# Study on Flexural Behaviour of Box Section Bamboo-Steel Composite Beams

Authors: Qifeng Shan; Jialiang Zhang; Keting Tong; Yushun Li
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

To take full advantages of the bamboo and cold-formed thin-walled steel, a new type of box section beam combined with bamboo and steel channel was proposed in this paper. Five composite beams with different parameters were tested to evaluate the effects of bamboo plywood thickness of composite beams and thickness and sectional dimension of steel channel. The results of experiment showed that the proposed composite beams exhibited excellent flexural bearing capacities and stiffness. The increase of bamboo plywood thickness and sectional dimension of steel channel could improve bearing capacity and flexural stiffness of composite beams, while the increase of steel thickness could enhance the bearing capacity and safety margin of composite beams. Furthermore, a new method to predict the deformation and bearing capacities of composite beams was proposed and matched well with the experimental results.


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## Body

## 1. Introduction

With the development of the society, green, sustainable, and ecologically materials are required to be employed for the construction. Wood and bamboo are one of environment-friendly building materials. Furthermore, wood and bamboo have the advantages of light weight, high strength, and good seismic resistant performance as construction materials.However, the resources of wood are relatively rare all over the world due to the long growth cycle; thus, the usage of wood is limited. A more environment-friendly building material such as bamboo need to be developed to replace wood.Bamboo, which has good mechanical performance, has been used by humans for thousands of years. In addition, China has a very rich resource of bamboo [1]. However, the applications of raw bamboo material are limited in civil engineering due to its dimensional instability, irregular shape, and difficult connection [2]. With the development of processing technic, bamboo plywood can be made with good mechanical properties by modified processing of raw bamboo [3–5]. However, the structure members made by modified bamboo had lower bearing capacity compared with the steel members under the same dimensions [6, 7], which meant bamboo members needed more materials to attain the same bearing capacity. Therefore, the bamboo structure members strengthened by other materials such as steel bars [8, 9], fiber polymer [10], and FRP sheets or grid [11–14] were designed and investigated in the recent years.Thin-walled cold-formed steel is one of the common construction materials with ultrahigh strength, while the steel members generally cannot reach its ultimate strength due to the buckling. Based on these considerations, a new bamboo-steel composite structure is proposed. The bamboo-steel composite structure is made up of bamboo plywood and cold-formed thin-walled steel through epoxy resin. The bamboo-steel composite structure can take the advantages of light weight and high strength of the two materials, while avoiding the disadvantages of easy buckling of cold-formed thin-walled steel. The research studies had showed the cooperation of the two materials could effectively improve the mechanical performance of the composite members [15–19].In this study, a new type of box section bamboo-steel composite beam, which consisted of four pieces of bamboo plywood and two pieces of cold-formed thin-walled steel channel, is proposed. Then, five composite beams proposed above were tested. The flexural behaviours of the composite beams were analysed and compared. The influence of the bamboo plywood thickness and the thickness and sectional dimension of steel channel were also studied in this paper.


## 2. Experiment Programs and Results

### 2.1. Material Properties

Cold-formed thin-walled steel employed in this paper was made of steel sheets, which were processed by a professional steel structure factory. The thickness (ts), yield stress (fy), ultimate stress (fu), and Young’s modulus (Es) of steel sheets were measured according to [20], as shown in Figure 1(a). The mechanical properties of the steel are listed in Table 1.Figure 1
Test of material properties. (a) Test for steel sheet. (b) Test for bamboo plywood.
(a)(b)Table 1
Material properties of cold-formed thin-walled steel.
ts (mm)Es (GPa)fy (MPa)fu (MPa)1.352062553951.75206275405There is no material test standard to be made for bamboo plywood in China; hence, the modulus of elasticity (Eb) and the modulus of rupture (σ) of bamboo plywood were measured according to the standard of wood-based panels [21], which is shown in Figure 1(b). The mechanical properties of bamboo plywood are listed in Table 2.Table 2
Material properties of bamboo plywood.
tb (mm)Eb (MPa)σ (MPa)15.148583817.667844625.0690556Note:tb is the thickness of bamboo plywood.


