Long-Term Loading Experimental Research of Prestressed Glulam Beams Based on Creep Influence

Abstract

In this paper, long-term loading tests of ten prestressed glulam beams were carried out for 45 days, using the loading method of three-point hanging heavy objects. We analyzed the influence of prestressed steel wire numbers and total preloading force on parameters such as failure mode of beams, variation of steel wire stress, and long-term deflection of mid-span. When the total prestress was constant and the number of steel wires was 2, 4, and 6, the total stress of steel wires decreased by 33.07%, 37.26%, and 50.04%, respectively, after long-term testing for 45 days. The ratio of mid-span deflection to total deflection was 61.5%, 54.8%, and 40.9% respectively. When the number of steel wires was constant and the values of total prestress were 0, 3.079 kN and 6.158 kN, the total stress decreased by 28.90%, 36.59%, and 36.63%, respectively, after long-term loading. The ratio of long-term deflection of mid-span to total deflection was 60.7%, 54.8%, and 39.3%, respectively. The more steel wires, the greater the value of total prestress and the loss of total stress, the smaller the mid-span long-term deflection. After the test, we analyzed and fitted the test data to obtain the specific numerical of the creep coefficient θ under normal conditions, and the formula for calculating the long-term stiffness of the glulam beams based on the creep effects is proposed.

1. Introduction

Wooden houses have a series of advantages such as low carbon, environmental friendliness, ecological livability, and superior seismic performance. It is a popular and promising architectural form [1,2,3]. Glued wood material has unlimited section size, scattered defects, high available strength, and can make full use of small-diameter wood and low-quality wood. It is a common material in modern wood structures [4,5]. As the main stressed member in wood structure, the traditional glued wood beam has some disadvantages, such as the material compressive strength can not be fully developed, the failure form is brittle tensile failure, the deflection is too large when bending, and the section size is controlled by deformation [6]. For this reason, a new composite member prestressed glued wood beam with prestressed tendons in tension and glued wood in compression is proposed [7,8,9,10,11]. On the other hand, creep is a basic characteristic of wood and is a key factor affecting the long-term mechanical behavior of glulam beams, and the force of beam is more complicated due to the prestress applied. Therefore, defining long-term performance of prestressed glulam beams for promoting this excellent composite member and promoting the development of wood structure has important academic value and social significance.

At present, domestic and foreign scholars in the related fields mainly focus on the creep characteristics of wood, creep deformation of components, and creep buckling of wood structures [12,13]. The above research provides a reference for this paper from the aspects of test methods and considerations, and also reflects the necessity of carrying out the long-term performance test of prestressed glued wood beams.

In this paper, two groups, a total of 10 prestressed glulam beams were subjected to a 45-day long-term loading test. We compared the failure mode of the beams under the influence of creep, the variation of the steel wires’ stress, and the long-term deflection of the beams, studying the influence of the number of steel wires and the total pre-force value on the mechanical behavior of glulam beams. We give the creep coefficient that reflects long-term deflection growth of glulam beams and establish the long-term deflection formula for prestressed glulam beams.

2. Experimental Design

2.1. Specimen Design and Grouping

According to the relevant standards at home and abroad and the geometric scale of 1:4, 10 prestressed glued wood beams with the size of 3150 mm × 100 mm × 100 mm were designed and manufactured [14,15,16]. Northeast larch was selected as the beam body material when the glued wood beam was made (research shows that northeast larch has good bending resistance. The bending strength of northeast larch selected in this paper is 59.88 MPa, the elastic modulus is 11,240.43 MPa, and the tightness is 32.94%), and the low relaxation 1570 prestressed steel wire with a diameter of 7 mm was selected as the prestressed reinforcement. According to the number of steel wires and the total preload value, the test beam was divided into two groups A and B, as shown in

Table 1. Basic information of test component.

Group A			Group B
Beam Number	Number of Steel Wires	Total Prestress (kN)	Beam Number	Number of Steel Wires	Total Prestress (kN)
LA1-1	2	3.079	LB1-1	4	0
LA1-2	2	3.079	LB1-2	4	0
LA2-1	4	3.079	LB2-1	4	3.079
LA2-2	4	3.079	LB2-2	4	3.079
LA3-1	6	3.079	LB3-1	4	6.158
LA3-2	6	3.079	LB3-2	4	6.158

Note: In the table, beam LA2-1 and beam LB2-1, beam LA2-2 and beam LB2-2 are exactly the same. Different numbers are used due to the different purpose of the test.

