Study on Profitability of Combining Wood and CFRP into Composite Based on Mechanical Performance of Bent Beams

Abstract

The paper attempts to estimate the profitability of combining wood and CFRP into a composite (BSH-CFRP), intended to be used in load-bearing beams, including mechanical performance and prices of constituent materials. Prices of glue laminated timber (BSH) and CFRP tapes over the years were provided by ABIES Poland Ltd. and S&P Poland Ltd. companies. Referring to the uncertainty of wood prices on the market, two levels of BSH prices were adopted. A prediction of the beams’ mechanical behaviour was made based on the analytical model prepared by the author. The calculated members varied in width, height and length and included twelve types of CFRP tapes (different thickness, width and modulus of elasticity) glued between wooden lamellas. The total cost of each BSH-CFRP beam was compared to the total cost of the corresponding BSH beam in GL24h class, which led to calculating a cost multiplier. Consecutively, the multiplier was referred to the standard class improvement of BSH according to the bending stiffness and load-bearing capacity. A cloud of points got from many analyses resulted in obtaining exponential approximating functions. The averaged results led to general conclusions that at the assumed price level, improving the BSH standard class by using CFRP tapes was associated with a 1.86 BSH cost in the case of expensive wood or 2.81 in the case of cheap wood. Improving class by two was connected with the 3.55 BSH cost for expensive wood, and 6.79 for cheap wood. At present, the profits from composing wood with CFRP appear to be not very high in terms of their price. However, they can radically increase, especially when wood cutting limits are imposed on manufacturing companies, which significantly reduce the available timber for construction use.

1. Introduction

Nowadays, composites are used in various industry branches. Combining materials with unique properties allows the optimization of the load-bearing elements and to adapt their strength to the expected loads. The current literature is rich in static studies of composites composed of wood and CFRP, conducted by various research centres around the world. Both strengthening the existing structures and testing newly manufactured elements are carried out. A general review of reinforcing techniques for wooden girders has been presented, for example, by Schober [1] and Franke [2]. Only a cumulative summary of the research conducted on bent beams of full rectangular cross-sections reinforced with CFRP materials, as they most directly concern the topic, is presented in the paper. The first identified method of strengthening the existing structural members is the near-surface mounting of CFRP bars with epoxy glue (Figure 1). Such studies were carried out, among others, by Raftery [3] and Bergner [4]. Bars can be pre-stressed as well, which was proposed by Yang [5].

The second way is to reinforce wood with CFRP mats, tapes or strips. This can be done on a variant width of the cross-section, as angles or the letter U (Figure 2). Such reinforcements were analysed, among others, by Andor [6], de la Rosa Garcia [7], Rescalvo [8], Nadir [9], Vahedian [10], Brunetti [11], Subhani [12] and Zhang [13]. CFRP tapes can be pre-stressed as well, which was investigated by Halicka [14,15].

The last method of strengthening the girders is cutting the cross-section and gluing the CFRP strips into the prepared incisions (Figure 3). This approach was checked by Jankowski [16], Nowak [17] and Morales-Conde [18].

Another group of reinforced wooden elements is beams made by joining wood with CFRP at the stage of their production, by gluing CFRP tapes between wooden lamellas in various arrangements (Figure 4). The necessity to apply an adequate pressure of the composite components to obtain a strong adhesive layer determines using CFRP tapes or strips only. Such studies were carried out, among others, by Raftery [19,20], Glisović [21], Yang [22], He [23] and the author of this paper [24,25,26,27].

The usefulness of connecting glue laminated timber with fibre reinforced polymers (CFRP), presented in this paper, and benefits of the mechanical performance of the elements are unquestionable. They lead to a high increase in the stiffness and load-bearing capacity of structural members. The research is both current and constantly developed, which proves the significant importance of the topic presented. However, the literature is silent about the production issues and cost profitability of merging these two materials together. The problem in technology is that production lines for classical BSH material should be improved and partially changed. It is strictly connected with difficulties in cutting materials with completely different properties. Saws used in wood production blunt when twenty times stiffer CFRP material meets their way. Another problem is the blunting of planers when planning side surfaces with a protruding CFRP tape.

Technological aspects are hard to estimate before performing many empirical tests. However, estimating the cost of load-bearing beams made of wood-CFRP composites, including their mechanical performance and prices of constituent materials, is possible and achieved in the paper.