### 2.2. Test Specimens

The main design parameters of box section bamboo-steel composite beams were thickness of bamboo plywood and thickness and sectional dimension of thin-walled steel channel. B-1 and B-2 were designed to investigate the influence of bamboo plywood thickness. B-3 and B-4 were designed to study the effect of steel channel thickness of composite beams. To investigate the effect of steel channel dimension, B-5 was designed as a comparison with B-3. The thickness of bamboo plywood (tb) was 15.1 mm, 17.6 mm, and 25.0 mm, and the thickness of thin-walled steel channel, namely, ts (both web and flange), was 1.35 mm and 1.75 mm, and dimensions of steel channel cross-section (flange width × web height, bs x hs) were 30  mm × 135  mm, 40  mm × 135  mm, and 40  mm × 175  mm, respectively. The length of five specimens (B-1 to B-5) was designed as 2.44 m, while the calculated span (l) of specimens was 2.2 m. The section of the composite beam is exhibited in Figure 2, and the parameters of specimens are listed in Table 3.Figure 2
Section form of composite beam: (i) bamboo plywood and (ii) cold-formed thin-walled steel channel.Table 3
Parameters of specimens.
Specimenstb (mm)ts (mm)bs × hs (mm)b × h (mm)l (m)B-115.11.3530.0 × 135.090.2 × 165.22.2B-225.01.3530.0 × 135.0110.0 × 185.02.2B-317.61.3540.0 × 135.0115.2 × 170.22.2B-417.61.7540.0 × 135.0115.2 × 170.22.2B-517.61.3540.0 × 175.0115.2 × 210.22.2Note:b and h represent the width and height of box section, respectively.


### 2.3. Specimen Preparation

The box section bamboo-steel composite beams consist of two cold-formed thin-walled steel channel and four bamboo plywood, which is bonded with epoxy resin. The section form of composite beams is shown in Figure2 and the specific manufacturing processes are as follows. First, polish the interface between thin-walled steel and bamboo plywood to remove zinc coating layer of steel and glaze layer of bamboo plywood. Then, wipe the polished steel and bamboo plywood with alcohol pads to ensure the bonding surface clean. After that, apply the epoxy resin evenly on the surface of bamboo plywood and fix the bamboo plywood and the steel channel with fixtures to make sure that two materials are bonded effectively. Besides, symmetrically place heavy objects on the bond surface to improve the quality of bond. The pressurization process lasted for two days and the curing time lasted for 7 days. The finished specimens are shown in Figure 3.Figure 3
Specimens of composite beam. Note: one specimen was omitted due to the invalid result.


### 2.4. Test Setup and Instrumentation

A four-axis universal testing machine was adopted in this study, as shown in Figure4(a). The mechanical jack was applied for monotonous gradation loading with the step of 5 kN. The force sensor was employed to measure the compressive load. Specimens can still bear load after local failure because of good entirety, and the test was terminated when the beam cannot bear higher level load. The four-point flexure loading scheme was adopted. Clear distance between two supports was 2.2 m, two equivalent loading points were 800 mm from the end of beam, and length of pure bending sections was 600 mm.Figure 4
Test setup. (a) Photograph. (b) Diagrammatic view (all dimensions in mm).
(a)(b)Five strain gauges were evenly arranged at the web of midspan of beam. Displacement sensors were installed at support point, loading point, midspan, and midpoint between the support and the loading point to measure vertical deflection under the load. Figure4(b) shows the scheme of loading device of the test.Data of strain gauges and displacement sensors was collected by the static strain test system. The load was supposed to be stable in the reading and observation process, and data collection should be carried out after the instrument readings were stable.


## 2.1. Material Properties

Cold-formed thin-walled steel employed in this paper was made of steel sheets, which were processed by a professional steel structure factory. The thickness (ts), yield stress (fy), ultimate stress (fu), and Young’s modulus (Es) of steel sheets were measured according to [20], as shown in Figure 1(a). The mechanical properties of the steel are listed in Table 1.Figure 1
Test of material properties. (a) Test for steel sheet. (b) Test for bamboo plywood.
(a)(b)Table 1
Material properties of cold-formed thin-walled steel.
ts (mm)Es (GPa)fy (MPa)fu (MPa)1.352062553951.75206275405There is no material test standard to be made for bamboo plywood in China; hence, the modulus of elasticity (Eb) and the modulus of rupture (σ) of bamboo plywood were measured according to the standard of wood-based panels [21], which is shown in Figure 1(b). The mechanical properties of bamboo plywood are listed in Table 2.Table 2
Material properties of bamboo plywood.
tb (mm)Eb (MPa)σ (MPa)15.148583817.667844625.0690556Note:tb is the thickness of bamboo plywood.


