# Compressive Strength Properties Perpendicular to the Grain of Hollow Glue-Laminated Timber Elements

^{*}

## Abstract

**:**

_{c,90}equal to 1.0. For load actions at the edge and the middle of the element, k

_{c,90}factors were obtained with a value closer to those obtained for full cross-section, which indicates the same phenomenology, regardless of cross-sectional weakening. At the same time, the factors in the stronger axis are lower by about 10%, and in the weaker axis by about 30% compared to those prescribed by the Eurocode. Experimental research was confirmed by FEM analysis. Comparative finite element analysis was performed in order to provide recommendations for future research and, consequently, to determine the optimal cross-section form of the hollow GL timber element. By removing the holes in the central part of the cross-section, the stress is reduced. The distance of the holes from the edges defines the local cracking. Finally, if the holes are present only in the central part of the element, the behavior of the element is more favorable.

## 1. Introduction

#### 1.1. State-of-the-Art

_{ef}, characteristic compressive strength perpendicular to the grain f

_{c,90, k,}and the factor k

_{c,90}, which considers the load configuration, the possibility of splitting, and the degree of compressive deformation [3]. The effective contact area A

_{ef}should be determined considering an effective contact length parallel to the grain, where the actual contact length, l, at each side is increased by 30 mm.

_{c,90}should be taken as 1.0, unless the conditions in the following paragraphs apply. In these cases, the higher value of k

_{c,90}specified may be taken, with a limiting value of 1.75. For members on continuous supports, provided that l

_{1}≥ 2 h (see Figure 1a), the value of k

_{c,90}should be taken as 1.25 for solid softwood timber and 1.5 for glued laminated softwood timber, where h is the depth of the member and l is the contact length. For members on discrete supports, provided that l

_{1}≥ 2 h (see Figure 1b) the value of k

_{c,90}should be assumed to be 1.5 for solid softwood timber and 1.75 for glued laminated softwood timber if l ≤ 400 mm. Leijten et al. [4] pointed out the inconsistencies of the mentioned discontinuities and determined the coefficient k

_{c,90}based on empirical results. Finally, they proposed modified expressions for k

_{c,90,}using the physical model of Van der Put [7].

_{c,90, k}, (CSPG) plays an important role and frequently governs the structural design. Obviously, CSPG depends on the type of wood and varies in radial and tangential directions [8,9,10]. Hoffmeyer et al. [11] concluded that the combined role of tensile and shear stresses perpendicular to the grain occurs in compression specimens of solid as well as glued laminated wood, where, at the design level, the 5% characteristic strength is not significantly different. Gehri [12] presented a study to verify the relationship between compressive strength and wood density, which is particularly evident when comparing healthy wood to rotten or insect-deteriorated wood [13]. Although wood is recognized as a building material due to highly technical-material characteristics in the direction parallel to the grains, it is necessary to note that elongated cells of the wood are stiffer and stronger when loaded along the axis of the cell rather than when loaded across it [14,15]. So, the modulus of elasticity in the direction perpendicular to the grain decreases by 30 times and strength by eight times for softwood and three times for hardwood [16].

_{c,90, k}value, the European (CEN) testing standard EN408 prescribes a method in which a block of timber is loaded in uniform compression over its entire surface. On the other hand, the American (ASTM) test standard D143 is based on the approach in which the test piece is a timber block, and the load is applied in the middle through a steel plate, where the test is primarily intended to simulate the behavior of a wood joint resting on a wall or foundation and does not intend to determine a physically correct perpendicular to grain strength [4]. In the absence of any physical model to modify the results and to account for situations deviating from the test set-up, modification factors were established and reported by Kunesh [17]. Madsen et al. [18] also took an interest in the relationship between deformation and compressive strength and recognized shortcomings of the ASTM method. Furthermore, Leijten [19] pointed out that in the Scandinavian countries, the standard characteristic bearing strength for a spruce wood element has double or even triple value than the stress at the proportional limit determined by tests, making values reported in the European standards questionable and very conservative. Further investigation is presented in [20]. Considering the above, the problem of a unified approach to determining the standard strength is obvious.

_{c,90, max,}and 0.4 F

_{c,90, max}as intersections with the curve, needs to be defined. Finally, the ultimate load capacity, F

_{c,90, max}is defined as the intersection of curve and line (2), which is offset by 1% of the standardized specimen depth h and parallel to the line (1). The force corresponding to the upper limit of the linear segment of the load/displacement (F-∆h) curve is known as the proportional limit F

_{c,90, prop}[29].

