Creep test results of glulam members under compression and bending were studied in this paper. The creep tests were conducted to investigate the influence of the stress level and relative eccentricity on the creep deformation of glulam members. The test results showed that the creep deformation trends of glulam members under long-term compression and bending loading were similar; the creep deformation increased with increases in both the stress level and relative eccentricity. However, the relative creep deformation decreased with the increase in both the stress level and relative eccentricity under long-term loading, and a five-parameter creep model was proposed to analyse the creep mechanism of glulam members under compression and bending. The good fitness of the test results indicated that the five-parameter model was able to accurately simulate the creep deformation of glulam compression-bending members. Moreover, a numerical model was developed using the creep equation, which was related to the parameter

Under the global trend of the increasing importance of environmental protection and sustainable development, timber, due to its low-carbon, renewable and favourable mechanical properties, has been considered the first choice of construction material for green buildings. The strain of timber increases with time under the continuous action of its self-weight or an external load, owing to its anisotropic viscoelastic characteristic. This phenomenon is known as creep. The deformation effect caused by creep will affect the overall deformation of a structure and result in the loss of structural strength [

In recent years, researchers have studied the creep properties of timber and timber components. Zhou et al. [

Some researchers have noted the effects of temperature and humidity on the creep properties of timber. Moutee et al. [

Large-span timber lattice shell structures have been widely used in large-span timber structure construction engineering in recent years. Some large-span lattice shell buildings have been successfully constructed, such as the Savill Garden gridshell. In a large-span timber lattice shell structure, the members are subjected to both compression and bending. Therefore, it is urgent to carry out research on the compression-bending creep deformation of timber. Research on timber creep in China and abroad has focused on the bending, tensile compression creep and mechanical adsorption deformation of timber, as well as the influence of temperature and humidity. Research on the compression-bending creep deformation of glulam has not yet been carried out. Therefore, glulam compression-bending members were used in this study to investigate the influence of the stress level, relative eccentricity and other factors on mid-span creep deformation. Twelve long-term creep specimens were designed and tested. Eccentric loading creep tests were carried out according to the relevant codes. A five-parameter model based on experimental data fitting was established to describe the creep characteristics of timber. It was verified that this five-parameter model can simulate the creep deformation of flexural members and predict the creep deformation of flexural members over 50 years.

The glulam considered in this study was made of Douglas fir. The physical properties of the Douglas fir were measured according to the timber property test standard [^{3}, the tensile strength parallel to the grain was 98.71 MPa, the compressive strength parallel to the grain was 39.43 MPa, the shear strength in the radial direction was 9.04 MPa, the shear strength in the tangential direction was 8.16 MPa, the bending strength was 33.70 MPa, and the elastic modulus in the longitudinal direction was 11495 MPa.

The glulam creep tests were carried out at the Timber Structure Laboratory of Nanjing Tech University. The dimensions of the specimens were determined by ASTMD143-94 (2000) [

Specimens | Influence factors | |
---|---|---|

Stress ratio | Relative eccentricity | |

L1-L3 | 0.35 | 0.6 |

L4-L6 | 0.2 | 0.6 |

L7-L9 | 0.2 | 1.2 |

L10-L12 | 0.2 | 0 |

A customized device was used for this work, and the load was applied by a jack. The diagram of the test device is shown in

To avoid the lateral deviation of the specimens and satisfy the actual stress state of the specimens, the two ends of each specimen were fixed with bolted steel-timber-steel connections. In the test, pressure was applied to both ends of the specimens through the test device, so that the specimen could be effectively connect to the test device during the test. Additional dial gauges were placed in the middle and at both ends of the specimen to measure the lateral displacement in the initial stage of the test so that the specimen position could be adjusted to ensure that no lateral deviation occurred. The details are shown in

Referring to the calculation method of the bearing capacity of compression-bending members in GB/T 50708-2012 [

The loading environment had a constant temperature of (20 ± 2)°C and RH of (65 ± 3)%, as shown in

Creep phenomenon is shown in

To ensure the reliability of the test results, the average value of test specimens for each group is adopted. Meanwhile, relative creep deformation is used to analyse creep data to clarify the relation between creep deformation and different stress ratios. Relative creep deformation is the ratio between creep deformation and initial deformation, and its equation is as follows:

where

The creep deformation curves and the relative creep deformation curves of the glulam members under different stress levels are shown in

The creep deformation of these specimens follows a certain pattern. In the first 30 days of loading, the mid-span deflection increased rapidly, and the components were in the initial creep stage at this time. Then, the increase in deflection deformation gradually decreased and entered the steady-state creep stage.