## 2.2. Test Specimens

The main design parameters of box section bamboo-steel composite beams were thickness of bamboo plywood and thickness and sectional dimension of thin-walled steel channel. B-1 and B-2 were designed to investigate the influence of bamboo plywood thickness. B-3 and B-4 were designed to study the effect of steel channel thickness of composite beams. To investigate the effect of steel channel dimension, B-5 was designed as a comparison with B-3. The thickness of bamboo plywood (tb) was 15.1 mm, 17.6 mm, and 25.0 mm, and the thickness of thin-walled steel channel, namely, ts (both web and flange), was 1.35 mm and 1.75 mm, and dimensions of steel channel cross-section (flange width × web height, bs x hs) were 30  mm × 135  mm, 40  mm × 135  mm, and 40  mm × 175  mm, respectively. The length of five specimens (B-1 to B-5) was designed as 2.44 m, while the calculated span (l) of specimens was 2.2 m. The section of the composite beam is exhibited in Figure 2, and the parameters of specimens are listed in Table 3.Figure 2
Section form of composite beam: (i) bamboo plywood and (ii) cold-formed thin-walled steel channel.Table 3
Parameters of specimens.
Specimenstb (mm)ts (mm)bs × hs (mm)b × h (mm)l (m)B-115.11.3530.0 × 135.090.2 × 165.22.2B-225.01.3530.0 × 135.0110.0 × 185.02.2B-317.61.3540.0 × 135.0115.2 × 170.22.2B-417.61.7540.0 × 135.0115.2 × 170.22.2B-517.61.3540.0 × 175.0115.2 × 210.22.2Note:b and h represent the width and height of box section, respectively.


## 2.3. Specimen Preparation

The box section bamboo-steel composite beams consist of two cold-formed thin-walled steel channel and four bamboo plywood, which is bonded with epoxy resin. The section form of composite beams is shown in Figure2 and the specific manufacturing processes are as follows. First, polish the interface between thin-walled steel and bamboo plywood to remove zinc coating layer of steel and glaze layer of bamboo plywood. Then, wipe the polished steel and bamboo plywood with alcohol pads to ensure the bonding surface clean. After that, apply the epoxy resin evenly on the surface of bamboo plywood and fix the bamboo plywood and the steel channel with fixtures to make sure that two materials are bonded effectively. Besides, symmetrically place heavy objects on the bond surface to improve the quality of bond. The pressurization process lasted for two days and the curing time lasted for 7 days. The finished specimens are shown in Figure 3.Figure 3
Specimens of composite beam. Note: one specimen was omitted due to the invalid result.


## 2.4. Test Setup and Instrumentation

A four-axis universal testing machine was adopted in this study, as shown in Figure4(a). The mechanical jack was applied for monotonous gradation loading with the step of 5 kN. The force sensor was employed to measure the compressive load. Specimens can still bear load after local failure because of good entirety, and the test was terminated when the beam cannot bear higher level load. The four-point flexure loading scheme was adopted. Clear distance between two supports was 2.2 m, two equivalent loading points were 800 mm from the end of beam, and length of pure bending sections was 600 mm.Figure 4
Test setup. (a) Photograph. (b) Diagrammatic view (all dimensions in mm).
(a)(b)Five strain gauges were evenly arranged at the web of midspan of beam. Displacement sensors were installed at support point, loading point, midspan, and midpoint between the support and the loading point to measure vertical deflection under the load. Figure4(b) shows the scheme of loading device of the test.Data of strain gauges and displacement sensors was collected by the static strain test system. The load was supposed to be stable in the reading and observation process, and data collection should be carried out after the instrument readings were stable.