2. Materials and Methods

The prediction of the behaviour of wood-CFRP composites compared to glue laminated timber beams was made based on the simplified analytical models. The detailed assumptions, experimental and numerical validation were given in the author’s earlier works prepared within the author’s PhD dissertation [24], published in 2021, and other articles [25,26]. Prices of glue laminated timber and CFRP tapes over the years were provided by the ABIES Poland Ltd. and S&P Poland Ltd. companies. The averages included the operating regions of the companies (Poland, Germany, Austria, Switzerland). The first quarter prices in 2022 were assumed for the analyses.

2.1. Models’ Assumptions

Only the main description and equations were presented in the paper. The material properties for wood were taken from the PN-EN 14080 standard [28] and for CFRP tapes as the producer declared [29]. Structural wood used in Poland is usually coniferous (Pine or Spruce) and called “softwood”. Both the species have similar mechanical properties. The one used in the calculations was GL24h glue laminated timber class. This means that the modulus of elasticity was equal to E_0,mean = 11.5 GPa, shear modulus G_mean = 0.65 GPa and bending strength f_m,k = 24 MPa.

Glue laminated timber beams without strengthening were noted as BSH and beams made of wood-CFRP composite as BSH-CFRP. Only one reinforcing technique was considered—CFRP tape glued above the bottom wooden lamella (Figure 4)—which was identified as the most effective. The properties of BSH beams may be calculated as for a simple rectangular cross-section, as shown in Figure 5. The cross-sectional area (A) and moment of inertia (J) should be calculated from Equation (1), consecutively.

$$A=bm{h}_L, J=\frac{b{\left(m{h}_L\right)}^3}{12}$$

(1)

For BSH-CFRP-beams, the equivalent area method should be used (Figure 6).

The equations to calculate the cross-sectional properties of BSH-CFRP-beams are Equations (2)–(6). The denotations used in the formulas are: S_x—cross-sectional static moment, A—cross-sectional area and J—total moment of inertia.

$$n=0.85\frac{E_{CFRP}}{E_{0,mean}}, S_x=S_{x,I}+S_{x,II}+S_{x,III},J=J_I+J_{II}+J_{III}, y_0=\frac{S_x}{A}$$

(2)

$$A=b\left[h_L\left(m+1\right)+n{t}_{CFRP}\right], S_{x,I}=bm{h}_L\left(h_L+t_{CFRP}+\frac{1}{2}m{h}_L\right)$$

(3)

$$S_{x,II}=nb{t}_{CFRP}\left(h_L+\frac{1}{2}{t}_{CFRP}\right), S_{x,III}=\frac{1}{2}b{h}_L{}^2$$

(4)

$$J_I=\frac{b{\left(m{h}_L\right)}^3}{12}+bm{h}_L{\left(h_L+t_{CFRP}+\frac{1}{2}m{h}_L-y_0\right)}^2$$

(5)

$$J_{II}=\frac{nb{t}_{CFRP}{}^3}{12}+nb{t}_{CFRP}{\left(y_0-h_L-\frac{1}{2}{t}_{CFRP}\right)}^2, J_{III}=\frac{b{h}_L{}^3}{12}+b{h}_L{\left(y_0-\frac{h_L}{2}\right)}^2$$

(6)

An estimation of the load capacity (P_max) for both presented types of the beams in four-point bending, where L is the length of the beam and f_m,k is wood bending strength according to standard wood class [28], may be completed using Equation (7):

$$P_{\max }=\frac{6J{f}_{m,k}}{L{y}_0}$$

(7)

Deflection in the middle of the beam (w_max) when the maximal force (P_max) is reached may be calculated from Equation (8). The main material’s properties are: E_0,mean—modulus of elasticity of wood in bending and G_mean—shear modulus of wood.

$$w_{\max }=\frac{23}{1296}\frac{P_{\max }{L}^3}{E_{0,mean}J}+\frac{1}{5}\frac{P_{\max }L}{G_{mean}A}$$

(8)

The results are planned to be presented as a comparison between reinforced and unreinforced beams. Because of that, only one static scheme is representative. The stiffness of the beam (K) may be defined as Equation (9):

$$K=\frac{P_{\max }}{w_{\max }}$$

(9)

2.2. Analysed Beams’ Cross-Sections

The straight structural members with full rectangular cross-section used in the construction had a length of 5–20 m and L/h ratio of 12–20, which gave a constraint, reducing the number of examples. The heights were constrained by the height of a single wooden lamella equal to 40 mm. In this work, beams’ widths were fixed at 100 mm, 120 mm and 150 mm by the produced CFRP tapes’ widths. Shear stresses in the analysed cases were not exceeded; the maximal effort was at the level of 60%. There occurred a high load capacity reserve in CFRP tapes in the case of the bottom wooden lamella crack: the maximal effort was at the level of 15%, which should prevent from a rapid collapse of the structural member in case of its overloading. The mechanical analyses were performed on many examples presented in

Table 1. Lengths and heights of the analysed beams.

