Adrian Bejan | Tree branches, equality in failure, from Design in Nature

Sep 26, 2025

The video explains how the evolution of solid structures follows the same logic as flow systems, aiming for efficiency, adaptability, and survival. The example of a beam under load introduces the connection between stiffness, strength, and material economy. From simple cantilever beams to tree branches and bones, the goal is always to minimize material while maintaining equal strength and stability throughout. The process of removing underused material leads to forms where stress is distributed uniformly, revealing nature’s preference for equality in failure and optimal use of resources.

The analysis begins with a beam loaded at its tip. Its stiffness is measured by how much it bends, and its strength by how much stress it can withstand before failure. These concepts, grounded in the work of early scientists like Navier and Cauchy, illustrate that every structure resists load through an internal balance of stress, where geometry and material properties determine performance.
The calculation shows that the highest stresses occur at the beam’s fixed end, where both the bending moment and the distance from the neutral axis reach their maximum. Cracks in balconies or branches appear there first, proving that local geometry controls vulnerability. The challenge in design is to reduce unused material without lowering stiffness or allowing stresses to exceed the allowable limit.
By gradually reshaping the structure to equalize stress, material is removed from areas that bear less load and added to those that bear more. This transformation leads to organic forms similar to bones or branches, which look irregular but are actually optimized for even stress distribution. These shapes are examples of “perfectly morphed” designs, where every part works equally hard.
Observations after a hurricane revealed that fallen branches were not just small or weak but of all sizes. This discovery demonstrated that the tree’s architecture had achieved equality in failure. Each branch, large or small, was loaded to the same maximum allowable stress, showing that nature builds for uniform readiness to fail rather than concentrating weakness in specific parts.
The conclusion links this principle of equal stress and proportional material use to broader patterns in nature. From single beams to branching trees and forests, the same rule of uniformity governs form and function. The result is a natural hierarchy of shapes that achieve maximum performance with minimum material, guided by the pursuit of structural harmony and balance.

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