Recent Advances in Engineering
Numerical Analysis of Hybrid Steel-Glass Beam
ONDREJ PESEK, JINDRICH MELCHER, MILAN PILGR
Institute of Metal and Timber Structures
Brno University of Technology
Veveri 331/95, 602 00 Brno
CZECH REPUBLIC
[email protected]; [email protected]; [email protected]
http://www.kdk.fce.vutbr.cz
Abstract: - The aim of this paper is testing of numerical modeling of steel-glass composite structure. New
hybrid steel-glass beam consists of steel flanges and glass web bonded together. The most important aspect of
all composite materials is to joint of different materials. Actually silicone, peroxide, acrylate and polyurethane
materials are use for steel and glass connecting. Load carrying capacity is directly dependent to quality of joint
of materials. In this paper perfect shear connection is consider. Numerical modeling was performed in software
based on final element method. Model of hybrid beam is consisting of 2D and 3D elements (two models). Span
of beam is 6 meters, depth is 300 mm. Flange has rectangular cross section with dimensions 150 and 10 mm.
Thickness of web is 8 mm. (this dimensions are equivalent to IPE300). Linear and nonlinear solutions were
performed. The same beam was calculated by analytical method. Results (deflections, normal stress and shear
stress) from numerical modeling were compared with analytical calculation results.
Key-Words: - Structural glass, hybrid steel-glass beam, composite material, shear connection, analytical
analysis, final element method
structural glass (Table 1). Shear stress in I-beam
web is relatively low and, for this reason, it can be
made of structural glass.
Shear connection of materials of composite
structures (made of materials with different value of
Young's modulus) is the key for utilization of
favorable properties of both materials.
1 Introduction
Glass structures are modern and very popular in
today's architecture. Structural glass as building
material has some unfavorable material properties.
For economical and safe design of structural glass
members is necessary to know its behaviour and
properties.
Currently glass structures are designed as load
carrying, not as earlier, when they were used only
for transparent building envelops. Glass structures
are designed for active load bearing same as
traditional concrete and steel structures.
Some unfavorable properties are possible to
eliminate by combination of several different
materials. Combination of different materials is
principle of composite material (utilize the
advantageous properties of both materials and
eliminate unfavorable properties of both materials).
In civil engineering there is steel-concrete
composite material well known.
Using of steel-glass composite structures is a new
trend in architecture. I-beam is a simple case of use
of steel-glass composite material. The beam is
consisting of steel flanges and glass web bonded
together by special materials. In bottom flange there
is maximal tensional normal stress. It is
advantageous to make tension flange of steel
because of low value of tension strength of
ISBN: 978-1-61804-137-1
Fig. 1 Hybrid Steel-Glass beam visualization
Shear connection between glass and steel is unsure
by special materials (epoxy, acrylate, polyurethane,
silicone).
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Recent Advances in Engineering
not grow of fail when element is in compression.
The compressive strength is irrelevant for all
structural applications, because an element’s tensile
strength is exceeded long before it is loaded to its
compressive strength [1].
For example characteristics values of tensile
strength for FTG, HSF and ANG are 120, 70 and 40
MPa respectively.
2 Materials of Steel-glass composite
A glass is an inorganic product of fusion, which has
been cooled to a rigid condition without
crystallization. Soda lime silica glass is the most
used in structures. For fire protecting glazing and
heat resistant glazing is borosilicate glass used.
Glass shows an almost perfectly elastic, isotropic
behaviour and exhibits brittle fracture. It does not
yield plastically, which is why local stress
concentrations are not reduced through stress
redistribution as is the case for other construction
materials like steel [1].
Base glass product is float glass (ANG). By
secondary processing thermal treatment we get heat
strengthened glass (HSG) and fully tempered glass
(FTG). Laminated (safety) glass is consisting of two
or more glass panes (it may be consisting of all
types) which are joined by PVB-foil.
Steel is an alloy made by combining iron, carbon
and other elements. Steel is elastic-plastic material,
which can yield plastically. Every physical and
material properties of steel are well known and will
not be discussed here.
In Table 1 there are summarized the most important
physical properties of soda lime silica glass and
structural steel.
Quantity
Symbol
Unit
Glass
Steel
Density
ρ
kg/m3
2500
7850
Young's modulus
E
GPa
70
210
Poisson's ratio
ν
-
0,23
0,3
Coefficient of
thermal expansion
α
K-1
9.10-6
12.10-6
Fig. 2 Stress-strain curves
3 Solution of composite structures
Composite structures are well known in civil
engineering. Steel-concrete structures are very
important and modern currently. Timber-concrete
composite is used in reconstruction of old buildings.
