Suitable Stiffening Systems for LiteSteel Beams with Web
Openings
Subjected to Shear
Poologanathan Keerthan and Mahen Mahendran
Science and Engineering Faculty
Queensland University of Technology, Brisbane, QLD 4000,
Australia
Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow
flange channel section produced using a simultaneous cold-forming
and dual electric resistance welding process. It is commonly used
as floor joists and bearers with web openings in residential,
industrial and commercial buildings. Their shear strengths are
considerably reduced when web openings are included for the purpose
of locating building services. A cost effective method of
eliminating the detrimental effects of a large web opening is to
attach suitable stiffeners around the web openings of LSBs.
Experimental and numerical studies were undertaken to investigate
the shear behaviour and strength of LSBs with circular web openings
reinforced using plate, stud, transverse and sleeve stiffeners with
varying sizes and thicknesses. Both welding and varying
screw-fastening arrangements were used to attach these stiffeners
to the web of LSBs. Finite element models of LSBs with stiffened
web openings in shear were developed to simulate their shear
behaviour and strength of LSBs. They were then validated by
comparing the results with experimental test results and used in a
detailed parametric study. These studies have shown that plate
stiffeners were the most suitable, however, their use based on the
current American standards was found to be inadequate. Suitable
screw-fastened plate stiffener arrangements with optimum
thicknesses have been proposed for LSBs with web openings to
restore their original shear capacity. This paper presents the
details of the numerical study and the results.
Keywords: LiteSteel beam, Web openings, Finite element analysis,
Shear strength, Plate stiffener, LSB stud stiffener, Sleeve
stiffener, Transverse stiffener, Hollow flanges, Cold-formed steel
structures.
Corresponding author’s email address: [email protected]
1. Introduction
The use of cold-formed steel members in low rise building
construction has increased significantly in recent times. There are
many significant benefits associated with the use of lightweight
cold-formed steel sections in residential, industrial and
commercial buildings. Thinner cold-formed steel sections with
varying geometry are continuously developed to suit various
requirements including higher moment capacities. The LiteSteel Beam
(LSB) shown n Figure 1(a) is a new cold-formed steel hollow flange
channel beam produced by OneSteel Australian Tube Mills [1]. It is
manufactured from a single strip of high strength steel using a
combined cold-forming and dual electric resistance welding process.
The effective distribution of steel in LSBs with two rectangular
hollow flanges results in a thin and lightweight section with good
moment capacity. The LSB has many applications and has become a
very popular choice in the flooring systems as shown in Figure 1(b)
[1]. Table 1 shows the details of LSB sections including their
dimensions.
Current practice in flooring systems is to include openings in
the web of floor joists or bearers so that building services can be
located within them. Without web openings, services have to be
located under the joists leading to increased floor heights.
Pokharel and Mahendran [2] recommended the use of circular web
openings in LSBs based on an investigation using finite element
analyses. Three standard opening sizes of 60, 102 and 127 mm are
used with the currently available LSBs [3]. The use of web openings
in a beam section significantly reduces its shear capacity due to
the reduced web area. Since about 88% of the shear force is
supported by the main web element of LSB [4], the use of web
openings can lead to significantly reduced shear capacities of
LSBs. Keerthan and Mahendran [5,6] investigated the shear behavior
and strength of LSBs with circular web openings using experimental
and numerical studies. They developed suitable design equations for
the shear capacity of LSBs with web openings by including both the
enhanced buckling coefficient and the post-buckling strength in
shear.
Since the loss of shear capacity of LSBs was found to be as high
as 60% [5] when the standard 127 mm web openings were used in
200x45x1.6 LSBs, the LSB manufacturers and researchers realized the
need to improve the shear capacity of LSB with web openings. There
are several methods used to improve the shear capacity of beams
with web openings. The most practical method is to increase the web
thickness. However, this may not be possible with cold-formed steel
sections as the thickness is governed by the manufacturing process.
A cost effective way to improve the detrimental effects of a large
web opening is to attach appropriate stiffeners around the web
openings. Currently available cold-formed steel design standards
[7,8] and steel framing standards [9] do not provide adequate
guidelines to facilitate the design and construction of stiffeners
for LSBs with large web openings. Hence experimental and numerical
studies were conducted to develop the most effective and economical
stiffener arrangement for LSBs with circular web openings subjected
to shear. Details of the experimental study and the results are
presented in [10]. In the numerical study, suitable finite element
models of LSBs with stiffened web openings were developed to
simulate their shear behaviour and capacity, and were validated by
comparing their results with experimental results reported in [10].
A detailed parametric study was then undertaken using the validated
finite element model to develop the optimum stiffening system for
the shear capacity of LSBs with web openings. This paper presents
the details of the development of finite element models of LSBs
with stiffened circular web openings subject to shear, and the
results. It includes a comparison of finite element analysis and
experimental results as well as the details of the new optimum
plate stiffener arrangement for LSBs.
2. Experimental Study of LSBs with Stiffened Web Openings
This section presents the important details of 17 shear tests of
simply supported back to back 200x45x1.6 LSBs under a three-point
loading arrangement as shown in Figure 2. The main focus was on the
use of plate stiffeners with varying fastening arrangements while
two tests included the use of LSB stud stiffeners. Table 2 shows
the details of test specimens while Figure 3 shows them with
various stiffener arrangements.
The first four specimens were not stiffened as seen in Table 2.
