# Analyses on Prestress Loss and Flexural Performance of the Laminated Bamboo Beam Applied with Prestressed BFRP Sheet

Authors: Qingfang Lv; Ye Liu; Yi Ding
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

Inspired by the studies about wooden beam applied with prestressed steel plate and bamboo beam strengthened by fiber-reinforced polymer (FRP), this paper aims to explore the applicability of the prestressed basalt fiber-reinforced polymer (BFRP) sheet to the laminated bamboo beam and the variation of the flexural performance of the laminated bamboo beam applied with prestressed BFRP sheet. Two series of tests were conducted in the present study. In the first series of tests, the prestress loss of the prestressed BFRP sheet was classified and analyzed based on measured strains and deflections, which led to a derivation of the effective prestressed force considering the prestress loss. Analyses showed that the recommended value of prestress loss compared with the initial prestressed force was 22.0% based on the existing test data in the specimen preparation stage. In the second series of tests, the static loading test was performed to investigate the flexural performance of the laminated bamboo beam applied with prestressed BFRP sheet and analyze the difference between the laminated bamboo beams applied with prestressed and non-prestressed BFRP sheets. Test results showed that the no significant variation of the ultimate load and a reduction of the ultimate deformation capacity were caused by the application of the prestressed BFRP sheet.


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## Body

## 1. Introduction

As a traditional structural material [1], the bamboo is convenient to be locally obtained and has usually been utilized in building local houses in China, which has advantages such as saving costs, environmental friendliness, and recyclability [2–4]. In general, the tensile and compressive stresses of the bamboo are twice and 1.5 times than those of wood, respectively, and the strength to weight ratio of the bamboo is higher than wood and steel [5]. However, the mechanical properties of the raw and unprocessed bamboo material are unstable, with large discreteness [6]. Many inevitable defects can also be found in the unprocessed bamboo material, which results in a poor durability [7–9]. To utilize advantages of the raw bamboo and improve its material stability and performance, kinds of bamboo engineering material, including laminated bamboo [10, 11] and reconstituted bamboo [12, 13], have been proposed and studied, which is beneficial to reduce the material discreteness and enlarge practical applications of the bamboo [14].The stiffness-control design is often adopted for the modern bamboo structure [15], which limits the application of the bamboo engineering material. Therefore, to improve the practical utilization of the bamboo engineering material, the strengthening techniques [16–19] are recommended and of important necessity. Adding fibers into the bamboo engineering material during the processing stage can improve the strength of the bamboo engineering material. The mechanism of the fibers enriching the strength of the bamboo strip has been studied [20–22].Similar to the bamboo, the wood also encounters the difficulties in broadening its application due to the stiffness-control design. As early studied by Peterson [23], the prestressed steel plate was used to strengthen the wooden glulam beam. However, the incompatible elastic moduli of steel and wood resulted in the significant deformation of the wood and large prestress loss. Compared with the steel, the elastic modulus of the basalt fiber-reinforced polymer (BFRP) is relatively small [24], which may have a better cooperative working performance with bamboo engineering material [25]. A recent study conducted by Wei et al. showed that the application of the fiber-reinforced polymer (FRP) can be effective in improving the flexural performance of bamboo beams [26].Inspired by the above studies, this paper explores the application of the prestressed BFRP sheet in the laminated bamboo beam. In order to obtain the reliable performance of the laminated bamboo beam applied with the prestressed BFRP sheet, the prestress loss is firstly investigated. Until now, the standard prestress tensioning method had not been formed, and various prestress loss would be resulted from different tensioning facilities and methods. Based on the prestress tensioning method proposed in this paper, the prestress loss was classified and calculated. Referable studies included the prestress loss in the posttensioned CFRP sheet-strengthened concrete beam [27, 28]. Secondly, the flexural performance of the laminated bamboo beam applied with the prestressed BFRP sheet is studied, which is valuable for the formation of the design of such structure.


## 2. Material Properties

### 2.1. Material Test on Laminated Bamboo considering Size Effect

The mechanical properties of the bamboo engineering material were found to be related to the dimension of the tested specimen. In order to take the size effect into consideration, one laminated bamboo beam specimen with a dimension (b × h × l) of 50 mm × 150 mm × 3000 mm was tested first, almost the same dimension with the beam used in the laminated bamboo beam applied with prestressed BFRP sheet to be investigated in the following section. Details of the material test specimen are listed in Table 1, and the four-point bending test setup for the material test specimen is depicted in Figure 1.Table 1
Material properties of the laminated bamboo considering size effect.
Type
l (mm)
l
0 (mm)
a (mm)
b (mm)
c (mm)
h (mm)
E
m (N/mm2)
f
m (N/mm2)
Laminated
3000
2700
900
50
150
150
11329.5
61.2
Note. l is the total length of the material test specimen; c is the distance between the end of the beam and support, which is set to avoid the stress concentration at the corner of the laminated beam.Figure 1
Material test setup.The flexural modulus,Em, and flexural stress, fm, of the laminated bamboo can be obtained based on(1)Em=aΔF48IΔω3l02−4a2,fm=aFuh4I,where a is the distance between the support and loading point; l0 is the clear span of the laminated bamboo beam between two supports; ΔF is the loading increment; Δω is the deflection increment corresponding to the loading increment; I equal to bh3/12 is the moment of inertia of the laminated bamboo beam, where b and h are the width and height of the laminated bamboo beam, respectively; and Fu is the maximum applied load during the material test. The flexural modulus, Em, and the flexural stress, fm, for the laminated bamboo are calculated and listed in Table 1 based on the material test.


### 2.2. Material Test on BFRP Sheet

The BFRP sheet with density of 300 g/cm2 was provided by the Basalt Fiber Center of Southeast University. Six BFRP sheets with a nominal thickness of 0.147 mm were tested under tension per ACI 440 [29], where the BFRP sheet was impregnated with epoxy resin adhesive L-500. The tensile strength and the flexural strengths of the epoxy resin adhesive L-500 were 48.8 MPa and 77.5 MPa, respectively. Failure photos of the six BFRP sheets are shown in Figure 2. Test results showed that the average ultimate tensile strain, elastic modulus, ultimate tensile stress, and standard tensile stress were 2.51%, 73.8 GPa, 1725.4 MPa, and 1563.2 MPa. The mechanical behavior of the BFRP sheet was considered as elastic and linear.Figure 2
Failure photos of BFRP sheets under standard tension testing.The above test on mechanical properties of the BFRP sheet was based on the standard testing specimen. However, the possible variation of mechanical properties of the BFRP sheet with long span and large width is not clear until now, which is of important necessity to be evaluated. One test was thus conducted to assess the tensile performance of two layers of BFRP sheets with a length of 3000 mm and width of 50 mm after impregnated with epoxy resin adhesive L-500. The control tensile force was 12.0 kN. The strain distributions of the BFRP sheet along the length direction were detected based on three groups of strain gages, and each group is composed of three strain gages, as shown in Figure3.Figure 3
Layout of strain gages for BFRP sheets with long span and large width.The load-strain curve of the two layers of BFRP sheets is shown in Figure4, where the ordinate of the figure is average strain obtained from strain gages in the group B attached in the middle of the BFRP sheet. The significant fluctuation can be observed during the loading history due to the manual compression processing of the adhesive. Before the control tensile force, no failure was found in the BFRP sheet. Besides, the strain distributions along the length direction were relatively even based on detected strain variation. The calculated elastic modulus was 72.97 GPa close to that obtained from the standard test specimen, which demonstrated that the long span and large width did not affect the basic mechanical properties of the BFRP sheet.Figure 4
Load-average strain curve obtained from strain gages in group B.


## 2.1. Material Test on Laminated Bamboo considering Size Effect

The mechanical properties of the bamboo engineering material were found to be related to the dimension of the tested specimen. In order to take the size effect into consideration, one laminated bamboo beam specimen with a dimension (b × h × l) of 50 mm × 150 mm × 3000 mm was tested first, almost the same dimension with the beam used in the laminated bamboo beam applied with prestressed BFRP sheet to be investigated in the following section. Details of the material test specimen are listed in Table 1, and the four-point bending test setup for the material test specimen is depicted in Figure 1.Table 1
Material properties of the laminated bamboo considering size effect.
Type
l (mm)
l
0 (mm)
a (mm)
b (mm)
c (mm)
h (mm)
E
m (N/mm2)
f
m (N/mm2)
Laminated
3000
2700
900
50
150
150
11329.5
61.2
Note. l is the total length of the material test specimen; c is the distance between the end of the beam and support, which is set to avoid the stress concentration at the corner of the laminated beam.Figure 1
Material test setup.The flexural modulus,Em, and flexural stress, fm, of the laminated bamboo can be obtained based on(1)Em=aΔF48IΔω3l02−4a2,fm=aFuh4I,where a is the distance between the support and loading point; l0 is the clear span of the laminated bamboo beam between two supports; ΔF is the loading increment; Δω is the deflection increment corresponding to the loading increment; I equal to bh3/12 is the moment of inertia of the laminated bamboo beam, where b and h are the width and height of the laminated bamboo beam, respectively; and Fu is the maximum applied load during the material test. The flexural modulus, Em, and the flexural stress, fm, for the laminated bamboo are calculated and listed in Table 1 based on the material test.


