# A Novel Z Profile of Pultruded Glass-Fibre-Reinforced Polymer Beams for Purlins

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Optimum Profile of the Purlin

^{2}”. The live load was approximated to be “958 N/m

^{2}”, the rain load was “196 N/m

^{2}”, and the wind load was “993 N/m

^{2}”. Furthermore, the distance between two purlins was estimated to be 1.6 metres. Table 1 shows the intended loads on the purlin structure.

_{P}+ Q

_{S}+ Q

_{L}or Q = Q

_{P}+ Q

_{S}+ Q

_{R}+ Q

_{W}; where is the biggest

_{allowable}= 1/180

^{2}), C is the farthest point at the cross-section of the purlin and the neutral axis or z-z axis (m), I

_{z-z}is the moment of inertia of the cross-section of the purlin and the neutral axis (m

^{4}), V is the shear force at both fixed ends of the structure (N), Q is the area moment of the z-z axis (Nm), Â is the cross-section area above or below z-z axis (m

^{2}), ŷ is the centre gravity of the cross-section area above or below z-z axis from the z-z axis (m), δ is the deflection (m), and E is the modulus of elasticity of the pultruded GFRP material in the longitudinal direction (N/m

^{2}).

_{max}were “2037 N/m” and “13,750 Nm”, respectively.

_{t}), modulus of elasticity (E), and shear strength at the longitudinal axis (τ

_{L}) were “400 MPa”, “22 GPa”, and “40 MPa”, respectively [35]. As depicted in Figure 2, the purlin structure will produce one principal stress in the direction of the longitudinal axis of the purlin (x-x axis) and a deflection in the direction of the axis perpendicular to the longitudinal axis of the purlin (y-y axis). The stress and the deflection must be limited for the structure to be declared safe. Pultruded GFRP materials are brittle materials and do not have yield strength like steel. Therefore, the design stress (σ

_{d}) used as a safety limit in the FE approach analysis was 80% of the tensile strength or “320 MPa”. Then, the analysis used a theoretical-analytic approach using allowable stress by taking a safety factor of 3, because this considers the stress concentration due to the bolt holes [36] at the supports at both ends of the purlin. Thus, the allowable stress (σ

_{allowable}) was “106.67 MPa”. The flexural stress was calculated using Equation (3). As described above, the failure of flexural stress mode occurs at both ends of the supports. On the other hand, the failure of the shear mode is caused by shear forces at both ends of the purlin structure. The most significant shear stress will occur at the line of the neutral axis (z-z axis) and at the plane where the longitudinal axis (x-x axis) is present. Equation (4) is the formula for calculating shear stress. Maximum deflection occurs in the middle of the span of the purlin structure and is calculated by Equation (5). Referring to Table 9.5.b of ACI 318-19 [37], the magnitude of the deflection was limited to L/180, as shown in Equation (6).

#### 2.2. Purlin Prototypes and Structures

^{2}” stitched mat of Jushi EMK450 (Changzhou Zhongjie Composites Co., Ltd., Changzhou, China). Meanwhile, the polymer matrix was a mixture of 100 parts by weight of orthophthalic unsaturated polyester resin (UPR) SHCP 3316QN (PT SHCP Indonesia, Surabaya, Indonesia), five elements by weight of alumina trihydrate (ATH) H-WF-08A (PT Justus Kimiaraya, Jakarta, Indonesia), five parts by weight of light-grey pigments HM IP 7 (PT Mata Pelangi Chemindo, Jakarta, Indonesia), and one and a half parts by weight of catalyst benzoyl peroxide BENZOXE-N (PT Kawaguchi Kimia Indonesia, Jakarta, Indonesia). Fibre and matrix weight percentages in the composite were 55–60% and 45–40%, respectively [35]. All these materials were procured from PT Intec Persada, Indonesia.

#### 2.3. Finite Element Analysis of the Purlin Structure

## 3. Results

#### 3.1. Purlin Profile

_{z-z})

_{min}, was calculated as “31.640 × 10

^{−6}m

^{4}”or “31.640 × 10

^{6}mm

^{4}”.