In Specimen 5, the web openings were stiffened with plate
stiffeners based on AISI’s [9] minimum stiffening requirements. The
plate stiffener thickness was equal to that of 200x45x1.6 LSB while
the plate stiffener extended 25 mm beyond the web opening edges.
The plate stiffener was fastened to the LSB web with No.12 Tek
screws at 25 mm spacing with an edge distance of 12.5 mm as shown
in Figure 3 (a). This stiffener arrangement was defined as
“Arrangement 1” (20 screws). Test Specimen 6 was assembled similar
to Test Specimen 5, but with a total of 8 screws at 63.5 mm spacing
along the plate stiffener edges with an edge distance of 12.5 mm
(Figure 3 (b)). This screw fastening arrangement was defined as
“Arrangement 2”. Since the plate stiffeners with a thickness equal
to the LSB web thickness (1.6 mm) did not restore the original
shear capacity, two and three 1.6 mm plate stiffeners were used in
Specimens 7 and 8, respectively. The plate stiffeners’ heights were
also increased to match the clear LSB web height of 168 mm, which
led to plate stiffener sizes of 152x168x3.2 mm and 152x168x4.8 mm.
These two specimens were fastened using Arrangement 2 with screws
located in the middle as implied by AISI [9] recommendations. Hence
the edge distance along the horizontal edges was 16.5 mm instead of
12.5 mm while its spacing along the vertical edges was 67.5 mm
instead of 63.5 mm due to the increased height of plate
stiffeners.
In Specimen 9, 200x45x1.6 LSB stud stiffeners were used with 102
mm web openings while 200x45x1.6 LSB stud stiffener and 177x168x1.6
mm plate stiffener were used in Specimen 10 with 127 mm web
openings. In these tests, the stiffener heights were again
increased to that of clear web. Arrangement 2 of eight screws was
used in Specimen 9, but the edge distances and screw spacings were
16.5 mm and 67.5 mm. Improved Arrangement 3 with four additional
screws in the diagonal direction (12 screws in total) was used in
Specimen 10. The additional screws in the diagonal direction were
located at 10 mm from the web opening edge. To increase the shear
capacity further, 3 mm thick and 202 mm wide plate stiffeners were
used for the full web height of Specimens 11 and 12 (Figures 3 (c)
and (d)). As in Specimen 10, four additional screws were used to
attach these 202x168x3.0 mm plate stiffeners along the diagonal
direction. The screws were located in the middle on each side of
the plate stiffener, which led to the edge distances of 25 mm and
16.5 mm and spacings of 67.5 mm and 76 mm in Test 11 (Figure 3
(c)). However, in Specimen 12, the edge distances were 12.5 mm and
16.5 mm (Figure 3 (d)). This stiffener arrangement of using 12
screws with a reduced edge distance of 12.5 mm was defined as
“Arrangement 4”. In Specimen 13, 202x168x3.0 mm plate stiffeners
were welded to LSBs to determine whether welding instead of
screw-fastening would produce higher shear capacities. Specimen 14
was used to investigate the use of thicker (5 mm) and wider (227
mm) plate stiffeners for larger 127 mm web openings. Two 2.5 mm
plates of 227x168 mm dimensions were screw fastened using 12 screws
in Arrangement 3 as in Specimen 11. Specimen 15 was similar to
Specimen 14, but the plate stiffeners were attached using screws
located on a circular format as shown in Figure 3 (e) (Arrangement
5). In Specimen 16 the plate stiffener width was reduced to 177 mm
based on AISC’s [9] recommendations while three 1.6 mm plate
stiffeners were used. Specimen 17 with the smallest web opening of
60 mm was stiffened with only one 1.6 mm plate stiffener.
3. Finite Element Analyses of LSBs with Stiffened Web
Openings
3.1. Description of Finite Element Model
This section describes the development of suitable finite
element models to investigate the ultimate shear behaviour and
strength of LSBs with stiffened web openings. For this purpose, a
general purpose finite element program, ABAQUS Version 6.7 [11],
which has the capability of undertaking geometric and material
non-linear analyses of three dimensional structures, was used.
Finite element models were developed first with the objective of
accurately simulating the actual test members’ physical geometry,
loads, constraints and mechanical properties reported in the
experimental study [10]. However, they were also developed for LSBs
with other stiffener types such as transverse and sleeve
stiffeners. Shear test results of back to back LSBs were similar to
those obtained from single LSBs with a shear centre loading [4].
Hence in this study, finite element models of single LSBs with a
shear centre loading and simply supported boundary conditions were
used to simulate the shear tests of back to back LSB with stiffened
web openings.
The cross-section geometry of the finite element model was based
on the measured dimensions, thicknesses and yield stresses of 17
tested LSBs reported in [10]. Table 2 gives the measured dimensions
of the test beams made of 200x45x1.6 LSBs, where tw and d1 are the
base metal thickness and the clear web height. The measured yield
stresses of web, and inside and outside flange elements were 452.1,
491.3 and 536.9 MPa, respectively. For LSBs d1 is defined as the
clear height of web instead of the depth of the flat portion of web
measured along the plane of the web as defined in AS/NZS 4600 [7]
for cold-formed channel sections. The reasons for this are given in
[4]. Table 2 also provides the diameters of web openings (dwh) used
in the models. Since the effect of including the rounded corners in
LSBs on the shear buckling behaviour and capacity was found to be
negligible [12], right angle corners were used in the finite
element models used in this study.
