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The use of non-renewable resources by the construction industry has several environmental consequences, contributing to excessive energy consumption and loss of materials. So, the construction sector is always in search of improvement and methods that innovate the existing techniques, aiming at the use of alternative and sustainable materials. Bamboo is a perennial plant with fast growth rate and low cost that has great physical and mechanical characteristics that assure its performance in the building environment. The use of beams with total or partial replacement of steel by bamboo has been well studied, due to the possibility of using the same design methods used in reinforced concrete beams, since the bamboo-reinforced beams meet the Bernoulli-Kirchoff bending theory. The objective of the work was to adapt a design procedure into an electronic spreadsheet for bamboo reinforced concrete beams subjected to four-point bending, with rectangular section, according to Brazilian Standard NBR 6118 (2014). The spreadsheet was tested based on other authors taking into consideration a steel double reinforcement. The resulting values were equivalents to those obtained by the authors, validating the efficiency of the worksheet. This methodology aims to optimize the design process of beams and enable the substitution of steel by bamboo, highlighting the validation, from the structural point of view, obtained by the authors.

The employment of non-renewable resources in the construction field results in environmental consequences, contributing to the excessive consumption of energy and substantial material losses. Thus, the construction sector is in an ongoing search for improvement and innovation in their techniques, aiming the utilization of sustainable and alternative materials.

According to [

Reference [

Since the 70s, some bamboo species are being studied and analyzed as reinforcement and molds for structural elements [

According to [

The bamboo’s structural performance is impaired due to certain anatomy particularities, presenting low shear strength parallel to the fibers and irregular geometry. Besides that, the lignin present in its composition is a target to xylophagous insects [

On the internodes, the fibers are axially oriented to the growth direction, diverging from the axis and concentrating on the nodes, which enables the diaphragm formation, giving lateral stability to the culm [

In its natural state, being an organic material, bamboo is susceptible to organic decay. Nowadays, there are numerous treatments for bamboo’s preservation. The durability of the material is ensured by protection against fungal rot, attack by insects and cracks with wood preservatives [

The bamboo’s largest utilization difficulty as reinforcement is its water absorption rate. When in contact with fresh concrete and during the curing process, the excess of water is absorbed by the bamboo, which swells. After the

curing process, the bamboo loses the water and shrink, impairing the adherence with concrete.

Waterproofing treatments that do not damage the interface between concrete and bamboo, such as Asphalt paints, bituminous materials, and epoxy resins, are commonly used in this type of work [

According to [

The ideal quantity of bamboo in a given cross-section varies between 1.25% and 8.33%, depending on various aspects [

In this context, the objective was to adapt a beam design system, using an electronic spreadsheet tool, to include and replace the bending reinforcement for bamboo.

The proposed design routine in the present study was based in the Brazilian standard [

The input data are insert according to the project established values, basics for any structural design.

The cross-section’s height (h) and width (b_{w}), the element’s length (l) are necessary measurements. Then, the spreadsheet can determine the loading points (a) and the working height (d), equivalent to the distance between the gravity center of the reinforcement and the compressed edge of the cross-section.

The concrete used for beams should have a compressive strength of, at least, 15 MPa for non-structural applications. Generally, the compressive strength varies between 25 and 50 MPa for structural concrete in beams.

The steel rebars used as reinforcement for concrete structural elements are classified by its characteristic yield stress (f_{yk}) divided into classes of 250 MPa (CA-25), 500 MPa (CA-50) and 600 MPa (CA-60), categorized by the Brazilian standard [

Without any tests or the manufacturer’s instructed values, the Young modulus (E_{s}) is admitted equal to 210 GPa, as stated by the [

The tensile strength admitted for the bamboo (σ_{_bamboo}) should be obtained by experimental tests, due to its variability, linked to species, maturity, and climatic conditions.

The output data are generated based on the input cited on the previous section, by the equations shown in this section, initially obtaining the steel reinforcement area and its correspondent bamboo reinforcement area.

The equations are obtained by constitutive law of materials (Materials Resistance) considering the internal balance of efforts. The external load (bending moment M_{d}) are balanced with internal binaries, represented by the representative strength of compressed concrete (R_{cc}) and the representative strength of tensile steel (R_{st}), distance to a length (z).