The final deformation of the specimens increased with increasing stress level. When the stress ratio increased from 0.2 to 0.35, the mid-span final deformation of the specimens increased from 0.8595 mm to 1.5445 mm, an increase of approximately 0.685 mm.

When the stress ratio increased from 0.2 to 0.35, the instantaneous deformation of the specimens increased by approximately 121.95%, and the creep deformation of the specimens increased by approximately 27.55%, far less than the increase in the instantaneous deformation. Thus, it can be inferred that the difference in the final deformation between the stress ratios of 0.2 and 0.35 was mainly caused by instantaneous deformation rather than creep deformation.

The relative creep deformation of the specimens decreased with increasing stress level. When the stress ratio increased from 0.2 to 0.35, the relative creep deformation decreased from 81% to 46%, a decrease of 35%. This phenomenon occurred because the transverse deformation of the specimens caused by the bending moment was restricted due to the pressure applied by the device. When the specimen was subjected to a long-term bending moment, one side of the specimen was in tension, and the other side was in compression, which led to transverse creep deformation. However, when the specimen was subjected to long-term vertical compression and bending, the creep deformation of the tensile side of the specimen was restricted by the long-term compression. Therefore, the creep deformation of a specimen under compression and bending was less than that of an identical specimen under pure bending. The relative creep deformation of a specimen under compression and bending decreased with increasing stress ratio.

The creep curves and relative creep deformation curves of the glulam members under different relative eccentricity rates are shown in

The creep deformation of these specimens with different relative eccentricities exhibits a certain pattern.

The final deformation of the specimens increased with increasing relative eccentricity. When the relative eccentricity increased from 0.6 to 1.2, the final deformation of the specimens increased from 0.8595 mm to 1.5995 mm, an increase of 0.74 mm.

When the relative eccentricity increased from 0.6 to 1.2, the instantaneous deformation of the specimens increased from 0.4748 mm to 1.099 mm, an increase of approximately 131.47%, and the creep deformation of the compression-bending component increased from 0.3847 mm to 0.5005 mm, an increase of approximately 30.10%, which is far less than that of the instantaneous deformation. Thus, it can be inferred that the difference in the final deformation between the cases of 0.6 and 1.2 relative eccentricity was mainly caused by instantaneous deformation rather than creep deformation.

The relative creep deformation of the specimens decreased with increasing relative eccentricity. When the relative eccentricity increased from 0.6 to 1.2, the relative creep deformation decreased from 81% to 45%, a decrease of approximately 36%. The reasons for this phenomenon were that the transverse deformation caused by the bending moment was restricted by the pressure and that the connection between the specimens and test device was semi-rigid. When the specimen was subjected to a long-term bending moment, the rotation angle generated at the two ends of the specimen increased, and the connections at the two ends of the component produced a counterforce to suppress this tendency. This caused the specimen to be compressed on only one side, causing the specimen to eventually shift towards the side that is not compressed, and resulting in a reduction in the specimen’s mid-span creep. Therefore, with increasing relative eccentricity, the long-term bending moment of the component and the counterforce of the connection increased. This resulted in a reduction in the specimen’s mid-span creep and a decrease in the relative creep deformation.