ABAQUS has several element types to simulate the shear behaviour
of beams with stiffened web openings. The shell element in ABAQUS
called S4R5 was selected as it has the capability to simulate the
shear behaviour of thin steel beams such as LSBs. This element is
thin, shear flexible, isometric quadrilateral shell with four nodes
and five degrees of freedom per node, utilizing reduced integration
and bilinear interpolation scheme.
R3D4 rigid body elements were used to simulate the restraints
and loading in the finite element models of LSBs with stiffened web
openings. The R3D4 element is a rigid quadrilateral with four nodes
and three translational degrees of freedom per node. Finite element
modelling was undertaken using MD PATRAN R2.1 pre-processing
facilities using which the model was created and then submitted to
ABAQUS for the analysis. The results were also viewed using MD
PATRAN R2.1 post-processing facilities.
In order to fully understand the shear behaviour of LSBs with
stiffened web openings, several important issues were considered
when deciding these parameters such as the ratio of the depth of
web openings to clear height of web (dwh/d1), types and thicknesses
of stiffeners, number of self-drilling Tek screws used to fasten
the stiffeners to the web and their spacing.
3.2. Finite Element Mesh
In finite element analyses (FEA), selection of mesh size and
layout is critical. It is desirable to use as many elements as
possible in the analysis. However, such an analysis will require
excessive computing time and resources. In this research, adequate
numbers of elements were chosen for both flanges and web based on
detailed convergence studies to obtain sufficient accuracy of
results without excessive use of computing time. Convergence
studies showed that an element size of 5mm x 5mm provided an
accurate representation of shear buckling and yielding
deformations. An element length of 5 mm in the longitudinal
direction was found to provide suitable accuracy for all the LSB
sections. In order to get accurate results, Paver Mesh was applied
around the LSB web and stiffener openings. The geometry and finite
element mesh of a typical LSB with stiffened web openings is shown
in Figure 4.
Plate and LSB stud stiffeners were connected to the web elements
of LSB using screw fasteners as shown in Figure 5 (c). These
stiffeners were modelled using 5mm x 5mm S4R5 elements and were
connected to the web of LSB using Tie MPC. Tie MPC makes the global
displacements and rotations as well as all other active degrees of
freedom equal at the two connected nodes. If there are different
degrees of freedom active at these nodes, only those in common will
be constrained. This Tie MPC was used to simulate all the screw
connections used in installing the stiffeners.
3.3. Material Model and Properties of LSB
The ABAQUS classical metal plasticity model was used in all the
analyses. This model implements the von Mises yield surface to
define isotropic yielding, associated plastic flow theory, and
either perfect plasticity or isotropic hardening behaviour. When
the measured strain hardening in the web element was used in FEA,
the shear capacity improvement was less than 1% [4]. Hence it was
not considered in our analyses. Tensile coupon tests were conducted
for the batch of LSBs from which the test beam specimens were
taken. Tensile coupons taken from the web and inside and outside
flanges of 200x45x1.6 LSB sections were tested to determine the
average yield stresses reported earlier. These measured yield
stresses were used in FEA. Since the plate stiffeners were taken
from the LSB web, the measured web yield stresses were used in the
modeling of plate stiffeners. The LSB stud stiffeners used in the
tests were taken from the same batch of LSBs. Hence the measured
yield stresses of web, inside and outside flange elements of LSBs
were used in the modeling of LSB stud stiffeners. The elastic
modulus and Poisson’s ratio were taken as 200,000 MPa and 0.3,
respectively.
3.4. Loads and Boundary Conditions
Simply supported boundary conditions were implemented in the
finite element models of LSBs with stiffened web openings. They
were used at the supports to provide the following
requirements:
· Simply supported in-plane - Both ends fixed against in-plane
vertical deflection but unrestrained against in-plane rotation, and
one end fixed against longitudinal horizontal displacement.
· Simply supported out-of-plane - Both ends fixed against
out-of-plane horizontal deflection, and twist rotation, but
unrestrained against minor axis rotation.
In order to provide simply supported conditions for the shear
panel, the following boundary conditions were employed.
Left and right supports: ux = 0 x = 1 Mid-span loading point: ux
= 1 x = 1
uy = 1 y = 0 uy = 0 y = 0
uz = 1 z = 0 uz = 1 z = 0
Note: ux, uy and uz are translations and θx, θy and θz are
rotations in the x, y and z directions, respectively. 0 denotes
free and 1 denotes restrained.
The vertical translation was not restrained at the loading
point. Figure 5 shows the applied loads and boundary conditions of
the model. Single point constraints and concentrated nodal forces
were used in the finite element models to simulate the experimental
boundary conditions and applied loads as closely as possible. In
order to prevent twisting, the applied point load and simply
supported boundary conditions were applied at the shear centre
using rigid body reference node. Shear test specimens included a 10
mm thick and 75 mm wide plate at each support to prevent lateral
movement and twisting of the section. These stiffening plates were
modelled as rigid bodies using R3D4 elements. In ABAQUS [11] a
rigid body is a collection of nodes and elements whose motion is
governed by the motion of a single node, known as the rigid body
reference node. The motion of the rigid body can be prescribed by
applying boundary conditions at the rigid body reference node.
Hence simply supported boundary conditions were applied to the node
at the shear centre in order to provide an ideal pinned
support.