#### 1.2. Objectives

_{c,90}, taking into account the load configuration, the possibility of splitting, and the degree of compressive deformation, depending on support and load type, several other test set-ups involving loading of the specimens’ proportional rectangular surface only at the edge parts, as well as only at central parts, was investigated.

## 2. Materials and Methods

#### 2.1. Test Setup

_{min}of 100 mm, and the surface that is fully loaded b × l of 25,000 mm

^{2}is defined, to achieve a volume of 0.01 m

^{3}for the tested specimens. In addition to the specimens prescribed by the standard, additional specimens were defined and loaded on the edge and in the middle part of the element, in order to determine the distribution of force along the specimens.

_{0}(approximately 0.6 h), is located centrally in the specimen height and no closer than b/3 of the loaded ends of the specimen, as shown in Figure 3.

_{c,90, max, est}or F

_{c,90, max}was reached within (300 ± 120) s. The test was stopped after reaching the compressive strength of the timber elements. This rate was determined from the results of preliminary tests.

_{c,90}is determined from the equation:

_{c,90}= F

_{c,90,max}/bl,

- f
_{c,90}—compression strength (N/mm^{2}) - F
_{c,90,max}—maximal compression load parallel to the grain (N) - b—width (mm)
- l—length (mm)

#### 2.2. Type and Number of Samples

#### 2.3. FEM Description

^{2}. The loading scheme and boundary conditions for FEM can be seen in Figure 8.

## 3. Results

#### 3.1. Experimental Work

#### 3.2. FEM Analysis

_{c,90, k}for MP-209 mm was determined to be 4.07 MPa (in the upper corner), and for ME-209 mm, f

_{c,90,k}= 1.83 MPa. Those stresses initially appeared in the upper corner and on the perimeter of the holes in the case of hollow GL specimens, which was also confirmed in the FE mode (Figure 11). By evaluating the results of the FEM analysis, the initial σ

_{z}stress for MP-209 mm was 4.067 MPa (Figure 11a) for the value of failure load 106.7 kN (Table 4) and 1.869 MPa (Figure 11b) for MP-209 mm specimen and the value of failure load 47.7 kN (Table 4). Furthermore, in Figure 10a,d, the failure mode and primary cracks are shown. This was also confirmed by the FEM model (check the stress trajectories in Figure 11).

## 4. Discussion

#### 4.1. Experimental Work

_{c, 90}factors are given in Table 3.

#### 4.2. FEM Analysis

^{2}. When the first row of cavities had been removed (Figure 12b), it minimally affected the stress distribution; however, although at the bottom of the sample the stress was lower, the maximum stress was similar to the first one (3.155 N/mm

^{2}). By removing the holes on the next lamella (Figure 12c), the stress distribution was more favorable both locally and globally, especially at the bottom part of the specimen.

^{2}, while the stress in the second model was 3.301 N/mm

^{2}.

^{2}) and, the stress distribution is more favorable because there are no stress concentrations in the central part. When the holes in each subsequent lamella are omitted (Figure 14b,c), the global stress distribution was more favorable, but due to the smaller number of holes, slightly higher stress occurred at the edges of the ellipse, caused by the flow of the principal stresses.

## 5. Conclusions

_{c,90}equal to 1.0. For load action at the edge of the element, the factor k

_{c,90}= 1.24 was obtained, as lower by 20% than the value prescribed in Eurocode 5 [3] of 1.55. For the load action at the middle of the element, the factor k

_{c,90}= 1.45 was obtained, which is lower by 12% than the value prescribed in [3] of 1.66. The CSPG of softwood, for a hollowed laminated cross-section loaded in the direction of the stronger axis, decreases by about 55% compared to the full cross-section, with a value of 1.83 MPa, and for hardwood, it decreases by about 50%, to a value of 6.58 MPa, with the coefficient k

_{c,90}equal to 1.0. For load actions at the edge and the middle of the element, k

_{c,90}factors were obtained with a value closer to those obtained for full cross-section, which indicates the same phenomenology, regardless of cross-sectional weakening.

