# Comparison of Theoretical and Laboratory Out-of-Plane Shear Stiffness Values of Cross Laminated Timber Panels

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Theoretical Methods

#### 2.1.1. Timoshenko Beam Theory

^{2}/12 (Mindlin) [10], or values as a function of the Poisson’s ratio (Cowper) [11]. The lay-up with the alternating grain orientation of CLT leads to a more complicated transverse shear strain distribution and therefore the values mentioned above are not applicable for CLT.

#### 2.1.2. Shear Analogy Method

#### 2.2. Laboratory Tests

#### 2.2.1. Material and Conditioning

#### 2.2.2. Modal Panel Tests

#### 2.2.3. Bending Tests

#### 2.2.4. Planar Shear Tests

^{2}in an environment with a temperature above 20 °C for at least 12 h. In the test, a load was applied to the aluminum plates at a displacement rate of 0.5 mm/min. The relative displacement between the two aluminum plates during the tests were measured by two LVDTs. The recorded displacement was used to determine the global shear moduli of the CLT panels. The test setup can be seen in Figure 5.

#### 2.2.5. Evaluation of the Effective Shear Stiffness

## 3. Test Results

#### 3.1. Single-Layer Tests

#### 3.2. CLT Panel Tests

#### 3.3. Shear Stiffness Results

_{(ratio)}and SA

_{(ratio)}), the other one was based on the overall average out-of-plane shear moduli parallel to the grain (${G}_{13}$) and the average out-of-plane shear moduli perpendicular to the grain (${G}_{23}$) of the corresponding group (FEG or SEG) from the planar shear tests (TBT

_{(test)}and SA

_{(test)}). The used shear modulus parallel to the grain on a single-layer was ${G}_{13}=813.9$ N/mm

^{2}, in the minor direction shear moduli of ${G}_{23}=261.8$ N/mm

^{2}for FEG layer panels and ${G}_{23}=188.5$ N/mm

^{2}for SEG layer panels were used. The overall average out-of-plane shear modulus parallel to the grain (${G}_{13}$) was used for both panel types since it is assumed that the existence of edge-gluing has no negative effect on the ${G}_{13}$ value even though the FEG group shows a smaller ${G}_{13}$ value compared to the SEG group. The calculated values were compared with the shear stiffness values determined by planar shear tests (Planar) (Equation (10)) and the flexure tests (Flex) (Equation (13)).

_{(test)}and SA

_{(test)}). The shear stiffness evaluated by planar shear tests shows better agreement with the calculated values based on the single-layer planar shear tests, with the planar shear test values generally showing lower values than the calculated values. The FEG layer based results produce more consistent values compared to the SEG layer based tests. The stiffness values determined by flexure tests show better agreement with the values calculated by common ratios, while showing relatively low values in general.

## 4. Discussion

_{(ratio)}and SA

_{(ratio)}). It can be seen that the two approaches lead to similar shear stiffness values with the Timoshenko beam theory usually yielding higher shear stiffness values. Furthermore, it can be seen in the figures showing the results for the major strength direction (Figure 7 and Figure 9) that the agreement of the two methods increases with the number of layers. Figure 7, Figure 8, Figure 9 and Figure 10 show the strong influence of the ${G}_{13}/{G}_{23}$ ratio on the comparison of the two calculation methods. It can be seen that the two different property sets used for the calculations, namely the commonly used property ratios ${G}_{13}={E}_{11}\text{}/16$ and ${G}_{23}={G}_{13}\text{}/10$ and the average single-layer ${G}_{13}$ and ${G}_{23}$ values from laboratory tests show significant differences. The main reason is that the properties evaluated in the planar shear tests are usually substantially higher than the ones determined by the property ratios. For the average modulus of elasticity ${E}_{11}$ of a single-layer evaluated in the modal tests the property ratios yield shear moduli of ${G}_{13}=658.5$ N/mm

^{2}and ${G}_{23}=65.9$ N/mm

^{2}, while the average values from the planar shear test are ${G}_{13}=813.9$ N/mm

^{2}and ${G}_{23}=261.8$ N/mm

^{2}for FEG layer panels and ${G}_{23}=188.5$ N/mm

^{2}for SEG layer panels. Based on the planar shear test results the property ratio based approach leads to about 21% lower ${G}_{13}$ values and 75% (FEG) to 66% (SEG) lower ${G}_{23}$ values.

