Glass Struct. Eng.
https://doi.org/10.1007/s40940-021-00156-8
RESEARCH PAPER
Cantilevered laminated glass balustrades: the Conjugate
Beam Effective Thickness method—part I: the analytical
model
Laura Galuppi · Adam J. Nizich
Received: 21 January 2021 / Accepted: 22 June 2021
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
Abstract The proper assessment of shear coupling is
necessary for the evaluation of laminated glass perfor-
mance between the bounding layered and monolithic
limits. The most common simplified design approach
consists in defining the effective thickness, i.e., the
thickness of a monolithic section with equivalent flexu-
ral properties. Cantilevered laminated glass balustrades
are common applications of structural glass. However,
the use of existing effective thickness methods presents
strong limitations for their design. Here, the conju-
gate beam effective thickness (CBET) method is pre-
sented, based on the conjugate beam analogy recently
proposed to evaluate the response of inflected lami-
nates formed by external elastic beams bonded by an
adhesive ply. The conjugate beam analogy, applied to
laminated glass beams, allows accurate evaluation of
the shear stress transmitted by the interlayer, based on
the response of a monolithic conjugate beam, with the
option to constrain relative sliding of plies at a beam
end. Once the shear coupling is known, the effective
thickness may be evaluated with the proposed CBET
model by comparing the maximum stress and deflec-
tion of the laminated beam with a monolithic Euler–
Bernoulli beam. The CBET method’s formulas can be
L. Galuppi
Department of Engineering and Architecture, University of
Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy
A. J. Nizich (B )
Simpson Gumpertz and Heger Inc., 1625 Eye Street NW,
Suite 900, Washington, DC 20006, USA
e-mail: ajnizich@sgh.com
readily applied to evaluate the maximum stress and can-
tilever free-end deflection for different load and bound-
ary conditions, representative of cantilevered laminated
glass balustrade supported in a U-profile.
Keywords Laminated glass · Balustrades · Glass
design · Effective thickness · Analytical methods
Abbreviations
CBET Conjugate Beam Effective Thickness
EET Enhanced Effective Thickness
PVB Polyvinyl butyral (a safety glass inter-
layer)
Geometric and material parameters
L Length of the the cantilever span
a Length of simply-supported span
b Beam width
d Distance from free end of cantilevered
span
i = 1, 2 Glass ply numbering
h
i
Thickness of the i th glass ply
t Thickness of the interlayer
x , y , z Axial, through-the-thickness and lateral
beam directions
E Young’s modulus of glass
G Secant shear modulus of the interlayer
ν Poisson’s ratio
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