Analytical solution of these composites structures is
reliable and can be use at steel-glass composite.
Table 1 Material properties
One of the most important properties of any
structural material is the strength. The theoretical
tensile and compressive strength of glass is
exceptionally high and may reach 32 GPa. The
relevant tensile strength for engineering is much
lower. The reason is that glass is brittle material.
The tensile strength of glass depends very much on
mechanical flaws on the surface. A glass element
fails as soon as the stress intensity due to tensile
stress at the tip of one flaw reaches its critical value.
The tensile strength of glass is not a material
constant, but it depends on many aspects (on the
condition of the surface, the size of glass element,
the action history, the residual stress, the
environmental conditions etc.) [1].
The compressive strength of glass is much larger
than the tensile strength, because surface flaws do
ISBN: 978-1-61804-137-1
Fig. 3 Types of steel-glass I-beams
In Fig. 3 there are shown some types of connecting
of steel and glass at hybrid I-beam (a – using steel
channel section, b – using two steel angle sections, c
- direct connection, d – tongue and groove
connection). In all cases, both materials are bonded
by special material as silicone, epoxy, acrylate and
polyurethane.
Without perfect shear connection materials behave
as separate members (Fig. 4a) and slip between
flanges and web has nonzero value. If shear
connection is perfect, we can take advantage of
favorable material properties (Fig. 4b) and slip is
zero. Such composite structure shows low values of
deformations.
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It is necessary to check effective width (beff) of the
bonded part (Fig. 6). Due to effect of shear lag it is
possible to include only effective width into crosssectional characteristic.
Actually value of slip is depending on used
connection material and their thickness. In practice,
there is low nonzero value of slip because of
imperfect bonded.
4 Example of hybrid steel-glass beam
Consider a simple beam made of hybrid steel-glass
material. Length of span is 6000 mm and beam is
subjected to uniform linear load q = 10 kN.m-1 (Fig.
7).
Cross-section has I shape and consist of steel
flanges (both 150 x 10 mm) and glass web (280 x 8
mm) connected together by direct connection (Fig.
3c). Total depth of beam is 300 mm (Fig.9).
Fig. 4 Principle of shear connection
Analytical solution of composite steel-glass
beam is based on the elastic solution of steelconcrete beams. Whole hybrid cross-section is
substituted by an ideal steel cross-section and
cross-sectional properties are computed for this
ideal cross-section.
Fig. 7 Example description
The different between normal stress at extreme steel
and glass fibres (σ1, σ3 and σ2, σ4) depends on ratio
of Young's modulus of used materials.
For this example is considered with perfect shear
connection between steel flanges and glass web –
the slip = 0 (Fig. 8d). In Fig. 8 there are shown
bended glass beam consisting of two glass panes
(8a), stress redistribution for glass panes without
jointing material (8b), stress redistribution for glass
panes connected by real jointing material (8c) and
stress redistribution for glass panes perfectly
connected (8d). The same principle is valid for
steel-glass bonding.
Fig. 6 Principle of shear lag
Fig. 8 PVB Shear connection behaviour
Fig. 5 Stress distribution in composite structure
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Influence of beam stability (lateral flexural
buckling) is not considered. The structure is
designed so that lateral buckling cannot occur. Glass
units are modeled as monolithic.
In hybrid steel-glass beams there joint is not made
from PVB-foil. The material used in this case is not
specified. It is not necessary if we consider perfect
shear connection.
Fig. 9 I-beam dimensions and stresses
4.1 Analytical solution
As was noted above, glass is perfect elastic material
and do not yield plastically. For this reason, elastic
computation is considered only.
In analytical computation there is actually 3D
problem converted to 1D problem. The supports and
loads are situated in the x-axis of the beam.
Determination of internal forces (Fig.7):
1
1
M = ⋅ q ⋅ L2 = ⋅ 10 ⋅ 6 2 = 45 kNm
8
8
1
1
V = ⋅ q ⋅ L = ⋅ 10 ⋅ 6 = 30 kN
2
2
The ratio of Young's modulus of steel and glass:
Determination of cross-sectional characteristics:
n=
A f ,bottom = A f ,upper = 150 ⋅10 = 1500 mm 2
Aw = 280 ⋅ 8 = 2240 mm2
Esteel 210000
=
=3
E glass
70 000
Aw
= 3747 mm 2
n
= 1500 ⋅ (10 2 ) = 7500 mm 3
Aequi = A f ,bottom + A f , upper +
It means that composite section is computed as only
steel section. Glass parts of cross-section are derived
by equivalent parts made of steel.