## 2.2. Material Test on BFRP Sheet

The BFRP sheet with density of 300 g/cm2 was provided by the Basalt Fiber Center of Southeast University. Six BFRP sheets with a nominal thickness of 0.147 mm were tested under tension per ACI 440 [29], where the BFRP sheet was impregnated with epoxy resin adhesive L-500. The tensile strength and the flexural strengths of the epoxy resin adhesive L-500 were 48.8 MPa and 77.5 MPa, respectively. Failure photos of the six BFRP sheets are shown in Figure 2. Test results showed that the average ultimate tensile strain, elastic modulus, ultimate tensile stress, and standard tensile stress were 2.51%, 73.8 GPa, 1725.4 MPa, and 1563.2 MPa. The mechanical behavior of the BFRP sheet was considered as elastic and linear.Figure 2
Failure photos of BFRP sheets under standard tension testing.The above test on mechanical properties of the BFRP sheet was based on the standard testing specimen. However, the possible variation of mechanical properties of the BFRP sheet with long span and large width is not clear until now, which is of important necessity to be evaluated. One test was thus conducted to assess the tensile performance of two layers of BFRP sheets with a length of 3000 mm and width of 50 mm after impregnated with epoxy resin adhesive L-500. The control tensile force was 12.0 kN. The strain distributions of the BFRP sheet along the length direction were detected based on three groups of strain gages, and each group is composed of three strain gages, as shown in Figure3.Figure 3
Layout of strain gages for BFRP sheets with long span and large width.The load-strain curve of the two layers of BFRP sheets is shown in Figure4, where the ordinate of the figure is average strain obtained from strain gages in the group B attached in the middle of the BFRP sheet. The significant fluctuation can be observed during the loading history due to the manual compression processing of the adhesive. Before the control tensile force, no failure was found in the BFRP sheet. Besides, the strain distributions along the length direction were relatively even based on detected strain variation. The calculated elastic modulus was 72.97 GPa close to that obtained from the standard test specimen, which demonstrated that the long span and large width did not affect the basic mechanical properties of the BFRP sheet.Figure 4
Load-average strain curve obtained from strain gages in group B.


## 3. Preliminary Design for the Laminated Bamboo Beam Applied with Prestressed BFRP Sheet

### 3.1. Prestress Control

When the initial prestress was relatively too high for the laminated bamboo beam applied with prestressed BFRP sheet, the following problems may be expected: (1) relatively large initial deflection, (2) relatively large slip between the BFRP sheet and laminated bamboo beam, and (3) the fracture or significant creep of the BFRP sheet under high prestress. When the initial deflection was large, the laminated bamboo beam applied with prestressed BFRP sheet may be in the antiarch state in the normal use state. Therefore, it is of important necessity to determine the appropriate range of the initial prestressed force of the BFRP sheet to avoid the above problems.The recommended initial deflection caused by the initial prestressed force of the BFRP sheet was defined asLt/500 based on the principle of the initial deflection caused by initial prestressed force equal to the deflection resulted from the dead load, where the dead load was taken as 0.15 kN/m2 and Lt is the total length of the laminated bamboo beam. For a certain initial prestress level, the calculated initial deflection can be compared with the recommended initial deflection, Lt/500, to determine whether the initial prestress level is appropriate. When the prestress loss was neglected and the elastic state of the laminated bamboo beam was assumed, the initial antiarch value, ωi, caused by the initial prestressed force can be calculated as expressed in equation (2), where the contribution of the BFRP sheet to the moment of inertia is not considered because the BFRP sheet is in the compressive zone.(2)ωi=MiLt28EmI,where Mi is the initial moment caused by the initial prestressed force and is expressed in the following equation:(3)M=fiAh2,where fi is the initial prestress level and A is the cross section area of the BFRP sheets and is 2 × 0.147 mm × 50 mm for two layers of BFRP sheets with nominal thickness of 0.147 mm and width of 50 mm.When the initial prestress level is 35% of the standard tensile stress of the BFRP sheet,ftk, the calculated initial antiarch value is 4.1 mm less than Lt/500. When the initial prestress level is 0.50ftk, the calculated initial antiarch value is 5.9 mm almost reaching Lt/500. Therefore, the value of the initial prestress is defined as 0.50ftk (11.49 kN, 781.6 MPa) in this paper. To compensate for the prestress loss, a 5% super tension is adopted, which finally leads to a recommended initial prestressed force of the BFRP sheet of 12.0 kN.


### 3.2. Bond Slip Verification

The bond slip between the BFRP sheet and the laminated bamboo should be checked to confirm the reliability of the employment of the prestressed BFRP sheet to the laminated bamboo beam when the bonding material is adopted as the epoxy resin adhesive L-500. Based on test results of a series of double shear tests on the bond behavior between the two-layer BFRP sheets and laminated bamboo (width of 50 mm and bond length of 300 mm) listed in Table2, it is found that the average ultimate bond strength (36.7 kN) is far more than the recommended initial prestressed force (12.0 kN) [30]. The strain variation of the BFRP sheet is limited within the 100 mm range away from the loaded end. It is found that the bond slip value caused by the initial prestressed force is small, which is calculated as 0.08 mm under a force of 12 kN.Table 2
Test results of double shear test.
Specimen label
Bonding material
Ultimate loadPu
JQ1
L-500
36.5 kN
JQ2
L-500
38.5 kN
JQ3
L-500
35.0 kN


## 3.1. Prestress Control

When the initial prestress was relatively too high for the laminated bamboo beam applied with prestressed BFRP sheet, the following problems may be expected: (1) relatively large initial deflection, (2) relatively large slip between the BFRP sheet and laminated bamboo beam, and (3) the fracture or significant creep of the BFRP sheet under high prestress. When the initial deflection was large, the laminated bamboo beam applied with prestressed BFRP sheet may be in the antiarch state in the normal use state. Therefore, it is of important necessity to determine the appropriate range of the initial prestressed force of the BFRP sheet to avoid the above problems.The recommended initial deflection caused by the initial prestressed force of the BFRP sheet was defined asLt/500 based on the principle of the initial deflection caused by initial prestressed force equal to the deflection resulted from the dead load, where the dead load was taken as 0.15 kN/m2 and Lt is the total length of the laminated bamboo beam. For a certain initial prestress level, the calculated initial deflection can be compared with the recommended initial deflection, Lt/500, to determine whether the initial prestress level is appropriate. When the prestress loss was neglected and the elastic state of the laminated bamboo beam was assumed, the initial antiarch value, ωi, caused by the initial prestressed force can be calculated as expressed in equation (2), where the contribution of the BFRP sheet to the moment of inertia is not considered because the BFRP sheet is in the compressive zone.(2)ωi=MiLt28EmI,where Mi is the initial moment caused by the initial prestressed force and is expressed in the following equation:(3)M=fiAh2,where fi is the initial prestress level and A is the cross section area of the BFRP sheets and is 2 × 0.147 mm × 50 mm for two layers of BFRP sheets with nominal thickness of 0.147 mm and width of 50 mm.When the initial prestress level is 35% of the standard tensile stress of the BFRP sheet,ftk, the calculated initial antiarch value is 4.1 mm less than Lt/500. When the initial prestress level is 0.50ftk, the calculated initial antiarch value is 5.9 mm almost reaching Lt/500. Therefore, the value of the initial prestress is defined as 0.50ftk (11.49 kN, 781.6 MPa) in this paper. To compensate for the prestress loss, a 5% super tension is adopted, which finally leads to a recommended initial prestressed force of the BFRP sheet of 12.0 kN.


## 3.2. Bond Slip Verification

The bond slip between the BFRP sheet and the laminated bamboo should be checked to confirm the reliability of the employment of the prestressed BFRP sheet to the laminated bamboo beam when the bonding material is adopted as the epoxy resin adhesive L-500. Based on test results of a series of double shear tests on the bond behavior between the two-layer BFRP sheets and laminated bamboo (width of 50 mm and bond length of 300 mm) listed in Table2, it is found that the average ultimate bond strength (36.7 kN) is far more than the recommended initial prestressed force (12.0 kN) [30]. The strain variation of the BFRP sheet is limited within the 100 mm range away from the loaded end. It is found that the bond slip value caused by the initial prestressed force is small, which is calculated as 0.08 mm under a force of 12 kN.Table 2
Test results of double shear test.
Specimen label
Bonding material
Ultimate loadPu
JQ1
L-500
36.5 kN
JQ2
L-500
38.5 kN
JQ3
L-500
35.0 kN


