Strength Estimation and Reinforcement of Glue-Laminated Timber Beams with Circular Through-Hole

Transcription

1 Strength Estimation and Reinforcement of Glue-Laminated Timber Beams with Circular Through-Hole Kazumi Hijikata 1, Hideki Idota 2, Naoko Tsujimoto 3 ABSTRACT: The purpose of this study is to establish a simple and effective way to reinforce glue-laminated timber beams with a circular through-hole having a diameter that is at least 1/3 the beam height. Experiments with bend and shear s and finite element analyses were used to determine the stress fields and fracture conditions around the hole and estimate the maximum strength of the beams. Beams with the hole were found to have 6 to 8% of the yield strength of beams without the hole. In the experiments, it was observed that fractures occurred at the point where the tensile stress exceeds the tensile strength of the beam. This indicates that reduction of the tensile stress around the hole is needed. Based on these results, we propose two reinforcement methods, one using wooden boards and the other using toothed steel plates, for timber beams with a hole. The effectiveness of the proposed methods is shown by the experimental results. KEYWORDS: laminated timber beam, penetration hole, reinforcement methods, experiment, finite element method, tensile stresses, wooden boards, toothed steel plates, screws, bend, shear 1 INTRODUCTION 12 In the structural design of wooden houses, long span beams are increasingly being used to provide large rooms that can adapt to changing lifestyles and generations. A laminated timber beam of large height and length is commonly used in such designs. For example, in a room requiring a water supply and drainage, such as a bathroom or kitchen, through-holes are needed in the beam to run plumbing inside the ceiling without increasing the story height. Several studies on the strength estimation of a laminated timber beam with a hole have been reported [1-6]. However, there are few reports on reinforcement techniques for such a beam [7-9]. Therefore, there are currently no established reinforcement methods for beams with a hole. In actual building construction, one method has been to attach steel plates around the hole with a large quantity of screws. However, screws cut into the fiber of the timber, and a large quantity of 1 Kazumi Hijikata, Office of SHAWOOD-HOME Design & Department, SEKISUIHOUSE, Ltd, TOWER EAST, UMEDA SKY BUILDING, , OYODONAKA, Kita-ku, Osaka, , Japan. kazhijik@ga.sekisuihouse.co.jp 2 Hideki Idota, Department of Architecture and Design, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, , Japan. Idota@nitech.ac.jp 3 Naoko Tsujimoto, Kanagawa Sales Administration Headquarters SEKISUIHOUSE, Ltd, SHINAGAWA GRAND CENTRAL TOWER, , MINATOMINAMI, Minato-ku, Tokyo, 18-75, Japan. tsujimoto14@sekisuihouse.co.jp screws can degrade the beam strength, and consequently provides inefficient reinforcement. The purpose of this study is to propose a simple and effective reinforcement method for a laminated timber beam with a hole having a diameter that is at least 1/3 the beam height. First, the stress fields around the hole are examined by experiments as well as the finite element method. Considering the stress distribution, we propose two types of reinforcement methods. The effects of these reinforcement methods are evaluated by an experiment. 2 EXERIMENTS 2.1 TEST SECIMENS Bending s and shear s on a laminated timber beam with a circular through-hole were carried out to determine the strength, the stress field around the hole and the fracture type near the hole. The specimens are shown in Table 1. The parameters of the experiment are beam height and presence and position of the hole. Beam heights of 33 and 39 mm were used. The positions of the in the beam of height 33 mm are 55 and 4 mm. The positions of the hole in the beam of height 39 mm is 25 mm. The specimens are named as follows. M and S denote the bend and shear, respectively, and 33 and 39 denote the beam height. H and N indicate specimens with and without a hole, respectively. The terms e55, e4, e25 express the eccentric distance of the hole from the center of the beam, where center is the center of gravity of the beam

