Bridging The Divide Between The Modulus Of Elasticity Obtained From Direct Test And Flextural Test Methods: Paper 1 Central Point Load

Abstract

The modulus of elasticity E is a fundamental material constant which is usually determined from experimentation and is an index of the stiffness of the material. The Direct Tensile or compressive test method is usually used for the determination of this constant, while the flexural test method is an indirect test method. Three samples of each of Glass, Mahogany timber, Massonia timber, Cotton timber, Iroko timber, Y16 steel, Y12 steel, Y10 steel and R12 steel were tested in flexure with a central point load in a simply supported arrangement. The respective deflections were recorded via dial gauges for each incremental load and repeated when unloading. The average load and deflection are back substituted into the deflection equation of a point loaded simply supported beam and the circular beam theory equation from where E₁ and E₂ are obtained respectively. For all the materials tested           (Glass, Timber and Steel), It was discovered that the ratio E₂/E₁ was 1.5. This raises the question of which of the two equations is correct. However the surprising constant of E₂/E₁ = 1.5 informed the need to get the average of E₁ and E₂ as the required E. This way the average E so obtained compares with quoted E from the direct Tensile or compressive test methods for the various Engineering materials tested. Therefore within the limits of experimental errors, E_Direct = 1.25 E_Flexure.

Keywords: Young’s Modulus, Tensile Test, Flexural Test, Deflection, Moment, Circular Bending Theory