# Cost Factor Analysis for Timber–Concrete Composite with a Lightweight Plywood Rib Floor Panel

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions [26,27].

## 2. Materials and Methods

_{con,fin}and E

_{tim,fin}are, respectively, the effective value of the elastic modulus of concrete and timber for long-term calculations, MPa; E

_{con,t0}is the modulus of elasticity of concrete at the moment when the concrete reaches the design strength or the load is applied to the concrete for the first time, MPa; ψ

_{con}is the coefficient taking into account the effect of the composite action of the material on the effective creep coefficient of concrete, which in the case of service class 1 and full composite action is taken as interpolation of recommended in the new design rules for TCC values and can be obtained by Equation (5); φ(∞,t

_{0}) is creep coefficient for long-term condition and can be obtained by Equation (3); E

_{tim}is mean value of elastic modulus of timber, MPa; ψ

_{tim}= 1 is a factor that takes into account the effect of the composite action of the material on the effective creep factor of the wood; and k

_{def}is a factor for the evaluation of creep deformation taking into account the relevant service class according to Eurocode 5.

_{0}) is the creep coefficient for the long-term condition; f

_{cm}is the mean compressive strength of concrete at the age of 28 days, MPa; t

_{0}is the time when a load is applied on the structure, days; φ

_{RH}is a factor considering the effect of relative humidity on the creep coefficient, which can be calculated from Equation (4).

_{0}is the notional size of the member equal to the height of the concrete layer, mm; f

_{cm}is the mean compressive strength of concrete at the age of 28 days, MPa.

_{con}is the coefficient considering the effect of the composite action of the material on the effective creep coefficient of concrete, in the case of service class 1 and full composite action; φ(∞, t

_{0}) is the creep coefficient for a long-term condition.

_{sls}is the fictitious load, kN/m; ε

_{sh}is the concrete’s drying and autogenous shrinkage inelastic deformation at the 90% level, which in the case of the cement of strength class CEM 42,5 N can be calculated from Equation (7); C

_{p,sls}is the coefficient, which for TCC with rigid connection between timber and concrete layers, i.e., the coefficient of composite action γ = 1, can be calculated from Equation (8).

_{cm}is the mean compressive strength of concrete at the age of 28 days, MPa; RH is relative humidity of the ambient environment, %; RH

_{0}= 100%; f

_{ck}is the characteristic compressive strength of the concrete at the age of 28 days, MPa.

_{1}and A

_{1}are, respectively, the elastic modulus and area of concrete cross-section, kNm

^{2}and m

^{2}; E

_{2}and A

_{2}are, respectively, the elastic modulus and area of timber base cross-section, kNm

^{2}and m

^{2}; z is the distance of the centres of gravity of the concrete and timber base cross-sections, m; L is the span of the panel, m.

_{L}and (EI)

_{T}, respectively, in the longitudinal and transverse directions of the floor, is shown in Figure 6.

_{CLT}and h

_{c}are, respectively, CLT and concrete layer heights, m; P

_{CLT}and P

_{c}are, respectively, CLT and usable strength class concrete price, EUR/m

^{3}; P

_{c, C20}is the price of concrete of strength class C20, used as the base price, EUR/m

^{3}; B

_{1}is a one-meter-wide strip of the panel, m.

_{c}/P

_{c,C20}ratios are summarised in Table 3. The prices used for the analysis are based on the Latvian market at the turn of the year 2021/2022. The use of additional protection layers—for example, fire-rated plasterboards- is required to meet the fire safety requirements of both CLT and plywood panel solutions. This solution allows the relatively easy replacement of such layers if it is necessary in comparison with charred CLT floor solution without additional protection layer. Fire protection layers are not considered in the cost factor analysis.

_{i}is the height of the layer or rib; P

_{i}is the price of the respective material, EUR/m

^{3}; b and L are, respectively, panel width and span, m; n

_{long}and n

_{trans}are the number of longitudinal and transverse ribs; indexes pu, pl are, respectively, the upper and lower plywood layers; indexes t and c are, respectively, the timber and concrete layers; P

_{c,C20}is the price of concrete of strength class C20, used as the base price, EUR/m

^{3}; B

_{1}is a one-meter-wide strip of the panel, m.