_{c,90}equal to 1.0. For load action at the edge of the element, the factor k

_{c,90}= 1.42 was obtained, as lower for 30% than the value prescribed in [3] of 2.07. For load action at the middle of the element, the factor k

_{c,90}= 1.46 was obtained, which is lower by 35% than the value prescribed in [3] of 2.21. The CSPG of softwood, for a hollowed laminated cross-section loaded in the direction of the weaker axis, decreases by about 55% compared to the full cross-section, with a value of 1.90 MPa, and for hardwood, it decreases by about 55%, to a value of 6.75 MPa, with the coefficient k

_{c,90}equal to 1.0. It can be concluded that the properties are similar to the situation when the cross-section is loaded in the direction of the stronger axis.

_{c,90}factors are approximately similar for hollowed and full cross-sections. However, in order to better understand it, it is necessary to study the stress distribution and force path in more detail using the DIC measurement method. As mentioned in the introduction, the factor k

_{c,90}is difficult to determine unequivocally for different boundary conditions. This research presented that the values given in European standards [3] still cannot be applied uniformly. So, further research is necessary for the correction of factors regarding the type of wood, type of section, etc.

## 6. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Individual lamellae of the element with elliptical holes and the cross-section of the assembled hollow glued laminated timber element.

**Figure 6.**Positioning and loading of specimens, considering the axis direction and boundary conditions: (

**a**) Specimen loaded over the entire surface in the strong-axis direction (four groups); (

**b**) specimen loaded over the entire surface in the weak-axis direction (four groups); (

**c**) specimen loaded on the edge in the strong-axis direction (three groups); (

**d**) specimen loaded on the edge in the weak-axis direction (three groups); (

**e**) specimen loaded in the middle area in the strong-axis direction (three groups); (

**f**) specimen loaded in the middle area in the weak-axis direction (three groups).

**Figure 9.**Characteristic load-displacement curves for each group of specimens: (

**a**) Standardized specimens; (

**b**) specimens loaded on edge of the element; (

**c**) specimens loaded in the middle of the element.

**Figure 10.**Failure modes characteristic for group of specimens: (

**a**) ME-209 mm; (

**b**) TE-209 mm; (

**c**) ME-400 mm; (

**d**) MP-209 mm; (

**e**) TP-209 mm; (

**f**) MP-400 mm.

**Figure 12.**Results of FEM analysis—stress: (

**a**) Completely perforated timber element; (

**b**) the first lamella without cavities; (

**c**) the second lamella without cavities.

**Figure 13.**Results of FEM analysis—stress: (

**a**) Each subsequent lamella without cavities; (

**b**) alternating arrangement of holes, type 1; (

**c**) alternating arrangement of holes, type 2.

**Figure 14.**Results of FEM analysis—stress: (

**a**) The central part without cavities; (

**b**) the central part and each subsequent lamella without cavities; (

**c**) the outer part and each subsequent lamella without holes.

**Figure 15.**Results of FEM analysis—stress: (

**a**) The central part with cavities; (

**b**) the central part and each subsequent lamella with cavities; (

**c**) normal—without cavities.

Width (mm) | Length (mm) | Height (mm) | Weight (g) | Density (kg/m^{3}) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Avg. | CoV. (%) | St. Dev. | Avg. | CoV. (%) | St. Dev. | Avg. | CoV. (%) | St. Dev. | Avg. | CoV (%) | St. Dev. | Avg. | CoV. (%) | St. Dev. | |

SoftwoodM1–M12 | 119.3 | 0.19 | 0.22 | 120.1 | 0.30 | 0.36 | 119.0 | 0.22 | 0.27 | 657.9 | 1.52 | 9.99 | 385.7 | 1.42 | 5.47 |

HardwoodT1–T12 | 119.3 | 0.21 | 0.25 | 119.9 | 0.35 | 0.42 | 118.5 | 0.89 | 1.06 | 1337.4 | 1.35 | 18.08 | 789.4 | 1.60 | 12.60 |

Moduli | Symbol | Value (N/mm^{2}) |
---|---|---|

Modulus of elasticity parallel | E_{0, mean} | 11,500 |

Modulus of elasticity perpendicular | E_{90, mean} | 300 |

Shear modulus | G_{mean} | 650 |

Modulus of elasticity parallel | E_{0,05} | 9600 |

Modulus of elasticity perpendicular | E_{90,05} | 250 |

Shear modulus | G_{05} | 540 |

**Table 3.**List of CSPGs for different load modes and boundary conditions with associated k

_{c,90}factors.