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2.2. Loading Device and Arrangement of Measuring Points

Due to the large size and large number of beams for long-term test, a long-term loading test device was designed by ourselves, as shown in Figure 1. The device is composed of eight steel columns, four steel beams numbered 1, and two steel beams numbered 2. Each two steel columns and one steel beam numbered 1 are connected by bolts, and the steel beam numbered 2 is erected on it to form a support, and then the wooden beam is placed on the steel beam numbered 2 for loading. The device can carry out long-term bending test on five wooden beams at the same time, with high efficiency. The bearing capacity and stiffness of the device are large, which has little influence on the test results; the distance between supports can be adjusted according to the length of the test beam, which has good applicability.

The long-term tests in this paper are carried out after the short-term test (through the three-point loading test, the short-term bending tests of 36 prestressed high-strength glued wood beams in four groups were carried out to study the effects of the number of prestressed steel wires and the prestress value on the bending performance of prestressed high-strength glued wood beams). Before that, the measured flexural capacity of prestressed glued wood beams has been obtained. According to the relationship between bearing capacity R and load effect S, the long-term load is determined to be 30% ultimate bearing capacity obtained from the short-term loading test. The long-term test load of prestressed glulam beams is shown in

Table 2. Basic information of test component.

Number	LA1-1	LA1-2	LA2-1	LA2-2	LA3-1	LA3-2
Loading Value (kN)	3.35	3.35	4.35	4.35	6.35	6.35
Number	LB1-1	LB1-2	LB2-1	LB2-2	LB3-1	LB3-2
Loading Value (kN)	2.20	2.20	4.35	4.35	6.35	6.35

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According to the relevant standard [17] and the previous tests [18,19], the loading time was adjusted to 45 days. In order to ensure the unchanged loading value during the test, the long-term load was applied by using heavy weight. To prevent local pressure failure at the loading point, we placed the steel base plate on the upper surface of the three-point of the beam, and placed a small wooden block on the steel base plate, as shown in Figure 2.

In order to collect the displacement at both ends of the beam and the midspan, a total of 3 displacement meters needed to be arranged at both ends of the beam and the midspan. At the same time, an additional mechanical dial indicator needed to be placed on the upper surface of the midspan of the beam to check the deflection change in the midspan of the beam. After that, five strain gauges were evenly arranged along the two sides of the beam span, and two strain gauges were evenly arranged on the top surface. Finally, one strain gauge was arranged at the three-point of each prestressed steel wire to collect the stress in the beam span and the stress changes in the steel wire. The layout position of displacement gauge and strain gauge is shown in Figure 2.

The screw thread tensioning and transverse tensioning method proposed in document [7] was used to apply prestress to the test beam. At the same time, the multi-functional static strain test system of jm3813 model was started to collect data synchronously. After reaching the expected preload, we started hanging heavy objects on the beam and implement loading, and continued to collect data. According to the development law of long-term deformation of the beam, the method of dense in front and sparse in rear was used for data collection. In order to avoid data loss caused by unexpected factors such as power failure, a mechanical dial indicator was set for manual reading. The time schedule of data collection is shown in

Table 3. Interval of data acquisition.

Test Time	Interval of Machine Acquisition	Interval of Manual Acquisition
Day 1	0.25 h/time	0.25 h/time
Day 2, 3	0.25 h/time	0.5 h/time
Day 4, 5	0.5 h/time	1 h/time
Day 6, 7	0.5 h/time	2 h/time
Day 8~14	1 h/time	4 h/time
Day 15~45	2 h/time	12 h/time

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3. Test Results and Analysis

3.1. Experimental Phenomena

Every 10 days, we observed the prestressed glulam beams and recorded the experimental phenomena. On the 10th day, prestressed glulam beams showed very small cracks between the laminates near the knot. Since then, cracks have developed slightly but tend to stabilize quickly, as shown in Figure 3.

