# Optimizing Lumber Densification for Mitigating Rolling Shear Failure in Cross-Laminated Timber (CLT)

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{3}with a coefficient of variation (COV) of 6%.

#### 2.2. Methodology for Densification

#### 2.3. Bending Test Procedure

_{max}) and shear stresses (τ

_{max}) were determined by Equations (1) and (2), respectively. Additionally, the apparent modulus of elasticity (E

_{app}) was computed using Equation (3). To compute E

_{app}, the deflection (Δ) was measured in a linear region utilizing an LVDT positioned at the bottom center of the CLT span.

_{max}is the maximum bending load (N) at failure, L is the span length (mm), b is the width of the panel (mm), h is the thickness of the beam (mm), and Δ is the mid-span deflection at the instance of bending load P. To compute the apparent modulus of elasticity (E

_{app}) given in Equation (3), the slope of the load–defection curve in the linear region was used as P/Δ.

#### 2.4. Required Densification to Meet MRSS

_{max}) exceeds the tensile bending strength (i.e., MOR), likewise, shear strength should be ample to withstand the maximum developed shear stress. The MOR at tensile failure for both single lumber and CLT constructed from the same species and grade of lumber should be identical under equivalent loading conditions. During rolling shear failure, however, the maximum shear stress (τ

_{max}) exceeds the shear strength. Hence, the minimum required shear strength (MRSS) of the mid-layer must be higher than the maximum shear stress developed (τ

_{max}) in CLT at the time of tensile failure to avoid rolling shear failure. Therefore, using Equations (1) and (2), the minimum required shear strength of the transverse mid-layer to shift rolling shear failure to tensile failure in CLT can be computed in terms of bending strength as given in Equation (4).

## 3. Results

#### 3.1. Shear Strength Assessment of Non-Densified Lumber

#### 3.2. Effect of Densification on Failure Mode and Rolling Shear Strength

^{3}with a COV of 5% after densification. The average dimension of CLT specimens with a densified mid-layer (D) was as follows: a span length of 838 mm, a width of 139 mm, and a total thickness of 104 mm. The thickness of the non-densified and densified specimens was not much different. The densification of the mid-layer lumber reduced the thickness to 31.75 mm; however, during fabrication the total depth of CLT was comparable to the non-densified sample. Similarly, for the densified samples, the short-span bending test results have been presented in Table 2 with the failure mechanism for each sample. The bending properties, i.e., MOR, τ

_{max}, and E

_{app}, have been calculated using Equations (1), (2) and (3), respectively, and tabulated in Table 2.

