Full-culm bamboo has been used for millennia in construction. Specific connections are normally required to suit its unique morphology and nonuniform structure. Presently, the use of full-culm bamboo is limited in the construction industry as a result of a lack of information and test standards about the use and evaluation of full-culm connections. This study aims to further explore this area by investigating the failure modes in bamboo bolt connections in uniaxial tension by considering fiber direction in finite element analysis. Three types of bolt configurations of varying permutations, namely, single, dual, and orthogonal, were investigated. An orthotropic material was used as a constitutive model in finite element formulation to capture the inhomogeneity prevailing in bamboo culm. From the strain-field analysis of a hollow-inhomogeneous model representing bamboo, shear-out failure was dominant, as a localized area equivalent to the bolt diameter was affected due to high material orthotropy with high axial strength but weak radial and tangential strength. Bearing failure is assumed to precede shear-out failure at the bolt–bamboo contact interface, as the embedding strength was affected by localized strain concentration. The strain distribution in various bolt arrangements was found to vary between bolted connections of inhomogeneous-hollow geometry of bamboo and the ones of inhomogeneous-solid geometry representing timber. The observation in this study highlights the need for alternative design criteria to specifically assess the damage mechanism in bamboo connections.Abstract
As one of the oldest construction materials, bamboo has been widely used as a reliable structural material in rural houses and bridges in several Asian and Latin American countries in the past millennia. It has attracted much attention in recent years because of its distinctive sustainability attributes and excellent mechanical characteristics. Unlike timber, bamboo has a fast growth rate, and those with optimum strength can be harvested after reaching maturity in 3 to 4 years (Liese 1987). In terms of mechanical strength, it outperforms timber based on its high strength-to-weight ratio (Ashby et al. 1995). Even so, its unlimited use in the construction industry is hindered because of natural variation in its morphology and by a lack of standards and building codes, hence restricting its use to basic structures (Gatoo et al. 2014). One area with a notable shortfall of applicable standards is for bamboo connections. To maximize the use of bamboo in building construction, specific connection types are normally required as a result of its inherent structural nonuniformity and unique morphology comprised of a round, hollow, and tapered structure (Correal 2016).
Several types of bamboo connections, ranging from traditional to modern types, have been developed with varying load-carrying capacity. Their efficacy rests on the types of fasteners used and the orientation of joined members (Correal 2016, Hong et al. 2019). Janssen (2000) has proposed three criteria for the classification of joints: (1) joints involving contact between full cross sections or connected via joining elements linked to cross sections, (2) collecting forces within the hollow section or from the outside of the culm, and (3) the alignment of the joining element with respect to fiber direction. In addition, the strength and efficacy of the joint is specifically affected by the type of connector, the end shape of the bamboo culms, and the internode filling material (Janssen 2000). The dowel connection, which uses a steel bolt as a connector, is one of the most widely used connections in bamboo given its simplicity and reliability. The load capacity of the dowel-type connection is influenced by several factors, namely, bolt diameter, bolt strength, bamboo diameter, direction of loading, and moisture content, among others (Li et al. 2020, Sotayo et al. 2020, Wang and Yang 2020). It has been found that the direction of loading parallel to main and side bamboo culms yielded the best results in comparison to perpendicular loading members. In addition, the compressive strength parallel to grain was found to decrease with increasing moisture content as observed in other cellulose-reinforced composite material similar to bamboo (Yang et al. 2020). In general, bamboo tends to behave nonlinearly in conditions of excessive humidity above 60 percent and linearly in conditions of humidity below 40 percent (Askarinejad et al. 2015). Additionally, the variation in culm morphology, such as tapered geometry and fiber density, which increases with height, also influences the strength of the culm connection (Correal 2016).