## 3. Test Results and Discussion

### 3.1. Failure Characteristics and Test Observations

All the five specimens showed the similar failure modes. The failure processes for specimen could be divided into two stages. The first stage began with the application of load. As the load increased to about 50% of the ultimate load, the sporadic sound could be heard due to the extrusion and tension of bamboo plywood. However, no crack could be found on the surface during the first stage. During the second stage, initial debonding cracks could be observed with slight degumming sound in the interface between thin-walled steel and bamboo plywood. With the increase of applied load, the cracks continued to appear and propagated along the interface. As the load was about to reach the ultimate load, the specimens failed due to the local damage and debonding between bamboo plywood and steel channel. However, no overall debonding could be found during the experiment.Figure5 shows the failure characteristics of specimens. The difference between B-1 and B-2 is the thickness of bamboo plywood. B-1 failed due to the extrusion of upper bamboo flange (Figure 5(a)), while the upper bamboo flange of B-2 could bear more pressure with thicker bamboo plywood. Debonding at upper flange near the support could be observed when B-2 failed (Figure 5(b)). The difference between B-3 and B-4 is the thickness of steel channel, while they exhibited the similar failure characteristics, both of them failed due to the extrusion of bamboo plywood and local buckling of steel channel in the compression zone of the midspan section (Figures 5(c) and 5(d)). The steel channel dimension of B-5 is larger than that of B-3. Unlike the B-3, the failure of B-5 attributed to the debonding between bamboo plywood and steel channel (Figure 5(e)), and local buckling of steel channel could be found near the support point (Figure 5(f)); thus, the specimen could not resist more load.Figure 5
Failure characteristics of composite beams. (a) Extrusion of upper bamboo flange of B-1. (b) Debonding near support of B-2. (c) Extrusion of upper bamboo flange of B-3. (d) Extrusion of upper bamboo flange of B-4. (e) Debonding of B-5. (f) Local buckling near support of B-5.
(a)(b)(c)(d)(e)(f)


### 3.2. Load-Deflection Curves and Bearing Capacity

The load-deflection curves for specimens B-1 to B-5 are shown in Figure6. The deflection here is the deflection of midspan, which is recorded by displacement sensor. As can be seen from Figure 6, the curves of each specimen could be divided into two stages, i.e., the elastic stage and elastic-plastic stage. During the elastic stage, the deflection of the specimen increased linearly with the increase of the load. At this stage, bamboo plywood and thin-walled steel worked together, and the overall performance of composite beam was good. Once the applied load reached approximately 50% of the ultimate load, the flexural stiffness of specimens gradually decreased due to the partial debonding of interface. The curves went into elastic-plastic stages, and the deflection of composite beam increased more, the load-deflection curves showed nonlinear behaviour. There was no obvious descending section in each curve, and the load could keep near the ultimate load before the specimen failed. Thus, the composite beam had enough safety margin.Figure 6
Load-deflection curves for specimens B-1 to B-5.The limit state of members can be divided into two states, i.e., the ultimate limit state and the serviceability limit state. The members cannot meet the safety requirements when exceeding the ultimate bearing capacity. And the members cannot meet the suitability and durability requirements when exceeding the serviceability limit state. For flexural members, the flexural capacity calculation is controlled by the ultimate limit state, while the deflection calculation is controlled by the serviceability limit state. The bearing capacity of bamboo-steel composite flexural members (such as composite floors and composite beams) is high, and the deflection is also large. Thus, the bearing capacity under serviceability limit state is controlled by the rigidity condition. The deflection of box section bamboo-steel composite beam under serviceability limit state should be calculated by l/250 of span length according to the standard in China [22]. The main test results are shown in Table 4. The bearing capacity of composite beam under serviceability limit state is close to or exceeds half of that, under the ultimate limit state.Table 4
Calculation results of specimens.
SpecimensPu (kN)Mu (kN·m)δmax (mm)Mu′ (kN·m)δ (mm)Mu′/MuB-135.014.035.805.688.800.41B-265.026.025.4711.408.800.44B-360.024.021.1610.768.800.45B-470.028.031.7611.728.800.42B-570.028.017.1017.648.800.63Note:Pu is the ultimate applied load; Mu is the ultimate flexural bearing capacity; δmax is the deflection of midspan corresponding to Pu; Mu′ is the flexural bearing capacity in serviceability limit state; δ is the deflection of midspan in the serviceability limit state.


### 3.3. Strains Distribution at Midspan Section

Five strain gauges were arranged evenly at midspan of composite beams to measure the changes of strain along the height of beams under different loads. It was found that the cross-sectional strain curves of each beam were similar. Taking specimen B-3 as example, the average strain distribution along the height at midspan, which is shown in Figure7, changed almost linearly, and the position of neutral axis of section was at the centre of beam height, which indicated that the midspan sectional deformation of the composite beam accorded with the plane-section assumption.Figure 7
Strain distribution at midspan section of B-3.


