-
Effective Steel Area of Fully Embedded Cold-Formed Steel Frame
in
Composite Slab System under Pure Bending
Yee Ling Lee1,a, Cher Siang Tan1,b, Yeong Huei Lee1,c, Shahrin
Mohammad1,d, Mahmood M. Tahir1,e, Poi Ngian Shek1,f
1Faculty of Civil Engineering,Universiti Teknologi Malaysia,
81310 Johor Bahru, Johor, Malaysia.
[email protected],
[email protected],
[email protected],
[email protected],
[email protected], [email protected]
Keywords: Effective cross sectional area, cold-formed steel,
lipped channel sections, bending resistance, composite slab,
built-up hollow section
Abstract In conjunction with the promote of Industrial Building
System (IBS) in Malaysia building
construction, precast units such as slab, beam and column were
widely used. This paper reports on the
determination of the effective cross sectional area of the
proposed cold-formed sections that
embedded in precast concrete slab. The cold-formed steel
sections are single and double lipped
channel section, with 100mm in depth, 50 mm width, 12 mm lips
length and 1.55 mm thickness. In
order to determine the flexural capacity of the composite slab
system, it is necessary to identify the
effective cross sectional area of the section contributes to
load-carrying of the slab system. The
calculation method was based on the effective width method
concept from BS EN 1993-1-3 and BS
EN 1993-1-5. Four types of cold-formed steel frame profiles that
embedded in the concrete to form a
new type of composite slab system were used to study in this
paper. The four types of cold-formed
steel section configuration are S1-SV, S2-SH, S3-DV and S4-DH.
From the analytical calculation,
S3-DV has the highest effective cross-sectional area, which it
only consists of 2% ineffective area for
load-carry capacity. Besides that, single lipped section S2-SH
fully utilized the cross sectional in
carrying load. It can be concluded that S3-DV is predicted to
have highest bending resistance than
other three types of configuration with condition that the
reliability of the prediction need to verify as
other factors such as shear bonding and shifted neutral axis
happened due to combination of concrete
and cold-formed section which, will also contribute the strength
capacity of the composite slab
system.
Introduction
Past over several decades, composite structure are mostly used
in bridge engineering [1] and
building construction [2, 3], where steel beam or girders act
compositely with concrete slab. In recent
years, the application of cold-formed steel composite concrete
floor system has gained popularity in
small commercial and residential construction [4].
Conventionally, the slab system construct in
residential and small commercial building are using precast
concrete slab, the normal conventional
reinforced concrete slab system or the composite deck slab
system, which the concrete poured onto
the cold-formed steel decking.
In this study, the reinforcement bar inside the conventional
slab system will be fully replaced by
using the cold-formed steel section. There were four types of
composite slab configurations studied in
this research. The first type of the slab configuration was
three single cold-formed C-channel section
placed vertically and form as a steel frame (namely S1-SV)
whereas the second type of configurations
was three single cold-formed C-channel section placed
horizontally and form as a steel frame (namely
S2-SH). For the third type and fourth type of the slab
configuration, both cold-formed C-channel
sections placed together to formed as rectangular section and
positioned vertically for third type slab
configuration (namely S3-DV) and positioned horizontally for the
fourth type slab configuration (
namely S4-DH). All types of slab configuration as mentioned are
shown in Fig. 1. In order to obtain
Applied Mechanics and Materials Vols. 284-287 (2013) pp
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(2013) Trans Tech Publications,
Switzerlanddoi:10.4028/www.scientific.net/AMM.284-287.1300
All rights reserved. No part of contents of this paper may be
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Universiti Teknologi Malaysia, Johor Bahru,
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the flexural capacity of the composite slab, the effective cross
sectional area of the cold-formed
section is important as to determine the effective area that the
cold-formed section will utilized to
resists the bending action of the slab. The objective of this
study is to determine the effective cross
sectional area of the proposed cold-formed sections that
embedded in the precast concrete slab from
theoretical calculation.
Figure 1. The cross sectional view of the four types of slab
configuration
Analytical Investigation
It is necessary to determine the dimensional properties of the
cold-formed section before the calculation of section resistance to
bending, compression or other loading [5]. Effective section
properties refer to the fictitious cross section that has been
reduced in area. From the effective cross-section, a clear model
for the ineffective location in cross-section in carrying load can
be identified and perception of neutral axis shift in the section
due to local-buckling can be obtained.
The calculation of the effective cross-section area is based on
the concept of effective width method. According to BS EN 1993-1-3
[8], there are three important issues that need to be considered
before analytical calculation, which are the core steel thickness,
mid-line theory and impart of corner radii. In this study, the core
steel thickness is using standard zinc coating with 275 g/m
2, where the
coating thickness is 0.02 mm on each surface. The entire
dimension in calculating section properties were calculated based
on the mid-line method, which each of the element length reduced
its nominal value of either t/2 or t. The cold-formed C-section
used in all types of slab configuration is 100 mm web depth, 50 mm
flange width, and 12 mm lip length and 1.55 mm thickness. Fig. 2
shows the mid-line dimension for the lipped C section.
