A Study of the Elastic Behaviour of Some Natural Materials under Applied Bending Loads

Abstract

The development of theoretical models relating the elastic moduli to strains, for generally rectangular cross-sections of dual moduli material beams under pure bending, is presented in this paper. Theoretical validation of the models developed, is done by applying the developed expressions to single modulus material beams and confirming that the models reduce to the known expressions for simple bending. Experimental validation of the models developed, is done on the basis of the 3-point bend test, using the known single moduli materials, aluminium and mild steel. Testing is then conducted on limestone, marble, African mahogany wood and teak wood, which are all naturally occurring materials that are suspected of being dual moduli. The results obtained confirm coincidence of the neutral and centroidal axes for aluminium and mild steel beams under pure bending moment, as is expected of single modulus materials. The results further show the neutral and centroidal axes for limestone, marble, African mahogany wood and teak wood not to be coincident, thus indicating that these materials possess dual moduli properties under externally applied pure bending moments. The location of the neutral axis for these latter materials is seen in certain cases to vary with the magnitude of the applied bending moment. It is recommended from the results obtained in this work that, in designing with wood and limestone, the compressive and tensile elastic moduli, as well as the movement of the neutral axis with changes in the magnitudes of the applied loads, should all be considered.

KEYWORDS:           Dual Moduli, 3-Point Bend Test, Limestone, Marble, African Mahogany and Teak