3.5. Fastener Modelling
Fasteners play an important role in the shear behaviour of LSBs
with stiffened web openings. This study assumed that screw fastener
failure is unlikely to occur as confirmed by our experimental study
[10]. Considering this observation, the screw fasteners connecting
the stiffeners to the LSB were not explicitly modelled. Instead
they were simulated using Tie MPCs, which make all active degrees
of freedom equal on both sides of the connection.
The web side plates at the supports were connected using high
strength steel bolts (M16 8.8/S) to avoid bolt failures during
testing. Our shear tests [10] confirmed that there were no bolt or
plate failures. Therefore these web side plates were modelled as
rigid bodies using R3D4 elements.
3.6. Initial Geometric Imperfections
The local plate imperfections in LSBs were found to be less than
the currently accepted fabrication tolerance of d1/150 [4].
However, the fabrication tolerance limit of d1/150 was used in the
numerical modelling of LSBs as the preliminary analyses showed that
the effect of local plate imperfection (from d1/300 to d1/150) on
the shear capacity of LSB with stiffened web openings was small.
The critical imperfection shape was introduced by ABAQUS
*IMPERFECTION option with the shear buckling eigenvector obtained
from an elastic buckling analysis.
3.7. Residual Stresses
The residual stresses in the LSB sections produced using the
dual electric resistance welding and cold-forming processes have
unique characteristics. The residual stress models of conventional
steel sections are therefore not suitable for LSB sections. Details
of the residual stress tests and an idealized residual stress model
developed for computer analyses are presented in [13]. Preliminary
FEA showed that the effect of residual stresses on the shear
capacity of LSBs without openings is less than 1% [14]. Therefore
the effect of residual stresses on the shear capacity of LSBs with
stiffened web openings is also likely to be very small. It was thus
decided to neglect the residual stresses in the FEA.
3.8. Analysis Methods
Both elastic buckling and nonlinear static analyses were used.
Elastic buckling analyses were used to obtain the eigenvectors for
the inclusion of initial geometric imperfections. Nonlinear static
analyses, including the effects of large deformation and material
yielding, were used to investigate the shear behaviour of LSBs
until failure. The RIKS method in ABAQUS was also included in the
nonlinear analyses. It is generally used to predict geometrically
unstable nonlinear collapse of structures. In using the RIKS method
in this study, the solution of nonlinear equations was achieved by
the Newton-Raphson method, in conjunction with a variable
arc-length constraint to trace the instability problems associated
with nonlinear buckling of beams. Following parameters were used in
the non-linear analyses of LSB with stiffened web openings: Maximum
number of load increments = 100, Initial increment size = 0.01,
Minimum increment size = 0.000001, Automatic increment reduction
enabled, and large displacements enabled.
4. Validation of Finite Element Models of LSB with Stiffened Web
Openings
The accuracy of the developed finite element models of LSBs with
stiffened web openings was investigated by comparing the non-linear
analysis results with those obtained from the shear tests of LSBs
with stiffened web openings [10]. Seventeen finite element models
were constructed using the material and geometric properties from
experimental testing (Table 2) and the results were compared with
test results, with particular attention given to the ultimate load,
load-deflection curves and failure modes. These comparisons were
intended to establish the validity of the shell element model in
the modelling of initial geometric imperfections and shear
deformations, and associated material yielding. The accuracy of
local plate imperfection magnitude and finite element mesh density
was also established.
Table 2 presents the ultimate shear capacity results from FEA
and a comparison of these results with the corresponding
experimental results. The mean and COV of the ratio of test to FEA
ultimate shear capacities are 0.97 and 0.021. This indicates that
the finite element model developed in this study is able to predict
the ultimate shear capacity of LSBs with stiffened web openings
with very good accuracy.
In the experimental study, five screw fastening arrangements
were considered as shown in Figure 3 [10]. Figure 6 shows the FEA
results in the form of load versus deflection for 200x45x1.6 LSB
with 127 mm stiffened web openings (Test Specimen 14) while Figures
7 (a) and (b) show them for 200x45x1.6 LSB with 102 mm stiffened
web openings (Test Specimens 11 and 12) and compare them with
corresponding experimental results. Figures 8 and 9 show the shear
failure modes of Test Specimens 11 and 12, respectively, while
Figures 10 (a) to (c) show the failure modes of Test Specimens 13,
15 and 17, respectively. The shear capacity of Test specimen 13 was
considerably increased due to the additional welded plate
stiffener. Hence it failed due to combined shear and bending as
shown in Figure 10 (a). These figures demonstrate a good agreement
between the results from FEA and experiments and confirm the
adequacy of the developed finite element model in predicting the
ultimate load, deflections and failure modes of LSBs with stiffened
web openings.
5. Finite Element Analyses of LSBs with Different Types of
Stiffeners
The overall objective of this research is to develop the most
effective and economical stiffening arrangements for LSBs with web
openings subjected to shear. In this section, the use of different
types of stiffeners, namely, plate stiffeners, LSB stud stiffeners,
sleeve stiffeners and transverse stiffeners, was investigated by
using finite element analyses.
5.1. Transverse Stiffeners
Transverse stiffeners are generally used in hot-rolled steel
sections and are welded to the web. Welding in cold-formed steel
sections is difficult and hence this stiffener is not a practical
option. However, it was investigated due to its popularity in
traditional steel design. Transverse stiffeners improved the shear
strength by reducing the aspect ratio of the web panel. The
geometry and finite element mesh of a typical LSB with transverse
stiffeners is shown in Figure 4 (b), which shows that two steel
plates are attached to the web on either side of the opening at 20
mm from the edge of the web opening.