Figure 2. Mid-line dimension for lipped C section and effective
properties for flanges and web under pure bending
Geometrical properties need to be check after determining the
mid-line dimension of the C section.
This steps is essentially need to done to make sure that the
geometrical proportions as stated in BS EN 1993-1-3 [6] clause 5.2
pass the checking so that the design method in BS EN 1993-1-3 [6]
can be used. Besides that, the influence of round corner radii can
be ignore in the calculation with the condition that the internal
radius of the cold-formed steel section stated in BS EN 1993-1-3
[6] clause 5.1 need to be satisfied.
After all the geometrical properties checking are checked and
satisfied with the applied standard, the effective properties of
each the elements can be studied by using BS EN 1993-1-3[6] .
(a) S1-SV (c) S3-DV (d) S4-DH (b) S2-SH
(a) Gross cross sectional (b) Mid-line dimension view (c)
Effective properties of flanges and web
Applied Mechanics and Materials Vols. 284-287 1301
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Effective Properties of a Lipped C section under Bending about
the Major Axis. There are two
types of embedded cold-formed steel sections that bending about
the major axis, which were S1-SV
and S3-DV. For S1-SV, it is calculated using single lipped
section while for S3-DV, the calculation
based on using built-up rectangular section. Both the
calculation procedure was almost the same. The
effective cross section for the single lipped C section in
bending for S1-SV is as shown in Fig. 2.
There are three steps on the calculation of effective properties
of the compression flange and lip.
For the first step of the calculation, effective width of the
compression flange and the effective width
of the edge stiffener were determined. The effective width of
the compression flange is
beff =bp1 , be1 = be2 = 0.5beff (1)
Where the reduction factor, in BS EN 1993-1-5 [7] clause
4.4,
(2)
As for the effective width of the edge stiffener calculation,
the buckling factor is determined based
on BS EN 1993-1-3[8] clause 5.5.3.2(5a). The effective width is
given by, Ceff =Cp
Where the reduction factor, is as Eq. 3,
(3)
For the second step, it is used to determine the reduction
factor that allowing for the effects of the
distortional buckling. The elastic critical stress of the
distorsional buckling for the edge stiffener is
calculated as
(4)
Where, (5)
And effective second moment, (6)
Thickness reduction factor for the edge stiffener is calculated
based on the relative slenderness of
the edge stiffener as follow,
(7)
For the Third step, according to BS EN 1993-1-3 [6] clause
5.5.3.2(3), as the reduction factor for
the stiffener is less than 1,iterations are required to refine
the value of the reduction factor. The
iteration stops when the reduction factor d converges and hence
the calculation of the reduced
thickness for the stiffener is, tred = t d
After obtained the effective properties of the compression
flange and lip, effective properties of the
web can be obtained by getting the position of neutral axis with
regard the flange in compression.
Equations 2 were used to obtain the effective web, heff as, heff
= hp
The effective properties of the whole cross section, second
moment of the effective sectional area
and effective section modulus can be obtained after effective
length of compressive flange, lip and
web had been calculated.
As for the calculation of effective cross sectional area for
S3-DV, all the steps of calculation are
same as S1-SV but the second step and third step of calculation
is being ignored as the built-up
rectangular section does not have the edge stiffener.
tcb
tbbbb
effe
ee
p)(
2/
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)(22)(21212
++
+++=
effe
effeff
eff
effe
eff
e
effe
scb
cctc
cb
ctb
tctbI
scr
ybd
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2
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hp
hp
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,
, 188.0
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cp
=
4
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KEI=
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=
1302 Innovation for Applied Science and Technology
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Effective Properties of a Lipped C section under Bending about
the Minor Axis. There are two
types of embedded cold-formed steel section bending about the
minor axis namely S2-SH and S4-DH.
For S2-SH, it is calculated using single lipped C-Section while
for S4-DH, the calculation based on
using built-up rectangular section. The effective cross section
for a single section of S2-SH bending in
minor axis is as shown in Fig. 3. The formulae for the
calculation for the effective properties bending
about minor axis are not much different as the calculation on
bending in major axis.
Figure 3. Effective properties of flanges and web under
bending
For calculating effective properties of S2-SH, which bending
under minor axis, the calculation
steps are simpler. Calculating on the effective properties of
the lips by using the Eq. 2 is the first step
of the calculation. There is then will be the calculation on the
effective width of the part of the flange
in compression. The position of effective neutral axis with
regard the lip in compression is
determined. Hence, by using Eq. 2, the effective width of
flanges can be obtained. The web is not need
to be calculated as the web is in tension zone and it is fully
effective. From the obtained effective
width of lips, flanges and web, the effective cross sectional
area, effective second moment of area and
effective elastic modulus about minor axis can be
determined.
