Buckling Design of glass elements under compression

Andreas Luible
Michel Crisinel

1. Introduction

The increasing demand in modern architecture for more slender and lighter structures requires the use of new construction materials. Glass, a material that has been used for a long time in windows as a filling material, has much to offer in this regard due to its very high compressive strength and transparency. For this reason, there is a growing trend to extend the use of glass to load carrying elements. Due to their high slenderness and high compressive strength, such elements tend to fail
because of instability (i.e. column buckling). At the moment little knowledge exists about the load
carrying behaviour of glass structural elements, and existing design methods for other materials (i.e. steel) cannot be directly transferred to glass panels, because influences of the following aspects must be investigated in a different way for glass:

• production tolerances (i.e. glass thickness)

• initial deformations,

• the visco-elastic Poly-Vinyl-Butyral foil interlayer (PVB) used for laminated safety glass,

• the ideal elastic material behaviour without plastic deformability or strain hardening effect as it is the case for steel, and

• the ultimate breaking stress in glass, which is not a material property but depends on the embedded compressive surface stress due to the tempering process, the degree of damage of the glass surface and the load duration.

The main objective of the research work being conducted [1] is to develop a design method for stability-critical load carrying glass elements which may fail due to lack of stability, i.e. column buckling, plate buckling and lateral torsional buckling.

2. Column Buckling of Glass Elements

Loss of stability (bifurcation buckling) means the instantaneous failure of a structure after the
critical load Ncr,K (Fig 1) is exceeded. In reality the critical load can never be obtained because of
the out-of-straightness of the bar and/or the eccentricity e of the applied load. The maximum load
NK is the point where the maximum stresses in the material due to the lateral deformations are reached. For the design of structural elements under compression, the fundamental study of the difference between the critical load Ncr,K and the maximum load NK is necessary.

3. Column Buckling Models for Glass

To study the column buckling behaviour analytical models based on the second order differential equation of compressed bar and numerical models were developed. The model for laminated glass takes into account the visco-elastic material behaviour of the PVB-interlayer.

4. Experimental Investigation

The test arrangement represents the ideal column buckling case with two pinned column ends. The second order differential equation solution showed good agreement with the performance of single layered glass in the tests. The visco-elastic finite element model was able to describe the time and
temperature dependent load carrying behaviour of the laminated glass elements.

5. Main results and conclusions

The column buckling strength of a compressed glass element depends mainly on the initial deformation, the glass thickness and the shear stiffness of the PVB foil interlayer. Failure occurs when the maximum tensile stress due to loading exceeds the embedded compressive surface stress
plus the tensile strength of the annealed float glass. The load carrying behaviour of laminated safety
glass in compression depends strongly on the temperature and the load duration due to the shear connection with the visco-elastic PVB interlayer. Investigations showed that this shear connection, which can be simplified on the safe side with an elastic approach, might only be taken into account for short-term loading like wind and impact. The design of single layered glass and laminated safety
glass might be carried out either with column buckling curves based on geometric slenderness or by means of direct second order stress analysis. The latter seems to be the more convenient approach especially when additional bending moments are applied. The dispersion of the glass thickness from the nominal value as well as the initial deformation of the glass members might be taken into
account in design by the values given in the paper. For further simplification the cross section of a
laminated safety glass structural element can be modelled as a monolithic cross section with an
effective thickness.

6. Acknowledgement

The work presented in this paper was primarily conducted with the support of the Swiss National Science Foundation (SNF) and the industry partners Glas Trösch (Bützberg, Switzerland) and Verre Industriels Moutiers - VIM (Moutier, Switzerland).

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The Authors

Dr. Andreas Luible Senior Engineer YUANDA Europe Ltd Andreas Luible finished his doctoral theses at the EPFL Lausanne about stability problems of load carrying glass elements in 2004.He obtained his civil engineering degree from the Technical University... Read more