_{max}) corresponds to the bending strength (MOR) of the sample. This observed bending strength value averaged 47.45 MPa, closely aligning with the initial value reported by Pradhan et al. [36]. This observation underscores the fact that the bending strength of CLT is predominantly governed by the bending strength of the bottom layer. Moreover, it was observed that the mid-layer-densified specimens failed in tensile strength at the bottom longitudinal layer, resulting in the development of an average maximum shear stress of 4.45 MPa, which was 48% higher than that of non-densified lumber. Despite both cases having similar moments of inertia due to their comparable thickness, it is noteworthy that the apparent modulus of elasticity for the mid-layer-densified specimens was 10% higher than that of the non-densified specimens.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Kawaai, Y.; Takanashi, R.; Ishihara, W.; Ohashi, Y.; Sawata, K.; Sasaki, T. Out-of-plane shear strength of cross-laminated timber made of Japanese Larch (Larix kaempferi) with various layups and spans. J. Wood Sci.
**2023**, 69, 33. [Google Scholar] [CrossRef] - Brandner, R.; Flatscher, G.; Ringhofer, A.; Schickhofer, G.; Thiel, A. Cross laminated timber (CLT): Overview and development. Eur. J. Wood Wood Prod.
**2016**, 74, 331–351. [Google Scholar] [CrossRef] - Kumar, C.; Li, X.; Subhani, M.; Shanks, J.; Dakin, T.; McGavin, R.L.; Ashraf, M. A Review of Factors Influencing Rolling Shear in CLT and Test Methodology. J. Test Eval.
**2022**, 50, 1634–1656. [Google Scholar] [CrossRef] - Forest Products Laboratory (US). Wood Handbook: Wood as an Engineering Material; General Technical Report FPL-GTR-282; Department of Agriculture, Forest Service, Forest Products Laboratory: Madison, WI, USA, 2021.
- Ehrhart, T.; Brandner, R. Rolling shear: Test configurations and properties of some European soft- and hardwood species. Eng. Struct.
**2018**, 172, 554–572. [Google Scholar] [CrossRef] - Aicher, S.; Christian, Z.; Hirsch, M. Rolling shear modulus and strength of beech wood laminations. Holzforschung
**2016**, 70, 773–781. [Google Scholar] [CrossRef] - Li, M.; Dong, W.; Lim, H. Influence of Lamination Aspect Ratios and Test Methods on Rolling Shear Strength Evaluation of Cross-Laminated Timber. J. Mater. Civ. Eng.
**2019**, 31, 04019310. [Google Scholar] [CrossRef] - Gui, T.; Cai, S.; Wang, Z.; Zhou, J. Influence of aspect ratio on rolling shear properties of fast-grown small diameter eucalyptus lumber. J. Renew. Mater.
**2020**, 8, 1053–1066. [Google Scholar] [CrossRef] - Nero, R.; Christopher, P.; Ngo, T. Investigation of rolling shear properties of cross-laminated timber (CLT) and comparison of experimental approaches. Constr. Build. Mater.
**2022**, 316, 125897. [Google Scholar] [CrossRef] - Pradhan, S.; Entsminger, D.E.; Mohammadabadi, M.; Ragon, K.; Nkeuwa, W.N. The effects of densification on rolling shear performance of southern yellow pine cross-laminated timber. Constr. Build. Mater.
**2023**, 392, 132024. [Google Scholar] [CrossRef] - Zhou, Y.; Shen, Z.; Li, H.; Lu, Y.; Wang, Z. Study on in-plane shear failure mode of cross-laminated timber panel. J. Wood Sci.
**2022**, 68, 36. [Google Scholar] [CrossRef] - Dong, W.; Wang, Z.; Zhou, J.; Gong, M. Experimental study on bending properties of cross-laminated timber-bamboo composites. Constr. Build. Mater.
**2021**, 300, 124313. [Google Scholar] [CrossRef] - Kumar, C.; Faircloth, A.; Shanks, J.; McGavin, R.L.; Li, X.; Ashraf, M.; Subhani, M. Investigating Factors Influencing Rolling Shear Performance of Australian CLT Feedstock. Forests
**2023**, 14, 711. [Google Scholar] [CrossRef] - Bendtsen, B.A. Rolling shear characteristics of nine structural softwoods. For. Prod. J.
**1976**, 26, 51–56. [Google Scholar] - Li, M. Evaluating rolling shear strength properties of cross-laminated timber by short-span bending tests and modified planar shear tests. J. Wood Sci.
**2017**, 63, 331–337. [Google Scholar] [CrossRef] - Fellmoser, P.; Blaß, H.J. Influence of rolling shear modulus on strength and stiffness of structural bonded timber elements. In Proceedings of the CIB-W18 Meeting, Edinburgh, UK, 31 August–3 September 2004. [Google Scholar]
- Dumail, J.-F.; Olofsson, K.; Salmén, L. An Analysis of Rolling Shear of Spruce Wood by the Iosipescu Method. Holzforschung
