Abstract:

The work verifies the morphological variation of strength in various sizes of solid timber beam in order to ascertain their respective volumetric strength mode at the three (3) perpendicular directions. In this work, a mathematical tool known as Volume Integral was adopted to analyze the volumetric strength mode of timber in mutually perpendicular axes of three (3) batches (A, B & C) having five (5) different sizes of solid timber beam respectively and thereafter, morphological values generated were used in determination of ultimate bending strength assuming Ekki lophira alata, as the timber specie. The result of the analysis showed that increase in timber morphology increases the volumetric strength mode. Also that the maximum volumetric strength for all the sizes of the solid timber beam analyzed occurred at the tangential axis which is perpendicular to the grain direction and tangent to the growth ring (x-direction) followed by the volumetric strength of the  radial axis which is also perpendicular to the grain direction and normal to the growth ring (z-direction). While the least volumetric strength occurred at the longitudinal axis which is parallel to the grain direction (y-direction). This is because solid timber beam has its highest and weakest volumetric strength zone at the tangential and longitudinal directions respectively and the strength varies from specie to specie. Furthermore, it was discovered that Volume Integral (∫_VFdv  = ∫_(x_1)^(x_2)?∫_(y_1)^(y_2)?∫_(z_1)^(z_2)?Fdzdydx) is a good mathematical tool to analyze the morphological variation of volumetric strength mode in structural timber beam because it shows the respective  volumetric strength behavior at the  respective principle axes (tangential, longitudinal and radial directions respectively) of the timber member.