Lateral Confinement Reinforcement of Timber Under Perpendicular-to-Grain Compression

Abstract

One of the most common issues encountered in the rehabilitation of timber-structured buildings is the crushing of elements subjected to compression perpendicular to the grain. This crushing results in differential settlements that decrease comfort and, in some cases, compromise the habitability of the building. This study analyzed a reinforcement method involving the lateral confinement of timber members using two metallic side plates. Experimental tests were conducted with various configurations of the bolts used to fix the plates. In addition, several finite element models were developed and validated to extend the scope of the analysis virtually. An initial reinforcement proposal was examined, in which the metal plates were allowed to move vertically with the wood’s deformation. This setup achieved only a 26% reduction in deformation. Subsequently, an enhanced reinforcement system was tested, wherein the plates were anchored to the lower vertical stud, preventing their vertical movement. This configuration significantly enhanced performance, achieving maximum deformation reductions of up to 53%. Finally, in the improved reinforcement system, the load distribution among the bolts was analyzed to support their structural design.

1. Introduction

The crushing of elements subjected to compression perpendicular to the grain is a prevalent issue encountered during the rehabilitation of existing buildings with heavy timber-framed walls. This phenomenon typically manifests in sill plates and capitals due to the concentration of stresses at their intersections with the vertical studs, both upper and lower, as illustrated in Figure 1.

Figure 2 illustrates real-life instances of this pathology in existing buildings in Madrid.

The issue of compression perpendicular to the grain in timber is not exclusive to existing buildings; it also affects new constructions, as demonstrated by several recent studies [1,2,3]. With the increasing use of timber in construction and the growing height of timber buildings, addressing the problem of wood crushing is essential to prevent differential settlements that could compromise the building’s habitability and stability. Therefore, it is crucial to address this issue during the design phase, prior to the building’s commissioning.

In recent years, several research projects have been conducted to provide reinforcement solutions for new construction based on the use of elements that directly support compressive stresses. For instance, metal components such as structural screws or glued-in rods [4,5,6,7,8,9], plates [10], and even densified wood dowels have been utilized [11,12,13].

The behavior of timber under compression perpendicular to the grain is complex and non-intuitive. Unlike failures due to tensile or shear stresses, which often lead to brittle collapse, compression perpendicular to the grain typically results in a ductile failure mode characterized by progressive deformation rather than immediate structural collapse. This behavior is commonly represented by a three-segment stress–strain curve [14,15,16,17] with a very marked central phase of plastic deformation (Figure 3):

A.

Elastic segment: wood displays elastic behavior, which remains linear over the entire range except at the terminal segment.

B.

Plastic segment: buckling of the cell walls and thus yielding of the fibres with macroscopically evident crushing under a small load increase.

C.

Hardening segment: the cell walls break, occupying the empty cell lumen, causing the fibres to accumulate and densify, thereby increasing the strength of the whole. The increase in strength continues until the fibres finally break under compression (around 225 MPa for Picea abies [18]).

Although the compression of wood may not lead to structural collapse, it significantly impacts the building’s habitability by substantially reducing its comfort levels. For instance, it is common for the supports of floor slabs over timber-framed facades to have lower elevations compared to those over brick masonry facades, resulting in floor unevenness within the dwelling.

In previous laboratory tests involving compression perpendicular to the grain, it has been observed that wood experiences slight swelling at the center of the load application area, as shown in Figure 4. Building upon this phenomenon, the present study focuses on investigating the effects of lateral confinement on elements subjected to perpendicular compression, aiming to design reinforcements that mitigate wood crushing.

This lateral bulging has also been observed by other researchers, who have highlighted the influence of the growth ring arrangement on the deformed shape of the specimen [19]. Additionally, experiments have been conducted on perpendicular compression, laterally confining the specimen to understand the behavior of wood under axial, biaxial, and triaxial compression [20]. These studies have confirmed that lateral confinement reduces deformation and enhances the recovery of the specimen’s initial shape once the load is removed.