## 3.1. Failure Characteristics and Test Observations

All the five specimens showed the similar failure modes. The failure processes for specimen could be divided into two stages. The first stage began with the application of load. As the load increased to about 50% of the ultimate load, the sporadic sound could be heard due to the extrusion and tension of bamboo plywood. However, no crack could be found on the surface during the first stage. During the second stage, initial debonding cracks could be observed with slight degumming sound in the interface between thin-walled steel and bamboo plywood. With the increase of applied load, the cracks continued to appear and propagated along the interface. As the load was about to reach the ultimate load, the specimens failed due to the local damage and debonding between bamboo plywood and steel channel. However, no overall debonding could be found during the experiment.Figure5 shows the failure characteristics of specimens. The difference between B-1 and B-2 is the thickness of bamboo plywood. B-1 failed due to the extrusion of upper bamboo flange (Figure 5(a)), while the upper bamboo flange of B-2 could bear more pressure with thicker bamboo plywood. Debonding at upper flange near the support could be observed when B-2 failed (Figure 5(b)). The difference between B-3 and B-4 is the thickness of steel channel, while they exhibited the similar failure characteristics, both of them failed due to the extrusion of bamboo plywood and local buckling of steel channel in the compression zone of the midspan section (Figures 5(c) and 5(d)). The steel channel dimension of B-5 is larger than that of B-3. Unlike the B-3, the failure of B-5 attributed to the debonding between bamboo plywood and steel channel (Figure 5(e)), and local buckling of steel channel could be found near the support point (Figure 5(f)); thus, the specimen could not resist more load.Figure 5
Failure characteristics of composite beams. (a) Extrusion of upper bamboo flange of B-1. (b) Debonding near support of B-2. (c) Extrusion of upper bamboo flange of B-3. (d) Extrusion of upper bamboo flange of B-4. (e) Debonding of B-5. (f) Local buckling near support of B-5.
(a)(b)(c)(d)(e)(f)


## 3.2. Load-Deflection Curves and Bearing Capacity

The load-deflection curves for specimens B-1 to B-5 are shown in Figure6. The deflection here is the deflection of midspan, which is recorded by displacement sensor. As can be seen from Figure 6, the curves of each specimen could be divided into two stages, i.e., the elastic stage and elastic-plastic stage. During the elastic stage, the deflection of the specimen increased linearly with the increase of the load. At this stage, bamboo plywood and thin-walled steel worked together, and the overall performance of composite beam was good. Once the applied load reached approximately 50% of the ultimate load, the flexural stiffness of specimens gradually decreased due to the partial debonding of interface. The curves went into elastic-plastic stages, and the deflection of composite beam increased more, the load-deflection curves showed nonlinear behaviour. There was no obvious descending section in each curve, and the load could keep near the ultimate load before the specimen failed. Thus, the composite beam had enough safety margin.Figure 6
Load-deflection curves for specimens B-1 to B-5.The limit state of members can be divided into two states, i.e., the ultimate limit state and the serviceability limit state. The members cannot meet the safety requirements when exceeding the ultimate bearing capacity. And the members cannot meet the suitability and durability requirements when exceeding the serviceability limit state. For flexural members, the flexural capacity calculation is controlled by the ultimate limit state, while the deflection calculation is controlled by the serviceability limit state. The bearing capacity of bamboo-steel composite flexural members (such as composite floors and composite beams) is high, and the deflection is also large. Thus, the bearing capacity under serviceability limit state is controlled by the rigidity condition. The deflection of box section bamboo-steel composite beam under serviceability limit state should be calculated by l/250 of span length according to the standard in China [22]. The main test results are shown in Table 4. The bearing capacity of composite beam under serviceability limit state is close to or exceeds half of that, under the ultimate limit state.Table 4
Calculation results of specimens.
SpecimensPu (kN)Mu (kN·m)δmax (mm)Mu′ (kN·m)δ (mm)Mu′/MuB-135.014.035.805.688.800.41B-265.026.025.4711.408.800.44B-360.024.021.1610.768.800.45B-470.028.031.7611.728.800.42B-570.028.017.1017.648.800.63Note:Pu is the ultimate applied load; Mu is the ultimate flexural bearing capacity; δmax is the deflection of midspan corresponding to Pu; Mu′ is the flexural bearing capacity in serviceability limit state; δ is the deflection of midspan in the serviceability limit state.