As for type S4-DH, the calculation procedure is same as S2-SH.
Since S4-DH is built-up
rectangular section, the only differences in calculation is that
S4-DH apply the calculation for the
effective width of web in compression instead of lips in
compression in S2-SH by using Eq. 2 to
determine the effective width of web in compression.
Results and Discussion
From the calculation as above analytical method, the effective
cross sectional area for four types of embedded cold-formed steel
section configuration in concrete under pure bending is determined.
Table 1 shows the result of the obtained calculation from the above
mentioned analytical procedure.
Table1. Result of the calculated effective cross-sectional area
Type Effective Cross-sectional Area (mm
2) Gross Cross-Sectional Area (mm
2) Percentage Differences
(%)
S1-SV 933 987 5.5%
S2-SH 987 987 0%
S3-DV 1748 1784 2%
S4-DH 1573 1784 11.8%
From Table 1, it can be seen that the effective area of built-up
rectangular section is much higher
than single lipped C section. S3-DV had the highest effective
cross sectional area which is 1748 mm2.
As compared with S4-DH, only 2% of ineffective area in carrying
loads in S3-DV. S4-DH has large ineffective area, which is 11.8%
from the gross cross sectional area. This is because in S4-DH, the
cold-formed steel section was placed horizontally and hence the
compression is acting on the top web of the section. This resulted
in large reduction on the web length as if compare with the flange
in compression. Hence, the effective area of S4-DH is lower than
S3-DV.
As for the comparison of the single lipped section between S1-SV
and S2-SH, S2-SH is fully utilized the cross sectional area for
load carrying capacity. The 5.5% different is due to compression
lips of S2-SH is shorter than the compression flange in S1-SV.
There is an ineffective area happened on compressive flange hence,
reduced the gross cross sectional area of S1-SV.
Applied Mechanics and Materials Vols. 284-287 1303
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Since S3-DH had the highest effective cross sectional area among
the four types cold-formed steel configuration, so it can be
predict that S3-DH will have the highest load carrying capacity in
the precast concrete if compare to other three types of
configuration.
Conclusions
The effective steel area of fully embedded cold-formed steel
sections in composite slab system had
been obtained from the calculation. From the analytical
calculation mentioned as above, it can be
concluded that:
It is important to consider the effective cross sectional area
of the cold-formed steel section as
it can identify the ineffective area for load carry on the steel
section.
S3-DV has the highest effective cross sectional area as the
cold-formed steel section is in
built-up rectangular section and the ineffective area on the
compressive flange is lower than the
ineffective area on the compressive web of S4-DH.
The effective area of S2-SH is fully utilized for load-carrying
capacity. This is due to the lips
and the flange in compression zone is fully effective and
compare with the S1-SV, which there is
ineffective area on the flange in compression.
The load carrying capacity for the composite slab in this study
only limit the load is fully acting on
the effective area of cold-formed section. Further study on
determine the load-carrying capacity of the
composite slab need to be study. Other parameter such as the
shear bonding between the concrete and
cold-formed steel section, the effect of the shift neutral axis
of the composite system due to the
combination of concrete and the cold-formed steel are need to be
consider in order to get a more
reliable load-carrying capacity of the slab.
Acknowledgments
The reported research is funded by Universiti Teknologi Malaysia
(Vot 00J10, 01J09 and 05J76)
and Ministry of Higher Education, Malaysia (MOHE). The technical
and financial supports are
gratefully acknowledged.
References
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Association of State Highway
and Transportation Officials, Washington DC, 2005.
[2] C.E. Ekberg, R.M. Schuster, Floor System with Composite from
Reinforced Concrete Slabs.
IABSE Final Report, New York, 1968, pp. 385-394.
[3] M.L. Porter, C.E. Ekberg, Design Recommendations for Steel
Deck Floor Slabs. Journal of
Structural Division 102(ST11), (1976) 21-36.
[4] B.S. Lakkavalli and Y. Liu, Experimental Study of Composite
Cold-formed Steel C-Section
Floor Joists. Journal of Constructional Steel Research 62 (2006)
995-1006.
[5] A.G.J. Way and M.D. Heywood, Design of Light Steel Sections
to Eurocode 3 (ED 005).The
Steel Construction Institute, UK, 2012.
[6] BSI. BS EN 1993-1-3:2006: Design of Steel Structures.
General Rules. Supplementary Rules for
Cold-Formed Members and Sheeting. British Standard Institute,
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[7] BSI. BS EN 1993-1-5:2006: Design of Steel Structures. Plated
Structural Elements. British
Standard Institute, UK, 2006.
1304 Innovation for Applied Science and Technology
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Innovation for Applied Science and Technology
10.4028/www.scientific.net/AMM.284-287
Effective Steel Area of Fully Embedded Cold-Formed Steel Frame
in Composite Slab System underPure Bending
10.4028/www.scientific.net/AMM.284-287.1300