The neutral line position (x) was obtained by the Equation (1).

x = 1.25 × d × ( 1 − 1 − M d 0.425 × b w × d 2 × f c d ) (1)

Being:

M_{d} is the bending moment by a ponderation coefficient (kN.cm);

f_{cd} is Compressive strength (kN/cm^{2});

b_{w} is the cross-section width (cm);

x is the distance between the compressed edge and the point without deformation and stress (cm);

d is the working height (cm).

The representative strength of compressed concrete (R_{cc}) was obtained by the Equation (2).

R c c = 0.68 × f c d × b w × x (2)

Being:

f_{cd} is Compressive strength (kN/cm^{2});

b_{w} is the cross-section width (cm);

x is the distance between the compressed edge and the point without deformation and stress (cm);

R_{cc} is the representative strength of compressed concrete (kN).

The representative strength of tensile steel (R_{st}) was obtained by the Equation (3).

R s t = A s × f y k (3)

Being:

f_{yk} is the characteristic yield stress (kN/cm^{2});

b_{w} is the cross-section width (cm);

x is the distance between the compressed edge and the point without deformation and stress (cm);

R_{st} is the representative strength of tensile steel (kN).

The bending moment (M_{d}) was obtained by the Equation (4).

M d = 0.68 × f c d × b w × x × ( d − 0.4 x ) (4)

Being:

M_{d} is the bending moment by a ponderation coefficient (kN.cm);

f_{cd} is Compressive strength (kN/cm^{2});

b_{w} is the cross-section width (cm);

x is the distance between the compressed edge and the point without deformation and stress (cm);

d is the working height (cm).

The Service bending moment (M_{k}) can be estimated in the Equation (5), dividing the bending moment by a ponderation coefficient.

M k = M d γ f (5)

Being:

M_{k} is the bending moment (kN.cm);

M_{d} is the bending moment by a ponderation coefficient (kN.cm);

γ_{f} is the Load ponderation coefficient.

The acting load (P) was determined from the Equation (6) that links the load to the Service bending moment (M_{k}) and the element distributed weight (q).

M k = P × a + q × l 2 8 (6)

Being:

M_{k} is the bending moment (kN.cm);

P is the acting load (kN);

a is the distance of acting load (P) from support (cm);

q is the element distributed weight (kN/cm);

l is the element length (cm).

The steel reinforcement area (A_{s}) was determined without the safety coefficients, according to Equation (7).

A s = M k / ( d − 0.4 x ) × f y k (7)

Being:

A_{s} is the steel reinforcement area (cm^{2});

M_{k} is the bending moment (kN.cm);

d is the working height (cm);

x is the distance between the compressed edge and the point without deformation and stress (cm);

f_{yk} is the characteristic yield stress (MPa).

The corresponding bamboo reinforcement area was obtained by the equality of the needed force in the steel to resist the Service bending moment Equation (8) and the force admitted by a given bamboo area in Equation (9). It’s very important to observe, the steel area can be partially or total replaced by bamboo. The combination with bamboo and steel could be made carefully, observing the total tensile strength R_{st}. This combination must be respecting the correlation shown in Equation (10).

σ steel = F / A s (8)

Being:

σ_{steel} is the mean tensile stress of steel (kN/cm^{2});

F = Acting force on the steel reinforcement (kN);

A_{s} is the steel reinforcement area (cm^{2}).

σ bamboo = F / A b (9)

Being:

σ_{bamboo} is the mean tensile stress of bamboo (kN/cm^{2});

F it the acting force on the bamboo reinforcement (kN);

A_{b} is the equivalent bamboo area (cm^{2}).

σ bamboo × A b + σ steel × A s R s t ≥ 1 (10)

Being:

σ_{bamboo} is the mean tensile stress of bamboo (kN/cm^{2});

σ_{steel} is the mean tensile stress of steel (kN/cm^{2});

A_{s} is the steel reinforcement area (cm^{2}).

A_{b} is the bamboo area (cm^{2}).

The vertical displacement (D_{máx}) limited by [

D max = l / 250 (11)

Being:

D_{máx} is the maximal vertical displacement allowed (cm);

l is the element length (cm).

The validation was made by comparison with [

In this study, the authors prepared 6 beams, three being reinforced with bamboo and the other three being reinforced with steel. The dimensions adopted were: 12 cm × 40 cm (width × height) for the cross-section and a total length of 300 cm, but an admitted length of 290 cm between supports. The concrete compressive strength was adopted as 25 MPa and the steel utilized was classified as CA-50.