Before unloading (test for 45 days), the prestressed glulam beams were observed, photographed again. And archiving the test results, as shown in Figure 4.

The Figure 3 and Figure 4 show that since the purpose of a long-term test is to provide the basis for the design of serviceability limit state, the long-term load applied was the service load, which is different from the failure load of the beam. Therefore, in the course of the experiment, there were obvious failure phenomena such as cracks and folds except for obvious changes in deflection.

3.2. Stress Variation of Prestressed Steels

In the long-term loading test, the change of the steel wire stress is an important index of the mechanical behavior of the prestressed glulam beam. In this test, the change of the steel wire stress was caused by two parts: one is the relaxation of the steel wire and the other is the creep of the glued wood. Previous studies have shown that when the initial stress of prestressed steel wire is less than 0.5 times the ultimate tensile strength Ry, the steel wires’ relaxation phenomenon is not obvious. Because of the maximum stress of the prestressing steel wire in this experiment σ = 0.32 Ry < 0.5 Ry, the stress change caused by steel wire relaxation is ignored and the stress change of steel wire is caused all by the creep of the glued wood.

For the test beams of A and B, the stress of all steel wires in a beam, that is, the curve named relationship between the total stress of steel wires and the change of time, is shown in Figure 5.

It can be seen from Figure 5 that the total stress of beams LA1, LA2, and LA3 decreased by 33.07%, 37.26%, and 50.04%, respectively, from the initial loading to the end of the test. Therefore, the stress loss of steel wire increased with the increase of the number of steel wire when the prestress was constant. The greater the number of wires, the greater the bearing capacity of the beam and then the greater the external load applied. From the angle of sectional stress, the stress of the glued wood part became greater and greater, which led to greater creep of the glued wood. Therefore, the steel wire stress dropped significantly. The stress of beams LB1, LB2, and LB3 decreased by 28.90%, 36.59%, and 36.63%, respectively. We can see that the greater the pre-force, the greater the loss of steel wire stress when the number of steel wires is the same. This is because the greater the pre-force, the greater the stress suffered by the glued wood part. In the same way, the greater creep, the greater the drop in wire stress.

In order to clarify the rate of change of the wire stress, the initial stress of the wire was zeroed, and the curve which shows the relationship between relative stress value and time was obtained, as shown in Figure 6.

As can be seen from Figure 6, with the increase of the number of wires, the stress of wire decreased rapidly while the prestress was constant. And as time goes on, the drop rate of wire stress was constantly expanding. This shows that the more wires, The faster speed of development of glued wood creep. However, when the number of steel wires was the same, the beam with large prestress only descended faster at the initial stage of loading and the dropping speed of the stress was basically the same at the later stage of loading between three beams. This shows that the influence of prestress on the cross section’s stress distribution is not as obvious as the number of steel wire. Moreover, as the timber enters the plastic, the phenomenon of stress distribution occurs and the influence of the prestress on the creep development speed is getting smaller and smaller.

3.3. Deflection Variation of Mid-Span

In long-term loading tests, the development of mid-span deflection is an important index of the deformation performance of prestressed glulam beams. By observing and recording the data of each batch of beams for 45 days, the curve of total deflection of the beams A and B with time can be obtained as shown in Figure 7.

For the convenience of comparison, we rule that deflection towards down is positive. On contrast, it is negative. The initial mid-span deflection is negative because of the prestress applied and the beam shows inverted arch. After the infliction of the external load, the instant deflection of the beam is short-term deflection, and after long-term loading for 45 days, the additional deflection of the beam is the long-term deflection; the sum of two is the total deflection of the beam. The short-term, long-term, and total deflection values of the beams in A and B are shown in

Table 4. Short-term, long-term, and total deflection values of prestressed glulam beams.