L/h	21.43	18.75	16.67	15.00	13.64	12.50
Length (m)	Height (mm) (Number of Wooden Lamellas)
6	280 (7)	320 (8)	360 (9)	400 (10)	440 (11)	480 (12)
12	650 (14)	640 (16)	720 (18)	800 (20)	880 (22)	960 (24)
18	840 (21)	960 (24)	1080 (27)	1200 (30)	1320 (33)	1440 (36)

, both for reinforced and unreinforced beams.

Based on these examples, the ratios of maximal force and deflection between BSH and BSH-CFRP beams could be calculated. It will give the answer of what the influence of CFRP tapes is compared to unreinforced glue laminated timber beams both in stiffness and load-bearing capacity. After calculating the mechanical properties, cross-sectional areas of wood and CFRP tapes were estimated. Based on this information and materials’ prices, it was possible to find the girders’ costs and cost ratios between BSH and BSH-CFRP beams.

2.3. Materials’ Prices

Calculating the profitability of the composite material is possible only when recent materials’ prices are known. Average year prices of the materials as BSH—GL24h class wood (Figure 7) and CFRP tapes (Figure 8) over the years 2016–2022 were provided by the ABIES Poland Ltd. and S&P Poland Ltd. companies.

The trend of glue laminated timber prices is clearly increasing and prices of CFRP tapes are keeping rather stable. Further and more detailed economical predictions can be made based on more sophisticated data. However, they are not a part of this paper. The article considered only two possibilities: when BSH was relatively cheap (ca. 290 EUR/m³) and relatively expensive (ca. 630 EUR/m³). The price of one running meter of 1 mm² of CFRP tape was assumed stable as an average: 0.24 EUR for SM tape and 0.38 EUR for HM tape. SM are tapes with a lower modulus of elasticity (170 GPa) and HM are with the higher one (210 GPa). It is worth mentioning that the given prices are net prices.

3. Results and Discussion

The presentation of results is divided into several parts. The first one shows the costs of the constituent materials used in the analysed beams. The next one presents the increases in stiffness (K_incr) and load-bearing capacity (P_incr) of the analysed cases. The last one comprises a results discussion.

3.1. Costs of the Constituent Materials

The calculated costs of the materials used in the beams are presented in the subsequent

Table 2. BSH volume and CFRP tape cross-sectional area for the beams (compared to Table 1).

L/h			21.43	18.75	16.67	15.00	13.64	12.50
Length L(m)	Width (mm)	CFRP Tape Cross-Sectional Area t = 1.2 mm/t = 1.4 mm (mm2)	BSH Volume (m3)
6	100	120/140	0.168	0.192	0.216	0.240	0.264	0.288
	120	144/168	0.202	0.230	0.259	0.288	0.317	0.346
	150	180/210	0.252	0.288	0.324	0.360	0.396	0.432
12	100	120/140	0.672	0.768	0.864	0.960	1.056	1.152
	120	144/168	0.806	0.922	1.037	1.152	1.267	1.382
	150	180/210	1.008	1.152	1.296	1.440	1.584	1.728
18	100	120/140	1.512	1.728	1.944	2.160	2.376	2.592
	120	144/168	1.814	2.074	2.333	2.592	2.851	3.110
	150	180/210	2.268	2.592	2.916	3.240	3.564	3.888

,

Table 3. Costs of CFRP tapes used in the analysed beams.

Length (m)	Width (mm)	S&P C-Laminate/1.2 mm (EUR)		S&P C-Laminate/1.4 mm (EUR)
6	100	173	202	274	319
	120	207	242	328	383
	150	259	302	410	479
12	100	346	403	547	638
	120	415	484	657	766
	150	518	605	821	958
18	100	518	605	821	958
	120	622	726	985	1149
	150	778	907	1231	1436

,

Table 4. Costs of “cheap” BSH used in the analysed beams.

