h/ h/ h/ h/ h/ Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

13 Figures 7 and 8 show the distributions of interlaminar shear stress of the five-laer and seven-laer CLT beams (E/E = 0, respectivel, compared to the equidirectional laminated timber beams (E/E =. For the five-laer, seven-laer, and equidirectional laminated timber beams (E/E =, the shear stress followed approimatel a parabolic distribution along the depth of section. This was consistent with the fact that the shear stress of the isotropic material beam followed a parabolic distribution along the depth of the section height. The shear stress of the orthogonal laminated timber beam did not continue to follow the parabolic distribution along the depth of the section, but showed a balanced value along the height variation. The maimums, located in the neutral laer, were about 87 and 93% of.5 times that of the average shear stress, respectivel. Fig. 7. Distributions of interlaminar shear stress of fivelaer CLT beam (E/E = 0 and equidirectional laminated timber beam (E/E = along height of the section Fig. 8. Distributions of interlaminar shear stress of seven-laer CLT beam (E/E = 0 and equidirectional laminated timber beam (E/E = along the height of section nterlaminar Shear Strength of CLT According to the data in Table, the maimum interlaminar shear stress of CLT beam was epressed as k eff (5 A Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

14 where Keff is defined as the ratio between the maimum interlaminar shear stress and.5 times of the average shear stress on the cross section of CLT beam, Keff is related to E/E, the number of orthogonal laminated laers and the locations of the laers in the section, The elastic modulus ratio E/E of CLT was usuall larger than 0. Therefore, the correction coefficient Keff in the formula depended mainl on the number of laers of CLT (Table. When the three-laer CLT was loaded in the three-point bending test, the interlaminar shear failure surface was close to the lower support and near the interface between the parallel and perpendicular laers. Here, the bending moment was small, and the shear stress was Q = P/. Therefore, the normal bending stress, which was small relative to the shear stress, could be ignored. The interlaminar damage surface was near the interface between the parallel and perpendicular laers, inclining to the parallel laer. Given =h/6, the correction coefficient Keff 0.9. n the three-point bending test, the interlaminar shear strength of the three-laer CLT could be epressed as 3Pma 0.9 (6 4bh where is the interlaminar shear strength of CLT (MPa, Pma is the maimum load in the load-displacement curve (N, b is the width of specimen (mm, and h is the thickness of specimen (mm. According to Table, for the five-laer CLT, Keff 0.8, while for seven-laer CLT, Keff Therefore, the interlaminar shear strength of the five-laer CLT could be 3Pma epressed as 0.8, while the interlaminar shear strength of the seven-laer CLT 4bh 3Pma could be epressed as bh Table. nterlaminar Shear Strength Test Results of Three-laer CLT Hemlock with Grade along the Main Strength Direction Specimen No. Pma (kn nterlaminar Shear Strength (MPa Average (Coefficient.06 (8.8% of Variation Average nterlaminar Shear Strength (MPa Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

15 Tables and 3 show the interlaminar shear strengths of the three-laer CLT hemlock with Grades and along the main strength direction as determined b the test. Table 3. nterlaminar Shear Strength Test Results of Three-laer CLT Hemlock with Grade along the Main Strength Direction Specimen nterlaminar Shear Pma(kN No. Strength (MPa Average (Coefficient of Variation.73 (.0% Average nterlaminar Shear Strength (MPa The hemlocks are classified according to EL values. For hemlock CLT of Grades and, the interlaminar shear strengths were.06 and.73 MPa, respectivel, with a difference of 9%. Therefore, the interlaminar shear strength of CLT was positivel correlated with the elastic modulus of the CLT parallel laer. This eplains the importance of wood classification in engineering applications. CONCLUSONS. For the beams with equidirectional laminated timber, the shear stress followed approimatel a parabolic distribution along the height of rectangular section. The shear stresses on the upper and lower edge points of the section were equal to zero. On the neutral laer, the shear stress reached the maimum, namel.5 times that of the average shear stress of the section.. The shear stress of CLT beam no longer approimatel follows a parabolic distribution along the height of rectangular section. With the increase of CLT laers, the shear stress on the cross section tends to be more uniforml distributed. The maimum shear stress is less than.5 times of the average shear stress on the cross section. ts value is related to number of laers, parallel laer, perpendicular laer and the ratio between elastic modulus of parallel and perpendicular laer E/E. 3. During the three-point bending test, the CLT short span beam ehibited three failure modes, namel perpendicular laer rolling shear, CLT interlaminar, and parallel laer bending failures. Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