## 3.3. Strains Distribution at Midspan Section

Five strain gauges were arranged evenly at midspan of composite beams to measure the changes of strain along the height of beams under different loads. It was found that the cross-sectional strain curves of each beam were similar. Taking specimen B-3 as example, the average strain distribution along the height at midspan, which is shown in Figure7, changed almost linearly, and the position of neutral axis of section was at the centre of beam height, which indicated that the midspan sectional deformation of the composite beam accorded with the plane-section assumption.Figure 7
Strain distribution at midspan section of B-3.


## 4. Parametric Analysis

### 4.1. Effect of Bamboo Plywood Thickness

The bamboo plywood thickness of B-2 was increased from 15.1 mm (thickness of B-1) to 25 mm, as comparing B-1 and B-2, both of which had the same geometrical dimensions of the steel channel. Load-deflection curves (Figure8) show that the ultimate load of B-2 was increased from 35 kN of B-1 to 65 kN. And the deflection of B-2 was also significantly smaller than that of B-1 under the same load. This may attribute to the fact that the ticker bamboo plywood has great contribution to the sectional moment of inertia, which could improve the flexural stiffness and bearing capacity. Thus, with the increase of bamboo flange and web thickness of the composite beam, the ultimate load and flexural stiffness of composite beams can be greatly improved.Figure 8
Effect of bamboo plywood thickness on load-deflection curves.


### 4.2. Effect of Thickness and Sectional Dimension of Steel Channel

The load-deflection curves of B-3 and B-4 are compared in Figure9, and it can be found that the increased thickness of thin-walled steel can improve ultimate load and safety margin of composite beams, while having little effect on flexural stiffness. Because the sectional area of steel is far less than that of bamboo plywood in composite beams, the thicker steel channel has little contribution to the sectional moment of inertia. Thus, the thickness of steel channel has little influence on the flexural stiffness of beams. However, the ultimate stress of steel (fu) is larger than the rupture modulus of bamboo plywood (σ) according to Table 1 and Table 2. Therefore, the bearing capacity of the composite beam can be improved effectively by increasing the thickness of steel channel.Figure 9
Effect of steel channel thickness on load-deflection curve.Similarly, the load-deflection curves of B-3 and B-5 are compared in Figure10, and it can be found that the increase of the height of steel channel could improve the ultimate bearing capacity and flexural stiffness. That is because the increase of height of steel channel can increase both the inertia moment and area of cross-section effectively.Figure 10
Effect of sectional dimension of steel channel on load-deflection curve.


## 4.1. Effect of Bamboo Plywood Thickness

The bamboo plywood thickness of B-2 was increased from 15.1 mm (thickness of B-1) to 25 mm, as comparing B-1 and B-2, both of which had the same geometrical dimensions of the steel channel. Load-deflection curves (Figure8) show that the ultimate load of B-2 was increased from 35 kN of B-1 to 65 kN. And the deflection of B-2 was also significantly smaller than that of B-1 under the same load. This may attribute to the fact that the ticker bamboo plywood has great contribution to the sectional moment of inertia, which could improve the flexural stiffness and bearing capacity. Thus, with the increase of bamboo flange and web thickness of the composite beam, the ultimate load and flexural stiffness of composite beams can be greatly improved.Figure 8
Effect of bamboo plywood thickness on load-deflection curves.


## 4.2. Effect of Thickness and Sectional Dimension of Steel Channel

The load-deflection curves of B-3 and B-4 are compared in Figure9, and it can be found that the increased thickness of thin-walled steel can improve ultimate load and safety margin of composite beams, while having little effect on flexural stiffness. Because the sectional area of steel is far less than that of bamboo plywood in composite beams, the thicker steel channel has little contribution to the sectional moment of inertia. Thus, the thickness of steel channel has little influence on the flexural stiffness of beams. However, the ultimate stress of steel (fu) is larger than the rupture modulus of bamboo plywood (σ) according to Table 1 and Table 2. Therefore, the bearing capacity of the composite beam can be improved effectively by increasing the thickness of steel channel.Figure 9
Effect of steel channel thickness on load-deflection curve.Similarly, the load-deflection curves of B-3 and B-5 are compared in Figure10, and it can be found that the increase of the height of steel channel could improve the ultimate bearing capacity and flexural stiffness. That is because the increase of height of steel channel can increase both the inertia moment and area of cross-section effectively.Figure 10
Effect of sectional dimension of steel channel on load-deflection curve.