2 Table 1: Test specimens Test Bending Beam Specifications Specimens h Φ e n (mm) (mm) (mm) M-33-N M-33-H-e M-33-H-e4 4 6 M-39-N M-39-H-e S-33-N S-33-H-e S-33-H-e4 4 3 S-39-N S-39-H-e h : beam height Φ : diameter of hole e : eccentric distance of the hole n : the number of specimens without the hole. The value 13 in the Φ column is the size of the hole, if one is present. The number of specimens for each is in the n column. The tree species of the specimens is spruce. According to the Japanese Agricultural Standards, the strength specification is JAS E-F33. The standard strength of bending and shearing and the Young's modulus are shown in Table 2. This Young's modulus is a value for the strong axes. The cross section of each specimen is shown in Table 3. Beam width D is mm, and diameter Φ of the hole is 13 mm. For the beam height of 33 mm, 11 pieces of laminas were laminated, and for the beam height of 39 mm, 13 pieces of laminas were laminated. The distribution of the stiffness of a lamina constituting a beam is determined by the cross section. The hole is positioned so that it avoids a floor joist. For drainage pipes, an incline is needed. For these specimens, the hole is positioned lower than the center of gravity of the beam. The cross-section characteristics of each specimen are shown in Table 3. In this table, I Table 2: Material strength Material Strength(N/cm 2 ) Species Spec σ b τ E Spruce JAS E-F σ b :bending strength τ :shear strength E :Young's modulus is the geometrical moment of inertia, Z is the section modulus, and A is the area of the cross section. The value in parentheses expresses the ratio for the crosssection characteristics of specimens that does not include a hole. 2.2 TEST SETU Figures 1-1 and 1-2 show the setup for the bend and shear, respectively. The reaction force is realized by the ground and steel frame. Figures 2-1 and 2-2 show the specimen for each. For the bend (Figures 1-1 and 2-1), the load is added using a pressurization beam. An equal bending moment acts on the section including the hole. The beam of the bend is a simple beam of span 4, mm. The hole is established at the center in the length direction. The load acts at positions 5 mm to the right and left of the hole. For the shear (Figures 1-2 and 2-2), a concentrated load is applied to a simple beam of span 3, mm. The hole is 3 mm from the support point. The input load is applied 6 mm from the supported point. The shear force of 8% of the input load acts on the section, including the hole. Monotonic loading is applied to the beam by a 5 tf oil jack. The loading is carried out until the beam is fractured throughout the thickness. The lateral support installed near the supported point prevents out-of-plane deformation of the specimens. The load is measured by a load cell attached to the oil jack. A wire displacement gauge is attached to both sides of the beam to calculate flexural deformation. The flexural deformation is the average of the measurements of both sides. Table 3: Characteristics of specimen cross sections h 33 mm 39 mm Specimens M-33-N M-33-H-e55 M-33-H-e4 M-39-N M-39-H-e25 S-33-N S-33-H-e55 S-33-H-e4 S-39-N S-39-H-e25 Cross Section 33 Stiffness Stiffness I (.72) (2) (.94) Z (.59) 1551 (.71) (8) A (1) 24 (1) (7) 1: I=Geometic Moment of Inertia (cm 4 ), 2: Z=Section Modulus (cm 3 ), 3: A=Section Area (cm 2 ) Stiffness Stiffness Stiffness

3 Steel Frame Steel Frame 5tf Oil Jack 5tf Oil Jack ressurization Beam Lateral Load Cell Lateral Lateral Load Cell Lateral Specimens Specimens 支承部 支承部 支承部 支承部 Figure 1-1: Test setup for the bend /2 /2 Loading oint Loading oint Figure 1-2: Test setup for the shear 6 24 Loading oint oint Disp. Gauge1, 2 oint Figure 2-1: Bend specimen oint Disp. Gauge1, 2 oint Figure 2-2: Shear specimen 2.3 TEST RESULTS Shown in Table 4 are the results of the experiments. max is the maximum strength, y is the yield strength, and K is the initial stiffness. The values shown are the average of each. Figure 3 shows the parameters for the calculation of yield strength y and initial stiffness K. The X-axis is displacement, and the Y-axis is load. y is the value of the Y coordinate at the intersection of lines I and III. Line I links.1 max and max. Line II links max and.9 max. III is the gradient of straight line II and is also a tangent line of the load - deformation curve. IV is the straight line parallel to the X-axis and passing through y. The point of intersection of straight line IV and the load - deformation curve is R. oint R has coordinates ( y, y ). The initial stiffness K is the gradient of straight line V. Straight line V passes through coordinate R and the origin. Figures 4-1 and 4-2 shows several examples of the load - deformation curves of the bend and the shear, respectively. In each graph, the vertical axis shows the load, and the horizontal axis shows the deformation. The data of the beams with and without the hole are plotted. The black and white triangles denote the yield strength of the specimen. Table 4: Test results (kn) Test Specimens max y K I V III II (kn) (kn) (kn/cm) max M-33-N max M-33-H-e Load - deformation curve Bending M-33-H-e M-39-N IV I : Line to link.1 max and max y R II : Line to link max and.9 max M-39-H-e III : The tangent line that have gradient of II to S-33-N max the load-deformation curve S-33-H-e IV : The arallel line in X passes through the S-33-H-e point of intersection of I and III S-39-N max V : Line to link R and the origin S-39-H-e O y max : Maximum Strength (mm) y : Yield Strength K : Initial stiffness Figure 3: Calculation of y and K

