Advances in Laminated Glass Engineering
Capacity of imperfect fins with continuous lateral restraints
Presented on October 13, 2022 at Facade Tectonics 2022 World Congress
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Overview
Abstract
The stability of monolithic glass fins is reasonably well defined; as an elastic material it behaves in a similar manner to other elastic materials such as steel, for which there are many equations of different forms which give similar results. Special care is required for continuous restraint to the tension flange. Equations presented in Australian Standard AS1288 Glass in Buildings – Selection and Installation1 (AS1288) have been used successfully for many years for monolithic fins when used with the strength model of AS1288, but require closer examination when using laminated fins and/or strength models that allow higher levels of stress. This paper presents strategies for analysis of beams with laminated glass and flexible buckling restraints, such as structural silicone.
Authors
Richard Green PE (WA, NY, TX, CO, OR, MT), M.IEAUST CPEng, NER(Aus), APEC Engineer, IntPE(Aus), RBP(Vic)
Principal - Owner
Green Facades LLC
Richard@GreenFacadesLLC.com
Keywords
Introduction
Australian Standard AS12881 (Appendix C) contains stability options for unrestrained monolithic beams (fins), beams with intermediate restraints, and continuously restrained beams. The latter case is perhaps the most common. The source of the formula for the continuously restrained case is not cited and reputedly has origins in rectangular timber joist equations which assume a rigid fixity to the diaphragm providing the restraint. However, when the restraint is flexible, such as structural silicone, the formula can be non-conservative due to change of buckling load and development of secondary stresses from minor axis bending. The magnitude of the second-order stress is a function of the level of imperfection present in the construction. AS1288 has worked relatively well when used in combination with the stress levels in AS1288, because the stress limit for fins is relatively conservative, employing a glass type factor of 2.5 for fully tempered glass instead of 4.0 in ASTM E13002. If using higher stresses for design, without the ‘buffer’ of lower stresses in AS1288, a more accurate formula for the stability is required and second-order effects need to be taken into consideration.
Kala3 provides a derivation of moment capacity of beams for a given stress level and level of imperfection, geometric parameters, and elastic buckling moment. The derivation only holds true for the elastic range, but glass is elastic to fracture and as rectangular fins are doubly symmetric, the compression limits and tension limits are the same magnitude (axial loads are not considered at this point.) Finite element modelling has found the equation to have good agreement for the tension-controlled stress failure.
Bedon4 et al., demonstrates that a wavelength approach can be taken to glass fins with continuous elastic lateral restraints. The approach assumes the critical half-wavelength must be the length of member divided by an integer and requires testing for a number of integers to find the most critical one. Bedon5 proposes separate equations for tension flange and compression flange restraint, however by selecting a suitable sign convention the two equations can be unified.
Laminated glass further adds to the complexity of the problem. The Wöffel-Bennison effective thickness model in E13002 only correctly predicts the stiffness of simply supported beams under uniformly distributed load, with important inputs including: the length of the member, thickness of the interlayer, and shear stiffness of the interlayer for a given temperature and duration. However, this bending effective thickness significantly over-predicts the torsional stiffness of the glass fin and is non-conservative for stability calculations. Galuppi5 offers an Enhanced Effective Thickness which includes additional parameters for torsional effective thickness that are strongly influenced by the width of the fin.
With a combination of effective section properties and stiffnesses, a stability model that accounts for flexibility of the restraint, and a method of accounting for second-order stresses due to imperfections, this method predicts a more realistic capacity of glass beams and fins.
Method for Analysis of Glass Fins
Form of Equation of Elastic Buckling Used for Unrestrained Fins
There are many forms of the critical elastic buckling formula (also known as Euler Buckling Moment) available. The form used
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Summary
The use of stability equations in AS1288 have been found to be non-conservative for some circumstances such as continuous elastic restraint by structural silicone. The Wöffel-Bennisson effective thickness model in
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Rights and Permissions
[1) Australian Standard AS1288 Glass in Buildings – Selection and Installation, Standards Australia GPO Box 476 Sydney NSW 2001 Australia.
[2] ASTM E1300 - Standard Practice for Determining Load Resistance of Glass in Buildings, ASTM International. West Conshohocken, PA
[3] Zdeněk Kala - Elastic Lateral-Torsional Buckling of Simply Supported Hot-Rolled Steel I-Beams with Random Imperfections, 11th International Conference on Modern Building Materials, Structures and Techniques, MBMST 2013, Procedia Engineering 57 ( 2013 ) 504 – 514, www.sciencedirect.com
[4] Chiara Bedon, Jan Belis, Claudio Amadio - Structural assessment and lateral-torsional buckling design of glass beams restrained by continuous sealant joints. Engineering Structures, August 2015.
[5] Chiara Bedon - Lateral-torsional buckling (LTB) method for the design of glass fins with continuous lateral restraints at the tensioned edge. Composite Structures, Volume 266, 15 June 2021, 113790
[6] Laura Galuppi, Gianni Royer-Carfagni Enhanced Effective Thickness of multi-layered laminated glass, Composites: Part B 64 (2014) 202–213
[7] NCCI SN-003-EN-EU NCCI: Elastic critical moment for lateral torsional buckling, by Access Steel. https://eurocodes.jrc.ec.europa.eu/doc/WS2008/SN003a-EN-EU.pdf
[8] Adam Nizich, Laura Galuppi Enhanced Effective Thickness Method for Cantilevered Laminated Glass Balustrades. Glass Performance Days 2019, pp398-401.
[9] EN 16612: Glass in building. Determination of the lateral load resistance of glass panes by calculation
[10] CEN/TS 19100-1 Design of glass structures - Part 1: Basis of design and materials