## 4. Specimen Preparation

The main process of the preparation for the laminated bamboo beam applied with prestressed BFRP sheet is summarized as follows:(1)
Impregnating and interfacial treatment: Two layers of BFRP sheets were impregnated with epoxy resin adhesive L-500. For ease of applying the initial prestress force to the BFRP sheet, a special fixture which was composed of two steel plates with two bolt holes shown in Figure5(a) was introduced after 2-day cure of the epoxy resin adhesive L-500. When the special fixture was connected to the end of the BFRP sheet, the prestressed force applied by the tensioning equipment can be exerted to the special fixture and then transferred to the BFRP sheet. Besides, the plum blossom notches were made on the surface of the laminated bamboo beam to increase the bond between the BFRP sheet and laminated bamboo beam.(2)
Applying prestressed force: Firstly, both of the BFRP sheet and surface of the laminated bamboo beam were coated with the structural adhesive and then pressed together. Then, graded prestressed forces, including four force levels of 5 kN, 8 kN, 19 kN, and 11.49 kN (or 12.0 kN), were applied to the BFRP sheet. The load holding duration for each level of prestressed force was about 2 minutes, and the BFRP sheet was pressed to make the distribution of the structural adhesive even during the holding duration.(3)
Releasing BFRP sheet: Both ends of the laminated bamboo beam were constructed with the structural measurement shown in Figure5(b), which was characteristic as two steel plates connected by four bolts and aimed at avoiding the delamination between the BFRP sheet and laminated bamboo beam due to the shear stress and normal stress [31, 32]. After 7-day curing of the epoxy resin adhesive L-500, the BFRP sheet between the beam end and tensioning equipment was cut, which meant that the BFRP sheet was released and the prestressing was finished. The representative specimen of the laminated bamboo beam applied with prestressed BFRP sheet after completion is shown in Figure 6.Figure 5
Specimen preparation: (a) special fixture for BFRP sheet and (b) structural measurement.
(a)
(b)Figure 6
The photo of the laminated bamboo beam applied with prestressed BFRP sheet.In the present study, the whole tensioning system at the tensioned and fixed ends is depicted in Figure7. Nine components were involved in this system, which were independent reaction system, special fixture for BFRP sheet, tensioning fixture, reaction cylinder, anchor bolt, bearing plate, center hole jack, anchor nut, and force transducer. The anchor nut was used to keep the jack in place at the tensioned end and fasten the tensioning fixture at the fixed end. When the applied force reached the target initial prestressed force, the anchor bolt depicted in Figure 7(a) would be fixed in order to dismount the center hole jack.Figure 7
Assembly of tensioning system: (a) tensioned end, (b) tension fixture, and (c) fixed end.
(a)
(b)
(c)


## 5. Prestress Loss in the Laminated Bamboo Beam Applied with Prestressed BFRP Sheet

### 5.1. Definition of Prestress Loss

Taking the release of the prestressed BFRP sheet as a dividing line, the specimen can be divided into preparation stage and storage stage. The former is defined as the preparation process of the specimen until the release of the BFRP sheet and the latter is recognized as the specimen to be stored or used after the release. Based on different stages, types of the prestress loss observed in the laminated bamboo beam applied with prestressed BFRP sheet are summarized as follows.In specimen preparation stage, (1)σl1 was caused by the deformation of the tensioning equipment and the bond slip between the tensioning fixture and BFRP sheet; (2) σl2 was caused by the retraction of the BFRP sheet due to tightening of the anchor bolt; (3) σl3 was caused by the friction between the BFRP sheet and laminated bamboo beam; (4) σl4 was caused by the relaxation of the BFRP sheet after reaching the target initial prestressed force and before the release of the BFRP sheet; (5) σl5 was caused by the elastic deformation of the laminated bamboo beam at the time of the release of BFRP sheet; and (6) σl6 was caused by the bond slip between the BFRP sheet and laminated bamboo beam due to the release of the BFRP sheet.In specimen storage stage, (1)σl4 was caused by the further relaxation of the BFRP sheet after releasing of the BFRP sheet; (2) σl7 was caused by the creep of the structural adhesive; and (3) σl8 was caused by the creep of the laminated bamboo beam.


### 5.2. Measurement of Prestress Loss

In order to quantitatively measure the prestress loss in the laminated bamboo beam applied with prestressed BFRP sheet, three specimens including P-1, P-2, and P-3 were tested in this section, details of which are listed in Table3. Specimen P-1 without structural measurement in Figure 5(b) was monitored at the preparation stage, and specimens P-2 and P-3 with structural measurement were tested until the storage state. The strains of the BFRP sheet and loads at tensioned and fixed ends during the preparation and storage stages were monitored by strain gages shown in Figure 8 and force transducers depicted in Figure 7, respectively. The deflections of the specimens were also measured.Table 3
Specimens for measuring the prestress loss.
Label
b × h × l (mm)
F
0 (kN)
b
f (mm)
ε
0
Preparation stage
Storage stage
P-1
50 × 150 × 2978
12.02
51.2
10820
2-9 11 : 38 to 2-13 9 : 09
—
P-2
50 × 150 × 2978
12.54
51.9
11135
2-18 10 : 45 to 2-24 9 : 08
2-24 9 : 08 to 3-03 8 : 11
P-3
50 × 150 × 3000
12.54
51.1
11310
3-03 11 : 35 to 3-10 8 : 55
3-10 8 : 55 to 3-14 8 : 55
Note. F
0 is the actual load applied at the tensioned end, which is the target initial prestressed force; bf is the width of the BFRP sheet; ε0 is the calculated initial strain caused by the initial prestressed force; 2-9 11 : 38 means the data were monitored at 11 : 38 on February 9.Figure 8
Strain gages for specimens P-1, P-2, and P-3 (the number in brackets is adopted for specimen P-3).


### 5.3. Test Results of Prestress Loss

The measured values related to the prestress loss in the three specimens are listed in Table4. Symbols in Table 4 are explained as follows: F′ is the measured load at the fixed end caused by F0; Fmin′ is the measured load at the fixed end before releasing the BFRP sheet; and ε0′ is the midspan initial strain caused by the initial prestressed force, which was the average value of strains of the BFRP sheet obtained from three strain gages at the midspan. The measured values of ε0′ agreed well with calculated values of ε0; ε1′ is the midspan strain of the BFRP sheet before the release of the BFRP sheet; ε2′ is the midspan strain of the BFRP sheet after the release of the BFRP sheet; ε3′ is the midspan strain of the BFRP sheet until the end of measurement of the storage stage; and ω0 is the theoretical initial deflection caused by F0, based on equation (2). Considering the effect of the structural measurement employed in specimens P-2 and P-3, ends of the two specimens were viewed as rigid, which were removed from the total length of the specimen in the calculation of ω0; ω′ is the deflection after the release of the BFRP sheet; ωmax′ is the final deflection until the end of measurement of the storage stage.Table 4
Measured results related to prestress loss.
Label
F′ (kN)
F
min
′ (kN)
ε
0
′ (με)
ε
1
′ (με)
ε
2
′ (με)
ε
3
′ (με)
ω
0 (mm)
ω′ (mm)
ω
max
′ (mm)
P-1
11.78
9.90
10288
9519
9053
–
6.29
–
–
P-2
12.02
10.49
9811
8113
7449
5991
4.54
3.04
4.15
P-3
12.08
10.82
10093
8916
8324
8108
4.62
3.53
3.77


### 5.4. Quantitative Prestress Loss Analyses

#### 5.4.1. Prestress Loss in the Preparation Stage

The calculation of different types of prestress losses was conducted based on the preparation stage and storage stage, respectively. Firstly, the prestress losses occurred in the preparation stage were analyzed. In the present test, the interface between the tensioning fixture and BFRP sheet was rough and the tensioning equipment was rigid enough, which made the prestress lossσl1 small enough to be neglected. Both of the prestress losses σl2 and σl3 can be calculated by the difference between F′ and F0 after the completion of tensioning, which were 0.24 kN, 0.52 kN, and 0.46 kN for specimens P-1, P-2, and P-3, respectively. The ratios of the prestress losses σl2 and σl3 of the three specimens to the applied load at the tensioned end, F0, were 2.0%, 4.1%, and 3.7%, respectively.After reaching the target initial prestressed force and before the release of the BFRP sheet, the prestress lossσl4 can be calculated by monitoring the load variation at the fixed end, as shown in Figure 9. It is concluded that the prestress relaxation developed quickly at the initial stage. After 20 hours, the load variation caused by the prestress relaxation gradually became gentle. The prestress loss caused by the BFRP sheet relaxation and the ratio of the certain relaxation to the total relaxation under a certain period are listed Table 5. It can be found that the prestress loss σl4 caused by the relaxation of the BFRP sheet in the preparation stage was 10.0% to 15.6% of the applied load at the tensioned end F0 based on load variation. Within 2 hours, the prestress loss was about 30% of the total loss, and the prestress loss within 20 hours was around 50% to 70% of the total loss. Until 40 hours, the prestress loss reached almost 90% of the total prestress loss. The value of the prestress loss σl4 caused by the relaxation of the BFRP sheet in the preparation stage was related to the initial prestressed stress of the BFRP sheet, which explained that the prestress losses σl4 of specimens P-2 and P-3 with same structural measurement and similar initial prestressed stresses were similar. However, specimen P-1 without structural measurement had relatively larger prestress loss compared with other two specimens.Figure 9
Load variation at the fixed end.Table 5
Calculations for prestress lossσl4.
F
R (kN)
η
f (%)
η
F2h (%)
η
F20h (%)
η
F40h (%)
P-1
1.88
15.6
24.6
52.6
91.3
P-2
1.53
12.2
30.1
73.2
77.3
P-3
1.26
10.0
30.9
68.3
85.0
Note. F
R equal to (F′−Fmin′) is the load reduction value after reaching the target initial prestressed force and before the release of the BFRP sheet; ηf is the ratio of load reduction to the control prestressed force F0; ηF2h, ηF20h, and ηF40h are the ratios of the load reduction after 2 hours, 20 hours, and 40 hours to FR, respectively.When the prestressed BFRP sheet was released, both flexural and compressive deformations would result in the prestress lossσl5 of the specimen. In the present study, the flexural and compressive deformations were considered together based on the measurement of the strain variation of the BFRP sheet at the midspan and deflection of the laminated bamboo beam. As listed in Table 4, the values of strain reduction of the BFRP sheet at the midspan equal to (ε1′−ε2′) caused by the deformations of the laminated bamboo beam were 466 με, 664 με, and 592 με after the release of the BFRP sheet in specimens P-1, P-2, and P-3, respectively. In specimen P-1 without structural measurement, the prestress loss σl5 was 4.5% of the measured initial prestressed strain, ε0′, while in specimens P-2 and P-3, the prestress loss σl5 reached 5.9% to 6.8% of the measured initial prestressed strain, ε0′. Until now, the total prestress losses after releasing the BFRP sheet (σl1 + σl2 + σl3 + σl4 + σl5) for specimens P-2 and P-3 were 22.2% and 20.5%, respectively. Furthermore, in terms of the deflection of the laminated bamboo beam, the total prestress losses after releasing the BFRP sheet calculated as (ω0 − ω′)/ω0 for specimens P-2 and P-3 were 33.0% and 23.6%, respectively, which agreed well with the above analyses.The prestress lossσl6 in specimen P-1 without structural measurement was analyzed by the strain distribution along the laminated bamboo beam shown in Figure 10. The prestress loss σl6 concentrated within 100 mm away from the end of the specimen and then minimized quickly, which agreed well with the result obtained in Section 3.2. The large prestress loss at both ends due to the bond slip was observed in specimen P-1. However, due to the existence of the structural measurement at both ends in specimens P-2 and P-3, the strain variation due to the bond slip can be neglected, which means the prestress loss σl6 was neglected in the specimen with structural measurement.Figure 10
Strain distribution of specimen P-1 forσl6.