L/h			21.43	18.75	16.67	15.00	13.64
Length (m)	Width (mm)	Cost of “Cheap” BSH (EUR)
6	100	49	56	63	70	77	84
	120	59	67	75	84	92	100
	150	73	84	94	104	115	125
12	100	195	223	251	278	306	334
	120	234	267	301	334	367	401
	150	292	334	376	418	459	501
18	100	438	501	564	626	689	752
	120	526	601	677	752	827	902
	150	658	752	846	940	1034	1128

and

Table 5. Costs of “expensive” BSH used in the analysed beams.

L/h			21.43	18.75	16.67	15.00	13.64
Length (m)	Width (mm)	Cost of “Expensive” BSH (EUR)
6	100	106	121	136	151	166	181
	120	127	145	163	181	200	218
	150	159	181	204	227	249	272
12	100	423	484	544	605	665	726
	120	508	581	653	726	798	871
	150	635	726	816	907	998	1089
18	100	953	1089	1225	1361	1497	1633
	120	1143	1307	1470	1633	1796	1959
	150	1429	1633	1837	2041	2245	2449

.

3.2. IncreasesinStiffness and Load-Bearing Capacity

The increases in stiffness (K_incr) and load-bearing capacity (P_incr) of reinforced beams for each analysed case in relation to unreinforced beams, represented by Equation (10), are presented in

Table 6. Results for data: E_CFRP = 170 GPa, t_CFRP = 1.2 mm (S&P C-Laminate SM/1.2).

L/h			21.43	18.75	16.67	15.00	13.64
Length (m)	Stiffness /Load-Bearing Capacity	Increases of Stiffness and Load-Bearing Capacity (%)
6	Kincr	8.41	7.99	7.53	7.09	6.66	6.26
	Pincr	11.80	11.18	10.55	9.95	9.39	8.88
12	Kincr	5.86	5.30	4.82	4.40	4.05	3.73
	Pincr	7.98	7.23	6.59	6.06	5.60	5.21
18	Kincr	4.33	3.86	3.47	3.15	2.87	2.63
	Pincr	5.82	5.21	4.71	4.30	3.95	3.65

,

Table 7. Results for data: E_CFRP = 170 GPa, t_CFRP = 1.4 mm (S&P C-Laminate SM/1.4).

L/h			21.43	18.75	16.67	15.00	13.64
Length (m)	Stiffness /Load-Bearing Capacity	Increases of Stiffness and Load-Bearing Capacity (%)
6	Kincr	9.75	9.26	8.74	8.23	7.74	7.28
	Pincr	13.73	13.02	12.29	11.60	10.95	10.35
12	Kincr	6.81	6.16	5.60	5.12	4.71	4.34
	Pincr	9.30	8.42	7.69	7.07	6.54	6.08
18	Kincr	5.04	4.49	4.04	3.66	3.34	3.07
	Pincr	6.79	6.08	5.49	5.01	4.61	4.26

,

Table 8. Results for data: E_CFRP = 210 GPa, t_CFRP = 1.2 mm (S&P C-Laminate HM/1.2).

L/h			21.43	18.75	16.67	15.00	13.64
Length (m)	Stiffness /Load-Bearing Capacity	Increases of Stiffness and Load-Bearing Capacity (%)
6	Kincr	10.13	9.66	9.14	8.61	8.11	7.64
	Pincr	14.54	13.81	13.05	12.32	11.64	11.01
12	Kincr	7.15	6.48	5.90	5.40	4.96	4.58
	Pincr	9.90	8.97	8.19	7.53	6.96	6.47
18	Kincr	5.31	4.73	4.26	3.87	3.53	3.24
	Pincr	7.24	6.47	5.85	5.34	4.91	4.54

and

Table 9. Results for data: E_CFRP = 210 GPa, t_CFRP = 1.4 mm (S&P C-Laminate HM/1.4).

