This paper presents a method of measuring local slip in bamboo-reinforced concrete beams. Local slips (
Research on bamboo as reinforcing concrete has been done a lot and the majority of failures are the failure of adhesion between bamboo and concrete. The main factors causing adhesive failure are the lower elastic modulus of bamboo than concrete, hygroscopic properties, and the hydrolysis process. The difference in the modulus of elasticity of bamboo which is lower than concrete causes the concrete not to grip the bamboo reinforcement after the cement hydration process, which eventually occurs swelling [
There are many ways to prevent the hygroscopic process between bamboo reinforcement and concrete during the hydration process. The use of adhesives and waterproof coatings such as Sikadur 32 Gel [
Reinforced concrete bonds are formed by the mechanism of adhesion, friction, and mechanical interlock between reinforcement and concrete. The bond strength is strongly influenced by the fracture energy [
Bamboo has high elastic properties due to the high tensile strength of bamboo fibers. Archila et al. [
The reference for calculating the bond stress and slip of bamboo reinforcement with concrete is based on the reference for calculating the bond stress and slip of steel reinforcement. Several references are used as a basis including Diab et al. [
Diab et al. [
Siempu et al. [
Wang et al. [
This study discusses the slip calculation method on bamboo reinforced concrete beams (BRC) based on moment-curvature and bond-stress. Some of the difficulties in obtaining slip data between reinforcement and concrete from the experimental results are obtaining concrete elongation (
The specimens used in the study were eight pieces of bamboo reinforced concrete beam with single reinforcement. The size of the beams is 75 mm × 150 mm × 1100 mm. The geometry and reinforcement details of BRC beams are shown in
Bar type and concrete | Reinforcement size, |
Modulus of elasticity ( |
Tensile strength, (MPa) | Compressive strength, |
Poisson's ratio ( |
---|---|---|---|---|---|
Petung Bamboo ( |
15 × 15 | 17235.74 | 126.68 | – | 0.25 |
Concrete | – | 26324.79 | – | 31.31 | 0.20 |
There are 16 specimens of BRC beams, consisting of 4 variations of the area of bamboo reinforcement, namely 100 mm^{2}, 140 mm^{2}, 200 mm^{2}, and 450 mm^{2}. The BRC beam specimen has 2 strain gauges installed on the bamboo reinforcement to detect the elongation of the bamboo reinforcement as shown in
The elongation of bamboo reinforcement from the experimental results is obtained from the formula
The load is applied at a distance of ⅓L from the beam support, using the WF load spreader. The strain gauge is attached to the bamboo reinforcement with a distance of ½L from the span of the beam. The strain gauge is connected to a digital strain-meter. Hydraulic jacks are used for beam loading with a 200 kN load cell connected to the data logger. Crack patterns and failure patterns were observed and identified from the first crack to the collapse of the beam. Crack pattern data and loading history are used as input data for calculating slip through moment-curvature and bond stress. The test equipment setup and load scheme are shown in
Crack patterns and flexural behavior in steel-reinforced concrete beams are used as the basis for this method. How crack and bond-slip patterns occur is shown in
The basic formula for calculating the bond-stress (
Preparation for the calculation process is to carry out the flexural test to the BRC beam. A strain gauge is attached to the bamboo reinforcement. The data from the strain gauge readings were analyzed according to the loading stage and the cracking process. The calculation of elongation of bamboo reinforcement (
The local slip (
where,
The calculation of bond-stress and local slip through the curvature-moment using the Excel program based on
The calculation of curvature-moment using the Excel program as shown in the following link: https://bit.ly/3ltwPEb. In the program, there is a calculation of the internal forces before cracking, when cracks occur (
The calculation of bond-stress and the local slip of the first crack as shown in the following link: https://bit.ly/2UpCQFQ.
The calculation of bond-stress and the local slip of the second crack until rupture is shown in the following link: https://bit.ly/2Ukj2Uo.