Transverse stiffeners can be welded to either the web only or
both web and flange elements. Finite element analyses conducted to
determine the effect of this variation showed that additional
restraint provided by welding the transverse stiffeners to the
flanges gave only a 4% increase in the shear capacity. Hence
welding the transverse stiffeners to the web of LSBs is considered
sufficient.
In order to investigate the effect of the thickness of
transverse stiffeners on the shear capacity of LSB with web
openings, FEA of 200x45x1.6 LSBs with 60 and 127 mm web openings
were undertaken with varying transverse stiffener thicknesses.
Figure 11 shows the failure modes of LSBs with 3 mm transverse
stiffeners while Figure 12 shows the FEA results in the form of
shear capacity of LSBs versus thickness of transverse stiffeners.
Here the transverse stiffeners were only welded to the web element
of LSB. Table 3 shows the shear capacities of LSBs with 5 mm
transverse stiffeners. In this table, the shear capacities of LSBs
without and with web openings and stiffened web openings are
referred to as Vv, Vnl and Vnls, respectively. These results show
that the thickness of the transverse stiffeners does not play a
significant role on the shear capacity of LSB with web openings
(see Figure 12). This is due to the fact that the transverse
stiffeners mainly reduces the aspect ratio and does not contribute
to increasing the shear area of LSB with web openings. Both Figure
12 and Table 3 show that transverse stiffeners are not adequate to
restore the shear strengths of LSBs with larger web openings (127
mm). Hence the use of transverse stiffeners is not recommended for
LSBs with large web openings.
5.2. Sleeve Stiffeners
The sleeve stiffener was proposed based on its ability to
restrain the free edge of the web opening. This proposal was
adopted from conventional cold-formed steel designs where such
stiffeners are used to reduce the local buckling effects of free
edges. This stiffener is likely to have a greater effect on the
buckling strength of LSBs than the ultimate shear strength.
However, increasing the shear buckling capacity is also important.
The geometry and finite element mesh of a typical LSB with sleeve
stiffeners is shown in Figure 4 (c). In comparison with other
stiffeners, the sleeve stiffener is less practical as it requires
the sleeve to be formed during manufacturing or welded to the web.
However, welding thin cold-formed steel sections is to be avoided
as it can be detrimental in terms of heat effects and residual
stresses. Hence the use of sleeve stiffeners may complicate the
fabrication phase of LSB joists and bearers.
The thickness and length of sleeve stiffener that affects its
rigidity were considered as possible variables in FEA. The sleeve
stiffener thickness was considered to be the same as the LSB web
thickness. However, its length was varied (10, 20 and 25 mm) to
determine its effect on the shear capacity of 200x45x1.6 LSBs with
60 mm web openings. Table 4 shows the shear capacity results, which
show that the sleeve stiffener length (10 to 25 mm) did not play a
significant role on the shear capacity of LSB with web openings.
Table 5 shows the shear capacities of LSBs with varying web opening
sizes and 20 mm sleeve stiffeners, which indicate that sleeve
stiffeners are not adequate to restore the shear strengths of LSB
with larger web openings (102 and 127 mm). Hence the use of sleeve
stiffeners is not recommended for LSBs with large web openings.
Figure 13 shows the failure mode of 200x45x1.6 LSB with 60 mm web
openings and 20 mm sleeve stiffeners.
5.3. LSB Stud Stiffeners
The LSB stud stiffeners are LSBs with web openings that are
attached to the web. The LSB stud stiffener is attached to the web
around the opening by fastening with No.12 Tek screws. It is
capable of both reducing the aspect ratio and increasing the shear
area of LSB with web openings. The geometry and finite element mesh
of a typical LSB with LSB stud stiffener is shown in Figure 4
(d).
Effect of LSB stud stiffeners on the shear capacity of LSBs with
web openings was investigated using FEA and Tests 9 and 10, and the
results are shown in Table 2. As shown by the experimental study,
finite element analyses also showed that LSB stud stiffeners were
able to obtain about 80% of the shear capacity of LSB without web
openings (52 kN) in the case of 102 mm web openings. Since the
thickness of LSB stud stiffener is equal to the web thickness, LSB
stud stiffeners are not adequate to restore the shear strengths of
LSB with large web openings. Hence LSB stud stiffeners are not
recommended for LSBs with large web openings.
5.4. Plate Stiffeners
Plate stiffeners are plates with web openings that are attached
to the web (see Figures 4 (a) and 5). They are attached to the web
around the openings by fastening with No.12 Tek screws. In contrast
to the other types of stiffeners, the plate stiffener is capable of
both reducing the aspect ratio and increasing the shear area of LSB
with web openings. Our experimental studies [10] showed that plate
stiffeners were the best stiffener for LSBs with web openings.
However, the number of shear tests was limited. Hence in order to
determine the optimum plate stiffener sizes, finite element models
of LSBs with web openings stiffened with plate stiffeners in shear
were developed to simulate their shear behaviour and strength. They
were then validated by comparing their results with available test
results (Test Specimens 5 to 17) and used in a parametric study
(see Section 5.5).