#### 5.4.2. Prestress Loss in the Storage Stage

The further prestress loss can be caused by the creep of the structural adhesive and laminated bamboo beam, as well as the further relaxation of the BFRP sheet after release. Among the three factors, the creep is main reason for the prestress loss. As shown in Figure11(a), the strain variation of the BFRP sheet at the midspan was monitored in the storage stage. It can be found that the strain variation in specimen P-2 was around 1458 με and in specimen P-3 was about 216 με. The strain variation of the specimen P-2 became gentle after 100 hours of the release and the strain variation of the specimen P-3 was relatively stale after release. By comparing the strain variation and the measured initial prestressed strain, the prestress losses of specimens P-2 and P-3 were 14.9% and 2.1%, respectively.Figure 11
(a) Strain variation of specimens P-2 and P-3; (b) deflection variation of specimens P-2 and P-3.
(a)
(b)In Figure11(b), the midspan deflection variation is presented. A significant increase of the midspan deflection in specimen P-2 was observed, which developed from 3.04 mm to 4.15 mm as listed in Table 4. After 100 hours of the release, the deflection of the beam became stable. However, the midspan deflection variation of the specimen P-3 was stable after about 20 hours of the release, and the deflection only grew from 3.53 mm to 3.77 mm. Test results are relatively dispersed, which means that more measured data are required in the future study pointing at the prestress loss in the storage stage.


### 5.5. Effective Prestressed Force

The effective prestress,σpe, can be achieved by subtracting the prestress loss, σl, from the target initial prestressed force, σcon, which is specified in the following equation:(4)σpe=σcon−σl,where σl includes σl1, σl2, σl3, σl4, σl5, and σl6 in the preparation stage and consists of σl1, σl2, σl3, σl4, σl5, σl6, σl7, and σl8 in the storage stage. Based on analyses of prestress loss above, σl in the preparation stage is recommended as 22.0%. However, in the storage stage, due to lack of enough calibrated data, the recommended value of prestress loss is not available.


## 5.1. Definition of Prestress Loss

Taking the release of the prestressed BFRP sheet as a dividing line, the specimen can be divided into preparation stage and storage stage. The former is defined as the preparation process of the specimen until the release of the BFRP sheet and the latter is recognized as the specimen to be stored or used after the release. Based on different stages, types of the prestress loss observed in the laminated bamboo beam applied with prestressed BFRP sheet are summarized as follows.In specimen preparation stage, (1)σl1 was caused by the deformation of the tensioning equipment and the bond slip between the tensioning fixture and BFRP sheet; (2) σl2 was caused by the retraction of the BFRP sheet due to tightening of the anchor bolt; (3) σl3 was caused by the friction between the BFRP sheet and laminated bamboo beam; (4) σl4 was caused by the relaxation of the BFRP sheet after reaching the target initial prestressed force and before the release of the BFRP sheet; (5) σl5 was caused by the elastic deformation of the laminated bamboo beam at the time of the release of BFRP sheet; and (6) σl6 was caused by the bond slip between the BFRP sheet and laminated bamboo beam due to the release of the BFRP sheet.In specimen storage stage, (1)σl4 was caused by the further relaxation of the BFRP sheet after releasing of the BFRP sheet; (2) σl7 was caused by the creep of the structural adhesive; and (3) σl8 was caused by the creep of the laminated bamboo beam.


## 5.2. Measurement of Prestress Loss

In order to quantitatively measure the prestress loss in the laminated bamboo beam applied with prestressed BFRP sheet, three specimens including P-1, P-2, and P-3 were tested in this section, details of which are listed in Table3. Specimen P-1 without structural measurement in Figure 5(b) was monitored at the preparation stage, and specimens P-2 and P-3 with structural measurement were tested until the storage state. The strains of the BFRP sheet and loads at tensioned and fixed ends during the preparation and storage stages were monitored by strain gages shown in Figure 8 and force transducers depicted in Figure 7, respectively. The deflections of the specimens were also measured.Table 3
Specimens for measuring the prestress loss.
Label
b × h × l (mm)
F
0 (kN)
b
f (mm)
ε
0
Preparation stage
Storage stage
P-1
50 × 150 × 2978
12.02
51.2
10820
2-9 11 : 38 to 2-13 9 : 09
—
P-2
50 × 150 × 2978
12.54
51.9
11135
2-18 10 : 45 to 2-24 9 : 08
2-24 9 : 08 to 3-03 8 : 11
P-3
50 × 150 × 3000
12.54
51.1
11310
3-03 11 : 35 to 3-10 8 : 55
3-10 8 : 55 to 3-14 8 : 55
Note. F
0 is the actual load applied at the tensioned end, which is the target initial prestressed force; bf is the width of the BFRP sheet; ε0 is the calculated initial strain caused by the initial prestressed force; 2-9 11 : 38 means the data were monitored at 11 : 38 on February 9.Figure 8
Strain gages for specimens P-1, P-2, and P-3 (the number in brackets is adopted for specimen P-3).


## 5.3. Test Results of Prestress Loss

The measured values related to the prestress loss in the three specimens are listed in Table4. Symbols in Table 4 are explained as follows: F′ is the measured load at the fixed end caused by F0; Fmin′ is the measured load at the fixed end before releasing the BFRP sheet; and ε0′ is the midspan initial strain caused by the initial prestressed force, which was the average value of strains of the BFRP sheet obtained from three strain gages at the midspan. The measured values of ε0′ agreed well with calculated values of ε0; ε1′ is the midspan strain of the BFRP sheet before the release of the BFRP sheet; ε2′ is the midspan strain of the BFRP sheet after the release of the BFRP sheet; ε3′ is the midspan strain of the BFRP sheet until the end of measurement of the storage stage; and ω0 is the theoretical initial deflection caused by F0, based on equation (2). Considering the effect of the structural measurement employed in specimens P-2 and P-3, ends of the two specimens were viewed as rigid, which were removed from the total length of the specimen in the calculation of ω0; ω′ is the deflection after the release of the BFRP sheet; ωmax′ is the final deflection until the end of measurement of the storage stage.Table 4
Measured results related to prestress loss.
Label
F′ (kN)
F
min
′ (kN)
ε
0
′ (με)
ε
1
′ (με)
ε
2
′ (με)
ε
3
′ (με)
ω
0 (mm)
ω′ (mm)
ω
max
′ (mm)
P-1
11.78
9.90
10288
9519
9053
–
6.29
–
–
P-2
12.02
10.49
9811
8113
7449
5991
4.54
3.04
4.15
P-3
12.08
10.82
10093
8916
8324
8108
4.62
3.53
3.77