Failure of bamboo connections can occur in many ways, namely, due to material failure as a result of its inherent inhomogeneity or failure in the joining element. Full-culm bamboo in the external loading mode exhibits a complex deformation behavior as a result of its high anisotropy (Kappel et al. 2004, Spatz and Niklas 2013, Askarinejad et al. 2015, Deng et al. 2016, Huang et al. 2017, Trujillo et al. 2017, Zhang et al. 2017, Gauss et al. 2019). In previous studies, four types of prevalent modes of failure have been reported in timber and laminated wood and bamboo products involving bolted connections (Hong et al. 2020). These are bearing, net tension, shear-out, and cleavage (Coelho and Mottram 2015). In bearing failure, the contact area at the hole edge is affected and is expected to occur in a high width-to-hole diameter component, while in net-tension failure, sudden cracks orthogonal to the direction of loading propagate due to a small cross-sectional area. Shear-out failure occurs in bolt arrangements with short end distances and is characterized by shear stresses that occur along the shear-out planes, while cleavage failure occurs as the result of a combination of the latter and net-tension failure. Previous studies on failure analysis of bolted connections in axial tension in full-culm and laminated bamboo have resulted in longitudinal shear plug formation (Reynolds et al. 2016, Ramful 2018). However, as stated by Reynolds et al. (2016), conventional design rules and practices used to prevent split in timber products are not applicable to bamboo, as it exhibits different failure modes. The progressive deformation consisting of localized buckling of fibers and crushing of matrix in bearing failure is characterized by embedding strength (Olmedo and Santiuste 2012, Coelho and Mottram 2015, Hong et al. 2020). In bamboo laminates, the embedding strength parallel to grain exceeds that of perpendicular to grain (Sawata and Yasumura 2002, Eratodi et al. 2012). In addition, the embedding strength in bamboo laminates perpendicular to grain was found to further decrease with increasing bolt diameter (Zhou et al. 2018).
From previous studies, connections in bamboo laminates were found to be affected by several influential factors, namely, diameter of connectors, laminate thickness, direction of loading, and embedding strength (Cui et al. 2020, Hu and Zhang 2020). Even though the weaknesses of full-culm bamboo is well described in literature, the outcome due to its inhomogeneous material characteristics and unique geometry on mechanical performance of connections is limited. The lack of information on the full-culm connection is demonstrated by a lack of standards and building codes in this area, restricting its use in complex and modern construction. To overcome the material constraints in bamboo culms, the finite element method (FEM) has been widely used to investigate its material limitation and failure modes (Askarinejad et al. 2015, Keogh et al. 2015, Paraskeva et al. 2017). This study aims to address this gap by investigating the failure modes of bamboo bolt connections in uniaxial tension by considering fiber direction in FEM.
Finite Element Analysis of the Bamboo Connection
In this section, the bamboo–bolt connection was simulated in implicit mode in uniaxial tension in the commercial FEM software LS-DYNA (version 4.3; Livermore Software Technology, USA). The results of the hollow-inhomogeneous model of bamboo was compared with the solid-inhomogeneous model representing timber and with other models of homogeneous material characteristics.
Material properties and models
The homogeneous material in this study was based on a simple isotropic model assigned with engineering constants of an elastic material, as displayed in Table 1. From previous experimental investigation (Ramful et al. 2020), an average modulus of elasticity, E, of 15 GPa was obtained, while the Poisson ratio, ν, was determined from past literature data as 0.3 (Keogh et al. 2015). The engineering constants of an orthotropic material were used to simulate the inhomogeneous nature of bamboo, as displayed in Table 2. These values are estimates based on the optimized transverse isotropy of bamboo, which was assumed to have a longitudinal-to-transverse bending stiffness ratio of 100:4.5 (Ramful and Sakuma 2020). The bolt in this study was assumed as a rigid section such that it will not undergo any deformation. The study focused mainly on the damage mechanisms within bamboo culm material. In the rigid material setting, it was assigned a Young's modulus value much greater than bamboo material. The rigid material setting was selected in order to apply constraints in the global direction. The displacement of the bolt was thus restricted only to the axial direction to simulate the connection in the uniaxial tension mode. The material density was taken as 700 kg/m3 (Trujillo and Lopez 2016).
Geometrical modeling and boundary conditions
Three types of bolt configurations of varying permutation, namely, single, dual, and orthogonal, were selected in this study, as shown in Figure 1. One full solid cylindrical internode section was considered in this study, and the physical model was constructed based on morphological data of Madake bamboo (Phyllostachys bambusoides). The outer diameter, wall thickness, and intermodal length were taken as 100, 12, and 450 mm, respectively, for an internode count of 18 (Ghavami 2016). The bolt diameter, ϕB, was 9 mm with a clearance of 0.5 mm with the hole wall section. A displacement of 1 mm/min was applied to the rigid bolt by prescribed motion, as illustrated in Figure 1d. At the wall end, movement was restricted in the x, y, and z directions.
Citation: Forest Products Journal 71, 1; 10.13073/FPJ-D-20-00066
According to the Eurocode 5 standard, the embedding strength is calculated from the bolt diameter and the density as follows:
where
and feα is the embedding strength in MPa, k90 is the material constant when loaded perpendicular to grain, d is the bolt diameter in mm, ρ is the density in kg/m3, and α is the loading angle to grain direction (EN 1995-1-1 2004). In this study, the parameters d, ρ, and α were kept constant to minimize variability in strain field analysis in order to discern principal changes in terms of damage mechanisms and embedding strength due to the effect of geometry and the material model.