In Test Specimen 5, plate stiffener dimensions and screw
fastening arrangement were adopted based on AISI [9] (Arrangement
1). However, FEA and experimental results showed that it only
reached about 65% of the shear capacity of LSB without web openings
(34.8 and 33.6 kN vs 52 kN). Hence FEA and test results showed that
the plate stiffeners based on AISI [9] recommendations are not
adequate to restore the shear strengths of LSBs.
Test Specimens 5 and 6 with 152x152x1.6 mm plate stiffeners were
considered to investigate the effect of different screw spacings
(Arrangements 1 and 2). Both FEA and tests showed that using more
screws (20 versus 8 screws) increased the shear capacity of LSBs by
only 5% as shown in Table 2. Test Specimens 7 and 8 were conducted
to investigate the effect of using thicker (3.2 and 4.8 mm) plate
stiffeners of full web height (152x168 mm). In this case, both FEA
and test results showed that the shear capacities increased
considerably (Table 2).
Tests 11 and 12 of LSBs with 102 mm web openings were considered
with 3 mm plate stiffeners that were 202 mm wide (50 mm on either
side of the edge of web opening) and 168 mm height (full web
height). Both FEA and Test results showed that thicker and wider
stiffeners of full web height as used in these tests were able to
fully restore the shear capacity of LSBs (56.0 and 55.0 versus 54
kN in FEA and 54.5 and 52.5 kN vs 52 kN in tests). Test and FEA
results also showed that Arrangement 4 with reduced edge distances
of 12.5 mm led to a small reduction in the shear capacity. Hence
screw fastening Arrangement 3 used in Test 11 is recommended.
Test Specimen 13 with welded plate stiffeners failed at a higher
load due to combined shear and bending as shown in Figure 10. Both
FEA and test results (66.5 and 67 kN) showed that the shear
capacity of LSB with web openings can be improved to levels beyond
the shear capacity of a solid LSB section (54 and 52 kN) by welding
suitable plate stiffeners. Generally horizontal, vertical and
inclined stiffeners are welded to the web around the openings in
hot-rolled sections. Our FEA and test results show that plate
stiffeners can also be welded to improve the shear capacity of
cold-formed sections with large web openings. However, welding is
not recommended to avoid excessive heat and residual stress effects
on thin-walled cold-formed steel sections.
Test Specimens 14 and 15 with larger 127 mm web openings were
investigated to determine the required stiffener thickness. Five mm
plate stiffeners that were 227 mm wide (50 mm on either side of the
edge of web opening) and 168 mm height (full web height) were used.
Both FEA and test results showed that these plate stiffeners
fastened using Arrangements 3 and 5 were almost able to restore the
full shear capacity (93% of the shear capacity of LSB without web
openings). In this case, the depth of web opening to the clear
height of web ratio (dwh/d1) is 0.75, which is more than the
limiting value of 0.7 given in AS/NZS 4600 [7]. Hence it is
unlikely that such large openings will be used in practice.
Arrangement 5 (Figure 3(e)) is architecturally appealing, however,
it is not recommended due to additional installation costs.
Test Specimen 16 included 177x168x4.8 mm plate stiffeners, and
the shear capacity from FEA was only 36.8 kN due to the use of
plate stiffeners with reduced width (177 mm versus 227 mm).
However, for Test Specimen 17 with 60 mm web openings, 1.6 mm thick
plate stiffeners of 160x168 mm were able to restore the original
shear capacity (52.5 and 50.5 vs 52 kN). Both FEA and test results
show that AISI’s [9] recommendation for the minimum width of plate
stiffeners to be based on 25 mm on each side of web openings is not
adequate. This research has shown that the plate stiffeners should
extend 50 mm beyond all the edges of web openings.
In summary, FEA and test results show that plate stiffeners with
dimensions equal to web opening width and depth plus 100 mm, screw
fastened using Arrangement 3, are needed to restore the original
shear strength of 200x45x1.6 LSBs. Their thicknesses have to be a
minimum of 1.6 mm and 3.0 mm for these LSBs with 60 mm and 102 mm
web openings, respectively. However, detailed parametric studies
are needed to determine these parameters for other LSB sections.
Details of these parametric studies are given next.
5.5. Parametric Study of LSBs with Stiffened Web Openings (Plate
Stiffeners)
In this parametric study based on validated finite element
models, five LSB sections, 150x45x1.6 LSB, 150x45x2.0 LSB,
200x45x1.6 LSB, 300x75x2.5 and 300x75x2.0 LSB, with four web
opening sizes (60, 102, 119 and 127 mm), were selected with an aim
to determine the optimum plate stiffener thickness that increases
the shear capacity to that of LSB without web openings in each
case. The plate stiffener thickness was varied from 1.6 to 8 mm in
the models with an aspect ratio of 1.5. The ultimate shear
capacities obtained for varying ratios of dwh/d1 are given in
Tables 6 (a) to (d).