S f ,bottom
S f ,upper = 1500 ⋅ (300 − 10 2 ) = 442 500 mm 3
S w = 2240⋅ (300 − 10 − 280 2) = 336000 mm3
Notational convention in equations and figures:
• Quantity:
M
bending moment
V
shear force
A
area
S
static moment of area
I
moment of inertia
W
elastic modulus
σ
normal stress due to bending
τ
shear stress due to bending
δ
deflection
z
distance from the centre of gravity
• Subscripts:
f
flange
w
web
equi
equivalent
Sequi = S f , bottom + S f , upper +
eYequi =
I f ,upper
S equi
562000
= 150 mm
Aequi
3747
1
= I f ,bottom . = ⋅ 150 ⋅ 10 3 = 12500 mm 4
12
=
1
⋅ 8 ⋅ 280 3 = 14,635 ⋅ 10 6 mm 4
12
I f ,bot ,Yequi = I f ,bot + A f ,bot ⋅ z 2f ,bot = 31,55 ⋅ 10 6 mm 4
Iw =
I f ,up ,Yequi = I f ,up. + A f ,up ⋅ z 2f ,up = 31,55 ⋅ 10 6 mm 4
I w,Yequi = I w + Aw ⋅ z w2 = 14,635 ⋅ 106 mm 4
The check of the effective width of flanges:
I equi = I f ,Yequi +
beff ,1 = beff , 2 = l0 8 = 6000 8 = 750 mm
I w ,Yequi
n
= 67,978 ⋅ 10 6 mm 4
67,978 ⋅ 10 6
= 45,319 ⋅ 10 4 mm 3
z
150
I Yequi
67,978 ⋅ 10 6
W3 = W4 =
⋅n =
⋅3 =
z
140
= 145,668 ⋅ 10 4 mm 3
beff ,1 = beff , 2 = 750 mm ≤ b1 = b2 = 71 mm
W1 = W2 =
The flanges are relatively narrow due to the length
of the span and it is possible to include whole width
of flanges into cross-sectional characteristics. There
is no shear lag.
ISBN: 978-1-61804-137-1
Sw
= 562000 mm 3
n
237
I Yequi
=
Recent Advances in Engineering
upper flange in 3D model. In 2D model, there is
load situated into x-axis of beam (Fig. 10).
Both models were computed by linear and nonlinear
analysis. Deflection at mid-span, normal stresses in
the extreme steel and glass fibers and shear stress.
Numerical modeling solutions were compared with
analytical solutions and they are shown in Table 2.
Vertical deformations are shown in Fig. 11.a. In Fig.
11.b. there redistribution of normal stress σx is
shown. Both of them are from 3D modeling.
Normal stress due to bending at mid-span:
σ 1, 2 =
M
45 ⋅ 10
=
= 99,30 MPa
W1, 2 45,319 ⋅ 10 4
6
M
45 ⋅ 10 6
=
=
= 30,89 MPa
W3, 4 145,668 ⋅ 10 4
σ 3, 4
Shear stress due to bending at support:
V ⋅ Sy
τ1 =
I equi ⋅ b
τ2 =
τ3 =
V ⋅ Sy
I equi ⋅ b
V ⋅ Sy
I equi ⋅ b
=
30 ⋅ 103 ⋅ 29,59 ⋅ 10 4
= 16,41 MPa
67,98 ⋅ 10 6 ⋅ 8
=
30 ⋅ 103 ⋅ 21,75 ⋅ 10 4
= 12,00 MPa
67,98 ⋅ 10 6 ⋅ 8
=
30 ⋅ 103 ⋅ 21,75 ⋅ 104
= 0,64 MPa
67,98 ⋅ 106 ⋅ 150
Fig. 11 Deflection and normal stress
Deflection at mid-span:
In Fig. 12 there are redistributions of normal and
shear stresses at beam support from 2D and 3D
model respectively.
5
q ⋅ L4
δ =
⋅
= 0,01182 m = 11,8 mm
384 E steel ⋅ I equi
4.2 Numerical modeling
This problem was modeled in ANSYS software
based on finite element method. Beam (web and
flanges) were modeled by 2D elements
(SHELL181) and 3D elements (SOLID45).
Three dimensional problem is modeled in true
dimensions (Fig. 10c) but two dimensional model is
performed by axial dimensions with real constants thickness of web and flange (Fig. 10b).
Fig. 12 Stresses redistribution at support
In Fig. 13 there redistribution of normal and shear
stresses at mid-span of beam for 2D and 3D model
respectively are shown. The difference between
shear stresses redistribution from 2D and 3D
modeling is caused by different location of load.