## 5.4. Quantitative Prestress Loss Analyses

### 5.4.1. Prestress Loss in the Preparation Stage

The calculation of different types of prestress losses was conducted based on the preparation stage and storage stage, respectively. Firstly, the prestress losses occurred in the preparation stage were analyzed. In the present test, the interface between the tensioning fixture and BFRP sheet was rough and the tensioning equipment was rigid enough, which made the prestress lossσl1 small enough to be neglected. Both of the prestress losses σl2 and σl3 can be calculated by the difference between F′ and F0 after the completion of tensioning, which were 0.24 kN, 0.52 kN, and 0.46 kN for specimens P-1, P-2, and P-3, respectively. The ratios of the prestress losses σl2 and σl3 of the three specimens to the applied load at the tensioned end, F0, were 2.0%, 4.1%, and 3.7%, respectively.After reaching the target initial prestressed force and before the release of the BFRP sheet, the prestress lossσl4 can be calculated by monitoring the load variation at the fixed end, as shown in Figure 9. It is concluded that the prestress relaxation developed quickly at the initial stage. After 20 hours, the load variation caused by the prestress relaxation gradually became gentle. The prestress loss caused by the BFRP sheet relaxation and the ratio of the certain relaxation to the total relaxation under a certain period are listed Table 5. It can be found that the prestress loss σl4 caused by the relaxation of the BFRP sheet in the preparation stage was 10.0% to 15.6% of the applied load at the tensioned end F0 based on load variation. Within 2 hours, the prestress loss was about 30% of the total loss, and the prestress loss within 20 hours was around 50% to 70% of the total loss. Until 40 hours, the prestress loss reached almost 90% of the total prestress loss. The value of the prestress loss σl4 caused by the relaxation of the BFRP sheet in the preparation stage was related to the initial prestressed stress of the BFRP sheet, which explained that the prestress losses σl4 of specimens P-2 and P-3 with same structural measurement and similar initial prestressed stresses were similar. However, specimen P-1 without structural measurement had relatively larger prestress loss compared with other two specimens.Figure 9
Load variation at the fixed end.Table 5
Calculations for prestress lossσl4.
F
R (kN)
η
f (%)
η
F2h (%)
η
F20h (%)
η
F40h (%)
P-1
1.88
15.6
24.6
52.6
91.3
P-2
1.53
12.2
30.1
73.2
77.3
P-3
1.26
10.0
30.9
68.3
85.0
Note. F
R equal to (F′−Fmin′) is the load reduction value after reaching the target initial prestressed force and before the release of the BFRP sheet; ηf is the ratio of load reduction to the control prestressed force F0; ηF2h, ηF20h, and ηF40h are the ratios of the load reduction after 2 hours, 20 hours, and 40 hours to FR, respectively.When the prestressed BFRP sheet was released, both flexural and compressive deformations would result in the prestress lossσl5 of the specimen. In the present study, the flexural and compressive deformations were considered together based on the measurement of the strain variation of the BFRP sheet at the midspan and deflection of the laminated bamboo beam. As listed in Table 4, the values of strain reduction of the BFRP sheet at the midspan equal to (ε1′−ε2′) caused by the deformations of the laminated bamboo beam were 466 με, 664 με, and 592 με after the release of the BFRP sheet in specimens P-1, P-2, and P-3, respectively. In specimen P-1 without structural measurement, the prestress loss σl5 was 4.5% of the measured initial prestressed strain, ε0′, while in specimens P-2 and P-3, the prestress loss σl5 reached 5.9% to 6.8% of the measured initial prestressed strain, ε0′. Until now, the total prestress losses after releasing the BFRP sheet (σl1 + σl2 + σl3 + σl4 + σl5) for specimens P-2 and P-3 were 22.2% and 20.5%, respectively. Furthermore, in terms of the deflection of the laminated bamboo beam, the total prestress losses after releasing the BFRP sheet calculated as (ω0 − ω′)/ω0 for specimens P-2 and P-3 were 33.0% and 23.6%, respectively, which agreed well with the above analyses.The prestress lossσl6 in specimen P-1 without structural measurement was analyzed by the strain distribution along the laminated bamboo beam shown in Figure 10. The prestress loss σl6 concentrated within 100 mm away from the end of the specimen and then minimized quickly, which agreed well with the result obtained in Section 3.2. The large prestress loss at both ends due to the bond slip was observed in specimen P-1. However, due to the existence of the structural measurement at both ends in specimens P-2 and P-3, the strain variation due to the bond slip can be neglected, which means the prestress loss σl6 was neglected in the specimen with structural measurement.Figure 10
Strain distribution of specimen P-1 forσl6.


### 5.4.2. Prestress Loss in the Storage Stage

The further prestress loss can be caused by the creep of the structural adhesive and laminated bamboo beam, as well as the further relaxation of the BFRP sheet after release. Among the three factors, the creep is main reason for the prestress loss. As shown in Figure11(a), the strain variation of the BFRP sheet at the midspan was monitored in the storage stage. It can be found that the strain variation in specimen P-2 was around 1458 με and in specimen P-3 was about 216 με. The strain variation of the specimen P-2 became gentle after 100 hours of the release and the strain variation of the specimen P-3 was relatively stale after release. By comparing the strain variation and the measured initial prestressed strain, the prestress losses of specimens P-2 and P-3 were 14.9% and 2.1%, respectively.Figure 11
(a) Strain variation of specimens P-2 and P-3; (b) deflection variation of specimens P-2 and P-3.
(a)
(b)In Figure11(b), the midspan deflection variation is presented. A significant increase of the midspan deflection in specimen P-2 was observed, which developed from 3.04 mm to 4.15 mm as listed in Table 4. After 100 hours of the release, the deflection of the beam became stable. However, the midspan deflection variation of the specimen P-3 was stable after about 20 hours of the release, and the deflection only grew from 3.53 mm to 3.77 mm. Test results are relatively dispersed, which means that more measured data are required in the future study pointing at the prestress loss in the storage stage.


## 5.4.1. Prestress Loss in the Preparation Stage

The calculation of different types of prestress losses was conducted based on the preparation stage and storage stage, respectively. Firstly, the prestress losses occurred in the preparation stage were analyzed. In the present test, the interface between the tensioning fixture and BFRP sheet was rough and the tensioning equipment was rigid enough, which made the prestress lossσl1 small enough to be neglected. Both of the prestress losses σl2 and σl3 can be calculated by the difference between F′ and F0 after the completion of tensioning, which were 0.24 kN, 0.52 kN, and 0.46 kN for specimens P-1, P-2, and P-3, respectively. The ratios of the prestress losses σl2 and σl3 of the three specimens to the applied load at the tensioned end, F0, were 2.0%, 4.1%, and 3.7%, respectively.After reaching the target initial prestressed force and before the release of the BFRP sheet, the prestress lossσl4 can be calculated by monitoring the load variation at the fixed end, as shown in Figure 9. It is concluded that the prestress relaxation developed quickly at the initial stage. After 20 hours, the load variation caused by the prestress relaxation gradually became gentle. The prestress loss caused by the BFRP sheet relaxation and the ratio of the certain relaxation to the total relaxation under a certain period are listed Table 5. It can be found that the prestress loss σl4 caused by the relaxation of the BFRP sheet in the preparation stage was 10.0% to 15.6% of the applied load at the tensioned end F0 based on load variation. Within 2 hours, the prestress loss was about 30% of the total loss, and the prestress loss within 20 hours was around 50% to 70% of the total loss. Until 40 hours, the prestress loss reached almost 90% of the total prestress loss. The value of the prestress loss σl4 caused by the relaxation of the BFRP sheet in the preparation stage was related to the initial prestressed stress of the BFRP sheet, which explained that the prestress losses σl4 of specimens P-2 and P-3 with same structural measurement and similar initial prestressed stresses were similar. However, specimen P-1 without structural measurement had relatively larger prestress loss compared with other two specimens.Figure 9
Load variation at the fixed end.Table 5
Calculations for prestress lossσl4.
F
R (kN)
η
f (%)
η
F2h (%)
η
F20h (%)
η
F40h (%)
P-1
1.88
15.6
24.6
52.6
91.3
P-2
1.53
12.2
30.1
73.2
77.3
P-3
1.26
10.0
30.9
68.3
85.0
Note. F
R equal to (F′−Fmin′) is the load reduction value after reaching the target initial prestressed force and before the release of the BFRP sheet; ηf is the ratio of load reduction to the control prestressed force F0; ηF2h, ηF20h, and ηF40h are the ratios of the load reduction after 2 hours, 20 hours, and 40 hours to FR, respectively.When the prestressed BFRP sheet was released, both flexural and compressive deformations would result in the prestress lossσl5 of the specimen. In the present study, the flexural and compressive deformations were considered together based on the measurement of the strain variation of the BFRP sheet at the midspan and deflection of the laminated bamboo beam. As listed in Table 4, the values of strain reduction of the BFRP sheet at the midspan equal to (ε1′−ε2′) caused by the deformations of the laminated bamboo beam were 466 με, 664 με, and 592 με after the release of the BFRP sheet in specimens P-1, P-2, and P-3, respectively. In specimen P-1 without structural measurement, the prestress loss σl5 was 4.5% of the measured initial prestressed strain, ε0′, while in specimens P-2 and P-3, the prestress loss σl5 reached 5.9% to 6.8% of the measured initial prestressed strain, ε0′. Until now, the total prestress losses after releasing the BFRP sheet (σl1 + σl2 + σl3 + σl4 + σl5) for specimens P-2 and P-3 were 22.2% and 20.5%, respectively. Furthermore, in terms of the deflection of the laminated bamboo beam, the total prestress losses after releasing the BFRP sheet calculated as (ω0 − ω′)/ω0 for specimens P-2 and P-3 were 33.0% and 23.6%, respectively, which agreed well with the above analyses.The prestress lossσl6 in specimen P-1 without structural measurement was analyzed by the strain distribution along the laminated bamboo beam shown in Figure 10. The prestress loss σl6 concentrated within 100 mm away from the end of the specimen and then minimized quickly, which agreed well with the result obtained in Section 3.2. The large prestress loss at both ends due to the bond slip was observed in specimen P-1. However, due to the existence of the structural measurement at both ends in specimens P-2 and P-3, the strain variation due to the bond slip can be neglected, which means the prestress loss σl6 was neglected in the specimen with structural measurement.Figure 10
Strain distribution of specimen P-1 forσl6.