## 3. Results

^{2}and 3 kN/m

^{2}, respectively, and the highest quality vibration class are summarised in Table 5 and Table 6. In most cases, the check of long-term deformation for the CLT–concrete panels, which is marked as w

_{fin,ratio}and means the ratio of the calculated deflection to the limiting value accepted as 1/150 of the span, is crucial.

_{ratio}and means the ratio of the calculated response factor R to the limit value according to the Table 1 and Table 2, is decisive. The determined most cost-effective cross-sectional parameters for the plywood–concrete panel at two load area categories—A1 and B—are summarised in Table 7 and Table 8.

## 4. Discussion

## 5. Conclusions

- Cost factor reduction of the most cost-effective cross-sections up to 73% for multi-storey residential and 69% for office building floors.
- A significant reduction of the cost factors leads to an increase in the panel total height of an average of 25% for multi-storey residential buildings and 29% for office buildings.
- Choosing a plywood–concrete composite panel with the lowest possible cross-sectional height, which requires TCC checks, makes it possible to achieve panels of comparable size height to CLT–concrete panels. Up to 54% and 69% lower cost factor values for A1 and B category buildings are obtained for panels of almost equal height.
- Thin concrete layers can achieve the most cost-effective parameters of the plywood–concrete panels and low self-weight levels regardless of panel span.
- The self-weight reduction of 59% un 45% on average, respectively, for A1 and B category buildings for plywood–concrete composite panels with the most cost-effective cross-sections, is obtained in comparison with CLT–concrete composite panels.
- The proposed estimation algorithm of panel cost-effectiveness can be applied in the initial design stage, during which it is necessary to select the used structural solution and materials.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The proposed production method of the rigid connection between timber and concrete layers by gluing granite chips.

**Figure 2.**Cross-section of timber–concrete composite (TCC) with: (

**a**) cross-laminated timber (CLT); (

**b**) plywood rib panel.

**Figure 3.**The proposed production method of a rigid connection between timber and concrete layers [18].

**Figure 4.**The assumed variables for elements of the TCC cross-section, where B—width of the panel; L—length of the panel; h

_{c}—thickness of the concrete layer; h

_{l1}and h

_{l2}—thickness of the CLT layers; h

_{pu}and h

_{pl}—thickness of the upper and lower plywood layers; b

_{t}and h

_{t}—width and height of the timber rib.

**Figure 5.**TCC checks with corresponding load combinations, where ULS and SLS are ultimate and serviceability limit states; t—time point; w—deflection; σ—normal stresses; τ—shear stresses; E—elastic modulus; G—dead load; Q—live load; ψ

_{2}—share of the permanent live load at the total live load; F

_{u}—fundamental load combination; p

_{sls}—fictitious load evaluated shrinkage; indexes: PV—permissible value; conc—concrete; tim—timber; pwc—upper plywood layer; pwt—lower plywood layer; conn—the connection between the rib and upper plywood layer; k—characteristic values; d—design values; fin—effective values; woodbase—wood-based materials.

**Figure 6.**The algorithm of the vibration checks according to the forthcoming design rules “Vibrations.

**Figure 7.**Two types of effective sections for calculations, where H—the height of the panel; h

_{c}—the height of the concrete layer; h

_{pu}and h

_{pl}—the height of the upper and lower plywood layers; h

_{t}—the height of the timber rib; b

_{ef, T}is the effective width of the double-T section, equal to the smallest of a tenth of the panel span L with rib width b

_{t}and half of rib step s; the effective width of the C-type section b

_{ef,C}is half of b

_{ef,T}with ½ b

_{t}.

**Figure 8.**Design schemes for: (

**a**) the load-bearing capacity of the upper plywood layer per 80 kg assembly load F

_{a,d}and self-weight from concrete g

_{c,d}and plywood layers g

_{pu,d}; (

**b**) the deflection of the upper plywood layer from the self-weight of concrete g

_{c,k}and plywood layers g

_{pu,k}; (

**c**) the deflection of the concrete and top plywood layers from the self-weight of both layers and the useful uniformly distributed load q

_{k}, where s is the rib step; h

_{c}and h

_{pu}are thicknesses of concrete and upper plywood layers.

**Figure 9.**The view of timber–concrete composite with plywood rib panel with four longitudinal ribs and four rows of cross ribs.

