Suitable Stiffening Systems for LiteSteel Beams with Web Openings

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Nov 15, 2013 (3 years and 7 months ago)

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1


Suitable Stiffening System
s

for LiteSteel Beam
s

with Web Opening
s


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
commerc
ial 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
opening
s of LSBs
.

E
xperimental and numerical studies were undertaken to investigate the
shear beha
viour and strength of LSBs with

circular
web openings

reinforced using
plate,

stud
,
transverse and sleeve

stiffeners with varying s
izes and thicknesses
. Both welding and

varying

screw
-
fastening arrangements
were used to attach these stiffeners to the web

of LSBs
.
F
inite
element models of LSBs with
stiffened
web openings in shear were developed to simulate
the
ir

shear behaviour and str
ength of LSBs. They were t
hen 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

in
adequate.

Suitable s
crew
-
fastened plate
stiffener arrangements

with optimum thicknesses
have been proposed for LSB
s

with web
opening
s

to
restore the
ir

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:
m.mahendran@qut.edu.au





2


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 contin
uously developed to suit
various

requir
ements 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
lightw
eigh
t 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
LS
B 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 height
s
.
Pokharel

and
Mahendran
[2]

re
commended 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 signifi
cantly 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],
th
e use of web openings

can

lead to significantly reduced shear c
apacities

of

LSBs.
Keerthan and Mahendran
[5,
6]

investigated the shear behavior
and strength
of LSB
s

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 bucklin
g 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

3


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 stif
feners around the web openings
.

Currently available cold
-
formed stee
l desi
gn
standard
s

[7,8]

and
steel framing standard
s

[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 LSB
s

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 we
b openings were developed to
simulate their shear behaviour and capacity, and were validated by comparing thei
r 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 compar
ison of finite element analysis

and experim
ental
results

as well as the d
etails 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

the
m

with various stiffener arrangements.



The first four s
pecimens
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 th
at

of 200x45x
1.6 LSB while the
plate stiffener

extended 25 mm beyond
the
web opening
edge
s. The plate stiffener was
fastened to the
LSB
web with No.12 T
ek screw
s 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 simil
ar to Test Specimen 5
, but with a total
of 8
screws at 63.5 mm
spacing
along the plate stiffener
edges
with a
n edge distance of 12.5
mm (
Figure
3

(b)). This s
crew

fastening
arrangement was defined as “Arrangement 2”. Since

4


the plate stiffeners with a thick
ness equal to the

LSB web thickness (1.6 mm) did not restore
th
e original shear capacity
, two and three
1.6 mm plate stiffeners

were used in

Specimen
s

7

and 8, respectively. The plate stiffeners’ heights were also increased to match the clear LSB
web heigh
t of 168 mm, which led to plate stiffener sizes of 152x168x3.2 mm and
152x168x4.8
mm. These two specimens we
re fastened using
Arrangement
2

with screws

locate
d

in the middle as implied by AISI [9] recommendations. Hence

the edge distance
along the horizont
al 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 1
27

mm web openings.
In these tests, the stiffener heights were again increased to
that of clear web. Arrangement 2 of eight screws wa
s used in
Specimen 9
, but the edge
distances and screw spacings w
ere 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
. T
o increase the shear capacity further, 3 mm thick and
202 mm wide plate stiffeners
were use
d 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
a
ttach

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 distance
s

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
edg
e 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 LSB
s 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 ope
nings. Two 2.5 mm plates of 227x168 mm dimensions were screw fastened using 12
screws in Arrangement 3 as in
Specimen 11. Specimen

15 wa
s similar to
Specimen 14, but
the plate stiffeners were attached using

screws
located on a

circular format as shown in
F
igure
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
.


5



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 investig
ate 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 u
sed. 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

type
s such as transverse and sleeve stiffeners.
S
hear

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 base
d 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

LSB
s
, where

t
w

and d
1

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 MP
a
, respectively.
For LSBs
d
1

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 co
ld
-
formed channel
sections. The reasons for this are given in
[4]
.

Table 2 also provides the diameters of web
openings (d
wh
) used in the models. Since the effect of including the rounded corners in LSBs
on the shear buckling behaviour and capacity was foun
d 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 sele
cted as it has the
capability to simulate the shear behaviour of thin steel beams such as LSBs. This element is

6


thin, shear flexible, isometric quadrilateral shell with four nodes and five degrees of freedom
per node, utilizing reduced integration and

bili
near interpolation scheme.


R3D4 rigid body elements were used to simulate the restraints and loading in the finite
element models

of LSB
s

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
-
proc
essing facilities.


