STUDIES OF ELASTIC DEFORMATIONS IN LEONARDO’S MANUSCRIPTS

Abstract

Leonardo da Vinci (1452–1519) was the main figure of the Renaissance by his works in many fields of arts and sciences. It was in the same time mathematician, painter, architect and engineer. But his remarkable contributions were also in botany, music, philosophy, anatomy and physiology. Leonardo is revered for his technological ingenuity. "All our knowledge has its origins in our perceptions" he noted. Based on the natural ability to observe and understand the details of a phenomenon, he developed his power of attaining the gist in many fields of human knowledge. Briefly, this was a skill named intuition doubled by the gift of quickness and accurate talent to make drawings and sketches. His books of notes and manuscripts are the source of study for scientist, revealing continuously surprises. The paper presents some aspects of the Leonardo's contribution in the domain of "strength of materials" referring to the behavior of elastic bars. From the geometrical constructions he studied the qualitative aspects of beam bending, preparing to try the establishment of stresses causing the arch failure. Through experimental studies, Leonardo observed and annotated the phenomenon of elastic deformation of elastic springs.
Assuming that cross-section is rectangular, Leonardo concluded that plane sections remain plane and perpendicular to the midplane after deformation. This is the geometrical hypothesis of the Bernoulli-Euler beam theory, presented by Leonard approximately 250 years earlier.