Serial Number	Short-Term Deflection (mm)	Long-Term Deflection (mm)	Total Deflection (mm)
LA1	4.76	7.60	12.36
LA2	6.39	7.75	14.14
LA3	7.81	5.40	13.21
LB1	3.20	4.94	8.14
LB2	6.39	7.75	14.14
LB3	8.00	5.18	13.18

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It can be seen from Figure 7 that the ratio of long-term deflection of mid-span was 61.5%, 54.8%, and 40.9% respectively, while the prestress was the same and the number of steel wires increased from 2 to 6. The proportion of long-term deflection was 60.7%, 54.8%, and 39.3% respectively, when the number of steel wires was 4 and the prestress increased from 0 to 6.158 kN. It can be seen that, with the increase of the number of steel wires, the prestressing force increased, and the proportion of long-term deflection declined. This is because, with the number of steel wires and the value of prestress increasing, the creep of glulam and initial stiffness increases. Although both increase, the increase of initial stiffness has a more obvious effect on long-term deflection of mid-span. Therefore, the proportion of long-term deflection decreases.

In order to analyze the variation of long-term deflection of beam mid-span, we assume the deflection of each beam is zero after short-term deflection, and obtain the curve of long-term deflection of beams over time, as shown in Figure 8.

It can be seen from Figure 8 that the mid-span long-term deflection of beams A and B were 35–45% and 40–50%, respectively. Until the 23rd day, 65–75% and 70–80% were completed, respectively. We can see that the mid-span long-term deflection of beams changed rapidly in the early period of the experiment, decreased gradually in the later period, and tended to be stable, which agrees with the characteristics of the creep development of glued wood.

For group A, with the increase of the number of steel wires, the rate of increase of long-term deflection slowed down gradually. This shows that increasing the number of steel wires can effectively control the rate of change of mid-span long-term deflection. For group B, the increase rate of long-term deflection was relatively close. The increase of pre-applied force made the creep of glued wood larger, but at the same time, the force arm of the beam also increased, and the interaction of the two effects made the growth rate of long-term deflection relatively close.

3.4. Creep Coefficient θ

The relaxation of prestressed steel wire and the creep of glued wood will affect the change of deflection of prestressed glulam beams during long-term loading. In order to calculate the long-term deflection of prestressed glulam beams, the ratio of the final deflection of the beam to the short-term deflection is defined as the creep coefficient. The influence of creep on deflection is considered in design.

Due to the limited test time, the long-term deformation of beam did not stop completely. Therefore, the final value of long-term deformation of prestressed glulam beam was obtained by curve fitting and derivation. Fitting the curve in Figure 7 and taking the beam LA1 as an example, the fitting curve and the formula are shown in Figure 9.

After fitting analysis, the calculation formula of the deflection of A and B beams with time can be written as:

$$y=A+Bt-C{t}^2$$

(1)

Among them, the coefficients A, B, C are shown in

Table 5. Coefficient value corresponding to the deflection formula of beam A and B.

Serial Number	Coefficient
	A	B	C (×10−6)
LA1	1.766	0.011	4.622
LA2	3.889	0.016	8.510
LA3	5.289	0.010	4.347
LB1	4.085	0.010	5.171
LB2	3.889	0.016	8.510
LB3	−17.61	0.012	5.514

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From the above formula, the final value of long-term deflection can be obtained and summed with the short-term deflection of the beam to obtain the final value of the total deflection of the beam. The creep coefficient θ is the ratio of the final value of the total deflection to the short-term deflection. We obtain

Table 6. Final value of prestressed glulam beams’ long-term deflection and creep coefficient.

Serial Number	Final Value of Total Deflection (mm)	Short-Term Deflection (mm)	Long-Term Deflection (mm)	Creep Coefficient θ
LA1	13.14	4.76	8.38	2.51
LA2	14.51	6.39	8.11	2.27
LA3	13.89	7.81	6.08	1.78
LB1	8.92	3.20	5.72	2.79
LB2	14.51	6.39	8.11	2.27
LB3	13.29	8.00	5.29	1.74

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It can be seen from Table 6, when the total pre-force values are the same, that the greater the number of wires, the smaller the creep coefficient θ. When the number of steel wires is the same, the larger the total pre-force value, and the smaller the creep coefficient θ. In the test beams involved in this article, the number of steel wires and prestress values are within a reasonable range. At this time, the creep coefficient θ is in the range of 1.74 to 2.79. In engineering design, according to the actual number of steel wires and prestressing value, we obtained the values in Table 6.