**Figure 10.**All possible results as the panel’s height with the related cost factor, which correspond to the ultimate and serviceability limit states for a CLT–concrete composite panel with a span of 7 m.

**Figure 11.**CLT–concrete (CLTCC) and plywood–concrete (PWCC) panels in category A1 buildings: (

**a**) cost-factor dependence of the panel span; (

**b**) panel-height dependence of its span, where min H—panel with the lowest height at the corresponding lowest cost factor; min c—panel with the most cost-effective cross-section, and A—multi-storey residential building.

**Figure 12.**CLT–concrete (CLTCC) and plywood–concrete (PWCC) panels in category B buildings: (

**a**) cost-factor dependence of the panel span; (

**b**) panel-height dependence of its span, where min H—panel with the lowest height at the corresponding lowest cost factor; min c—panel with the most cost-effective cross-section, and B—office building.

**Figure 13.**Self-weight of 1 m wide strip dependence of the panel span for CLT–concrete (CLTCC) and plywood–concrete (PWCC) panel in category A1 buildings, where min c—panel with the most cost-effective cross-section, and A—multi-storey residential building.

**Figure 14.**Increase bending stiffness EIef and modal mass M* dependence of concrete layer height h

_{c}for plywood–concrete with constant plywood panel cross-section parameters.

Criteria | Floor Performance Level | ||||||
---|---|---|---|---|---|---|---|

I | II | III | IV | V | VI | VII | |

Stiffness: w _{1kN} (mm) ≤ | 0.25 | 0.5 | 0.8 | 1.2 | 1.6 | No | |

Acceleration and velocity: R ≤ | 4 | 8 | 12 | 16 | 24 | 0.5 |

Category of Use | Quality Level | ||
---|---|---|---|

Quality | Base | Economy | |

Multi-storey residential, A1 | I, II, III | IV | V |

Single house, A2 | I, II, III, IV | V | VI |

Office areas, B | I, II | III | IV |

Strength Class | C25 | C30 | C35 | C40 | C45 |
---|---|---|---|---|---|

Price, EUR/m^{3} | 106 | 108 | 109 | 110 | 111 |

P_{c}/P_{c,C20} | 1.019 | 1.038 | 1.048 | 1.058 | 1.067 |

Thickness | 6.5 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 35 | 40 | 45 | 50 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Price, EUR/m^{3} | 1238 | 1019 | 911 | 895 | 876 | 895 | 895 | 895 | 895 | 995 | 995 | 995 | 995 |

P_{pw}/P_{c,C20} | 11.90 | 9.80 | 8.76 | 8.61 | 8.42 | 8.61 | 8.61 | 8.61 | 8.61 | 9.57 | 9.57 | 9.57 | 9.57 |

**Table 5.**The most rational cross-sectional parameters of the CLT–concrete composite panel for category A1.

Span, m | 3 | 3.5 | 4 | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 | 7.5 | 8 | 8.5 | 9 | 9.5 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Height H, mm | 80 | 95 | 100 | 110 | 130 | 140 | 140 | 160 | 180 | 200 | 220 | 230 | 245 | 260 | 275 |

Cost factor c | 0.54 | 0.63 | 0.71 | 0.72 | 0.82 | 0.91 | 1.06 | 1.23 | 1.25 | 1.28 | 1.37 | 1.46 | 1.55 | 1.64 | 1.74 |

h_{CLT}, mm | 60 | 70 | 80 | 80 | 90 | 100 | 120 | 140 | 140 | 140 | 150 | 160 | 170 | 180 | 190 |

h_{c}, mm | 20 | 25 | 20 | 30 | 40 | 40 | 20 | 20 | 40 | 60 | 70 | 70 | 75 | 80 | 85 |

Concrete class | C20 | C20 | C20 | C45 | C45 | C45 | C40 | C25 | C45 | C45 | C45 | C45 | C45 | C45 | C45 |

Timber class | C24 | C20 | C24 | C24 | C24 | C24 | C24 | C22 | C24 | C24 | C18 | C22 | C24 | C24 | C24 |