4 /2 /2 18 /2 /2 18 y S-33-H-e55 18 y S-39-N y S-33-N M-39-H-e25 M-33-N 1 1 y y 1 1 y M-39-N y M-33-H-e4 6 M-33-H-e y 4 M-33-N 4 M-39-N 4 S-33-N 4 y S-39-H-e25 M-39-H-e25 y S-33-H-e4 S-39-N M-33-H-e55 S-33-H-e55 S-39-H-e25 2 M-33-H-e4 2 2 S-33-H-e (mm) (mm) (mm) (mm) M-33 series M-39 series S-33 series S-39 series Figure 4-1: Load-deformation curves of the bend Figure 4-2: Load-deformation curves of the shear (kn) (kn) (kn) (kn) In the bend s (Figure 4-1), the stiffness does not decrease dramatically even if the deformation is increased. It is thought that the specimen is fractured through the thickness. due to brittleness. In the M-39 series, the load - deformation relation of M-39-H-e25 almost agrees with that of M-39-N. In the shear s (Figure 4-2), the stiffness decreases gradually as the deformation increases. The beam with the hole broke soon after the stiffness decreased. Figures 5-1 and 5-2 show the relation of the section modulus and maximum strength of the bend and the shear, respectively. The horizontal axis (Z/Z ) is the ratio of each section modulus to the standard section modulus. The standard section modulus is the section modulus of the beam without the hole. Likewise, the standard maximum strength is the maximum strength of the beam without the hole, and so the vertical axis ( max / max ) is the ratio of the maximum strength of each specimen to the standard maximum strength. The black mark denotes a beam without the hole, and the white mark denotes a beam with the hole. The maximum strength is proportional to the section modulus except for the M-39 series. In both the bend and shear, the maximum strength of the beam has a high correlation with the section modulus. 2.4 STRESS FIELD AROUND THE HOLE Figure 6 shows the stress fields and cracks around the hole. The stress field is represented as a vector diagram of the principal stress. The direction of the arrow indicates the course of the principal stress, and the length of the arrow indicates the size of the principal stress. If the direction of the arrow is away from the core of the stress, the principal stress is tensile stress. If the direction of the arrow is toward the core of the stress, the principal stress is compressive stress. Hatching covers the domain where the tensile stress is most prominent. In the illustrations of the failure type, cracks shows the condition under which the beam was destroyed. For the bend, M-33-H-e55 and M-39-H-e25 are shown. The destruction in the bend occurred from the bottom of the hole and the right and left slippage at the upper part of the hole. In the shear, S-33-H-e55 and S-39-He25 are shown. The destruction in the shear occurred from the diagonal upper part of the hole in the loading point side and the diagonal lower part of the hole in the support point side. The stress field around the hole shows a tendency that is similar to the results reported in [1] for beams with the hole at the center of gravity. It is thought that the destruction occurs where the tensile stress is most prominent. max/max /2 /2 max/max /2 /2 max/max max/max M-33-N M-33-H-e55 M-33-H-e4 M-39-N M-39-H-e25 S-33-N S-33-H-e55 S-33-H-e4 S-39-N S-39-H-e Z/Z Z/Z Z/Z Z/Z M-33 series M-39 series S-33 series S-39 series Figure 5-1: Relation of the section modulus and maximum strength in the bend s Figure 5-2: Relation of the section modulus and maximum strength in the shear s