3.5. Calculation Formula of Long-Term Stiffness B

Because creep affects the long-term stiffness of the structure, it decreases with the increase of load time. Drawing lessons from our country “Concrete Structure Design Code” (GB50010-2010), we can determine the deflection influence coefficient θ in accordance with the test results, and then obtain the method of calculating the long-term stiffness B. Proposing formula for calculating the long-term stiffness B of prestressed glulam beams, the calculation diagram is shown in Figure 10. The beam span is L, before applying prestressing force, and the distance between mid-span steel wire and glulam beam bottom is h1. After applying prestressing force, the distance between the prestressed steel wire and glulam beam bottom is increased by h₂.

$$B=\frac{M_k}{(M_q\times (\theta -1)+M_k)}\times B_s=\frac{M_k}{(M_q\times (\theta -1)+M_k)}\times \frac{M}{(w_{1/2}-f_2)}$$

(2)

In the formula: B—The stiffness of flexural members considering the long-term effect of loading.

B_s—Short-term stiffness of prestressed flexural members calculated in accordance with standard combinations.

θ—Creep coefficient, As shown in Table 5.

M_k, M_q—Moment calculated according to the loading standard combination and quasi-permanent combination, take the maximum moment in calculation section.

M—Moment of mid-span, when the third point is loaded.

$$M=\frac{Fl}{\left(2\times 3\right)}=\frac{Fl}{6}$$

(3)

w_1/2—Mid-span deflection

$$w_{1/2}=\frac{23F{l}^3}{1296EI}$$

(4)

f₂—Mid-span arching value after applying prestress.

$$f_2=\frac{E_p{A}_p(h_1+h_2)L^3}{24E_m{I}_m}\times \left[\frac{1}{\sqrt{{\left(\frac{L}{2}\right)}^2+h_1^2}}-\frac{1}{\sqrt{{\left(\frac{L}{2}\right)}^2+{\left(h_1+h_2\right)}^2}}\right]$$

(5)

E_P—Elastic modulus of prestressed steel wire.

A_P—Reinforcement area of prestressed steel wire.

E_m—Elastic modulus of wood.

I_m—Section moment of inertia of test beam.

4. Conclusions

In this paper, through the long-term load test of prestressed high-strength glued wood beam, the variation law of prestressed steel wire and mid span deflection was obtained, and the prestressed steel wire, mid span deflection, and creep coefficient established θ, the relationship between the three. The calculation formula of the final deflection value is obtained by curve fitting, and the calculation formula of the long-term stiffness B of the wood beam based on the creep effect was proposed. The specific conclusions are as follows:

(1)

When the prestress value was unchanged and the number of prestressed steel wire was 2, 4, and 6, the steel wire stress decreased by 33.07%, 37.26%, and 50.04% from the beginning of loading to the end of the test. When the number of steel wires remained unchanged and the preload values were 0 kN, 3.079 kN, and 6.158 kN, the total stress of steel wires decreased by 28.90%, 36.59%, and 36.63%. With the increase of the number of steel wires, the preload value increased, and the stress loss of steel wires increased.

(2)

When the prestress value was constant and the number of prestressed steel wires were 2, 4, and 6, the ratios of mid-span long-term deflection of the beam to the total deflection were respectively 61.5%, 54.8%, and 40.9%. When the number of steel wires remained unchanged and the preload values were 0 kN, 3.079 kN, and 6.158 kN, the long-term deflection in the middle of the span accounted for 60.7%, 54.8%, and 39.3% of the total deflection, respectively. With the increase of the number of steel wires, the preload value increased and the proportion of long-term deflection decreased.

(3)

Through the analysis of the experimental data, fitting, and derivation, we obtained the value of the creep coefficient θ under normal conditions. The greater the number of wires, the greater the prestress value, and the smaller the value of θ. The other hand, when the number of steel wires was the same, the larger the total pre-force value, the smaller the creep coefficient θ. The formula for calculating the long-term stiffness B of wooden beams based on the creep effect was proposed.

There is still room for further improvement in the research of prestressed glued wood beams, including wood types, reinforcement ratio, and so on. The above conclusions can provide good data support for the follow-up study of prestressed high-strength glued wood beams.