Existing studies have found that the Maxwell, Kelvin-Voigt and standard linear solid models each have limitations in terms of reproducing the theoretical model [

The Burgers model is a four-element model obtained by connecting a Maxwell model and a Kelvin-Voigt model. As shown in

The strain in the Burgers model is composed of elastic strain, viscous strain and viscoelastic strain. To define the constant stress

where

The creep rate is as follows:

By calculating the limit value of the above equation, it was found that the strain rate tends to a certain value with increasing time, that is, the rate of change in the viscous part is constant. This means that creep will continue to develop over time and even cause damage in the timber, which is not applicable to predict long-term creep and will result in overestimation. Therefore, because the Burger model should satisfy the creep regularity of timber, a power function was introduced, which can provide a better numerical simulation description of creep regularity. The Burger model was changed into a five-parameter model [

The above equation can be simplified as follows:

The test data were fitted by MATLAB software, and the fitting results are shown in ^{2} exceeded 0.98. Therefore, it was concluded that the five-parameter model is suitable for simulating the creep deformation of glulam members under compression and bending.

Component groups | Initial values of fitting parameters | R^{2} |
||||||
---|---|---|---|---|---|---|---|---|

Specimens | Relative eccentricity | Stress ratio | ||||||

L1-L3 | 0.6 | 0.35 | 1.0538 | 0.07034 | 0.01649 | 0.1294 | 0.22081 | 0.98413 |

L4-L6 | 0.6 | 0.2 | 0.4748 | 0.22368 | 0.01723 | 0.05527 | 0.22055 | 0.98618 |

L7-L9 | 1.2 | 0.2 | 1.099 | 0.2 | 0.5 | 0.1 | 0.25 | 0.98872 |

The finite element software Abaqus was used to numerically simulate the long-term mechanical behaviour of the flexural members. In the creep analysis method of Abaqus, the strain hardening model can accurately simulate the creep of timber under constant temperature and humidity conditions. Its expression is as follows:

where

In the normal stress state, timber creep had a linear relationship with the stress change but was independent of the current strain. Therefore,

Since the deformation of the component in the creep test was very small and the stress change can be ignored,

where

The above formula was quite different from the creep model used in this paper, but it was similar to the power law model. The expression of the power law model is as follows:

When strain hardening was adopted in the finite element, the model parameters

where

Therefore, the power law model was adopted to fit the test data and obtain the parameters

Wood is an anisotropic material, and its mechanical properties are different in different grain directions. To effectively simulate the mechanical properties of compression-bending members, the anisotropy of timber was simplified to be orthotropic. The simulation of the elastic behaviour of wood timber was achieved by defining the engineering constants in Abaqus. In this simulation, the elastic modulus of glulam parallel to the grain adopted the measured value of 11,495 MPa, and the other elastic moduli in various directions were determined by the elastic modulus ratios, as recommended by the “Wood Handbook” (2010) [

The material properties of timber are listed in

Elastic modulus (MPa) | Shear modulus (MPa) | Poisson’s ratio | ||||||
---|---|---|---|---|---|---|---|---|

E1 | E2 | E3 | G12 | G13 | G23 | |||

11495 | 782 | 575 | 736 | 897 | 80.5 | 0.292 | 0.449 | 0.39 |

The power law model was used to fit the test data and obtain the required parameters, and the corresponding parameters are presented in

Component groups | Basic parameters | Abaqus parameters | ||||||
---|---|---|---|---|---|---|---|---|

Specimens | Relative eccentricity | Stress ratio | ||||||

L1-L3 | 0.6 | 0.35 | 0.15 | 0.21 | 2.74E-6 | –0.79 | 1 | |

L4-L6 | 0.6 | 0.2 | 0.145 | 0.35 | 4.41E-6 | –0.65 | 1 | |

L7-L9 | 1.2 | 0.2 | 0.074 | 0.34 | 2.19E-6 | –0.66 | 1 |

The finite element (FE) model of the specimen was established, and a 3D stress element (C3D8I) was adopted. The reference point was coupled with the compression surface at the end of the glulam member. The concentrated force was applied at the reference point. In addition, the two ends were simply supported. The FE model is shown in

By conducting the FE analysis of the glulam member under eccentric loading, the basic parameters

Component groups | Basic parameters | Variable factors | ||||||
---|---|---|---|---|---|---|---|---|

Specimens | Relative eccentricity | Stress ratio | Relative eccentricity | Stress ratio | ||||

L1-L3 | 0.6 | 0.35 | 0.15 | 0.21 | 1 | 1.75 | 1.03 | 0.6 |

L4-L6 | 0.6 | 0.2 | 0.145 | 0.35 | 1 | 1 | 1 | 1 |

L7-L9 | 1.2 | 0.2 | 0.074 | 0.34 | 2 | 1 | 0.51 | 0.97 |

Note: The change multiple is based on L4-L6.