5 Stress Field (At 29kN) Failure Type Stress Field (At 29kN) Failure Type M-33-H-e55 S-33-H-e55 Stress Field (At 29kN) Failure Type Stress Field (At 29kN) Failure Type M-39-H-e25 Figure 6: Stress fields and failure types around the hole S-39-H-e25 3 FINITE ELEMENT METHOD The purpose of this section is to confirm the stress field around the hole using the finite element method. The results of the analyses of this section and the experiments of the preceding section are utilized for the design of an effective reinforcement method. 3.1 ANALYTICAL MODEL ANSYS Structural, which is general-purpose software, was used for the finite element method. The element type was primary hexahedral, and the material was defined as an orthotropic elastic body. Table 4 lists the material properties. Young's modulus, oisson's ratio and shear modulus were set for the material property. On the coordinate axis, the X-axis is the lengthwise direction of the beam, and the Y-axis is the height Table 4: Material properties [1-11] Yong s Modulus (N/mm 2 ) [1] oisson s Ratio[11] Shear Modulus (N/mm 2 ) [1] X Y Z 4 8 XY YZ ZX XY YZ ZX direction of the beam, and the Z-axis is the width direction of the beam. Ten analytical models, shown in Table 5, were used. The dimensions of the beam were the same as those in the experiments. A linear static analysis was performed with an input load of 29 kn, which is the same as the stress field shown in Figure ANALYTICAL RESULTS Table 6 shows the stress fields around the hole resulting from the analyses. The case name having N at the end does not have a hole. Shown are vector diagrams: the direction and size of the principal stress are indicated with an arrow, and the hatching represents tensile stress, as in Figure 6. In the bending analysis of cases FM-33-N, FM-39-N (without the hole), the tensile stress is confirmed to be under the neutral axis of the beam. In FM-33-H-e55 and FM-33-H-e4, the tensile stress is confirmed at the lower part and upper part of the hole. In FM-39-H-e25, the tensile stress is confirmed at the lower part of the hole. In the shear analysis of FS-33-N, FS-39- N (without the hole), tensile stress is seen in the lower right part of the beam. In FS-33-H-e55, FS-33-H-e4, FS-39-H-e25 (with the hole), the tensile stress is confirmed at the upper right of the hole and the lower left of the hole. In addition, tensile stress is seen in the lower right part of the beam. Table 5: Analytical models Case FM- 33-N FM- 33-H-e55 Bending FM- 33-H-e4 FM- 39-N FM- 39-H-e25 FS- 33-N FS- 33-H-e55 FS- 33-H-e4 FS- 39-N FS- 39-H-e25 Model y y z x z x

6 Table 6: Test results FM-33-N FM-33-H-e55 FM-33-H-e4 FM-39-N FM-39-H-e25 Bending FS-33-N FS-33-H-e55 FS-33-H-e4 FS-39-N FS-39-H-e25 The stress distribution of FM-33-H-e55 and FM-39-He25 and FS-33-H-e55 and FS-39-H-e25 agrees with the stress distribution in the experiments, shown in Figure 6. In current studies of woody structures, the finite element method is not often used because judging the destruction is not considered easy. However, it is shown that inspection of the stress fields using the finite element method is possible. Based on the experimental results and analytical results, it is predicted that beam breaking occurs at the part where the tensile stress occurs. 4 REINFORCEMENT EFFECT The results of Sections 2 and 3 indicate the tensile stress around the hole should be reinforced. Therefore, reinforcement specifications were designed to restrict the tensile stress. The next section discusses the effects of the designed reinforcement specifications, as carried out in experiments. Type Figure Attaching W1 W A C B Douglas fir lumber Douglas fir lumber SS4 Steel plates SS4 Steel plates t=18mm t=18mm t=3.2mm t=2.3mm Gluing by isocyanate Attaching by 7 screws (36 toothed protrusions) Figure 7: Designs specifications for reinforcements C 34 A B 6 A B C rotrusion rotrusion Section 45 Section 15 rotrusion Section Figure 8: Toothed protrusions Table 8: Test specimens with the reinforcement Beam Specifications Reinforcing Specifications Specimens h Φ e Type t The number of n (mm) (mm) (mm) (mm) reinforced sides M-33-R-e55-W1D W1 18 Both sides 3 55 M-33-R-e55-1D Both sides M-33-R-e4-W2D W2 18 Both sides 3 4 M-33-R-e4-2S Single side 3 S-33-R-e4-2S Single side S-33-R-e4-2D Both sides 3 S-39-R-e25-2S Single side 3 h : beam height Φ : diameter of hole e : eccentric distance of the hole n : the number of specimens Test Bending

