Nonlinear computational framework for hybrid ductile glulam joists

Abstract

This paper starts by presenting a nonlinear algebraic analysis of hybrid glulam sections, including ductile compression-softening constitutive models obtained via regression analysis of material test data, to compute full-range admissible values of moment (M), co-existent curvature (κ) and excluded-area axial force (Fea) for the sections. The (M,κ,Fea) states, double-checked by treating the section alternately as discretised and as a continuum, are clustered into (M,κ) and (M,Fea) data-sets that permit regression-analysis of κ and Fea as polynomial functions of M. For any load on a glulam member the M profile is known, so κ(M) is a more efficient route to calculating deflections than is M(κ). The κ(M) and Fea(M) constitutive functions, which enable assessment of any section state without tedious recalculation, are fused with longitudinal compatibility and equilibrium requirements to predict the joists’ nonlinear responses up to ultimate. Using quartic or Glos compressive constitutive models, spreadsheet-coding of this framework is shown to predict nonlinear local (κ(M)) and global (load–deflection) responses close to test data, also axial and longitudinal-shear stress redistributions mimicking FE predictions for distributed- or point-loaded hybrid glulam joists comprising combinations of poplar, blue-gum, maritime-pine and larch. The results show that post-peak reductions on compressive stress–strain curves cause through-depth reversal of longitudinal-shear at high moments.