The reinforcement approach examined in this study represents a novel method not previously proposed for new construction projects. Traditionally, direct installation of pin-like elements, either metallic or wooden, is considered more effective for bearing localized compressive forces. However, lateral confinement may prove beneficial in rehabilitation projects where affected timber components are inaccessible from their upper and lower faces, as illustrated in Figure 2.

2. Materials and Methods

During the experimental phase, several reinforcement solutions were proposed, wherein the confinement of the specimens was achieved using 2 metal plates arranged laterally and connected by metal bolts. Perpendicular compression tests were conducted with varying bolt configurations.

2.1. Materials

A total of 12 glued laminated timber specimens measuring 120 × 120 × 360 mm were used, along with metal plates of 100 × 100 × 10 mm perforated with 10 mm diameter holes, 160 mm long steel bolts with a 10 mm diameter, 10 mm diameter nuts, and 10 mm diameter washers, as shown in Figure 5. All specimens were made of new timber, specifically spruce (Picea abies (L.) H. Karst), with a strength class of GL24h, as defined by standard EN 14080 [21]. The metal plates were made of S 235 JR steel, and the bolts were of steel grade 10.9.

2.2. Methods

A total of 12 destructive mechanical tests were tested in the laboratory with 4 different configurations to identify which one allowed the least crushing, with 3 tests conducted for each configuration. The first configuration was without reinforcement (C90SR), meaning no lateral plates were used to confine the specimen. The second configuration involved confining the specimen with 2 lateral metal plates joined by a single central bolt (C90RC). In the third configuration, the lateral metal plates were connected using 2 bolts placed in a horizontal line at a distance of twice the diameter from the edge (from centre of hole to edge, 20 mm) (C90RH). Finally, in the fourth configuration, the metal plates were joined with 2 bolts placed in a vertical line at a distance of twice the diameter (20 mm) from the edge (C90RV), as shown in Figure 6.

The bolt nuts were tightened until the metal plate came into contact with the wood, meaning that no pre-compression was applied to the wood in the direction perpendicular to the grain, as this could significantly affect the results.

The load was applied uniformly distributed on the upper metal plate in the negative vertical axis direction (downward), with a constant movement of the load head until failure was reached at 300 ± 120 s, in accordance with EN 408 [22]. The lower plate was embedded across its entire surface, while the upper plate could only move vertically along the axis (without rotation). The vertical displacement of the movable head was recorded using a Linear Variable Displacement Transducer (LVDT) attached to it.

Once the experimental phase was completed, a 3D model of each perpendicular compression test was developed using Dlubal RFEM software (version 5.34) for finite element (FE) numerical analysis. The goal was to create an FE model that accurately represents the experimental reality, allowing for an increased number of virtual tests. To validate the models, the crushing experienced by the specimen in the load range of 0.1–0.4 Fmax was calculated, as this is the reference range with linear-elastic behavior used in the standard [22]. Since the tests indicated that the maximum load was approximately 70 kN, the reference range of 7–28 kN was used.

In order for the finite element model to accurately represent the experimental behavior it is essential to properly define the material properties. Wood is an anisotropic material that is commonly considered as orthotropic, to simplify its analysis, with the following three orthotropic directions: longitudinal (L), radial (R), and tangential (T). To characterize the behavior of an orthotropic material in the linear-elastic range, it is necessary to define 12 elastic constants: 3 Young’s moduli: E_L, E_R and E_T; 3 shear moduli: G_LR, G_LT and G_RT; and 6 Poisson’s ratios: ʋ_LR, ʋ_LT, ʋ_RT, ʋ_TR, ʋ_RL, ʋ_TL. Of the 12 elastic constants, only 9 are independent; the remaining constants can be determined through known mathematical expressions derived from stress symmetry.

