Stability of glued and embedded Glass Panes: Dunkerley straight Line as a conservative Estimate of superimposed buckling Coefficients

We consider a rectangular glass pane as part of a stiffening and force-transmitting timber-glass composite building element. The glass pane is assumed to be both glued circumferentially and embedded into a timber substructure via block setting which enables a load transfer of horizontal forces via vitreous shear areas and compression diagonals within the glass. To verify the stability of the glass pane, the buckling coefficient has to be determined.In this note we first present a PDE model (based on linear elasticity) for the stress tensor within the glass pane and the eigenvalue problem for buckling of the pane. These two equations (in weak formulation) are then solved subsequently with the software COMSOL, i.e. the computed stress field is an input coefficient for the eigenvalue problem of the plate equation. We are interested in the critical load that implies buckling. It is determined by zero becoming an eigenvalue of the plate equation. Numerical results are presented for pane geometries between 1:1 and 4:1. We also find that an additional transversal surface pressure does not influence the critical buckling loads (at linear order).The maximum load is a non-linear function of the compression and shear forces applied at the boundary of the pane. To provide a simplified analysis for the practitioner, we prove that the Dunkerley straight line represents a conservative estimate for superimposed buckling coefficients and therefore for the critical buckling load. This mathematically rigorous proof is based on an application of the generalized Dunkerley theorem for eigenvalue problems.