Type of Cross-Section | MP | ME | TE | TP | ||||
---|---|---|---|---|---|---|---|---|

Specimen Length (mm) | f_{c,90, k}(MPa) | k_{c, 90} | f_{c,90, k}(MPa) | k_{c, 90} | f_{c,90, k}(MPa) | k_{c, 90} | f_{c,90, k}(MPa) | k_{c, 90} |

105 | 4.17 | 1.00 | 1.90 | 1.00 | 6.75 | 1.00 | 15.08 | 1.00 |

209 | 4.07 | 1.00 | 1.83 | 1.00 | 6.58 | 1.00 | 12.96 | 1.00 |

400 | 5.90 | 1.42 | 2.67 | 1.40 | 9.59 | 1.42 | / | / |

440 | 5.03 | 1.24 | 5.90 | 1.45 | 8.16 | 1.24 | / | / |

520 | 6.08 | 1.46 | 2.95 | 1.55 | 10.42 | 1.54 | / | / |

640 | 5.90 | 1.45 | 2.78 | 1.51 | 9.72 | 1.48 | / | / |

Specimen Length (mm) | Type of Cross-Section | Average Failure Force (kN) | CoV. (%) | St. Dev. | F_{max}-Ratioin Relation to ME | F_{max}-Ratioin Relation to TE |
---|---|---|---|---|---|---|

105 | ME | 45.2 | 9.07 | 4.1 | 1.00 | 0.54 |

MP | 118.4 | 7.09 | 8.4 | 2.62 | 1.41 | |

TE | 185.2 | 8.26 | 15.3 | 4.10 | 2.21 | |

TP | 622.19 | 6.22 | 38.7 | 13.77 | 7.43 | |

209 | ME | 47.7 | 5.03 | 2.4 | 1.00 | 0.54 |

MP | 106.7 | 9.09 | 9.7 | 2.24 | 1.22 | |

TE | 184.1 | 1.90 | 3.5 | 3.86 | 2.10 | |

TP | 453.80 | 2.29 | 10.4 | 9.51 | 5.17 | |

400 | ME | 87.3 | 9.51 | 8.3 | 1.00 | 0.31 |

MP | 219.3 | 8.76 | 19.2 | 2.51 | 0.78 | |

TE | 320.2 | 6.09 | 19.5 | 3.67 | 1.15 | |

TP | / | / | / | / | / | |

440 | ME | 75.3 | 1.73 | 1.3 | 1.00 | 0.39 |

MP | 157.4 | 8.64 | 13.6 | 2.09 | 0.82 | |

TE | 255.3 | 10.77 | 27.5 | 3.39 | 1.33 | |

TP | / | / | / | / | / | |

520 | ME | 126.5 | 5.06 | 6.4 | 1.00 | 0.24 |

MP | 282.4 | 5.24 | 14.8 | 2.23 | 0.54 | |

TE | 413.7 | 3.50 | 14.5 | 3.27 | 0.79 | |

TP | / | / | / | / | / | |

640 | ME | 106.9 | 8.70 | 9.3 | 1.00 | 0.31 |

MP | 196.0 | 4.23 | 8.3 | 1.83 | 0.57 | |

TE | 323.8 | 6.61 | 21.4 | 3.03 | 0.94 | |

TP | / | / | / | / | / |

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**MDPI and ACS Style**

Perković, N.; Barbalić, J.; Rajčić, V.; Duvnjak, I.
Compressive Strength Properties Perpendicular to the Grain of Hollow Glue-Laminated Timber Elements. *Polymers* **2022**, *14*, 3403.
https://doi.org/10.3390/polym14163403

**AMA Style**

Perković N, Barbalić J, Rajčić V, Duvnjak I.
Compressive Strength Properties Perpendicular to the Grain of Hollow Glue-Laminated Timber Elements. *Polymers*. 2022; 14(16):3403.
https://doi.org/10.3390/polym14163403

**Chicago/Turabian Style**

Perković, Nikola, Jure Barbalić, Vlatka Rajčić, and Ivan Duvnjak.
2022. "Compressive Strength Properties Perpendicular to the Grain of Hollow Glue-Laminated Timber Elements" *Polymers* 14, no. 16: 3403.
https://doi.org/10.3390/polym14163403