The stiffness values of the material (Young’s modulus and shear modulus) were obtained directly from the EN 14080 [21] standard for the strength class GL24h. Since the standard does not provide Poisson’s ratios, these were taken from the Wood Handbook [23] for Sitka spruce wood. Accordingly, the values used in the 3D finite element model were as follows:

• E_L: 11,500 MPa, E_R: 300 MPa, E_T: 300 MPa
• G_LR: 650 MPa, G_LT: 650 MPa, G_RT: 65 MPa
• ʋ_LR: 0.372, ʋ_LT: 0.467, ʋ_RT: 0.435
• ʋ_RL: 0.010, ʋ_TL: 0.012, ʋ_TR: 0.435

The mesh density of the finite element model was defined such that the edge length of the finite elements was 10 mm. Additionally, the software was instructed to automatically select either quadrilateral or triangular elements to optimize the element shape and avoid excessive distortion.

Once the FE models were validated, virtual tests were conducted by examining different bolt arrangements and quantities: with 4 bolts in 2 vertical rows, with 6 bolts in 3 vertical rows, and with 9 bolts in 3 vertical rows, as shown in Figure 7. In all configurations, the outer bolts were positioned so that their centers were located at a distance of twice the diameter from the edge (from the center of the hole to edge, 20 mm). The remaining bolts, the interior ones, were evenly distributed within the remaining space.

In the initial reinforcement proposal, the vertical displacement of the lateral plates was considered to occur simultaneously with the crushing of the wood. To improve the performance of the initial reinforcement, a second reinforcement was virtually tested, which prevented the lateral plates from descending. For this, it was assumed that the plates were fixed to the lower stud. The implementation of this improved reinforcement in the field would be feasible without significant difficulties. To account for this mechanical behavior in the FE models, a new displacement constraint was introduced, which consisted of preventing downward movement in the Z direction of the lateral plates.

Furthermore, it is worth noting that some reinforcements have been observed, such as the one shown in Figure 8, consisting of placing a metal plate on the exterior that directly connects the upper stud with the lower one. This reinforcement allows the load transfer from the upper stud to occur directly to the lower stud without the capital (or the sill plate) having to work in perpendicular compression. It is an effective reinforcement, but it is not always feasible to implement, especially when it requires penetrating intermediate floors. The second reinforcement proposed in this study would only connect the capital (or the sill plate) with the lower stud using lateral metal plates.

3. Results and Discussions

3.1. Initial Reinforcement

Figure 9 presents comparative graphs between the three reinforcement configurations and the unreinforced arrangement, derived from the experimental results of the destructive tests. The x-axis shows the displacement (or crushing) of the wood in millimeters, while the y-axis indicates the applied load in kilonewtons (kN).

It is observed that the central reinforcement slightly increases the stiffness by raising the slope of the elastic segment (segment A). The horizontal reinforcement similarly enhances the stiffness in segment A and also increases the load-bearing capacity by surpassing the load value of the unreinforced configuration. Finally, the vertical reinforcement is clearly the most effective of all, as it significantly improves both stiffness and strength.

The failure mode of the wood was similar across all tests, as shown in Figure 10. As the test progressed, the load head compressed the wood in the perpendicular direction until the longitudinal fibers fractured (by shear) and then continued compressing in the perpendicular direction until the material was fully plastified and densified.

The metal plates demonstrated sufficient thickness to prevent significant deformations during the tests. In contrast, the metal bolts exhibited different behaviors depending on the type of test. In the tests with central reinforcement (C90RC) and horizontal reinforcement (C90RH), the bolts operated exclusively in tension by preventing the separation of the metal plates. The position of the bolts along the specimen’s axis allowed the upper and lower compressions to be balanced without inducing any bending in the bolts (after the tests, the bolts could be manually removed from the holes without effort). However, in the tests with vertical reinforcement (C90RV), the bolts primarily experienced bending. The load transmitted from the end of the specimen, where the bolt was located, was greater than that from the opposite, more distant end, which was attenuated; this caused the bolt to bend. The upper bolt experienced a positive moment (concave deformation), while the lower bolt experienced a negative moment (convex deformation), as shown in Figure 11. This behavior was evident because the bolts were completely bent after the test (making manual recovery impossible).