Figure 14 shows the FEA results in the form of shear capacity of
LSB with 102 mm stiffened web openings versus number of screws
while Figure 15 shows the FEA results in the form of shear capacity
of LSB with stiffened web openings versus stiffener thickness for
200x45x1.6 LSB. Figure 14 indicates that plate stiffeners with 12
screws (Arrangement 3) provide the optimum screw fastening
arrangement. Figure 15 (b) shows that the optimum thickness of
plate stiffener is 3.0 mm for 200x45x1.6 LSB with 102 mm web
openings. Similarly, Figures 15 (a) and (c) show that 1.6 mm and 4
mm are the optimum plate stiffener thicknesses for 200x45x1.6 LSB
with 60 mm and 119 mm web openings, respectively. Experimental
results also confirmed that plate stiffeners with Arrangement 3 (12
screws) provided the optimum arrangement and 1.6 mm and 3.0 mm were
the optimum stiffener thicknesses for 60 mm and 102 mm web
openings, respectively. Figures 16 (a) to (c) show the FEA results
in the form of shear capacity of LSB versus stiffener thickness for
300x75x2.5 LSB and 300x75x2.0 LSB while Figure 17 shows these
results for 150x45x1.6 LSB and 150x45x2.0 LSB. The optimum plate
stiffener thickness in each case can be obtained from these
figures. Table 7 shows the optimum plate stiffener thicknesses for
the different LSB sections and web opening sizes.
Table 7 and Figure 18 show that 5 mm plate stiffeners fastened
using Arrangements 3 were almost able to restore the full shear
capacity (93%) of 200x45x1.6 LSB with 127 mm web openings. In this
case, the depth of web opening to the clear height of web ratio
(dwh/d1) is 0.75, which exceeded the limiting value of 0.7 in
AS/NZS 4600 [7]. In order to obtain the full shear capacity, the
depth of web opening to the clear height of web ratio (dwh/d1) was
limited to 0.7 based on FEA results.
6. Optimum Stiffener Systems for LSB with Web Openings Subjected
to Shear
In this section the optimum plate stiffener system was proposed
based on the numerical and experimental results reported in the
previous sections. It is proposed that the width of the optimum
plate stiffener is dwh+100 mm and its height is lesser of clear web
height (d1) and dwh+100 mm. These dimensions have been chosen for
practicality and allow a distance of 50 mm between the free edges
of the web opening and the plate stiffener. This optimum stiffener
arrangement is an improvement of the recommendations of AISI [9]
and Sivakumaran [15]. Table 8 shows the shear capacities of LSBs
using optimum plate stiffener arrangement (Arrangement 3 with No.12
screws). It shows that LSBs were able to restore the original shear
strength when the optimum stiffener arrangements were used around
the web openings. Keerthan and Mahendran [14] proposed suitable
predictive equations for the shear capacity of LSB without web
opening (Vv). These equations can be used for LSBs with stiffened
web openings when the optimum stiffening system proposed here is
used around the web openings. Keerthan and Mahendran’s [14] design
equations are also given in Appendix A of this paper for the sake
of completeness.
Figure 19 shows the plot of optimum plate stiffener thickness to
web thickness ratio (tSiff/tw) versus depth of web opening to clear
height of web (dwh/d1). Figure 20 shows the schematic diagram of
optimum plate stiffener arrangement for LSBs with web openings.
Suitable equations are also proposed to predict the sizes of
optimum plate stiffeners (Equations 1 to 3). Equations 1 to 3 were
developed so that they predict the required plate stiffener
thickness (tStiff) conservatively and thus ensure a safe design of
LSBs with stiffened web openings.
(1)
(2)
Lesser of and (3)
where
wstiff x hstiff = Width x Height of plate stiffener
7. Conclusions
This paper has presented a detailed investigation into the shear
behaviour of LSBs with stiffened web openings using finite element
analyses. Suitable finite element models were developed and
validated by comparing their results with experimental test
results. The developed nonlinear finite element model was able to
predict the shear capacities of LSBs with stiffened web openings
and associated deformations and failure modes with very good
accuracy. Both finite element analysis and experimental results
show that the plate stiffeners based on the recommendations of AISI
[9] are not adequate to restore the shear strengths of LSBs with
web openings. New plate stiffener systems with optimum sizes and
screw-fastening arrangements have been proposed to restore the
shear capacity of LSBs with web openings based on both experimental
and numerical parametric study results. It was found that the width
of the optimum plate stiffener is dwh+100 mm and its height is
lesser of the clear web height (d1) and dwh+100 mm while the
associated screw fastening is to be based on Arrangement 3 with 12
screws. Suitable predictive equations have been proposed for LSB
designers to determine the optimum plate stiffener thickness as a
function of dwh/d1.
Acknowledgements
The authors would like to thank Australian Research Council and
OneSteel Australian Tube Mills for their financial support, and the
Queensland University of Technology for providing the necessary
facilities and support to conduct this research project. They would
also like to thank Mr Christopher Robb and Mr Jamie Scott-Toms for
their valuable assistance in performing the shear tests of
stiffened LSBs. The authors would also like to thank Mr Ross
Dempsey, Manager - Research and Testing, OneSteel Australian Tube
Mills, for his technical advice and support to this research
project.
References
[1] LiteSteel Technologies (LST), OneSteel Australian Tube
Mills, Brisbane, Queensland, viewed 10 March, 2009, .
[2] Pokharel, N. and Mahendran, M. (2006), Preliminary
Investigation into the Structural Behaviour of LSB Floor Joists
Containing Web Openings, Research Report, Queensland University of
Technology, Brisbane, Australia.
[3] OneSteel Australian Tube Mills, (OATM) (2008), Design of
LiteSteel Beams, Brisbane, Australia.
[4] Keerthan, P. and Mahendran, M. (2010), Experimental Studies
on the Shear Behaviour and Strength of LiteSteel Beams, Engineering
Structures, Vol. 32, pp. 3235-3247.