## 5.4.2. Prestress Loss in the Storage Stage

The further prestress loss can be caused by the creep of the structural adhesive and laminated bamboo beam, as well as the further relaxation of the BFRP sheet after release. Among the three factors, the creep is main reason for the prestress loss. As shown in Figure11(a), the strain variation of the BFRP sheet at the midspan was monitored in the storage stage. It can be found that the strain variation in specimen P-2 was around 1458 με and in specimen P-3 was about 216 με. The strain variation of the specimen P-2 became gentle after 100 hours of the release and the strain variation of the specimen P-3 was relatively stale after release. By comparing the strain variation and the measured initial prestressed strain, the prestress losses of specimens P-2 and P-3 were 14.9% and 2.1%, respectively.Figure 11
(a) Strain variation of specimens P-2 and P-3; (b) deflection variation of specimens P-2 and P-3.
(a)
(b)In Figure11(b), the midspan deflection variation is presented. A significant increase of the midspan deflection in specimen P-2 was observed, which developed from 3.04 mm to 4.15 mm as listed in Table 4. After 100 hours of the release, the deflection of the beam became stable. However, the midspan deflection variation of the specimen P-3 was stable after about 20 hours of the release, and the deflection only grew from 3.53 mm to 3.77 mm. Test results are relatively dispersed, which means that more measured data are required in the future study pointing at the prestress loss in the storage stage.


## 5.5. Effective Prestressed Force

The effective prestress,σpe, can be achieved by subtracting the prestress loss, σl, from the target initial prestressed force, σcon, which is specified in the following equation:(4)σpe=σcon−σl,where σl includes σl1, σl2, σl3, σl4, σl5, and σl6 in the preparation stage and consists of σl1, σl2, σl3, σl4, σl5, σl6, σl7, and σl8 in the storage stage. Based on analyses of prestress loss above, σl in the preparation stage is recommended as 22.0%. However, in the storage stage, due to lack of enough calibrated data, the recommended value of prestress loss is not available.


## 6. Flexural Performance of the Laminated Bamboo Beam Applied with Prestressed BFRP Sheet

### 6.1. Test Protocol

Details of all tested laminated bamboo beams applied with prestressed BFRP sheet are listed in Table6. The height of the laminated bamboo beam is defined as the nominal height of the laminated bamboo beams applied with prestressed BFRP sheet, and the actual height is defined as the sum of the laminated bamboo beam height, thickness of the BFRP sheet, and thickness of the structural adhesive. The thickness of the structural adhesive was about 2–4 mm, and the thickness of the two layers of BFRP sheets after impregnated with epoxy resin adhesive L-500 was around 1.3 mm. In specimen B-1, the laminated bamboo beam was applied with non-prestressed BFRP sheet, while in specimens B-2 and B-3, the laminated bamboo beam was applied with prestressed BFRP sheet, aiming at investigating the mechanical mechanism related to prestress. Based on analyses of prestress loss above, all specimens were installed with structural measurement at beams’ ends. Besides, all specimens were tested shortly after the completion of the prestress tensioning, which meant that the creep of the structural adhesive, laminated bamboo beam, and further relaxation of the BFRP sheet were not taken into consideration for specimens B-2 and B-3.Table 6
Details of tested laminated bamboo beams applied with prestressed BFRP sheet.
Specimen label
b × h × l (mm)
l
0 (mm)
F
0 (kN)
b
f (mm)
σ
0 (MPa)
σ
pe (MPa)
ω′ (mm)
B-1
50 × 150 × 3000
2700
0
51.3
0
0
0
B-2
50 × 150 × 2978
2700
12.54
51.9
821.8
641.0
3.04
B-3
50 × 150 × 3000
2700
12.54
51.1
836.7
652.6
3.53
Note. l
0 is the distance between two supports; F0 is the actual applied prestressed force; bf is width of o BFRP sheet; σ0 is the initial prestressed stress of the BFRP sheet, which is recognized as the target initial prestressed stress, σcon; σpe is the effective prestress based on equation (4); ω′ is the measured initial deflection caused by the initial prestressed force after release of the BFRP sheet.The four-point bending test was adopted in the present experimental protocol shown in Figure12, where a 2 kN preload was applied to the specimen to verify the workability of the equipment, and then the specimen was loaded at a loading rate of 3 kN/min until failure. The layout of the strain gages and displacement transducers is shown in Figure 12. The measurement of the strain and deflection was taken after the completion of the prestressed tension. All data were automatically collected by TDS 530.Figure 12
Test setup and layout of strain gages and displacement transducers.


### 6.2. Test Results and Discussions

#### 6.2.1. Experimental Observations

The failure pictures of the laminated bamboo beam applied with non-prestressed or prestressed BFRP sheet are shown in Figure13. At the initial loading stage, no significant change can be observed in all specimens. The deflection increased distinctly after the proportional limit, and the obviously downward deformation was observed with the further increase of the applied load. When the specimen reached the ultimate load, the BFRP sheet and the bottom fibers of the laminated bamboo beam simultaneously fractured with an abrupt noise. As shown in Figure 13, the failure of the laminated bamboo beam applied with non-prestressed or prestressed BFRP sheet initiated from the loading point and propagated to a certain distance of the laminated bamboo beam.Figure 13
Failure photos of (a) overall and (b) local views for specimen B-1, (c) overall and (d) local views for specimen B-2, and (e) overall and (f) local views for specimen B-3.
(a)
(b)
(c)
(d)
(e)
(f)


#### 6.2.2. Load-Deflection Relationship

The load-deflection curves of specimens B-1, B-2, and B-3 are shown in Figure14, where the initial deflection caused by the prestressed force was subtracted from the measured deflection. The deflection at the midspan reached around 90 mm to 130 mm until failure, the ratio of which to l0 was about 1/30 to 1.4/30. It can be seen that the laminated bamboo beams applied with both non-prestressed BFRP sheet and prestressed BFRP sheet had good deformation capacity, which promised a good energy dissipation ability in all specimens.Figure 14
Load-deflection curves at the midspan.The ultimate loads of the three specimens were 29.5 kN, 29.0 kN, and 29.5 kN, respectively, which meant that the application of the prestressed force in the BFRP sheet did not affect the ultimate load. Until the failure point, the ultimate midspan deflections of specimens B-1, B-2, and B-3 were 131.41 mm, 96.41, and 96.41 mm, respectively. It is demonstrated that the ultimate deformation capacity of the laminated bamboo beam applied with prestressed BFRP sheet was reduced compared with that applied with non-prestressed BFRP sheet.As shown in Figure14, the stiffness of the three specimens was almost the same in the linear stage, but the stiffness of the laminated bamboo beam applied with prestressed BFRP sheet was relatively increased compared with specimen with non-prestressed BFRP sheet after the linear stage. It is found in Figure 15 that at the same applied load, the deflection of the laminated bamboo beams applied with prestressed BFRP sheet (specimens B-2 and B-3) was smaller than that of the laminated bamboo beam applied with non-prestressed BFRP sheet (specimen B-1). The employment of the prestressed BFRP sheet could increase the load bearing capacity under the same deflection.Figure 15
Midspan deflection under levels of loads.


#### 6.2.3. Load-Strain Curves

The load-strain curves of the three specimens are shown in Figure16. The strain data obtained from strain gages Y-1 and Y-2 monitored the strain variation of the top beam surface (compressive state) and from strain gages Y-7 and Y-8 monitored the strain of BFRP sheet (tensile state). As discussed in Section 3.2, the bond between the BFRP sheet and laminated bamboo beam was good enough to view the strain obtained from BFRP sheet as the strain of the bottom surface of the laminated bamboo beam. As seen from Figure 16, the linear strain variation can be observed in all specimens at the initial loading stage. This phenomenon accorded well with the elastic range of the load-deflection curves at the initial stage.Figure 16
Load-strain curves of the three specimens: (a) B-1, (b) B-2, and (c) B-3.
(a)
(b)
(c)Until the failure point, the maximum compressive and tensile strains of the specimen B-1 applied with non-prestressed BFRP sheet were −12345με and 9649 με, respectively. The maximum compressive strains of specimens B-2 and B-3 applied with prestressed BFRP sheet were respectively −10007 με and −10932 με, and the maximum tensile strains of the two specimens were 7004 με and 8120 με, respectively. In general, the maximum compressive strain was larger than the maximum tensile strain for all specimens. The failure of all specimens was explained as the tensile strain of the specimen reached the maximum tensile strain. Compared with the laminated bamboo beam applied with non-prestressed BFRP sheet, the ultimate tensile strain of the laminated bamboo beam applied with prestressed BFRP sheet dropped about 15.8% to 27.4%. This phenomenon was caused by the existence of the initial tensile strain in the prestressed BFRP sheet.