^{2}for the FEG panels and 188.5 N/mm

^{2}for the SEG panels. These values are significantly higher that the ${G}_{23}$ values commonly used in design. A lower ${G}_{13}$-to-${G}_{23}$ ratio leads to higher shear stiffness value in both, major and minor direction. Other research projects have suggested ${G}_{23}$ values around 135 N/mm

^{2}for the same and similar materials [16,17], which would lead to a ${G}_{13}$-to-${G}_{23}$ ratio of around 6.0 and therefore a better agreement to the shear stiffness values evaluated in the laboratory tests. It is interesting to see that the results from the flexure tests are not only lower than the results from the planar shear tests but that the percentage is consistently around −77% at a relatively low level of standard deviation. If this value can be confirmed by further test the shear stiffness of multi-layer CLT panels with symmetrical layup and constant layer thickness could be estimated by a combination of modal and bending test, which would lead to significantly lower testing efforts compared to the planar shear tests.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Planar shear tests for the ${G}_{13}$ and ${G}_{23}$ evaluation (here: ${G}_{13}$ of a 5-layer CLT panel).

Panel | Elastic Moduli | Span (mm) | Span-to-Thickness | Displacement Rate (mm/min) |
---|---|---|---|---|

Single-Layer | ${E}_{11}$ | 1100 | 57.9 | 8.0 |

${E}_{22}$ | 500 | 26.3 | 0.75 | |

3-Layer CLT | ${E}_{11}$ | 500 | 10.3–10.8 | 0.5 |

${E}_{22}$ | ||||

5-Layer CLT | ${E}_{11}$ | 500 | 6.2–6.7 | 0.5 |

${E}_{22}$ |

Panel Type | Test Method | Average & StDev | Density (kg/m^{3}) | ${\mathit{E}}_{11}$ (N/mm^{2}) | ${\mathit{E}}_{22}$ (N/mm^{2}) | ${\mathit{G}}_{12}$ (N/mm^{2}) | ${\mathit{G}}_{13}$ (N/mm^{2}) | ${\mathit{G}}_{23}$ (N/mm^{2}) |
---|---|---|---|---|---|---|---|---|

FEG | Modal | Average | 465.9 | 10,919.6 | 283.6 | 696.5 | - | - |

StDev | 25.7 | 1776.9 | 55.5 | 94.9 | ||||

Static | Average | 465.9 | 10,965.3 | 264.4 | 796.0 ^{1} | 753.4 ^{2} | 261.8 ^{3} | |

StDev | 25.7 | 1837.7 | 74.5 | 101.5 ^{1} | 80.1 ^{2} | 92.6 ^{3} | ||

SEG | Modal | Average | 401.2 | 10,152.0 | 60.8 | 482.8 | - | - |

StDev | 19.8 | 1428.8 | 18.5 | 68.2 | ||||

Static | Average | 401.2 | 10,655.5 | - | - | 874.5 ^{2} | 188.5 ^{3} | |

StDev | 19.8 | 1528.3 | 143.9 ^{2} | 74.0 ^{3} |

^{1}Results based on 28 FEG specimens.

^{2}Results based on 3 FEG specimen and/or 3 SEG specimen.

^{3}Results based on 9 FEG specimen and/or 9 SEG specimen.