## 5. Theoretical Calculation and Analysis

### 5.1. Midspan Deflection

The test showed that the steel and bamboo plywood of the bamboo-steel composite beam are both in the elastic stage under the serviceability limit state. Therefore, superposition principle can be employed to calculate the flexural stiffness (EI) of the composite beam [2], which is given by(1)EI=EfbIfb+EwbIwb+EsIs,where Efb, Ewb, and Es are the elasticity modulus of flange bamboo plywood, web bamboo plywood, and steel channel, respectively; Ifb, Iwb, and Is are the inertia moment of flange bamboo plywood, web bamboo plywood, and steel channel, respectively.Considering the different deflection calculation of composite components between test and theory, a coefficientβb is introduced in the formula for calculating the midspan deflection of the simply supported beam [23]. Thus, the midspan deflection (δ) of the composite beam under the serviceability limit state can be expressed as follows:(2)δ=βbpal248EI3−4al2,where the P is the applied load on the composite beam, a is the distance between the point of applied load and near support, l is the calculated span of composite beam, and EI is the flexural stiffness of composite beam.Figure11 showed the comparison of midspan deflections between experimental values and theoretical values calculated by equation (1) and equation (2). It can be observed that the calculated values matched well with the experimental values with less than 10% relative errors.Figure 11
Comparisons of midspan deflections between the experimental and calculated value (in serviceability limit state). (a) B-1. (b) B-2. (c) B-3. (d) B-4. (e) B-5.
(a)(b)(c)(d)(e)


### 5.2. Flexural Bearing Capacities

The test results showed that when the beam damaged, the upper flange of the cross-section was deboned, so the strength reduction factorγd (γd = 0.95) [2] of bamboo plywood was introduced to consider the debonding of upper flange. It also could be found that the strain of steel channel in the tension zone exceeded the yield strain (εs > 0.002) when the beam damaged, which indicated that the tension zone of the steel channel had reached the plastic stage while the other components were still in the elastic stage. Thus, the plastic ratio of steel channel γs (γs = 1.05) [24] was introduced to consider the plastic behaviour. Strain distribution at midspan section of specimens indicates that the midspan sectional deformation of specimens agrees with the plane-section assumption. The flexural bearing capacities (M) of box section composite beams are proposed based on the superposition principle, which is shown as follows:(3)M=Mb+Ms,Mb=γdσbWb,σb=εbEfb,Ms=γsfuWs,where Mb and Ms are the flexural bearing capacities of bamboo section and steel channel section, respectively; σb and εb are the failure normal stress and strain of bamboo plywood, respectively; Wb and WS are the elastic section modulus of bamboo plywood section and steel channel section, respectively; and fu is the ultimate stress of steel channel.The comparison of flexural bearing capacities between calculated values (M) and experimental values (Mexp) are shown in Table 5. It can be found that the calculated capacities matched well with the experimental values. Furthermore, the bamboo section contributes 40–63% of the total flexural bearing capacity of composite beams.Table 5
Comparison of flexural bearing capacities between calculated and experimental values.
SpecimensMb (kN·m)Ms (kN·m)M (kN·m)Mexp (kN·m)Mb/MMexp/MB-25.107.6512.7514.000.401.10B-312.787.6520.4326.000.631.27B-410.048.6918.7324.000.541.28B-512.0113.5325.5428.000.471.10B-610.2913.1723.4628.000.441.19