_{max}= (13,750 × 0.125)/(31.976 × 10

^{−6}) = “53.75 MPa” < σ

_{allowable}= “106.67 MPa” → OK

_{max}= (2037 × 9

^{4})/(384 × 22 × 10

^{9}× 31.976 × 10

^{−6}) = “0.0495 m” = “49.5 mm”

_{max}= 0.0495/9 = 1/181 < (δ/L)

_{allowable}= 1/180 → OK

#### 3.2. Purlin Prototypes and Structure

_{55–45}) and another purlin with ratio 60–40% (Z

_{60–40}). Barcol hardness examination on several points of the two samples’ surfaces yielded relatively similar results in the 55–60 range. Tensile tests were conducted following the ASTM D638 standard for the two samples in the longitudinal and transverse directions. Likewise, the shear strength test in the direction of the longitudinal axis of the bar was carried out according to the procedure described in Figure 3. Table 5 shows both samples’ longitudinal and transverse tensile properties and longitudinal shear strength.

#### 3.3. Finite Element Model of the Purlin Structure

^{2}; 0.34; 1000 N/mm

^{2}; 1940 kg/m

^{3}; 320 N/mm

^{2}; 0.15 W/mK; and 1400 J/kg K, respectively. The external force was loaded as a uniformly distributed force along the purlin, Q. Initially, we used the data properties in Table 2 as parameters input in the FE model of Figure 5. The properties are modulus of elasticity, Poisson’s ratio, shear modulus, mass density, tensile strength, thermal conductivity, and specific heat. The value taken for these parameters are, respectively, 22,000 N/mm

^{2}; 0.32; 1000 N/mm

^{2}; 1900 kg/m

^{3}; 320 N/mm

^{2}; 0.15 W/m K; and 1400 J/kg K. We compared the deflection of the end of the cantilever structure with the deflection of the experimental results as a reference. Next, we changed some properties of the FE model to obtain a deflection value similar to the experimental reference value. Finally, the properties modulus of elasticity, Poisson’s ratio, and mass density were adjusted to be, respectively, 20,400 N/mm

^{2}; 0.34; and 1940 kg/m

^{3}.

## 4. Discussion

_{60–40}, with a 60–40 reinforcement–matrix weight ratio. The pultruded GFRP purlin cross-section has a height (h) of “250 mm”, a width (w) of “100 mm”, and a thickness (t) of “8 mm”. The moment of inertia along the neutral axis (I

_{z–z}) was “31.976 × 10

^{−6}m

^{4}”.

_{60–40}pultruded GFRP material in Table 5 indicate “433 ± 21.24 MPa” longitudinal tensile strength, “22,440 ± 218 MPa” modulus of elasticity, and “45.5 ± 2.4 MPa” longitudinal shear strength.

_{60–40}pultruded GFRP beam was the optimum design for the nine-metre-span purlin to suit a new warehouse building in the fertiliser industry.

_{55–45}and Z

_{60–40}have reinforcement–matrix weight ratios of 55–60% and 45–40%, respectively, while the volume ratios are 41–47% and 59–53%.

_{60–40}, has yielded good results: the tensile properties were observed under the design requirements. When making pultruded composites, some researchers may use fibre with volume fractions from 40–80%, depending on the production methods [50,51]. The greater the amount of reinforcement, the higher the strength and stiffness of the resulting composite. E-glass longitudinal fibres provide the necessary strength and stiffness. Four E-glass stitched mats were included to provide adequate strength and rigidity in the transverse direction.

_{60–40}, the tensile strength in the transverse direction, as denoted in Table 5, was “70 ± 8.15 MPa”. The trial production verified the success of the design and production of the Z prototype purlins, which met the technical criteria. Furthermore, purlin assembly with bolt-nut connections and sag-rod stiffening, as shown in Figure 11 and Figure 12, demonstrated that the purlin roof-support structure functions properly.

## 5. Conclusions

## 6. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 13.**The correlation between force and deflection from experimental and FE models of the cantilever structure.