#### 6.2.4. Strain Distribution along Beam Height and Position of Neutral Axis

The strain distribution along the beam height (captured from strain gages Y-3, Y-4, Y-5, and Y-6) under different loads shown in Figure17 was analyzed to define the position of the neutral axis. The abscissa of the figure is the measured strain value and the ordinate is the distance between the strain gage and bottom surface of the beam. An almost linear strain distribution along the beam height at the midspan was finally obtained, and the plane section assumption is suitable for the laminated bamboo beam applied by non-prestressed or prestressed BFRP sheet.Figure 17
Strain distribution along beam height under different loads: (a) B-1, (b) B-2, and (c) B-3.
(a)
(b)
(c)Based on the detected strain values in Figure17, the positions of the neutral axis at the midspan under different loads are calculated in Table 7. It can be found that the position of the neutral axis was near the middle height of the laminated bamboo beam at the initial loading stage (5 kN). With the further increase of the applied load, the position of the neutral axis gradually went down. Until the ultimate load, the neutral axis of the specimen B-1 was around 0.39 of the laminated bamboo beam height, and the neutral axes of specimens B-2 and B-3 were between 0.43 and 0.44 of the laminated bamboo beam height. It is found that the neutral axis of the laminated bamboo beam applied with prestressed BFRP sheet was a little higher than that of the laminated bamboo beam applied with non-prestressed BFRP sheet under the same load.Table 7
Positions of neutral axis under different loads.
Load (kN)
B-1
B-2
B-3
h
l (mm)
h
l/h
h
l (mm)
h
l/h
h
l (mm)
h
l/h
5
72.97
0.49
73.90
0.49
75.26
0.50
10
72.15
0.48
73.82
0.49
75.37
0.50
15
69.99
0.47
73.67
0.49
75.02
0.50
20
65.82
0.44
72.05
0.48
73.62
0.49
25
61.89
0.41
68.82
0.46
69.86
0.47
P
u
57.93
0.39
65.49
0.44
63.86
0.43
Note. h
l is the distance between the neutral axis and the bottom surface of the laminated bamboo beam; Pu is the ultimate load.


## 6.1. Test Protocol

Details of all tested laminated bamboo beams applied with prestressed BFRP sheet are listed in Table6. The height of the laminated bamboo beam is defined as the nominal height of the laminated bamboo beams applied with prestressed BFRP sheet, and the actual height is defined as the sum of the laminated bamboo beam height, thickness of the BFRP sheet, and thickness of the structural adhesive. The thickness of the structural adhesive was about 2–4 mm, and the thickness of the two layers of BFRP sheets after impregnated with epoxy resin adhesive L-500 was around 1.3 mm. In specimen B-1, the laminated bamboo beam was applied with non-prestressed BFRP sheet, while in specimens B-2 and B-3, the laminated bamboo beam was applied with prestressed BFRP sheet, aiming at investigating the mechanical mechanism related to prestress. Based on analyses of prestress loss above, all specimens were installed with structural measurement at beams’ ends. Besides, all specimens were tested shortly after the completion of the prestress tensioning, which meant that the creep of the structural adhesive, laminated bamboo beam, and further relaxation of the BFRP sheet were not taken into consideration for specimens B-2 and B-3.Table 6
Details of tested laminated bamboo beams applied with prestressed BFRP sheet.
Specimen label
b × h × l (mm)
l
0 (mm)
F
0 (kN)
b
f (mm)
σ
0 (MPa)
σ
pe (MPa)
ω′ (mm)
B-1
50 × 150 × 3000
2700
0
51.3
0
0
0
B-2
50 × 150 × 2978
2700
12.54
51.9
821.8
641.0
3.04
B-3
50 × 150 × 3000
2700
12.54
51.1
836.7
652.6
3.53
Note. l
0 is the distance between two supports; F0 is the actual applied prestressed force; bf is width of o BFRP sheet; σ0 is the initial prestressed stress of the BFRP sheet, which is recognized as the target initial prestressed stress, σcon; σpe is the effective prestress based on equation (4); ω′ is the measured initial deflection caused by the initial prestressed force after release of the BFRP sheet.The four-point bending test was adopted in the present experimental protocol shown in Figure12, where a 2 kN preload was applied to the specimen to verify the workability of the equipment, and then the specimen was loaded at a loading rate of 3 kN/min until failure. The layout of the strain gages and displacement transducers is shown in Figure 12. The measurement of the strain and deflection was taken after the completion of the prestressed tension. All data were automatically collected by TDS 530.Figure 12
Test setup and layout of strain gages and displacement transducers.


## 6.2. Test Results and Discussions

### 6.2.1. Experimental Observations

The failure pictures of the laminated bamboo beam applied with non-prestressed or prestressed BFRP sheet are shown in Figure13. At the initial loading stage, no significant change can be observed in all specimens. The deflection increased distinctly after the proportional limit, and the obviously downward deformation was observed with the further increase of the applied load. When the specimen reached the ultimate load, the BFRP sheet and the bottom fibers of the laminated bamboo beam simultaneously fractured with an abrupt noise. As shown in Figure 13, the failure of the laminated bamboo beam applied with non-prestressed or prestressed BFRP sheet initiated from the loading point and propagated to a certain distance of the laminated bamboo beam.Figure 13
Failure photos of (a) overall and (b) local views for specimen B-1, (c) overall and (d) local views for specimen B-2, and (e) overall and (f) local views for specimen B-3.
(a)
(b)
(c)
(d)
(e)
(f)


### 6.2.2. Load-Deflection Relationship

The load-deflection curves of specimens B-1, B-2, and B-3 are shown in Figure14, where the initial deflection caused by the prestressed force was subtracted from the measured deflection. The deflection at the midspan reached around 90 mm to 130 mm until failure, the ratio of which to l0 was about 1/30 to 1.4/30. It can be seen that the laminated bamboo beams applied with both non-prestressed BFRP sheet and prestressed BFRP sheet had good deformation capacity, which promised a good energy dissipation ability in all specimens.Figure 14
Load-deflection curves at the midspan.The ultimate loads of the three specimens were 29.5 kN, 29.0 kN, and 29.5 kN, respectively, which meant that the application of the prestressed force in the BFRP sheet did not affect the ultimate load. Until the failure point, the ultimate midspan deflections of specimens B-1, B-2, and B-3 were 131.41 mm, 96.41, and 96.41 mm, respectively. It is demonstrated that the ultimate deformation capacity of the laminated bamboo beam applied with prestressed BFRP sheet was reduced compared with that applied with non-prestressed BFRP sheet.As shown in Figure14, the stiffness of the three specimens was almost the same in the linear stage, but the stiffness of the laminated bamboo beam applied with prestressed BFRP sheet was relatively increased compared with specimen with non-prestressed BFRP sheet after the linear stage. It is found in Figure 15 that at the same applied load, the deflection of the laminated bamboo beams applied with prestressed BFRP sheet (specimens B-2 and B-3) was smaller than that of the laminated bamboo beam applied with non-prestressed BFRP sheet (specimen B-1). The employment of the prestressed BFRP sheet could increase the load bearing capacity under the same deflection.Figure 15
Midspan deflection under levels of loads.


### 6.2.3. Load-Strain Curves

The load-strain curves of the three specimens are shown in Figure16. The strain data obtained from strain gages Y-1 and Y-2 monitored the strain variation of the top beam surface (compressive state) and from strain gages Y-7 and Y-8 monitored the strain of BFRP sheet (tensile state). As discussed in Section 3.2, the bond between the BFRP sheet and laminated bamboo beam was good enough to view the strain obtained from BFRP sheet as the strain of the bottom surface of the laminated bamboo beam. As seen from Figure 16, the linear strain variation can be observed in all specimens at the initial loading stage. This phenomenon accorded well with the elastic range of the load-deflection curves at the initial stage.Figure 16
Load-strain curves of the three specimens: (a) B-1, (b) B-2, and (c) B-3.
(a)
(b)
(c)Until the failure point, the maximum compressive and tensile strains of the specimen B-1 applied with non-prestressed BFRP sheet were −12345με and 9649 με, respectively. The maximum compressive strains of specimens B-2 and B-3 applied with prestressed BFRP sheet were respectively −10007 με and −10932 με, and the maximum tensile strains of the two specimens were 7004 με and 8120 με, respectively. In general, the maximum compressive strain was larger than the maximum tensile strain for all specimens. The failure of all specimens was explained as the tensile strain of the specimen reached the maximum tensile strain. Compared with the laminated bamboo beam applied with non-prestressed BFRP sheet, the ultimate tensile strain of the laminated bamboo beam applied with prestressed BFRP sheet dropped about 15.8% to 27.4%. This phenomenon was caused by the existence of the initial tensile strain in the prestressed BFRP sheet.


### 6.2.4. Strain Distribution along Beam Height and Position of Neutral Axis

The strain distribution along the beam height (captured from strain gages Y-3, Y-4, Y-5, and Y-6) under different loads shown in Figure17 was analyzed to define the position of the neutral axis. The abscissa of the figure is the measured strain value and the ordinate is the distance between the strain gage and bottom surface of the beam. An almost linear strain distribution along the beam height at the midspan was finally obtained, and the plane section assumption is suitable for the laminated bamboo beam applied by non-prestressed or prestressed BFRP sheet.Figure 17
Strain distribution along beam height under different loads: (a) B-1, (b) B-2, and (c) B-3.
(a)
(b)
(c)Based on the detected strain values in Figure17, the positions of the neutral axis at the midspan under different loads are calculated in Table 7. It can be found that the position of the neutral axis was near the middle height of the laminated bamboo beam at the initial loading stage (5 kN). With the further increase of the applied load, the position of the neutral axis gradually went down. Until the ultimate load, the neutral axis of the specimen B-1 was around 0.39 of the laminated bamboo beam height, and the neutral axes of specimens B-2 and B-3 were between 0.43 and 0.44 of the laminated bamboo beam height. It is found that the neutral axis of the laminated bamboo beam applied with prestressed BFRP sheet was a little higher than that of the laminated bamboo beam applied with non-prestressed BFRP sheet under the same load.Table 7
Positions of neutral axis under different loads.
Load (kN)
B-1
B-2
B-3
h
l (mm)
h
l/h
h
l (mm)
h
l/h
h
l (mm)
h
l/h
5
72.97
0.49
73.90
0.49
75.26
0.50
10
72.15
0.48
73.82
0.49
75.37
0.50
15
69.99
0.47
73.67
0.49
75.02
0.50
20
65.82
0.44
72.05
0.48
73.62
0.49
25
61.89
0.41
68.82
0.46
69.86
0.47
P
u
57.93
0.39
65.49
0.44
63.86
0.43
Note. h
l is the distance between the neutral axis and the bottom surface of the laminated bamboo beam; Pu is the ultimate load.