16 4. For the three-point bending tests of three-laer, five-laer, and seven-laer CLT short span beams, the interlaminar shear strengths could be uniforml epressed as 3Pma keff, where Keff values were 0.9, 0.8, and 0.93, respectivel, and Pma was 4bh determined b the maimum load of the load-displacement curve recorded in the threepoint bending tests. 5. The interlaminar shear strength of CLT was positivel correlated with the elastic modulus of the parallel laer. Grading the timbers according to the elastic modulus could improve the interlaminar shear strength of CLT. ACKNOWLEDGEMENTS This stud was funded b the Priorit Academic Program Development of Jiangsu Higher Education nstitutions (PAPD and the 07 Jiangsu Province Forestr Science and Technolog nnovation and Etension Fund (LYKJ[07]4. REFERENCES CTED ANS/APA PRG Standard for performance-rated cross-laminated timber, New York, USA. ASTM D Standard test methods of static tests of lumber in structural sizes, Pennslvania, USA. Cao, Y., Wang, Y. L., and Wang, Z. (06. Application and research progress of overseas cross-laminated timber (CLT construction, China Forest Products ndustr 3(, 3-7. DO: /j.issn Gagnon, S., Bilek, E. M., Podsto, L. Crespell, P., Gagnon, S., and Bilek, E. M. (0. CLT Handbook: Cross-laminated Timber, FPnnovation, New York, USA. Que, Z. L., Li, Z. R., and Wang, F. B. (07. Review of research and development status of cross-laminated timber used b medium high-rise structure in Europe, Building Structure 47(, DO:00-848X( Shao, B., and Ma, G. X. (988. Analsis of effect of shear on deformation of beams, Journal of Nanjing nstitute of Chemical Technolog 0(3, DO: /CN:3-670/N. Sikora, K. S., McPolin, D. O., and Harte, A. M. (06. Effects of the thickness of crosslaminated timber (CLT panels made from rish Sitka spruce on mechanical performance in bending and shear, Construction and Building Materials 6(7, DO: 0.06/j.conbuildmat Timoshenko, S., and Gere, J. (978. Mechanics of Material, Science Press, Beijing, China Wang, B. J., Pirvu, C., and Lum, C. (0. Cross-laminated timber manufacturing, in: Canadian CLT Handbook, FPnnovations, Quebec,Canada Wang, Z., Gao, Z. Z, and Cao, Y. (06. Dnamic measuring Poisson s Ratio μlt, μlr and μrt of lumbers b electrical method, Scientia Silvae Sinicae 5(8, DO:0.707/j Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

17 Wang, Y. L., Wang, Z., and Wang, J. H. (07. Research progress of the new generation of heav CLT wood structure building technolog, Journal of Northwest Forestr Universit 3(, DO: /j.issn Article submitted: Januar 9, 08; Peer review completed: March 7, 08; Revised version received and accepted: Ma 8, 08; Published: Ma 3, 08. DO: /biores Lu et al. (08. Cross-laminated timber shear, BioResources 3(3,

LECTURE 13 Strength of a Bar in Pure Bending

V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 13 Strength of a Bar in Pure Bending Bending is a tpe of loading under which bending moments and also shear forces occur at cross sections of a rod. f the bending