Self-weight, kN/m | 0.75 | 0.90 | 0.84 | 1.09 | 1.38 | 1.42 | 1.00 | 1.07 | 1.59 | 2.09 | 2.32 | 2.41 | 2.59 | 2.76 | 2.92 |

w_{fin,ratio} | 0.78 | 0.92 | 0.82 | 1.00 | 0.99 | 0.99 | 0.90 | 0.99 | 0.98 | 0.99 | 0.99 | 1.00 | 0.99 | 1.00 | 0.99 |

**Table 6.**The most rational cross-sectional parameters of the CLT–concrete composite panel for category B.

Span, m | 3 | 3.5 | 4 | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 | 7.5 | 8 | 8.5 | 9 | 9.5 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Height H, mm | 95 | 105 | 115 | 130 | 135 | 150 | 165 | 170 | 195 | 210 | 220 | 235 | 250 | 270 | 285 |

Cost factor c | 0.63 | 0.72 | 0.73 | 0.82 | 0.90 | 0.99 | 1.09 | 1.24 | 1.27 | 1.36 | 1.45 | 1.54 | 1.63 | 1.73 | 1.82 |

h_{CLT}, mm | 70 | 80 | 80 | 90 | 100 | 110 | 120 | 140 | 140 | 150 | 160 | 170 | 180 | 190 | 200 |

h_{c}, mm | 25 | 25 | 35 | 40 | 35 | 40 | 45 | 30 | 55 | 60 | 60 | 65 | 70 | 80 | 85 |

Concrete class | C20 | C20 | C20 | C20 | C45 | C35 | C45 | C45 | C40 | C45 | C45 | C45 | C45 | C45 | C45 |

Timber class | C24 | C24 | C24 | C24 | C24 | C24 | C24 | C24 | C24 | C20 | C24 | C24 | C24 | C24 | C24 |

Self-weight, kN/m | 0.92 | 0.96 | 1.21 | 1.38 | 1.30 | 1.46 | 1.63 | 1.34 | 1.96 | 2.13 | 2.17 | 2.34 | 2.51 | 2.80 | 2.97 |

w_{fin,ratio} | 0.69 | 0.71 | 0.95 | 0.99 | 0.93 | 1.00 | 0.99 | 0.98 | 1.00 | 1.00 | 0.99 | 1.00 | 0.99 | 0.99 | 0.99 |

**Table 7.**The most rational cross-sectional parameters of the CLT–concrete composite panel for category A1.

Span, m | 3 | 3.5 | 4 | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 | 7.5 | 8 | 8.5 | 9 | 9.5 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Height H, mm | 113 | 107.5 | 132.5 | 142.5 | 161 | 180.5 | 171 | 211 | 213 | 236 | 264 | 270 | 314 | 323 | 354 |

Cost factor c | 0.27 | 0.26 | 0.27 | 0.27 | 0.28 | 0.31 | 0.32 | 0.33 | 0.35 | 0.38 | 0.41 | 0.44 | 0.46 | 0.51 | 0.65 |

h_{pl}, mm | 9 | 6.5 | 6.5 | 6.5 | 6.5 | 6.5 | 12 | 9 | 9 | 9 | 9 | 15 | 9 | 18 | 21 |

h_{pu}, mm | 12 | 9 | 9 | 9 | 9 | 9 | 9 | 12 | 9 | 12 | 15 | 15 | 15 | 15 | 18 |

h_{t}, mm | 72 | 72 | 97 | 97 | 120 | 145 | 120 | 170 | 170 | 195 | 220 | 220 | 270 | 270 | 295 |

b_{t}, mm | 35 | 35 | 35 | 35 | 35 | 44 | 35 | 44 | 44 | 60 | 60 | 60 | 72 | 72 | 97 |

Ribs step s, m | 0.60 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.40 | 0.65 | 0.47 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | 1.0 |

h_{c}, mm | 20 | 20 | 20 | 30 | 25 | 20 | 30 | 20 | 25 | 20 | 20 | 20 | 20 | 20 | 20 |

Concrete class | C20 | C30 | C20 | C20 | C20 | C20 | C35 | C20 | C25 | C25 | C20 | C40 | C30 | C45 | C35 |

Timber class | C18 | C24 | C18 | C18 | C24 | C22 | C24 | C22 | C24 | C24 | C18 | C24 | C24 | C24 | C24 |