7 /2 /2 Loading oint Loading oint Both side 6 24 Reinforcement Loading oint Both side Reinforcement oint Disp. Gauge1, 2 oint Figure 9-1: Bend specimen with reinforcement Single Side oint Disp. Gauge1, 2 oint Single Side Figure 9-2: Shear specimen with reinforcement 4.1 TEST SECIMENS The designed reinforcement specifications are shown in Figure 7. Specimens identified by W1 and W2 are reinforcement made from Douglas fir lumber. The thickness is 18 mm. W1 and W2 are attached to the side of the beam by the adhesive isocyanate. To attain adhesion, compressive force was input for 3 minutes. The round part of W1 and W2 partially overlaps the hole of the beam. Specimens identified by 1 and 2 are steel plates with a toothed protrusion. The steel material is SS4, and the thickness is 2.3 mm or 3.2 mm. The round part of the plate partially overlaps the hole. 1 and 2 are attached to the side of the beam with seven screws. In this reinforcement method, the transmission of force to the steel plate is mainly performed by notched projections. The number of projections is 36, and the shape of each projection is a triangle that has a height of 5 mm and a width of 3.5 mm. The projection is pushed into the beam by a screw and penetrates between the fibers without cutting a lot of fiber. Because a projection is used as a substitute for a screw, the quantity of screws is reduced to avoid cutting off any fiber, which reduces the strength of the beam. The reinforcement method with minimal cutting of the fiber is effective in raising the strength of the beam. The three placements of the projections, shown in Figure 8, are the same as the direction of the principal stress around the hole. These projections resist the tensile stress that causes destruction of the beam. Bend s and shear s, described in Section 2, were again performed to determine the effect of the reinforcement. The same examination devices, also described in Section 2, were used. Table 8 lists the specimens. The reinforcements shown in Figure 7 were joined to either both sides or one side of the beam. W1 and 1 were used for M-33-H-e55, presented in Section 2. W2 and 2 were attached to M-33-H-e4 and S-33-He4 and S-39-H-e25. R in the specimen name identifies the reinforcement. D and S represent both sides and one side, respectively. Four specimens were used in the bend s, and three in the shear s. Figures 9-1 and 9-2 shows the bend specimen and shear specimen, respectively. The shape and strength specifications of the beam are the same as those of Section 2. The dark gray areas in the figures show the reinforcement. 4.2 TEST RESULTS The data shown in Table 9 are results of the experiments. Maximum strength ( max ) and yield strength ( y ) and initial stiffness (K) are listed in the result. Yield strength and initial stiffness were calculated by the method shown in Section 2.3. Figure 1 is photographs of the hole at the time of the destruction of M-33-R-e4-W2D, M-33- R-e4-2S, S-33-R-e4-2S and S-39-R-e25-2S. In M- 33-R-e4-W2D, W2 broke along the breaking line of the beam. In addition, the breaking that started from the upper part of the hole is remarkable. In the bend and the shear, the destruction shape of the beam with the reinforcement was the same as that of the beam without the reinforcement. Table 9: Test results Test Specimens No. max y K (kn) (kn) (kn/cm) M1 M-33-R-e55-W1D Bending M2 M-33-R-e55-1D M3 M-33-R-e4-W2D M4 M-33-R-e4-2S S1 S-33-R-e4-2S S2 S-33-R-e4-2D S3 S-39-R-e25-2S max : Maximum Strength y : Yield Strength K : Initial Stiffness M-33-R-e4-W2D S-33-R-e4-2S Figure 1: Failure conditions M-33-R-e4-2S S-39-R-e25-2S