**2000**, 54, 420–426. [Google Scholar] [CrossRef] - Aicher, S.; Dill-Langer, G. Basic considerations to rolling shear modulus in wooden boards. Otto-Graf-J.
**2000**, 11, 157. [Google Scholar] - Sretenovic, A.; Müller, U.; Gindl, W. Comparison of the in-plane shear strength of OSB and plywood using five point bending and EN 789 steel plate test methods. Eur. J. Wood Wood Prod.
**2005**, 63, 160–164. [Google Scholar] [CrossRef] - Xu, B.-H.; Zhang, S.-D.; Zhao, Y.-H.; Bouchaïr, A. Rolling Shear Properties of Hybrid Cross-Laminated Timber. J. Mater. Civ. Eng.
**2021**, 33, 04021159. [Google Scholar] [CrossRef] - Li, Q.; Wang, Z.; Liang, Z.; Li, L.; Gong, M.; Zhou, J. Shear properties of hybrid CLT fabricated with lumber and OSB. Constr. Build. Mater.
**2020**, 261, 120504. [Google Scholar] [CrossRef] - Li, H.; Wang, B.J.; Wang, L.; Wei, Y. An experimental and modeling study on apparent bending moduli of cross-laminated bamboo and timber (CLBT) in orthogonal strength directions. Case Stud. Constr. Mater.
**2022**, 16, e00874. [Google Scholar] [CrossRef] - Wang, Z.; Fu, H.; Gong, M.; Luo, J.; Dong, W.; Wang, T.; Chui, Y.H. Planar shear and bending properties of hybrid CLT fabricated with lumber and LVL. Constr. Build. Mater.
**2017**, 151, 172–177. [Google Scholar] [CrossRef] - Wang, Z.; Gong, M.; Chui, Y.-H. Mechanical properties of laminated strand lumber and hybrid cross-laminated timber. Constr. Build. Mater.
**2015**, 101, 622–627. [Google Scholar] [CrossRef] - Bahmanzad, A.; Clouston, P.L.; Arwade, S.R.; Schreyer, A.C. Shear Properties of Eastern Hemlock with Respect to Fiber Orientation for Use in Cross Laminated Timber. J. Mater. Civ. Eng.
**2020**, 32, 04020165. [Google Scholar] [CrossRef] - Buck, D.; Wang, X.A.; Hagman, O.; Gustafsson, A. Bending properties of Cross Laminated Timber (CLT) with a 45° alternating layer configuration. Bioresources
**2016**, 11, 4633–4644. [Google Scholar] [CrossRef] - Chui, Y.H. Simultaneous evaluation of bending and shear moduli of wood and the influence of knots on these parameters. Wood Sci. Technol.
**1991**, 25, 125–134. [Google Scholar] [CrossRef] - Cao, Y.; Street, J.; Mitchell, B.; To, F.; DuBien, J.; Seale, R.D.; Shmulsky, R. Effect of knots on horizontal shear strength in southern yellow pine. BioResources
**2018**, 13, 4509–4520. [Google Scholar] [CrossRef] - Tabarsa, T.; Chui, Y.H. Effects of hot-pressing on properties of white spruce. For. Prod. J.
**1997**, 47, 71. [Google Scholar] - Navi, P.; Girardet, F. Effects of thermo-hydro-mechanical treatment on the structure and properties of wood. Holzforschung
**2000**, 54, 287–293. [Google Scholar] [CrossRef] - Rassam, G.; Ghofrani, M.; Taghiyari, H.R.; Jamnani, B.; Khajeh, M.A. Mechanical performance and dimensional stability of nano-silver impregnated densified spruce wood. Eur. J. Wood Wood Prod.
**2012**, 70, 595–600. [Google Scholar] [CrossRef] - Kuai, B.; Wang, Z.; Gao, J.; Tong, J.; Zhan, T.; Zhang, Y.; Lu, J.; Cai, L. Development of densified wood with high strength and excellent dimensional stability by impregnating delignified poplar by sodium silicate. Constr. Build. Mater.
**2022**, 344, 128282. [Google Scholar] [CrossRef] - Pelit, H.; Yorulmaz, R. Influence of densification on mechanical properties of thermally pretreated spruce and poplar wood. Bioresources
**2019**, 14, 9739–9754. [Google Scholar] [CrossRef] - Ulker, O.; Imirzi, O.; Burdurlu, E. The Effect of Densification Temperature on Some Physical and Mechanical Properties of Scots Pine (Pinus sylvestris L.). Bioresources
**2012**, 7, 5581–5592. [Google Scholar] [CrossRef] - Yu, H.; Hse, C.Y.; Jiang, Z. Effect of PF impregnation and surface densification on the mechanical properties of small-scale wood laminated poles. In Proceedings of the Conference on Advanced Biomass Science and Technology for Bio-Based Products, Beijing, China, 23–25 May 2007; Hse, C.-Y., Jiang, Z., Kuo, M.-L., Eds.; Chinese Academy of Forestry, People’s Republic of China: Beijing, China, 2009; pp. 357–363. [Google Scholar]
- Pradhan, S.; Entsminger, E.D.; Mohammadabadi, M.; Ragon, K. Influence of densification on structural performance and failure mode of CLT under bending load. Bioresources
**2024**, 19, 2342–2352. [Google Scholar] [CrossRef]