The behavior of the bolts adequately explains the graphs shown in Figure 9. Thus, with 2 bolts arranged horizontally, the performance was expected to improve compared to a single bolt; however, this improvement was practically imperceptible because sufficiently thick plates were used. In other words, the metal plates experienced the stresses from the wood as it attempted to deform transversely, but they hardly deformed at all. Using thinner plates would likely have made the difference in crushing between the two types of tests more evident. On the other hand, with the vertical arrangement of the bolts, the crushing was less because the bolts provided additional stiffness (their own flexural rigidity) by working together with the wood.

To validate the FE models, the strains recorded during the experimental tests were compared with those computed by the software within the load interval of 0.1–0.4 Fmax (7–28 kN). The obtained results are presented in

Table 1. Reduction in crushing (within linear-elastic range) achieved with the initial reinforcement.

Test Type	Experimental Results (Side Plates No Fixed to the Lower Column)		FE Results (Side Plates No Fixed to the Lower Column)
	crushing (mm)	crush reduction (%)	crushing (mm)	crush reduction (%)
C90SR	0.495	---	0.415	---
C90RC	0.439	11	0.367	12
C90RH	0.436	12	0.362	13
C90RV	0.394	20	0.341	18
C904P	---	---	0.330	20
C906P	---	---	0.318	23
C909P	---	---	0.309	26

.

It is observed that, as previously discussed, the best configuration tested in the laboratory is C90RV, achieving a reduction in crushing of up to 20% compared to the unreinforced specimen, as shown in Figure 10. Comparing the numerically obtained values with the experimental results indicates that the finite element models exhibit crushings similar to those observed in reality. Furthermore, the percentage of improvement observed when transitioning from one configuration to the next is also quite similar. The minor discrepancies found are due to the stiffness values incorporated into the numerical models correspond to a GL24h class; however, due to the heterogeneity typically present in wood, the properties of the specimens used do not precisely match these normalized stiffness values. Therefore, it can be concluded that the developed models have sufficient accuracy to reliably conduct virtual testing.

In Table 1, the crush values obtained from the virtual tests of configurations C904P, C906P, and C909P are also presented. The reduction in crushing continues to increase when transitioning between configurations, from 11% in C90RC up to 26% in C909P.

The reinforcements carried out by other researchers on new construction (using pin-like elements arranged parallel to the load) achieved much greater stiffness increases [6]. For example, by using 6 metal screws with a length 10 times their diameter, a 55% reduction in deformation was observed in the linear-elastic segment.

Therefore, from a practical standpoint, the reduction achieved with the initial reinforcement appears insufficient to justify the high number of bolts required for this type of reinforcement. In other words, the proposed reinforcement to reduce wood crushing through confinement perpendicular to the grain is ineffective.

3.2. Enhanced Reinforcement

After confirming that the initial reinforcement, with its various configurations, did not significantly reduce wood crushing through confinement, an improved version of this reinforcement was proposed. The enhancement consisted simply of preventing the side plates from descending with the wood crushing. To achieve this, it was necessary for the plates to be continuous with the lower stud, thereby preventing their vertical displacement. An example of this solution is shown in Figure 12.

This reinforcement aimed to directly activate the bending action of the bolts, regardless of their position, thereby ensuring that the stiffness of the reinforcement was shared between the lateral confinement of the wood and the bending of the metal bolts, as shown in Figure 13.

In the FE models the improved reinforcement was simulated by adding a restriction to the vertical movement of the lateral plates. Specifically, vertical movement was prevented exclusively at the lower surface of the lateral plates to allow for possible bulging when confining the wood. The results are shown in

Table 2. Reduction in crushing (within linear-elastic range) achieved with the enhanced reinforcement.