FE mesh
The 3D model was designed and meshed on FEMAP (version 12.0.1a; Siemens Digital Industries Software, USA), a finite element model–building software, and tetrahedral mesh solid was applied, with finer mesh at the bolt-bamboo connection, as shown in Figure 2a.
Citation: Forest Products Journal 71, 1; 10.13073/FPJ-D-20-00066
Results and Discussion
Strain field analysis
The strain field results of various geometry-material models of three-bolt configurations in uniaxial tension are displayed in Figures 3 through 5. The observed variation in the strain field occurred as a result of change in material property, geometry, and bolt configurations. In this analysis, the applied displacement was resisted mainly by embedding strength in the surrounding material rather than shear in the connector, as the rigid bolt was considered.
Citation: Forest Products Journal 71, 1; 10.13073/FPJ-D-20-00066
Citation: Forest Products Journal 71, 1; 10.13073/FPJ-D-20-00066
Citation: Forest Products Journal 71, 1; 10.13073/FPJ-D-20-00066
Damage mechanisms
The main failure modes in the four types of geometry-material models of single-bolted connections due to axial tension are depicted in Figure 6. These were shear-out failure and net-tension failure. These failure modes observed in the four types of geometry-material models were recurrent in all three types of bolt configuration regardless of bolt permutations. In each failure mode, the effect due to homogeneous and inhomogeneous material characteristics can be easily distinguished from the side-by-side comparison. The effect of short-end distance on shear-out failure in this study was negligible, as the ratio of end distance to diameter, e/ϕB, was greater than 4 (Coelho and Mottram 2015). Shear-out failure, which occurred mainly in solid-inhomogeneous and hollow-inhomogeneous models, affected a localized area equivalent to the bolt diameter, as shown in Figures 6a and 6c. This phenomenon, which occurred in inhomogeneous material, can be explained by the high orthotropicity resulting in high strength axially but weak strength radially and tangentially.
Citation: Forest Products Journal 71, 1; 10.13073/FPJ-D-20-00066
In addition to shear-out failure in solid-inhomogeneous and hollow-inhomogeneous models, bearing failure is anticipated to occur at the bolt-member contact interface due to the effect of embedding strength. This is demonstrated by the region of strain concentration in the fringe plots of Figures 3b, 3d, 4b, 4d, 5b, and 5d. The progressive deformation associated with bearing failure due to the localized buckling of fibers and the crushing of matrix increases the deformation capacity of the connection (Olmedo and Santiuste 2012). This mode of failure is assumed to provide damage-tolerant bolted connections rather than brittle shear-out or net-tension failure modes (Coelho and Mottram 2015).
Net-tension failure occurred mainly in solid-homogeneous and hollow-homogeneous models, whereby the axial tensile forces exerted by the bolt uniformly affected the whole cross-sectional area, as shown in Figures 6b and 6d. Net-tension failure, which affected mainly homogeneous material, can be explained by the uniform load distribution across its cross section due to material uniformity. In net-tension failure, instantaneous cracks propagated in a direction transverse to that of axial loading and is assumed to be influenced by the cross-sectional area of the main member. From Figures 4a, 4c, 5a, and 5c, net-tension failure was found to be dominant in multirow bolted connections. This observation corresponds to previous reports that attributed this failure to high stress concentration originating from specific rows in successive arrangements (Mottram and Turvey 1998).
Analysis of strain distribution
The deformation due to bolt arrangements in various geometry-material models is quantitatively discussed by analyzing the maximum principal strain distribution in the periphery of the bolt-member contact interface. Figure 7 shows the distribution of maximum principal strain in terms of azimuthal angle, θ, along the transverse sliced sections A and B located at a distance of 25 mm from the bolt axis, as indicated in Figure 1b. The azimuthal angle is interpreted clockwise from the radial axis.
Citation: Forest Products Journal 71, 1; 10.13073/FPJ-D-20-00066
The distinct peaks at azimuthal angles 0°, 180°, 90°, and 270° (Figs. 7a, 7c–7f) in solid-inhomogeneous and hollow-inhomogeneous models demonstrate a narrowed region of strain concentration that is in line with the previous observation made about shear-out failure. This localized increase is assumed to further affect the embedding strength, leading to bearing failure. Furthermore, in dual configurations involving same geometry-material models, the strain distribution in the periphery of the first row was altered (Fig. 7c). The compressive effect induced by the second row restrained the full tensile effect on the first row, hence the reduction in strain as observed by the difference between Figures 7c and 7a. Conversely, the constant strain distribution around azimuthal angle θ in solid-homogeneous and hollow-homogeneous models (Figs. 7a, 7c–7f) confirmed the net-tension failure as previously discussed.
