At our last Tree Research Journal Club meeting, we discussed the only paper we could find with data on pruner design and tree wound response, comparing its findings to conventional gardening wisdom. Today, we’re examining another widely accepted arboricultural truth that has recently come under scrutiny: the often-repeated claim (including by us) that V-shaped codominant branch unions are inherently weaker than U-shaped unions.

The paper sparking today’s discussion is a relatively recent study:

Rust, S. 2023. Trees adjust the shape of branch unions to increase their load-bearing capacity. Forests. 14:1041.

What Was Done?

This study investigated the relative strength and underlying structure of tree forks through two main approaches. First, in mechanical testing, the author pulled apart 94 branch unions (81 European beech and 13 sycamore maple). As part of this effort, the author assessed how factors such as union shape (U- or V-shaped), included bark, bulges, hidden cracks, angle of branch attachment, and branch diameter ratio influenced branch union strength.

Second, the author compared the relative size and shape of the branch unions using 3D models derived from photographs of about 120 forks from various species. From these models the author measured the section moduli (see below for an explanation of this), an indicator of load-bearing capacity, at multiple points around the fork to better understand fork strength.

What Was Discovered?

There was no difference in breaking strength between U-shaped and V-shaped forks in either the beech or sycamore maple

trees. Regarding the other factors assessed, branch attachment angle had no significant effect on load-bearing capacity. The diameter ratio of branches and included bark showed mixed or limited effects depending on the species and were most concerning when hidden cracks were discovered after testing.

From his assessment using 3D scans of branch unions, Rust suggests that trees employ three mechanisms to strengthen forks: 1. Optimizing the shape of branches to increase their section modulus, 2. Increasing section modulus just below where the stems part, and 3. Increasing section modulus through the growth of lateral bulges (see graphical abstract below).

What in the world is a section modulus?

Section modulus is a ratio between two key factors. The first is the moment of inertia, which describes how the material is spread out in a shape—similar to how weight is distributed in an object. The second is the distance from the center (i.e., the neutral axis) to the outermost edge of the shape. When we divide the moment of inertia by this distance, we get the section modulus.

To visualize why section modulus matters, imagine two identical wooden planks. If you stand one on its edge (|) and lay the other flat (—) across a span, then step on them in the middle, the upright plank will be much harder to bend. Even though both contain the same amount of material, the standing plank is stronger because its wood is distributed farther from the center in relation to the direction of the applied pressure, increasing its section modulus. In trees, a higher section modulus at a fork means the tree has arranged its wood in a way that strengthens that area against bending forces, making it more resistant to breaking.

Conclusion

This research suggests that simple visual assessments based on fork shape (U vs. V) and angle of attachment may not reliably predict structural weakness. While diameter ratio and included bark have historically been better predictors of branch union strength, they were not significant factors given the species and conditions tested here. Finally, these results support current industry BMPs and qualification reference materials, which suggest that adaptive growth, like the lateral bulges observed in this study, indicates both an inherent weakness and the tree’s ability to compensate for that weakness with additional wood production.

Why We Like This Article

First and foremost, we are particularly interested in research on the strength of branch unions. Our team recently conducted a large, multi-language review of tree damage associated with tropical storms and discovered that many branch defects lacked real world data to justify their use in risk assessments. This finding surprised us—so much so that we decided to study these branch defects the next time a storm hit our area. Less than a year later, Hurricane Ian brought tropical storm-level winds to one of our past inventory sites, and none of the 1,518 trees with branch-related issues failed at their defect. Since then, we have been actively seeking new data on branch unions and branch strength.

Beyond the subject matter itself, there is nothing quite like a well-organized summary table to highlight where new findings fit within the existing literature. Table 1 from Rust’s paper summarizes how union shape (U vs. V), diameter ratio, branch angle, and the presence or absence of included bark influenced breaking strengths in ten past biomechanical assessments covering nine different species. The table reveals that none of the assessed factors are completely reliable predictors of relative branch strength (* indicates the factor was tested and found to weaken branches, while – indicates it was tested and had no impact on branch strength).

Minor Grievances

Overall, we appreciate this article but found a few aspects irksome. The study notes that about 120 3D models were generated, yet the exact count should be straightforward to report. It reminds us of a paper that looked at the health of “several hundred palms.” Also, analyzing breaking test data with multiple regression, rather than ANOVAs and correlations, would better account for interactions and reduce experimentwise error. Repeated independent tests increase the risk of false positives or negatives. Lastly, inconsistencies in treatment descriptions made the narrative harder to follow, requiring multiple readings for clarity.

Acknowledgements

A special thanks to Steffen Rust for choosing to publish his work in an open-access journal, enabling us to freely share the full article and republish the tables and figures above with proper attribution (see MDPI Open Access Information and Policy here).

About this Blog

Rooted in Tree Research is a joint effort by Andrew Koeser and Alyssa Vinson. Andrew is a research and extension professor at the University of Florida Gulf Coast Research and Education Center near Tampa, Florida. Alyssa Vinson is the Urban Forestry Extension Specialist for Hillsborough County, Florida.

The mission of this blog is to highlight new, exciting, and overlooked research findings (tagged Tree Research Journal Club) while also examining many arboricultural and horticultural “truths” that have never been empirically studied—until now (tagged Show Us the Data!).

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