The beams were designed to utilize the limit of both materials, disregarding all safety coefficients, facilitating the comparison between the results. The authors, through the use of the equations, determined the reinforcement needed to not get out of the situation of reinforcement failure. Then, the authors determined the equivalent bamboo reinforcement to compare the vertical displacements.

The bamboo’s tensile strength was determined by tensile stress test and obtained a final value of 192.20 MPa.

A design procedure for bamboo reinforced concrete beams with rectangular cross-section was elaborated following based on the schematics presented section 2. The input data is entered in the electronic spreadsheet, highlighted by the blue color in

As commented previously, all safety coefficients were disregarded, in order to enable comparison with [_{s} = 1.15) and concrete (γ_{c} = 1.4) can be manually inserted for consideration in the determination process, as stated by [

A comparative analysis suggests an approximation between the results obtained by this study and those obtained during the study realized by [^{2} of bamboo reinforcement.

Design spreadsheet for Reinforced concrete beams - Rectangular cross-section | |||||
---|---|---|---|---|---|

Simple bending | |||||

Input data | Output data | ||||

General data | Parameters | Single reinforcement | |||

q (kN/cm) | 1.2 | P (kN) | 31.09 | ϐx (cm) | 0.259 |

Steel | CA-50 | Mk (kN.cm) | 3131.70 | As (cm^{2}) | 3.12 |

Concrete | C25 | Md (kN.cm) | 4384.38 | Domain | 2 |

f_{yk} (Mpa) | 500 | fyd (kN/cm^{2}) | 43.48 | ρmin | 0.0015 |

f_{ck} (Mpa) | 25 | fcd (kN/cm^{2}) | 1.786 | Asmin (cm^{2}) | 0.74 |

b_{w} (cm) | 12 | d (cm) | 36 | Double reinforcement | |

h (cm) | 40 | ϐx = 0.45 | 0.45 | fyd' (kN/cm^{2}) | simple |

l (cm) | 290 | μlim (ϐx = 0.45) | 0.2509 | As' (cm^{2}) | simple |

d' (cm) | 4 | ϐx (Lim. Domain 2-3) | 0.259 | As (cm^{2}) | simple |

d'' (cm) | 4 | μlim (Domain 2-3) | 0.158 | ||

a (cm) | 96.67 | ϐx (Lim. Domain 3-4) | 0.628 | Solution | |

γ_{s} | 1.15 | μlim (Domain 3-4) | 0.32 | Single reinforcement | |

γ_{c} | 1.4 | Mdlim (ϐx = 0.45) (kN.cm) | 6967.85 | As' (cm^{2}) | simple |

γ_{f} | 1.4 | Mdlim (Dom. 3-4) (kN.cm) | 8886.86 | As (cm^{2}) | simple |

E_{s} (Mpa) | 210,000 | x (cm) | 9.324 | As (cm^{2}) | 3.20 |

Steel - bamboo equivalence | |||||

σ_{steel} (kgf/cm^{2}) | 5000 | F (Kgf) | 16,000 | ||

σ_{bamboo} (kgf/cm^{2}) | 1922 | Ab (cm^{2}) | 8.32 | ||

Dmáx. (cm) | 1.16 |

Data | Oliveira and Vito (2012) [ | Design procedure (spreedshet) |
---|---|---|

M_{d} (kNcm) | 4384.38 | 4384.38 |

M_{k} (kNcm) | 3131.70 | 3131.70 |

P (kN) | 31.09 | 31.09 |

A_{s} (cm^{2}) | 1.94 | 1.94 |

F (kgf) | 10,000.00 | 10,000.00 |

A_{b} (cm^{2}) | 5.2 | 5.2 |

Comparison tests validate the electronic spreadsheet’s procedure; thus, the design of reinforced concrete beams with rectangular cross-section in a four-point bending load can be realized in an optimized manner, obtaining a steel reinforcement area and an equivalent bamboo reinforcement area. Those results aim to support the diffusion of bamboo as a sustainable building material, capable of serving as reinforcement for concrete beams under bending efforts.

To the company Dias & Cardozo Engineering (D&C Engenharia) for partially financing the costs with the publication of this work, a very important private initiative for the promotion of research.

The authors declare no conflicts of interest regarding the publication of this paper.

Tokuda, E.N., de Toledo Viana, J., Amorim, G.A.N., Dias, R. and Bigotto, S. (2020) Design Procedure for Reinforced Concrete Beams and Reinforcement Replacement by Bamboo. Computational Water, Energy, and Environmental Engineering, 9, 37-47. https://doi.org/10.4236/cweee.2020.93004