The equations used in the calculation of bond-stress and local slip (Point B and Point C) based on the curvature-moment are as follows:
The peak bond-stress
where Φ’(
Local slip
Elongation of bamboo reinforcement
The total bond-force
The bamboo stress
Substituting
Bamboo strain
Results of integrating
In the calculation of
Substituting
Elongation of concrete
The results of photographic data of crack and slip patterns from the BRC beam experiment from the initial crack until collapse is shown in
The calculation results of bond-stress and local slip uses curvature-moment are shown in
The Excel program can be used directly by inputting material data, cross-sectional geometry data, initial cracking moments until the beam collapses, and the beam cracking process. The use of the Excel program on the links: https://bit.ly/3ltwPEb, https://bit.ly/2UpCQFQ, and https://bit.ly/2Ukj2Uo is carried out by still paying attention to
Control calculation of bond-stress and local slip with curvature-moment | ||||||
---|---|---|---|---|---|---|
Crack | Bond-stress, |
Local slip, |
||||
(1) | (2) | (3) | (4) | (5) | (6) | (7) |
First crack | – | – | 0 | 0 | 0.034 | 0 |
Crack 2 | 1.250 | 1.430 | 0.100 | 0.035 | 0.037 | 1.214 |
Crack 3 | 1.868 | 2.100 | 0.075 | 0.047 | 0.088 | 1.930 |
Crack 4 | 2.486 | 2.620 | 0.060 | 0.029 | 0.139 | 3.808 |
Crack 5 | 3.104 | 3.880 | 0.075 | 0.033 | 0.191 | 6.092 |
Crack 6 | 3.722 | 4.650 | 0.090 | 0.044 | 0.242 | 6.430 |
Crack 7 | 4.340 | 4.420 | 0.080 | 0.040 | 0.294 | 8.004 |
COLLAPSE 8 | 4.958 | 4.650 | 0.080 | 0.041 | 0.354 | 9.992 |
Meanwhile, the BRC beams as shown in
The relationship of bond-stress
In principle, this calculation method can be used only to control and validate models from experimental data. This method cannot be used for test methods whose purpose is to obtain the data needed for the model, because input data is highly dependent on experimental data. Calculation of the elongation of the concrete to be obtained still requires data from experimental results, such as crack pattern data. However, this method is a solution to establishing the elongation of the concrete and offers an alternative to using a concrete strain-gauge, which is mostly less accurate. And do not rule out the possibility of further research development; this method can predict a model–and evaluate the performance–of structural elements.
Based on the analysis and validation of experimental data using the slip calculation method based on the moment-curvature and bond-stress, several conclusions were obtained including: (1) The relationship of the bond-stress
This calculation method is useful for controlling, validating, and sensitivity analysis of the relationship model of bond-stress
This method is a solution for calculating concrete elongation (
Funding for this research was fully funded by Research Program, the Directorate of Research and Community Service, the Directorate General of Research and Technology Strengthening and Development of the Ministry of Research, Technology, and Higher Education of the Republic of Indonesia or DRPM of the Republic of Indonesia 2021.
Bond-stress (MPa)
The peak of bond-stress (MPa)
Local bond-stress (MPa)
Total bond-force (N)
Bond stress at a distance x away from the zero-slip section (MPa)
Shearing force of the beam (N)
Circumference of the cross-section of bamboo reinforcement
Distance from the maximum press fiber to the center of the bamboo tensile reinforcement area (mm)
Height of concrete stress block equivalent (mm)
The internal lever arm
A strain of bamboo reinforcement
Bamboo strain in cross-section Z
Bamboo strain function
Elongation of bamboo reinforcement (mm)
Elongation of concrete (mm)
Elongation of concrete due to the compressive force (mm)
Elongation of concrete due to bond force (mm)
Span length (at
½ crack distance the side left plus ½ crack distance the side right of the observation point as shown in
Bamboo reinforcement diameter (mm)
Bamboo stress at an uncracked section, bamboo stress at zero-slip point (N/mm^{2})
Bamboo stresses at cracked sections (N/mm^{2})
The stress of bamboo reinforcement at slip length (at the zero-slip point as shown in
The stress of bamboo reinforcement at slip length (at the crack point as shown in
Bamboo Reinforced Concrete
Steel Reinforced Concrete
Crack spacing (mm)
Distances from the cracked sections to zero slip point (mm)
Slip length or 1/2 the distance between two adjacent cracks (mm)
Local slips at the points where the peak bond stresses occur (mm)
Slip (mm)
Characteristic strength of concrete (MPa)
Bamboo stress at a distance x from zero-slip section (MPa)
Bamboo stress function at slip length (MPa)
Bamboo stress at zero-slip point (MPa)
Bamboo stress at a crack point (MPa)
Constitutive relationship
Modulus of elasticity of bamboo (N/mm^{2})
Bending moment at the supports in a continuous beam (N-mm)
Bending moment at mid-span in a continuous beam (N-mm)
Tension reinforcement ratio
Area of tensile reinforcement (mm^{2})
Beamwidth (mm)