## 5.1. Midspan Deflection

The test showed that the steel and bamboo plywood of the bamboo-steel composite beam are both in the elastic stage under the serviceability limit state. Therefore, superposition principle can be employed to calculate the flexural stiffness (EI) of the composite beam [2], which is given by(1)EI=EfbIfb+EwbIwb+EsIs,where Efb, Ewb, and Es are the elasticity modulus of flange bamboo plywood, web bamboo plywood, and steel channel, respectively; Ifb, Iwb, and Is are the inertia moment of flange bamboo plywood, web bamboo plywood, and steel channel, respectively.Considering the different deflection calculation of composite components between test and theory, a coefficientβb is introduced in the formula for calculating the midspan deflection of the simply supported beam [23]. Thus, the midspan deflection (δ) of the composite beam under the serviceability limit state can be expressed as follows:(2)δ=βbpal248EI3−4al2,where the P is the applied load on the composite beam, a is the distance between the point of applied load and near support, l is the calculated span of composite beam, and EI is the flexural stiffness of composite beam.Figure11 showed the comparison of midspan deflections between experimental values and theoretical values calculated by equation (1) and equation (2). It can be observed that the calculated values matched well with the experimental values with less than 10% relative errors.Figure 11
Comparisons of midspan deflections between the experimental and calculated value (in serviceability limit state). (a) B-1. (b) B-2. (c) B-3. (d) B-4. (e) B-5.
(a)(b)(c)(d)(e)


## 5.2. Flexural Bearing Capacities

The test results showed that when the beam damaged, the upper flange of the cross-section was deboned, so the strength reduction factorγd (γd = 0.95) [2] of bamboo plywood was introduced to consider the debonding of upper flange. It also could be found that the strain of steel channel in the tension zone exceeded the yield strain (εs > 0.002) when the beam damaged, which indicated that the tension zone of the steel channel had reached the plastic stage while the other components were still in the elastic stage. Thus, the plastic ratio of steel channel γs (γs = 1.05) [24] was introduced to consider the plastic behaviour. Strain distribution at midspan section of specimens indicates that the midspan sectional deformation of specimens agrees with the plane-section assumption. The flexural bearing capacities (M) of box section composite beams are proposed based on the superposition principle, which is shown as follows:(3)M=Mb+Ms,Mb=γdσbWb,σb=εbEfb,Ms=γsfuWs,where Mb and Ms are the flexural bearing capacities of bamboo section and steel channel section, respectively; σb and εb are the failure normal stress and strain of bamboo plywood, respectively; Wb and WS are the elastic section modulus of bamboo plywood section and steel channel section, respectively; and fu is the ultimate stress of steel channel.The comparison of flexural bearing capacities between calculated values (M) and experimental values (Mexp) are shown in Table 5. It can be found that the calculated capacities matched well with the experimental values. Furthermore, the bamboo section contributes 40–63% of the total flexural bearing capacity of composite beams.Table 5
Comparison of flexural bearing capacities between calculated and experimental values.
SpecimensMb (kN·m)Ms (kN·m)M (kN·m)Mexp (kN·m)Mb/MMexp/MB-25.107.6512.7514.000.401.10B-312.787.6520.4326.000.631.27B-410.048.6918.7324.000.541.28B-512.0113.5325.5428.000.471.10B-610.2913.1723.4628.000.441.19


## 6. Conclusions

In this paper, the flexural behaviour of box section bamboo-steel composite beams was experimentally investigated and theoretically analysed. Five box section bamboo-steel composite beams were tested, and the conclusion based on the results is summarized as follows:(1)
The box section bamboo-steel composite beams have an excellent structural integrity, and no overall failures can be observed in the interface between bamboo plywood and thin-walled steel channel. The composite beams could combine the advantages of light weight and high strength of bamboo plywood and steel, while the disadvantage of easy buckling of thin-walled steel are overcome.(2)
The midspan cross-section strain curve of composite beams showed that strains changed linearly along the height of cross-section; therefore, the plane-section assumption can be used to study the composite beams.(3)
The thickness of bamboo plywood, thickness, and sectional dimension of steel channel have varying degrees influence on bearing capacities, flexural stiffness, and safety margin of the box section bamboo-steel composite beams. The bearing capacity and flexural stiffness increased with the increase of the thickness of bamboo plywood and sectional dimension of steel channel, while the thickness of steel channel has little influence on the flexural stiffness. However, the thickness of steel channel can improve bearing capacity and safety margin of composite beams.(4)
The bearing capacity of composite beams under serviceability limit state is close to or exceeds half of that, under ultimate limit state, which indicated that the strength of both bamboo plywood and thin-walled steel channel was fully utilized. The proposed equations for predicting the deformation and bearing capacities of composite beams matched well with the experimental results.



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*Source: 8878776-2020-11-17.xml*