Test Type	FE Results (Side Plates Fixed to the Lower Stud)
	crushing (mm)	crush reduction (%)
C90SR	0.415	---
C90RC	0.287	31
C90RH	0.269	35
C90RV	0.256	38
C904P	0.226	46
C906P	0.208	50
C909P	0.193	53

.

It was observed that the improved reinforcement performed significantly better than the initial reinforcement, as it allowed for a reduction in crushing of up to 53% (in configuration C909P). Additionally, the configurations with 4 and 6 bolts already achieved a substantial reduction in crushing of 46% and 50%, respectively. These values are closer to those obtained in other studies for reinforcements in new construction [6].

Deriving a mathematical equation that relates to the crush reduction achieved for each configuration is challenging. This difficulty arises from the fact that not all configurations have the same number of bolts aligned with the direction of load application, i.e., the vertical axis. Nonetheless, it would be feasible to establish such a relationship for configurations C90RV, C904P, and C906P, as all of them feature two bolts (one at each end) aligned with the vertical load direction. Configuration C90RV has one line of two vertical bolts at the ends, configuration C904P has two lines of two bolts each, and configuration C906P has three lines of two bolts each. Thus, a relationship can be established between the reduction in bearing deformation and the number of lines (each consisting of two vertical bolts located at the ends), using the following logarithmic equation (Equation (1)). To do so, a simple regression analysis was performed for this purpose, yielding a coefficient of determination of R² = 0.998.

Crush reduction (%) = 10.989·ln (nº vertical lines with 2 bolts at the ends) + 38.103

(1)

On the other hand, in order to advance the practical application of the results, a simple methodology was developed to size the bolts (in the improved reinforcement) for any type of geometry with proportions similar to those in this study, as shown in

Table 3. Load multiplier factor, k_load, for bolt sizing in the enhanced reinforcement.

	C90RC	C90RH	C90RV		C904P		C906P		C909P
	Central bolt	Both bolts	Upper bolt	Lower bolt	Upper bolts	Lower bolts	Upper bolts	Lower bolts	Upper bolts	Central bolts	Lower bolts
f (mm)	0.178	0.162	0.251	0.075	0.213	0.066	0.190	0.050	0.162	0.086	0.050
Qreal (N/mm)	33.98	30.93	47.91	14.32	40.66	12.60	36.27	9.54	30.93	16.42	9.54
Qtrib (N/mm)	19.44	19.44	19.44	19.44	19.44	19.44	19.44	19.44	19.44	19.44	19.44
kload	1.75	1.59	2.46	0.74	2.09	0.65	1.87	0.49	1.59	0.84	0.49

. To do this, the actual load (Q_real) applied to each bolt in the FE models was obtained and compared with the load corresponding to its tributary area (Q_trib). The goal was to equalize both loads, for which a multiplying coefficient called k_load was determined. Thus, when designing a reinforcement, it would be sufficient to multiply k_load by Q_trib to obtain Q_real, which is the load used to size the bolts, as expressed in Equation (2).

Q_real = k_load·Q_trib

(2)

As previously mentioned, Q_real was obtained from the FE models. Specifically, the maximum deflection of each bolt was measured, and subsequently, Q_real was obtained by Equation (3) (elastic equation for a beam with fixed ends under a uniformly distributed load).

Q_real = f·384·E·I/L⁴

(3)

where Q_real is the load acting on the bolt in N/mm, f is the deflection at the center of the span in mm, E is the elastic modulus of the bolt in N/mm² (210,000 N/mm²), I is the moment of inertia of the bolt in mm⁴ (491 mm⁴), and L is the length of the bolt in mm (120 mm).