Panel Type | Density (kg/m^{3}) | ${\mathit{E}}_{11}$ (N/mm^{2}) | ${\mathit{E}}_{22}$ (N/mm^{2}) | ${\mathit{G}}_{12}$ (N/mm^{2}) | ${\mathit{G}}_{13}$ (N/mm^{2}) | ${\mathit{G}}_{23}$ (N/mm^{2}) | ||
---|---|---|---|---|---|---|---|---|

3-Layer | F E G | Calc. | 482 (13) | 10,601 (522) | 627 (95) | 725 (93) | - | - |

Modal | 11,471 (703) | 783 (118) | 853 (111) | - | - | |||

Static | 3502 (1182) | 612 (96) | - | 231 (47) | 165 (54) | |||

S E G | Calc. | 407 (27) | 9736 (1179) | 406 (31) | 486 (102) | |||

Modal | 9216 (1510) | 495 (52) | 353 (97) | |||||

Static | 2828 (767) | 417 (49) | - | 179 (961) | 115 (24) | |||

5-Layer | F E G | Calc. | 480 (11) | 9403 (1780) | 2649 (440) | 679 (79) | ||

Modal | 12,736 (3246) | 3192 (448) | 904 (142) | |||||

Static | 1344 (80) | 930 (48) | - | 212 (86) | 149 (38) | |||

S E G | Calc. | 405 (10) | 9264 (1003) | 2378 (298) | 485 (36) | |||

Modal | 13,355 (3430) | 2338 (481) | 361 (119) | |||||

Static | 1078 (57) | 712 (67) | - | 133 (51) | 111 (33) |

Panel Type | TBT_{(ratio)}/Planar (%) | SA_{(ratio)}/Planar (%) | TBT_{(test)}/Planar (%) | SA_{(test)}/Planar (%) | Flex/Planar (%) | ||
---|---|---|---|---|---|---|---|

Major | 3-Layer | Avg. | −55.7 | −61.0 | 53.3 | 26.8 | −77.3 |

StDev | 15.1 | 12.6 | 43.3 | 35.8 | 12.1 | ||

5-Layer | Avg. | −26.2 | −30.8 | 106.6 | 91.6 | −77.7 | |

StDev | 34.3 | 32.1 | 83.0 | 76.9 | 9.0 | ||

Total | Avg. | −40.8 | −46.9 | 78.2 | 57.0 | −77.5 | |

StDev | 29.2 | 27.9 | 69.2 | 66.3 | 10.6 | ||

Minor | 3-Layer | Avg. | 54.8 | - | 159.4 | - | −77.5 |

StDev | 53.9 | - | 103.8 | - | 14.6 | ||

5-Layer | Avg. | −56.3 | −64.8 | 47.7 | 16.6 | −76.2 | |

StDev | 12.1 | 10.3 | 38.4 | 30.7 | 6.3 | ||

Total | Avg. | 2.9 | −64.8 | 107.3 | 16.6 | −76.9 | |

StDev | 68.9 | 10.3 | 97.2 | 30.7 | 11.3 |

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**MDPI and ACS Style**

Niederwestberg, J.; Zhou, J.; Chui, Y.-H. Comparison of Theoretical and Laboratory Out-of-Plane Shear Stiffness Values of Cross Laminated Timber Panels. *Buildings* **2018**, *8*, 146.
https://doi.org/10.3390/buildings8100146

**AMA Style**

Niederwestberg J, Zhou J, Chui Y-H. Comparison of Theoretical and Laboratory Out-of-Plane Shear Stiffness Values of Cross Laminated Timber Panels. *Buildings*. 2018; 8(10):146.
https://doi.org/10.3390/buildings8100146

**Chicago/Turabian Style**

Niederwestberg, Jan, Jianhui Zhou, and Ying-Hei Chui. 2018. "Comparison of Theoretical and Laboratory Out-of-Plane Shear Stiffness Values of Cross Laminated Timber Panels" *Buildings* 8, no. 10: 146.
https://doi.org/10.3390/buildings8100146