L/h			21.43	18.75	16.67	15.00	13.64
Length (m)	Stiffness /Load-Bearing Capacity	Increases of Stiffness and Load-Bearing Capacity (%)
6	Kincr	11.72	11.19	10.59	9.99	9.41	8.86
	Pincr	16.91	16.07	15.20	14.35	13.56	12.82
12	Kincr	8.31	7.53	6.86	6.28	5.77	5.33
	Pincr	11.54	10.46	9.55	8.78	8.12	7.55
18	Kincr	6.17	5.51	4.96	4.50	4.11	3.77
	Pincr	8.44	7.55	6.83	6.23	5.73	5.30

. Individual rows and columns correspond to those in Table 1.

$$K_{incr}=\left(\frac{K_{BSH-CFRP}}{K_{BSH}}-1\right)\cdot 100\%, P_{incr}=\left(\frac{P_{\max ,\hspace{0.17em}BSH-CFRP}}{P_{\max ,\hspace{0.17em}BSH}}-1\right)\cdot 100\%$$

(10)

3.3. Study on Cost in Relation to Mechanical Properties of Reinforced and Unreinforced Beams

To compare the cost of beams, including mechanical properties, calculating a cost multiplier (C_T) was necessary, as determined by Equation (11):

$$C_T=\frac{C_{BSH-CFRP}}{C_{BSH}}$$

(11)

Looking at the increases in stiffness and load-bearing capacity as in the increasing glue laminated timber class, the cost increase in dependence on the BSH class increase was possible to be found. This can be substantial information, because these days, when demand for wood is high, acquiring a BSH class higher than GL24h is hard in a traditional production. Increasing stiffness by 5.22% leads to the BSH one class higher (GL26h), and 10.44% to two classes higher (GL28h), while one class growth in the case of load-bearing capacity may be completed by an 8.33% increase and 16.66% for two classes. When these features were known, based on the obtained results, creating a cloud of points representing the cost multiplier in dependence on class growth both for stiffness and load-bearing capacity was possible. Results presented in the mentioned manner are shown in Figure 9 and Figure 10.

Based on the point clouds, applying exponential approximating functions for both dependencies with a very good R² fitting factor could be achieved. For cheap and expensive wood, the formulas are Equations (12) and (13). They made it possible to collect data in one graph and describe the basic differences (Figure 11).

$$Stiffness:C_{T,cheap}=1.148\cdot e^{0.837\cdot x}, C_{T,expensive}=0.957\cdot e^{0.618\cdot x}$$

(12)

$$Load\hspace{0.17em}\hspace{0.17em}bearing\hspace{0.17em}\hspace{0.17em}capacity. C_{T,cheap}=1.193\cdot e^{0.917\cdot x}, C_{T,expensive}=0.984\cdot e^{0.677\cdot x}$$

(13)

As it can be seen in Figure 11, the cost of increasing the BSH class based on stiffness was close but was slightly different from this for the load-bearing capacity. For the stiffness, the cost multiplier with expensive wood for BSH one class growth (GL26h) was 1.78 and 3.29 for two classes (GL28h), while for cheap wood it was 2.65 and 6.12, consecutively. Equally, the load-bearing capacity with expensive wood for one class growth was 1.94 and 3.81 for two, while with cheap wood it was 2.98 and 7.47, consecutively.

To interpret the results in a clearer way, a column graph was prepared (Figure 12). It presents a BSH class increase in dependence on the wood price (cheap/expensive) and mechanical response (stiffness/load bearing capacity). For general summary, the results were averaged. It can be stated that improving the BSH standard class by one using CFRP tapes was associated with 1.86 BSH cost in the case of expensive wood or 2.81 in the case of cheap wood. Improving the class by two was connected with 3.55 BSH cost for the expensive wood, and 6.79 for the cheap wood.

From the point of view of structural design, the deflection condition was usually more important than the load capacity condition, because of the serviceability limit state. This made the stiffness a leading property for the results interpretation. Regardless of the dominant factor, the cost of increasing the class of beams in bending by one can be estimated as doubling the cost of the lower class structural member.

4. Conclusions

The paper discussed the cost of load-bearing beams made of wood-CFRP composites (BSH-CFRP) including their mechanical performance and prices of constituent materials. The total cost of each BSH-CFRP beam was compared to the total cost of the corresponding BSH beam in the GL24h class, which led to calculating a cost multiplier. Consecutively, the multiplier was referred to the standard class improvement of BSH according to the bending stiffness and load-bearing capacity. A cloud of points got from many analyses resulted in obtaining the exponential approximating functions. The averaged results led to general conclusions that the cost of increasing the class of beams in bending by one can be estimated as doubling the cost of the lower class element. At present, the profits from composing the GL24h glue laminated timber with CFRP appear to be not very high in terms of their price. However, they can radically increase, especially when wood cutting limits are imposed on manufacturing companies, which significantly reduce the available timber for construction use.