[5] Keerthan, P. and Mahendran, M. (2012), Shear Behaviour and
Strength of LiteSteel Beams with Web Openings, Journal of Advances
in Structural Engineering, Vol. 15, pp.197–210.
[6] Keerthan, P. and Mahendran, M. (2012), New Design Rules for
the Shear Strength of LiteSteel Beams with Web Openings, Journal of
Structural Engineering, ASCE, In Press.
[7] Standards Australia/Standards New Zealand (SA) (2005),
Australia/New Zealand Standard AS/NZS4600 Cold-Formed Steel
Structures, Sydney, Australia.
[8] American Iron and Steel Institute (AISI) (2007), North
American Specification for the Design of Cold-formed Steel
Structural Members, AISI, Washington, DC, USA.
[9] American Iron and Steel Institute (AISI) (2004), Supplement
to the Standard for Cold-Formed Steel Framing – Prescriptive Method
for One and Two Family Dwellings, 2001 Edition, American Iron and
Steel Institute, Washington, DC, USA.
[10] Mahendran, M. and Keerthan, P. (2012), Experimental Studies
of the Shear Behavior and Strength of LiteSteel Beams with
Stiffened Web Openings, Research Report, Queensland University of
Technology, Brisbane, Australia.
[11] Hibbitt, Karlsson and Sorensen, Inc. (HKS) (2007), ABAQUS
User’s Manual, New York, USA.
[12] Keerthan, P. and Mahendran, M. (2010), Elastic Shear
Buckling Characteristics of LiteSteel Beams, Journal of
Constructional Steel Research, Vol. 66, pp. 1309-1319.
[13] Seo, J.K, Anapayan, T and Mahendran, M. (2008),
Imperfection Characteristic of Mono- Symmetric LiteSteel Beams for
Numerical Studies, Proc. of the 5th International Conference on
Thin-Walled Structures, Brisbane, Australia, pp. 451-460.
[14] Keerthan, P. and Mahendran, M. (2011), New Design Rules for
the Shear Strength of LiteSteel Beams, Journal of Constructional
Steel Research, Vol. 67, pp. 1050–1063.
[15] Sivakumaran, K.S., (2008), Reinforcement Schemes for CFS
Joists Having Web Openings, Research Report, Department of Civil
Engineering, McMaster University, Ontario, Canada.
Appendix A: Proposed Design Equations for the Shear Strength of
LSBs [14]
for (Shear yielding) (A-1) for
(Inelastic shear buckling) (A-2)
for (Elastic shear buckling) (A-3)
where
where
For LSBs (A-4)
for (A-5)
for (A-6)
for (A-7)
for (A-8)
where kss, ksf = shear buckling coefficients of plates with
simple-simple and simple-fixed boundary conditions.
Direct Strength Method (DSM)
≤ 0.815 (A-9)
0.815< ≤ 1.23 (A-10)
> 1.23 (A-11)
where
(A-12)
(A-13)
(A-14)
1
70
.
0
24
.
0
1
£
<
d
d
wh
100
+
=
wh
Stiff
d
w
=
Stiff
h
1
d
100
+
wh
d
yw
v
t
t
=
yw
LSB
w
f
Ek
t
d
£
1
(
)
i
yw
i
v
t
t
t
t
-
+
=
25
.
0
yw
LSB
w
yw
LSB
f
Ek
t
d
f
Ek
508
.
1
1
£
<
(
)
e
yw
e
v
t
t
t
t
-
+
=
25
.
0
yw
LSB
w
f
Ek
t
d
508
.
1
1
>
yw
yw
f
6
.
0
=
t
ú
û
ù
ê
ë
é
=
w
yw
LSB
i
t
d
f
Ek
1
6
.
0
t
2
1
905
.
0
ú
û
ù
ê
ë
é
=
w
LSB
e
t
d
Ek
t
)
(
87
.
0
ss
sf
ss
LSB
k
k
k
k
-
+
=
(
)
2
1
34
.
5
4
d
a
k
ss
+
=
1
1
<
d
a
(
)
2
1
4
34
.
5
d
a
k
ss
+
=
1
1
³
d
a
(
)
(
)
(
)
1
1
2
1
39
.
8
44
.
3
31
.
2
34
.
5
d
a
d
a
d
a
k
sf
+
-
+
=
(
)
(
)
3
1
2
1
99
.
1
61
.
5
98
.
8
d
a
d
a
k
sf
-
+
=
1
=
yw
v
t
t
l
÷
ø
ö
ç
è
æ
-
+
=
l
l
t
t
815
.
0
1
25
.
0
815
.
0
yw
v
l
÷
ø
ö
ç
è
æ
-
+
=
2
2
1
1
25
.
0
1
l
l
t
t
yw
v
l
yw
yw
f
6
.
0
=
t
(
)
2
1
2
2
1
12
÷
÷
ø
ö
ç
ç
è
æ
-
=
d
t
E
k
w
LSB
cr
n
p
t
÷
÷
ø
ö
ç
ç
è
æ
÷
÷
ø
ö
ç
ç
è
æ
=
÷
÷
ø
ö
ç
ç
è
æ
=
LSB
yw
w
cr
yw
Ek
f
t
d
1
815
.
0
t
t
l
w
wh
Stiff
t
d
d
t
ú
û
ù
ê
ë
é
+
÷
÷
ø
ö
ç
ç
è
æ
=
035
.
0
52
.
3
1
