# Shrinkage Crack Patterns of Rectangular Timber Beams and Their Influence on Load-Bearing Capacity

## TL;DR

This study shows that multiple cracks in timber beams interact in complex ways, affecting load-bearing capacity differently than individual cracks, and symmetric cracks reduce strength less than asymmetric ones.

## Contribution

The study introduces three quantitative coefficients to evaluate crack damage effects and reveals the spatial coupling effect of multiple cracks in timber beams.

## Key findings

- Multiple cracks in timber beams have a spatial coupling effect rather than a simple superposition of individual cracks.
- Symmetric crack patterns cause a slightly smaller reduction in load-bearing capacity compared to asymmetric or single cracks.
- Deep shrinkage cracks do not completely eliminate the load-bearing capacity of timber beams.

## Abstract

What are the main findings?
When multiple cracks exist in a timber beam, their collective effect is not a simple superposition of individual cracks but a spatial distribution coupling effect;In beams with multiple cracks, symmetric crack patterns result in a slightly lower decline in load-bearing capacity than asymmetric or single-crack patterns;Even deep shrinkage cracks do not lead to a complete loss of capacity.

When multiple cracks exist in a timber beam, their collective effect is not a simple superposition of individual cracks but a spatial distribution coupling effect;

In beams with multiple cracks, symmetric crack patterns result in a slightly lower decline in load-bearing capacity than asymmetric or single-crack patterns;

Even deep shrinkage cracks do not lead to a complete loss of capacity.

What are the implications of the main findings?
The non-linear spatial coupling effect of multiple cracks implies that the assessment and repair of cracked timber beams must account for the overall crack pattern and interaction, rather than simply evaluating or summing the influence of individual cracks in isolation;The repair and reinforcement of cracked beams should consider the overall crack pattern, not just the deepest crack, since symmetric or multiple interacting cracks can alter the stress distribution and the overall degradation of structural performance;Even deeply cracked beams retain significant residual capacity, indicating that historical timber structures with shrinkage cracks may not require immediate replacement, allowing for more targeted and economical repair strategies.

The non-linear spatial coupling effect of multiple cracks implies that the assessment and repair of cracked timber beams must account for the overall crack pattern and interaction, rather than simply evaluating or summing the influence of individual cracks in isolation;

The repair and reinforcement of cracked beams should consider the overall crack pattern, not just the deepest crack, since symmetric or multiple interacting cracks can alter the stress distribution and the overall degradation of structural performance;

Even deeply cracked beams retain significant residual capacity, indicating that historical timber structures with shrinkage cracks may not require immediate replacement, allowing for more targeted and economical repair strategies.

This study used finite element simulation and theoretical analysis to predict the crack distribution patterns that may occur during the shrinkage cracking process of rectangular timber beams. Based on the predictions, experimental specimens with six typical crack distribution patterns (I–VI) were designed. Subsequently, a four-point bending test method was employed to conduct large-sample size fracture tests on a total of 1200 small-sized Pinus sylvestris var. mongolica specimens, quantifying the effects of the crack depth, location, and distribution patterns on the specimens’ load-bearing capacity. The results indicate that when multiple cracks exist in a timber beam, their collective effect is not a simple superposition of individual cracks but a spatial distribution coupling effect. Both the depth and location of the cracks play crucial roles in their interaction. This study introduces three coefficients for evaluating the influence of cracks on timber beams, namely the load-bearing capacity coefficient (R), the decline ratio of load-bearing capacity (D), and the comprehensive crack-influence coefficient (β), which can effectively quantitatively evaluate crack damage effects. The framework established in this study, which links shrinkage crack characteristics with the load-bearing capacity of timber beams, along with the experimental data provided, can serve as a reference for the safety evaluation and scientific maintenance of historical timber components and modern timber structures with shrinkage cracks.