As seen from the above table, when the relative eccentricity was 2 times larger than the base value, the corresponding value of

where

Finite element simulations were carried out. The modified basic parameters are summarized in

Component groups | Basic parameters | Abaqus parameter values | |||||
---|---|---|---|---|---|---|---|

Specimens | Relative eccentricity | Stress ratio | a | b | A | m | n |

L1-L3 | 0.6 | 0.35 | 0.145 | 0.20 | 2.52E-6 | –0.80 | 1 |

L4-L6 | 0.6 | 0.20 | 0.145 | 0.35 | 5.52E-6 | –0.65 | 1 |

L7-L9 | 1.2 | 0.20 | 0.074 | 0.35 | 2.21E-6 | –0.65 | 1 |

Note: Considering that the discreteness of timber results in different elastic moduli, the elastic modulus in the longitudinal direction of timber was determined with the above simulation method.

A comparison of the mid-span creep deformation between the FE analysis and test results is shown in

A comparison of the relative creep deformation results between the simulation and test is shown in

As specified in Eurocode 5 [

where

According to

Stress ratio | Relative eccentricity | Basic parameters | |
---|---|---|---|

0.20 | 0.6 | 0.145 | 0.35 |

0.25 | 0.6 | 0.145 | 0.28 |

0.30 | 0.6 | 0.145 | 0.23 |

0.35 | 0.6 | 0.145 | 0.20 |

0.40 | 0.6 | 0.145 | 0.175 |

Stress ratio | Relative eccentricity | Basic parameters | |
---|---|---|---|

0.2 | 0.6 | 0.145 | 0.35 |

0.2 | 0.9 | 0.097 | 0.35 |

0.2 | 1.2 | 0.0725 | 0.35 |

0.2 | 1.5 | 0.058 | 0.35 |

0.2 | 1.8 | 0.0483 | 0.35 |

Thus, the mid-span creep of the compression-bending members with different stress ratios and relative eccentricities are shown in

The fitting results of the relative creep deformation of the tested members with different stress ratios and relative eccentricities are shown in

The relative creep coefficient was also inversely proportional to the relative eccentricity.

where

Considering the effect of both the relative eccentricity and stress ratio, a parametric equation was obtained. The equation can be expressed as follows:

where

In this study, creep tests of glulam members under compression and bending were carried out to study the effects of the stress level and relative eccentricity on the mid-span creep deformation of these members. Based on the creep mechanism, the feasibility of the established five-parameter model for timber creep data fitting was verified. Finally, a numerical model was established based on the creep equation to simulate the test data, and the parameters

The creep deformation trends of glulam compression-bending components were similar and included an obvious initial creep phase and steady-state creep phase. The creep deformation of the tested glulam compression-bending members increased with increasing stress level and relative eccentricity. Therefore, it was necessary to control the stress level and relative eccentricity so that the excessive bending stress of glulam members could be avoided.

The relative creep deformation of the glulam compression-bending members decreased with increasing stress level and relative eccentricity. Because the initial creep deformation stage of the compression-bending members with a high stress level and large relative eccentricity was relatively short, the deformation of such a member quickly entered the steady-state creep stage, resulting in a relatively small final creep deformation.

The five-parameter model was suitable for simulating the creep performance of glulam compression-bending members due to its consideration of the observed creep mechanism. The accurate fitting results showed its potential to simulate the creep deformation of compression-bending members at the mid-span.

The creep equation in Abaqus software was used to simulate the long-term deflection of each specimen based on the proposed creep parameters. The simulation results of the creep deformation and relative creep deformation were in good agreement with the corresponding test results, showing that the proposed method was able to simulate the creep of glulam members.

The creep parameters

All authors contributed equally to this work.