# Buckling of laminated glass columns

J. Blaauwendraad

Delft University of Technology, Delft, The Netherlands

The buckling force of a laminated glass column is highly dependent on the shear stiffness of the soft foil which connects the two glass layers. The value of the buckling force is bounded by the lower limit when no foil is present (two separate glass planes) and the upper limit when the foil is infinitely stiff (the glass layers are ideally coupled). A formula for the buckling force should match these ultimate values. Three formulas for the buckling force of a laminated glass column exist. One of them produces the correct lower and upper limit, one produces the correct lower limit and a conservative upper limit and one produces a zero lower limit and conservative upper limit. The way they appear in the literature, the formulas do not provide engineering insight and do not contain a distinct parameter which controls the transition from the lower to the upper limit. In the present article, an alternative formula is derived on the basis of a set of three simultaneous differential equations, supposition of a sine/cosine displacement field, and the formulation of an eigenvalue problem. The new formula is simple and provides engineering insight. Its derivation yields a dimensionless parameter which controls the transition from the lower to the upper limit. The similarities and/or differences with the existing formulas are discussed. Subsequently, initial deformation of the glass layers is taken into account, transferring the stability problem into a strength problem, so that failure is governed by tensile strength. This allows straightforward computation of the stresses and a unity check to be done.

**Key words**: Laminated glass, buckling formulas, derivation