Fig. 10 Boundary conditions and load model
Fig. 13 Stress redistribution at mid-span
The models were meshed by 924 elements. Flanges
were meshes into 6 elements along the width, web
was meshed into 30 elements along the high and
both were meshed into 22 elements along the span
(Fig. 10).
In both of models, supports are modeled at bottom
flange. Load (stress at nodes) is situated axial at
ISBN: 978-1-61804-137-1
5 Discussion and Conclusion
In Table 2 there are the most important values of
normal and shear stresses. The symbol x means the
distance from support (x = 0 → stresses at support,
x = 3000 → stresses at mid-span) – Fig.7.
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Recent Advances in Engineering
σ1
σ2
σ3
[MPa]
σ4
τmax
Analytical
0,00
0,00
0,00
0,00
16,41
2D Num.
-44,19
91,99
-18,27
21,28
16,18
3000
546
273
0
x Solution
[mm]
3D Num.
-6,74
11,10
-2,87
0,63
13,70
Analytical
-17,07
17,07
-5,31
5,31
12,99
2D Num.
-10,62
14,07
-4,43
3,73
12,20
3D Num.
-15,45
20,67
-5,46
3,37
12,30
Analytical
-32,85
32,85
-10,22
10,22
11,68
2D Num.
-22,86
22,99
-9,32
9,88
11,36
3D Num.
-32,54
32,13
-10,33
10,39
11,30
Analytical
-99,30
99,30
-30,89
30,89
0,00
2D Num.
-70,27
70,24
-28,24
28,30
4.10-3
3D Num.
-98,99
99,07
-31,07
30,89
7.10-3
beam. The model of the beam would be modified in
the numerical computation.
3D model gives more accurate values of normal
stresses, but more accurate values of shear stresses
are given by 2D numerical modeling (related to the
analytical computation). These differences may be
caused by idealization of real beam into
computational model (dimensions at 2D model and
location of supports and load at both numerical
model).
Actually, the shear connection is imperfect and in
contact of steel and glass there slip occurs. It can be
modeled by 3D elements simply but it is very
difficult to take into account in analytical solution.
Furthermore, it is necessary to verify the beam
stability (lateral and torsional buckling).
Table 2
Acknowledgements:
This paper has been supported by the Czech
Ministry of Education, Youth and Sports in specific
research FAST-J-12-24/1699 and the Czech Science
Foundation within the research project GACR
P105/12/03141699 and within the frame of the
projects OPVK CZ.1.07/2.2.00/15.0428.
In Table 3 there are the maximal values (for
structural design) of displacement, normal stresses
in extreme steel and glass fibers and maximal values
of shear stresses.
Solution
δmax
[mm]
σsteel,max
[MPa]
σglass,max
[MPa]
τmax
[MPa]
Analytical
2D Numerical
3D Numerical
11,8
12,0
12,5
99,3
70,3
99,1
30,9
28,3
30,9
16,4
16,2
13,7
Table 3
References:
[1] Haldimann, M., Luible, E., Overend, M.:
Structural Use of Glass, Zurich, ETH Zurich,
2008, ISBN 3-85748-119-2.
[2] Pesek, O., Melcher, J.: Study of Behaviour of
Beams and Panels Based on Influence of
Rigidity. In Proceedings of Steel Structures and
Bridges 2012, Podbanske, Slovakia, 2012,
ISBN 978-80-89619-00-9.
[3] Kozak, J., Gramblicka, S., Lapos, J.: Composite
and Combined Steel-concrete Structures of
Buildings
(Spriahnute
a
kombinovane
ocelobetonove konstrukcie pozemných stavieb),
Bratislava: Jaga Group Publishing, 2000, ISBN
80-88905-32-x.
[4] Fremr, T.: Analysis of Hybrid Beams from
Glass and Steel in Respect to Residual Load
Capacity and Robustness. In Proceedings of
PhD Seminar of the Department of Steel and
Timber Structures 2010, Prague.
[5] Netusil, M., Eliasova, M.: Adhesively bonded
Hybrid Steel-glass Beams. In Proceedings of
ICSA 2010 – 1st Interrnational Conference on
Structures
&
Architecture,
Guimaraes,
Portugal, 2010, ISBN 978-0-415-49249-2.
For illustration, results from Table 3 are shown in
Fig.14. The values of stresses and deflections are in
mega Pascal and millimeters respectively.
Fig. 14 Results comparison
Actually, it is not possible to make the web of
hybrid steel-glass I-beam from one piece of glass
pane. Maximum dimension of glass member
depends on the type of glass (different
manufacturing processes). The length of the beam is
6 meters. Actually, the web consists of three pieces
of glass. Then it would be necessary to modify the
calculation according to the theory of Vierendeel's
ISBN: 978-1-61804-137-1
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