Derivation of the Bi-axial Bending, Compression and Shear Strengths of Timber Beams

Abstract

The derivation is given of the combined bi-axial bending, compression and shear strength of timber beams. As for other materials the elastic-full plastic limit design approach applies, which is known to precisely explain and predict uniaxial bending strength behaviour. The derivation is based on choosing the location of the neutral line. This provides the stress distribution in the beam cross section in the ultimate state for that case, making it possible to calculate the associated ultimate bending moments in both main directions and ultimate normal-and shear force. The derived general equations are simplified to possible elementary design equations, applicable for building regulation.

Exact Stability Calculation for Timber Beams and Columns

“…This failure criterion, derived in Chapter 2, is an applicable and systematized extension of [1]. Buckling is a three-dimensional problem due to initial eccentricities and because it never is possible to have deformations and loading actions to be precisely zero and thus to get exactly an two-dimensional planar structure and thus to get the possibility of bifurcation.…”

“…This therefore is the starting point for the derivations in [6] and is an improvement with respect to the old model, applied in [7], which was based on a limited ultimate compression strain and therefore did not explain and fit precisely to the data. The derivations in [6] of the following equations are based on choosing the location of the neutral line and calculate the associated ultimate bending moments and normal and shear forces. There are three cases to regard for the location of the neutral line.…”