A Young's Modulus Measurement Method Based on Approximate Polynomial of Large Deflection of Beams (Cantilever and Three Point Bending)

• Published in: Transaction of Japan Society of Spring Engineers Vol. 2020; no. 65; pp. 43 - 50
• Main Authors: HORIBE, Tadashi, SATO, Takeshi, KIMOTO, Hiroshi, MORI, Kotaro
• Format: Journal Article
• Language: Japanese
• Published: Tokyo Japan Society of Spring Engineers 31.03.2020; Japan Science and Technology Agency
• Subjects: Approximation; Beams (structural); Cantilever; Cantilever beams; Deflection; Elliptic functions; Exact solutions; Large deflection; Material testing; Mathematical analysis; Measurement methods; Modulus of elasticity; Piano wire; Polynomials; Thin plates; Three point bending; Young's modulus
• ISSN: 0385-6917; 1348-1479
• DOI: 10.5346/trbane.2020.43

A measurement method is established to determine the elastic modulus of slender, flexible beams when they are subjected to the large deflections. Specifically, the deflections of cantilever beam and simply supported beam is used to determine the modulus of elasticity, Young's modulus. Present method is based on approximate formulas for the nonlinear relation between deflection and load under large deflection. By using the approximate formulas, we can easily obtain the dimensionless load parameters corresponding to the deflection without employing elliptical functions. The approach is validated with experiments using a steel piano wire. While this approximation formulas are easy to use and simple, it has high-precise approximation to the exact solution, consisting from elliptic integrals. Present method is also applicable to flexible thin plates and extremely delicate materials in order to obtain a quick estimate of the material's elastic modulus.