**Figure 2.**Relationship between the minimum required shear strength (MRSS) and span-to-depth ratio (L/h) to avoid rolling shear failure in CLT fabricated from loblolly pine lumber #1 grade with an average MOR of 42.28 MPa.

**Figure 3.**Relationship between compression ratio and percentage of increment of rolling shear strength for loblolly pine shown by green bars and blue line. Reproduced from ref. [10].

S. No | Sample ID | P_{max} (N) | P/Δ (N/mm) | Apparent Modulus of Elasticity, E_{app} (MPa) | Rolling Shear Strength, τ_{max} (MPa) |
---|---|---|---|---|---|

1 | ND1 | 50,483 | 6896.85 | 8488.62 | 2.68 |

2 | ND2 | 62,048.6 | 7674.77 | 9435.65 | 3.22 |

3 | ND3 | 58,211.7 | 9300.82 | 11,587.4 | 3.06 |

4 | ND4 | 61,821.4 | 7420.48 | 9000.71 | 3.2 |

5 | ND5 | 67,046.5 | 7699.46 | 9506.11 | 3.48 |

6 | ND6 | 44,366.8 | 6951.67 | 8772.12 | 2.41 |

Average | 57,329.7 | 7657.34 | 9465.1 | 3 | |

COV | 13% | 10% | 11% | 12% |

S. No | Sample ID | P/Δ (N/mm) | P_{max} (N) | Modulus of Rupture (MPa) | Apparent Modulus of Elasticity, (MPa) | Maximum Shear Stress, (MPa) | Failure Mode |
---|---|---|---|---|---|---|---|

1 | D1 | 8738.31 | 83,548.35 | 45.08 | 10,205.05 | 4.24 | Tensile |

2 | D2 | 8276.33 | 78,239.92 | 42.21 | 9583.99 | 3.97 | Tensile |

3 | D3 | 8456.71 | 90,446.67 | 49.95 | 10,102.93 | 4.68 | Tensile |

4 | D4 | 9403.62 | 96,728.70 | 52.08 | 10,915.23 | 4.90 | Tensile |

5 | D5 | 9476.47 | 87,517.13 | 47.30 | 11,072.67 | 4.44 | Horizontal Shear |

6 | D6 | 9367.37 | 88,425.19 | 48.09 | 11,068.69 | 4.50 | Tensile |

Average | 8953.13 | 87,484.33 | 47.45 | 10,491.43 | 4.45 | ||

COV | 5% | 7% | 7% | 5% | 7% |

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**MDPI and ACS Style**

Pradhan, S.; Mohammadabadi, M.; Seale, R.D.; Thati, M.; Entsminger, E.D.; Nkeuwa, W.N.
Optimizing Lumber Densification for Mitigating Rolling Shear Failure in Cross-Laminated Timber (CLT). *Constr. Mater.* **2024**, *4*, 342-352.
https://doi.org/10.3390/constrmater4020019

**AMA Style**

Pradhan S, Mohammadabadi M, Seale RD, Thati M, Entsminger ED, Nkeuwa WN.
Optimizing Lumber Densification for Mitigating Rolling Shear Failure in Cross-Laminated Timber (CLT). *Construction Materials*. 2024; 4(2):342-352.
https://doi.org/10.3390/constrmater4020019

**Chicago/Turabian Style**

Pradhan, Suman, Mostafa Mohammadabadi, Roy Daniel Seale, Manikanta Thati, Edward D. Entsminger, and William Nguegang Nkeuwa.
2024. "Optimizing Lumber Densification for Mitigating Rolling Shear Failure in Cross-Laminated Timber (CLT)" *Construction Materials* 4, no. 2: 342-352.
https://doi.org/10.3390/constrmater4020019