Self-weight, kN/m | 0.69 | 0.66 | 0.67 | 0.91 | 0.80 | 0.69 | 0.97 | 0.73 | 0.86 | 0.76 | 0.78 | 0.83 | 0.83 | 0.89 | 0.99 |

w_{fin,ratio} | 0.98 | 0.91 | 0.74 | 0.94 | 0.77 | 0.62 | 0.81 | 0.57 | 0.66 | 0.55 | 0.50 | 0.46 | 0.40 | 0.36 | 0.30 |

vib_R_{ratio} | 0.62 | 0.99 | 0.94 | 0.99 | 0.99 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 0.97 | 0.87 | 0.81 | 0.73 | 0.62 |

**Table 8.**The most rational cross-sectional parameters of the CLT–concrete composite panel for category A1.

Span, m | 3 | 3.5 | 4 | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 | 7.5 | 8 | 8.5 | 9 | 9.5 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Height H, mm | 107.5 | 132.5 | 145 | 166 | 188 | 213.5 | 218 | 226 | 266 | 272 | 278 | 317 | 323 | 329 | 354 |

Cost factor c | 0.27 | 0.29 | 0.29 | 0.32 | 0.33 | 0.35 | 0.38 | 0.39 | 0.41 | 0.44 | 0.48 | 0.49 | 0.53 | 0.57 | 0.65 |

h_{pl}, mm | 6.5 | 6.5 | 9 | 12 | 9 | 6.5 | 9 | 12 | 9 | 12 | 18 | 12 | 18 | 21 | 21 |

h_{pu}, mm | 9 | 9 | 9 | 9 | 9 | 12 | 9 | 9 | 12 | 15 | 15 | 15 | 15 | 18 | 18 |

h_{t}, mm | 72 | 97 | 97 | 120 | 145 | 170 | 170 | 170 | 220 | 220 | 220 | 270 | 270 | 270 | 295 |

b_{t}, mm | 35 | 35 | 35 | 35 | 44 | 44 | 44 | 44 | 60 | 60 | 60 | 72 | 72 | 72 | 97 |

Ribs step s, m | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.40 | 0.43 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | 1.00 |

h_{c}, mm | 20 | 20 | 30 | 25 | 25 | 25 | 30 | 35 | 25 | 25 | 25 | 20 | 20 | 20 | 20 |

Concrete class | C30 | C20 | C20 | C20 | C20 | C20 | C20 | C20 | C20 | C30 | C25 | C30 | C25 | C45 | C35 |

Timber class | C24 | C20 | C22 | C18 | C20 | C24 | C24 | C24 | C22 | C24 | C24 | C24 | C24 | C24 | C24 |

Self-weight, kN/m | 0.67 | 0.68 | 0.94 | 0.84 | 0.84 | 0.86 | 1.00 | 1.14 | 0.91 | 0.95 | 0.98 | 0.86 | 0.89 | 0.93 | 0.99 |

w_{fin,ratio} | 0.86 | 0.71 | 0.82 | 0.66 | 0.61 | 0.55 | 0.61 | 0.66 | 0.49 | 0.49 | 0.49 | 0.41 | 0.42 | 0.42 | 0.39 |

vib_R_{ratio} | 0.99 | 1.00 | 1.00 | 0.97 | 1.00 | 0.99 | 0.98 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.93 |

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## Share and Cite

**MDPI and ACS Style**

Buka-Vaivade, K.; Serdjuks, D.; Pakrastins, L.
Cost Factor Analysis for Timber–Concrete Composite with a Lightweight Plywood Rib Floor Panel. *Buildings* **2022**, *12*, 761.
https://doi.org/10.3390/buildings12060761

**AMA Style**

Buka-Vaivade K, Serdjuks D, Pakrastins L.
Cost Factor Analysis for Timber–Concrete Composite with a Lightweight Plywood Rib Floor Panel. *Buildings*. 2022; 12(6):761.
https://doi.org/10.3390/buildings12060761

**Chicago/Turabian Style**

Buka-Vaivade, Karina, Dmitrijs Serdjuks, and Leonids Pakrastins.
2022. "Cost Factor Analysis for Timber–Concrete Composite with a Lightweight Plywood Rib Floor Panel" *Buildings* 12, no. 6: 761.
https://doi.org/10.3390/buildings12060761