Technical Loads | Constant Distributed Forces |
---|---|

Purlin weight (“7.25 kg/m” or “71 N/m”) | Q_{P} = “71 N/m” |

GFRP roofing sheet weight (“4 kg/m^{2}” or “39 N/m^{2}”) | Q_{S} = “63 N/m” |

Live load (“20 psf” or “97.6 kg/m^{2}” or “958 N/m^{2}”) | Q_{L} = “1532 N/m” |

Rain load (“20 kg/m^{2}” or “196 N/m^{2}”) | Q_{R} = “314 N/m” |

Wind load (“90 mph” or “993 N/m^{2}”) | Q_{W} = “1589 N/m” |

**Table 2.**Minimum mechanical properties of the pultruded GFRP beam material in the longitudinal direction.

Properties | Value |
---|---|

Tensile strength, σ_{t} | “400 × 10^{6} N/m^{2}” |

Design tensile strength, σ_{d} | “320 × 10^{6} N/m^{2}” |

Modulus of elasticity, E | “22 × 10^{9} N/m^{2}” |

Longitudinal shear strength, τ_{L} | “40 × 10^{6} N/m^{2}” |

Poisson ratio, ν | 0.32 |

Sub-Functions | Alternative Solutions | |||
---|---|---|---|---|

1st Solution | 2nd Solution | 3rd Solution | 4th Solution | |

Withstands corrosive environment | GFRP | KFRP | CFRP | Hybrid of G/K/C-FRP |

Withstands all technical loads | Pultruded beam with continuous roving and stitched mat reinforcement | |||

Compact for handling and shipping | Z profile | C profile | Ω profile | - |

Moment of Inertia (×10^{6} mm^{4}) | Thickness t (mm) | Height h (mm) | Width w (mm) | Cross-Section area A (mm^{2}) | |
---|---|---|---|---|---|

(I_{z}_{-z})_{min} | (I_{z}_{-z})_{actual} | ||||

31.640 | 31.956 | 40 | 180 | 70 | 9912 |

31.640 | 32.251 | 21 | 200 | 75 | 6468 |

31.640 | 32.058 | 14 | 220 | 80 | 4928 |

31.640 | 32.693 | 10 | 240 | 90 | 4000 |

31.640 | 31.976 | 8 | 250 | 100 | 3472 |

Tensile Properties | Samples Material | |
---|---|---|

Z_{55–45} | Z_{60–40} | |

Longitudinal tensile strength | “396 ± 24.02 MPa” | “433 ± 21.24 MPa” |

Longitudinal modulus of elasticity | “21,104 ± 198 MPa” | “22,440 ± 218 MPa” |

Transversal tensile strength | “76 ± 7.23 MPa” | “70 ± 8.15 MPa” |

Transversal modulus of elasticity | “6586 ± 82 MPa” | “6230 ± 69 MPa” |

Longitudinal shear strength | “41.8 ± 2.1 MPa” | “45.5 ± 2.4 MPa” |

Loads (kg) | Deflection at the Free End | ||
---|---|---|---|

Experimental Model (mm) | FE Model (mm) | Difference | |

0 | 0 | 0 | 0% |

46.39 | 4.4 | 4.53 | −2.96% |

69.59 | 7.0 | 6.80 | −2.86% |

92.78 | 9,0 | 9.07 | 0.78% |

115.98 | 110 | 11.35 | 3.18% |

139.18 | 13.0 | 13.61 | 4.69% |

162.37 | 16.5 | 15.88 | −3.76% |

185.57 | 19.0 | 18.15 | −4.47% |

208.76 | 22.0 | 20.42 | −7.18% |

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**MDPI and ACS Style**

Setyanto, D.; Antonio, Y.A.; Darmawan, M.; Ubaidillah, U.
A Novel Z Profile of Pultruded Glass-Fibre-Reinforced Polymer Beams for Purlins. *Sustainability* **2022**, *14*, 5862.
https://doi.org/10.3390/su14105862

**AMA Style**

Setyanto D, Antonio YA, Darmawan M, Ubaidillah U.
A Novel Z Profile of Pultruded Glass-Fibre-Reinforced Polymer Beams for Purlins. *Sustainability*. 2022; 14(10):5862.
https://doi.org/10.3390/su14105862

**Chicago/Turabian Style**

Setyanto, Djoko, Yohanes Adeatma Antonio, Marten Darmawan, and Ubaidillah Ubaidillah.
2022. "A Novel Z Profile of Pultruded Glass-Fibre-Reinforced Polymer Beams for Purlins" *Sustainability* 14, no. 10: 5862.
https://doi.org/10.3390/su14105862