## 6.2.1. Experimental Observations

The failure pictures of the laminated bamboo beam applied with non-prestressed or prestressed BFRP sheet are shown in Figure13. At the initial loading stage, no significant change can be observed in all specimens. The deflection increased distinctly after the proportional limit, and the obviously downward deformation was observed with the further increase of the applied load. When the specimen reached the ultimate load, the BFRP sheet and the bottom fibers of the laminated bamboo beam simultaneously fractured with an abrupt noise. As shown in Figure 13, the failure of the laminated bamboo beam applied with non-prestressed or prestressed BFRP sheet initiated from the loading point and propagated to a certain distance of the laminated bamboo beam.Figure 13
Failure photos of (a) overall and (b) local views for specimen B-1, (c) overall and (d) local views for specimen B-2, and (e) overall and (f) local views for specimen B-3.
(a)
(b)
(c)
(d)
(e)
(f)


## 6.2.2. Load-Deflection Relationship

The load-deflection curves of specimens B-1, B-2, and B-3 are shown in Figure14, where the initial deflection caused by the prestressed force was subtracted from the measured deflection. The deflection at the midspan reached around 90 mm to 130 mm until failure, the ratio of which to l0 was about 1/30 to 1.4/30. It can be seen that the laminated bamboo beams applied with both non-prestressed BFRP sheet and prestressed BFRP sheet had good deformation capacity, which promised a good energy dissipation ability in all specimens.Figure 14
Load-deflection curves at the midspan.The ultimate loads of the three specimens were 29.5 kN, 29.0 kN, and 29.5 kN, respectively, which meant that the application of the prestressed force in the BFRP sheet did not affect the ultimate load. Until the failure point, the ultimate midspan deflections of specimens B-1, B-2, and B-3 were 131.41 mm, 96.41, and 96.41 mm, respectively. It is demonstrated that the ultimate deformation capacity of the laminated bamboo beam applied with prestressed BFRP sheet was reduced compared with that applied with non-prestressed BFRP sheet.As shown in Figure14, the stiffness of the three specimens was almost the same in the linear stage, but the stiffness of the laminated bamboo beam applied with prestressed BFRP sheet was relatively increased compared with specimen with non-prestressed BFRP sheet after the linear stage. It is found in Figure 15 that at the same applied load, the deflection of the laminated bamboo beams applied with prestressed BFRP sheet (specimens B-2 and B-3) was smaller than that of the laminated bamboo beam applied with non-prestressed BFRP sheet (specimen B-1). The employment of the prestressed BFRP sheet could increase the load bearing capacity under the same deflection.Figure 15
Midspan deflection under levels of loads.


## 6.2.3. Load-Strain Curves

The load-strain curves of the three specimens are shown in Figure16. The strain data obtained from strain gages Y-1 and Y-2 monitored the strain variation of the top beam surface (compressive state) and from strain gages Y-7 and Y-8 monitored the strain of BFRP sheet (tensile state). As discussed in Section 3.2, the bond between the BFRP sheet and laminated bamboo beam was good enough to view the strain obtained from BFRP sheet as the strain of the bottom surface of the laminated bamboo beam. As seen from Figure 16, the linear strain variation can be observed in all specimens at the initial loading stage. This phenomenon accorded well with the elastic range of the load-deflection curves at the initial stage.Figure 16
Load-strain curves of the three specimens: (a) B-1, (b) B-2, and (c) B-3.
(a)
(b)
(c)Until the failure point, the maximum compressive and tensile strains of the specimen B-1 applied with non-prestressed BFRP sheet were −12345με and 9649 με, respectively. The maximum compressive strains of specimens B-2 and B-3 applied with prestressed BFRP sheet were respectively −10007 με and −10932 με, and the maximum tensile strains of the two specimens were 7004 με and 8120 με, respectively. In general, the maximum compressive strain was larger than the maximum tensile strain for all specimens. The failure of all specimens was explained as the tensile strain of the specimen reached the maximum tensile strain. Compared with the laminated bamboo beam applied with non-prestressed BFRP sheet, the ultimate tensile strain of the laminated bamboo beam applied with prestressed BFRP sheet dropped about 15.8% to 27.4%. This phenomenon was caused by the existence of the initial tensile strain in the prestressed BFRP sheet.


## 6.2.4. Strain Distribution along Beam Height and Position of Neutral Axis

The strain distribution along the beam height (captured from strain gages Y-3, Y-4, Y-5, and Y-6) under different loads shown in Figure17 was analyzed to define the position of the neutral axis. The abscissa of the figure is the measured strain value and the ordinate is the distance between the strain gage and bottom surface of the beam. An almost linear strain distribution along the beam height at the midspan was finally obtained, and the plane section assumption is suitable for the laminated bamboo beam applied by non-prestressed or prestressed BFRP sheet.Figure 17
Strain distribution along beam height under different loads: (a) B-1, (b) B-2, and (c) B-3.
(a)
(b)
(c)Based on the detected strain values in Figure17, the positions of the neutral axis at the midspan under different loads are calculated in Table 7. It can be found that the position of the neutral axis was near the middle height of the laminated bamboo beam at the initial loading stage (5 kN). With the further increase of the applied load, the position of the neutral axis gradually went down. Until the ultimate load, the neutral axis of the specimen B-1 was around 0.39 of the laminated bamboo beam height, and the neutral axes of specimens B-2 and B-3 were between 0.43 and 0.44 of the laminated bamboo beam height. It is found that the neutral axis of the laminated bamboo beam applied with prestressed BFRP sheet was a little higher than that of the laminated bamboo beam applied with non-prestressed BFRP sheet under the same load.Table 7
Positions of neutral axis under different loads.
Load (kN)
B-1
B-2
B-3
h
l (mm)
h
l/h
h
l (mm)
h
l/h
h
l (mm)
h
l/h
5
72.97
0.49
73.90
0.49
75.26
0.50
10
72.15
0.48
73.82
0.49
75.37
0.50
15
69.99
0.47
73.67
0.49
75.02
0.50
20
65.82
0.44
72.05
0.48
73.62
0.49
25
61.89
0.41
68.82
0.46
69.86
0.47
P
u
57.93
0.39
65.49
0.44
63.86
0.43
Note. h
l is the distance between the neutral axis and the bottom surface of the laminated bamboo beam; Pu is the ultimate load.


## 7. Conclusions

The laminated bamboo beam applied with prestressed BFRP sheet was investigated in this paper. Both prestress loss and flexural performance of the laminated bamboo beam applied with prestressed BFRP sheet were analyzed. Main conclusions are summarized as follows:(1)
A preliminary design of the laminated bamboo beam applied with prestressed BFRP sheet was discussed in this paper, including the reasonable controlled initial prestressed force and prevention of the bond slip. To overcome the deflection resulted from the dead load, the controlled initial prestress is recommended as 55% of the standard tensile stress of the BFRP sheet, including a 5% super tension. The bond slip between the BFRP sheet and the laminated bamboo is small and limited with the 100 mm range away from the loaded end.(2)
Considering the release of the prestressed BFRP sheet, the prestress loss was analyzed according to the specimen preparation stage and specimen storage stage. Based on analyses of prestress loss, the total prestress loss in the preparation stage is recommended as 22.0%, but more calibrated data are required to obtain an acceptable value for the prestress loss in the storage stage due to the diversity of the experimental data.(3)
The test results of four-point bending showed that the failure of the laminated bamboo beam applied with non-prestressed or prestressed BFRP sheet initiated from the loading point and propagated to a certain distance of the laminated bamboo beam, which can be explained as the tensile strain of the specimen reached the maximum tensile strain.(4)
The ultimate load of the laminated bamboo beam was not affected by the application of the prestressed BFRP sheet, but the ultimate deformation capacity of the laminated bamboo beam applied with prestressed BFRP sheet was reduced compared with that applied with non-prestressed BFRP sheet. The stiffness of the laminated bamboo beam applied with prestressed or non-prestressed BFRP sheet was almost the same in the linear stage, and then after the linear stage, the stiffness of the laminated bamboo beam applied with prestressed BFRP sheet became relatively larger.(5)
The maximum compressive strain was larger than the maximum tensile strain in all specimens. Based on the strain distribution along the beam height, the position of the neutral axis was found to be near the middle height of the beam at the initial loading stage and gradually went down with the increase of the applied load. The neutral axis of the laminated bamboo beam applied with prestressed BFRP sheet finally became higher than that of the laminated bamboo beam applied with non-prestressed BFRP sheet.



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*Source: 2319814-2019-04-30.xml*