The normalized values of the first row, based on corresponding maximum principal strain (6.33 × 10−3) obtained from the solid-inhomogeneous model in the single-bolt configuration, are shown in Table 3. The maximum principal strain distribution in inhomogeneous material models noticeably exceeded homogeneous ones and was specifically greater in solid as compared to hollow geometries. This difference between bolted connections of the inhomogeneous-hollow model of bamboo and the inhomogeneous-solid model representing timber is further pronounced in the second-row arrangement (Figs. 7d and 7f).
In a previous study, the failure observed in bamboo was reported to distinctly differ from solid wood structure with a higher ratio of wall thickness to radius. According to Huang et al. (2017), tubular plant materials inherit a high strength-to-weight ratio and low weight per unit length, enabling them to better resist deformation in various modes of loading in comparison to solid cylindrical materials of the same weight.
Future recommendation
As per the normalized embedding strength results in Table 4 according to the Eurocode 5 standard, the embedding strength of the material increases with density and decreases with increasing bolt diameter as well as when loaded perpendicular to the grain direction. Eurocode 5 uses a standard expression to estimate the embedment strength parallel to grain direction in various wood-related materials based simply on density and bolt diameter (EN 1995-1-1 2004).
However, due to the lack of provision for bamboo material in common standards such as Eurocode 5, the embedment strength due to varying bolt diameter and changes in loading with respect to grain direction has to be further researched for precise results. This will add to the establishment of specific standards for bamboo connections.
Conclusion
In this study, the damage mechanisms of three types of bolt–bamboo connections were investigated in uniaxial tension by considering fiber direction. The following conclusions were made from the strain-field analysis of the hollow-inhomogeneous model representing bamboo:
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Shear-out failure was dominant and affected a localized area equivalent to bolt diameter due to high material orthotropy, which provided high axial strength but weak radial and tangential strength.
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In addition to shear-out failure, bearing failure was anticipated to occur at the bolt–bamboo contact interface as the embedding strength was affected by localized strain concentration. A high width-to-hole diameter in bamboo is likely to further accentuate bearing failure.
This study provided useful insights by highlighting the damage mechanisms that prevailed in bolted connections of inhomogeneous-hollow geometry of bamboo as compared to the ones of inhomogeneous-solid geometry representing timber.
The strain distribution observed in these two unique geometry-material models varied according to bolt arrangements, underlining the need of alternative design criteria to specifically assess the damage mechanism in bamboo connections.
Further research in terms of numerical investigation supported by experimental results is required to establish relevant standards in bamboo building construction, as this study was limited to specific geometry and a unique mode of loading.
Schematic illustration of bolted connections evaluated: (a) single configuration, (b) dual configuration, (c) orthogonal configuration; and (d) boundary condition in axial tension mode setup.
Tetrahedral mesh solid of (a) bamboo model in single-bolt configuration (no. of elements: 93,929, no. of nodes: 142,649); (b) bolt model (no. of elements: 64,385, no. of nodes: 11,624).
Fringe plots of maximum principal strain of (a) solid-homogeneous, (b) solid-inhomogeneous, (c) hollow-homogeneous, and (d) hollow-inhomogeneous models in single-bolt configuration.
Fringe plots of maximum principal strain of (a) solid-homogeneous, (b) solid-inhomogeneous, (c) hollow-homogeneous, and (d) hollow-inhomogeneous models in dual-bolt configuration.
Fringe plots of maximum principal strain of (a) solid-homogeneous, (b) solid-inhomogeneous, (c) hollow-homogeneous, and (d) hollow-inhomogeneous models in orthogonal bolt configuration.
Schematic illustration of damage mechanisms in (a) solid-inhomogeneous, (b) solid homogeneous, (c) hollow-inhomogeneous, and (d) hollow-homogeneous models in single-bolt configuration.
Distribution of maximum principal strain in terms of azimuthal angle, θ, along the transverse sliced sections A and B in three-bolt configurations corresponding to (a), (c), and (e) first row, and (b), (d), and (f), second row.
Contributor Notes
The author is at Kyoto Institute of Technology, Kyoto, Japan (r.ramful@uom.ac.mu [corresponding author]). This paper was received for publication in October 2020. Article no. 20-00066.