On the other hand, Q_trib was calculated directly considering the tributary area of the bolt. With a diameter of 10 mm and a length of 120 mm, the tributary area is 10 × 120 = 1200 mm². Since the total area where the load is applied is 120 × 120 = 14,400 mm², and the applied load is 28,000 N, Q_trib is obtained using the expression: (1200/14,400) × 28,000 = 2333 N. Per unit length, this results in 2333/120 = 19.44 N/mm.

For example, if one wishes to size a bolt in the upper row within the C906P reinforcement configuration that receives a total load of 40,000 kN applied over an area of 100 × 100 mm, the following approach would be used. Considering bolts with a diameter of 8 mm and a length of 100 mm, Q_trib is calculated as (8 × 100)/(100 × 100) × 40,000/100 = 32 N/mm. To obtain Q_real, simply apply Equation (2): 1.87 × 32 = 59.84 N/mm.

As observed in Table 3, the load factor k_load for the upper bolts is greater than one, which would increase the load considered in the calculation, while for the lower bolts it is less than one. Since it is common to use bolts of the same diameter throughout, the diameter of the upper bolts would be used, as they are more heavily loaded.

Finally, by comparing Table 2 and Table 3, it is possible to identify the most suitable configuration, that is, the one that allows for the greatest reduction in wood crushing while also avoiding the use of numerous bolts and ensuring that they are not excessively loaded. In this regard, the C904P configuration appears to be the most optimized, as it reduces crushing by 46% and uses only 4 bolts.

4. Conclusions

The feasibility of reducing the crushing of compressed wood pieces in the direction perpendicular to the grain through confinement with lateral metal plates was analyzed. Destructive mechanical tests were conducted with different reinforcement arrangements: unreinforced (C90SR), reinforcement with lateral plates secured by a single central bolt (C90RC), with 2 horizontal central bolts (C90RV), and with 2 vertical central bolts (C90RV). Additionally, several finite element (FE) models were designed to extend the experimental campaign virtually by simulating the placement of 4, 6, and 9 bolts.

With the initial reinforcement proposed, the results showed a reduction in crushing of only 20%, 23%, and 26% with the placement of 4, 6, and 9 bolts, respectively. When comparing these values to other types of reinforcement, such as the use of pin-like elements arranged in the load direction, it indicated that the effectiveness of the reinforcement was quite limited.

In order to improve the performance of the initial reinforcement, an enhanced reinforcement was designed. This consisted simply in preventing the vertical displacement of the side plates, for which they were considered fixed to the lower stud. In the initial reinforcement, this displacement occurred jointly with the crushing of the wood. The performance of the enhanced reinforcement increased significantly, achieving a reduction in wood crushing of 46%, 50%, and 53% with the installation of 4, 6, and 9 bolts, respectively. Finally, taking into account the amount of material used, the most suitable configuration would be C904P, which uses only 4 bolts.

Additionally, for the configurations studied in the enhanced reinforcement, the load distribution among the bolts was analyzed to facilitate their design. As a result, a multiplication factor was obtained that allows determining the actual load carried by each bolt based on its position.

It can be concluded that this work presents a simple solution to reduce the crushing of wood components placed on-site, where access to the top and bottom faces is not possible. In new construction, it is more appropriate to use pin-like elements, as demonstrated by previously published research in the scientific literature. An additive model combining both reinforcement methods could improve the results; however, this would be the subject of analysis in future research. In this context, the economic cost of using a large number of reinforcement elements should be considered.

The experimental tests were conducted on pieces that were not previously compressed. In components placed on-site, already pre-crushed by perpendicular compression, the effectiveness of the lateral confinement reinforcement is likely to be lower. In the future, the experimental testing campaign will be expanded to include reclaimed wood with varying degrees of crushing, in order to adjust the results of this research, also considering the influence of the species, the density or number of bolts, their size and arrangement. Moreover, the influence of the adhesives used in the manufacture of glulam could be analyzed, as recent research has demonstrated that the adhesives used in Laminated Veneer Lumber (LVL) production can significantly contribute to enhancing its strength in aspects that are not typically considered in the structural verifications [24].