8 max/max Without hole Without hole max /2 /2 M1 M2 M3 M4 max of bend y/y Without hole y /2 /2 M1 M2 M3 M4 y of bend max/max Without hole max Without hole S1 S2 S3 max of shear y/y Without hole Without hole y S1 S2 S3 y of shear Figure 11-1: Maximum strength and yield strength in the bend s Figure 11-2: Maximum strength and yield strength in the shear s Figures 11-1 and 11-2 show the results of the reinforcement. The first and third graphs show the effect of the reinforcement on the maximum strength in the bend and shear s, respectively. The second and fourth graphs show the effect of the reinforcement on the yield strength in the bend and shear s, respectively. The vertical axis ( max / max or y / y ) of the graphs is the ratio of the maximum strength or yield strength of each specimen to the maximum strength or the yield strength of the beam without the hole. The horizontal axis shows the specimen names, listed in Table 9. In the bend (Figure 11-1), the reinforcement effect of all specifications is confirmed. The yield strength in M-33- R-e4-2S (M4) is the same as the strength of the beam without the hole. The reinforcement effects of M-33-Re55-W1D (M1) and M-33-R-e55-1D (M2), which are the specifications of different reinforcements, are at the same level. In the shear (Figure 11-2), the reinforcement effect of all specifications is confirmed. The yield strength of S-39-R-e25-2S (S3) is higher than the strength of the beam without the hole. The strength of S-33-R-e4-2D (S2), in which the reinforcement was attached on both sides, is higher than the strength of S- 33-R-e4-2S (S1), in which the reinforcement was attached only on one side. It is confirmed that the suggested reinforcements were effective for strength improvement of the beam with a hole. 5 CONCLUSIONS In this study, reinforcements were developed for a laminated timber beam having a through-hole with a diameter larger than at least 1/3 of the beam height, and the effects of the reinforcements were confirmed by experiment. It was thought that reinforcement around the hole improved the strength of the beam with the hole. To design the reinforcement, the stress field around the hole was examined by experiments and finite element analyses, and the relation of stress and destruction was shown. Fractures of the beam were found to occur when the stress around the hole exceeded the tensile strength of the beam. It was thought that most effective reinforcement would be restriction of the tensile stress around the hole. Therefore, two reinforcement designs were ed: 1) Wooden boards attached with adhesive 2) Toothed steel plates attached with seven screws. Both types of reinforcements were applied near the hole. The bend and shear results indicated that reinforcement is highly effective. In particular, the steel plate specifications are simple and easy to construct, and have high reinforcement performance. Because there are few screws, the steel plates do not cut off the fiber of the beam, and therefore the beam is strengthened effectively. In wooden structures in Japan, the evaluation and reinforcement method for a beam with a hole of diameter larger than 1/3 of the beam height have not yet been established. The establishment methods will be required in the future. In this study, the evaluation method of the beam with a hole of diameter larger than 1/3 of the beam height was not established. Nonetheless, the basic data for a finalized evaluation method was shown. The data of reinforcements in this study will contribute to future structural planning of long span wood beams with through-holes. ACKNOWLEDGEMENT The laminated timber beam was made in the Azai factory of Sekisui House, Ltd. The through-hole of the beam was processed in the Shiga Factory of Sekisui House, Ltd. The toothed steel plate was designed by Shinji Utsunomiya of Sekisui House, Ltd. The experiments were carried out at a site of Nagoya Institute of Technology by Satoshi Araki at Shimizu Corporation.

9 REFERENCES [1] Simon AICHER, Lilian HOFFLIN, New Design Model for Round Holes in Glulam Beams. roceedings of the 8 th World Conference on Timber Engineering, Vol.1, Finland, 24. [2] Naoko Tsujimoto et al. Experimental Study on Laminated Timber Beam with a Round Hole art1 Outline of Test. Summaries of Technical apers of Annual Meeting, C-1,Structures.III, AIJ, 26:19-2 [3] Kazumi Hijikata et al. Experimental Study on Laminated Timber Beam with a Round Hole art2 Test Results and Failure Conditions. Summaries of Technical apers of Annual Meeting, C- 1,Structures.III, AIJ, 26:21-22 [4] Naoko Tsujimoto et al. Experimental Study on Laminated Timber Beam with a Round Hole art3 Analysis evaluation of 3-demensional finite element method. Summaries of Technical apers of Annual Meeting, C-1,Structures.III, AIJ, 27:17-18 [5] Masahiko Karube et al. The Strength of GLT beams with Round Utility Holes. Summaries of Technical apers of Annual Meeting, C-1,Structures.III, AIJ, 2: [6] Masahiro Noguche et al. A Strength Calculation Method of The Timber With a Circular Hole. J. Struct. Constr. Eng., AIJ, Vol.74 No.64,: , 29 [7] Kohei Komatsu et al. Reinforcement of Glulam Beam with a lumbing Hole by Nailed-on- lywoods Gusset Method. roceedings of IWAS 25, Japan, 25: [8] Kazumi Hijikata et al. Experimental Study on Laminated Timber Beam with a Round Hole art4 Effect of Reinforcement in Bending Test. Summaries of Technical apers of Annual Meeting, C-1,Structures.III, AIJ, 27:19-2 [9] Kazumi Hijikata et al. Experimental Study on Laminated Timber Beam with a Round Hole art5 Effect of Reinforcement in Shering Test. Summaries of Technical apers of Annual Meeting, C- 1,Structures.III, AIJ, 28: [1] Architectural Institute of Japan, Standard for Structural Design of Timber Structures (in Japanese),26:42-45 [11] MARUZEN, WOOD INDUSTRY HANDBOOK (in Japanese), 24:

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