In order to fully und
erstand the shear behaviour of L
SB
s with stiffened web openings
,

several
important issues were considered when deciding the
se parameters such as the ratio

of the
depth of web openings to clear height of web (d
wh
/d
1
)
,
type
s 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 ele
ments as possible in the analysi
s. However, such an analysis will requi
re
excessive computing time and resources
. In this
research
, adequate numbers of elements were
chosen for both flanges and web based o
n detailed convergence studies
to obtain sufficient
accuracy of results without excessive use of computing time. Convergence studies
showed

that an elemen
t size of 5mm x 5
mm provided an accurate representation of shear buckling and
yielding deformations. A
n 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 we
re 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 the
se

nodes, only those
in
common will be constrained. This Tie MPC was used to simulate
all the

screw connections

used in installing the stiffeners
.


7



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 t
he 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 LSB
s

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 averag
e

yield stresses reported earlier
. The
se

measured yield stresses
were used in
FEA
.

Since
the
plate stiffeners were t
aken 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
elem
ents

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:
u
x

= 0


x

= 1 Mid
-
span loading point:

u
x

= 1


x

= 1


u
y


= 1


y

= 0


u
y

= 0


y

= 0



u
z


= 1


z

= 0




u
z

= 1



z

= 0


8


Note:
u
x
,
u
y

and
u
z

are translations and θ
x
, θ
y

and θ
z

are rotations in the x, y and z directions,
respectively. 0 deno
tes 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 speci
m
ens 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 ele
ments 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 conditio
ns 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
.
T
his study assumed that screw
fastener
failure is unlikely to occur as confirmed by o
ur
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 activ
e degrees of freedom equal on both sides of the connection.


The web side plates at the supports were connected using h
igh strength steel bolts (M16
8.8/S) to avoid bolt failure
s

during testing. Our
shear
tests

[10]
confirmed

that there were no
bolt

or p
late
failures. Therefore these web side plates were modelled as rigid bodies using
R3D4 elements.


3
.6
. Initial Geometric Imperfections

T
he local plate imperfections
in LSBs were found to be

less than the currently accepted
fabrication tolerance of d
1
/150

[4]
. However, the fabrication tolerance limit of d
1
/150 was

9


used in the numerical modelling of LSBs as the preliminary analyses showed that the effect of
local plate imperfection (from d
1
/300 to d
1
/150) on the shear capacity of LSB

with stiffened
web open
ings

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 residu
al stress model developed for computer a
nal
yses 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 c
apacity of LSBs with
stiffened
web openings is
also
lik
ely to be very
small. I
t was
thus

decided to neglect the residual s
tresses 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 imperfe
ctions. Nonlinear
static analyse
s, including the effects of large deform
ation and material yielding, were

used

to
investigate the shear

behaviour of LSB
s

until

failure. The
RIKS method in ABAQUS was
also
i
ncluded in the nonlinear analyse
s.
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 Newt
on
-
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 t
he non
-
linear analyses
of
LSB with
stiffened web openings
:

Maximum num
ber of load increments = 100,

Initial increment size =
0.01,

Minimum increment size = 0.000001,

Automatic increment reduction enabled, and large
displacements enabled.






10


4
.

Validation of Finite Element Models

of LSB with Stiffened Web Openings

T
he
accuracy of the
developed finite element model
s

of LSBs with stiffened web openings

was investigated by

comparing the non
-
linear a
nalysis results with those

obtained from

the

shear tests of LSBs with
stiffened web openings
[10].

Seventeen finite element
mo
dels were
constructed using the material and geometric properties from experimental testing (
Table 2)
and the
results were compared
with test results,

with pa
rticular attention given to the ultimate
load,
load
-
deflection curves

and

f
ailure m
odes.

These

com
parison
s 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 Figu
res 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, w
hile 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 bendi
ng 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 Ele
ment Analyse
s of LSBs with
Different

Type
s

of
Stiffeners


The overall objective of this research is to develop the
most
e
ffective and economical
stiffening

arrangement
s

for LSB
s

with web openings subjected to shear.

In this
section
,
the

11


use of
different

types of stiffeners, namely,
plate stiffener
s
, LSB stud stiffener
s
, sleeve
stiffener
s

and transverse stiffener
s
,

was

investigated

by using
finite element analyses
.



5
.1
.

Transverse Stiffener
s



Transverse stiffeners a
re

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

stiffener
s

is
shown in
F
igure
4

(b)
,
which

shows
that
two
steel
plates are attached to the web on either side
of the open
ing
at

20

mm

from the edge of the
web
opening.


T
ransverse 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
stiffener
s

to the flange
s

gave only a
4% increase in

the shear capacity.
Hence

welding the
transverse
stiffener
s

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 opening
s
,
FEA

of 200x45x1.6 LSBs with 60 and 127 mm web openings
were undertaken

with varying
transverse
stiffener thicknesses
.

Figure 11

shows the failure
mode
s

of LSB
s

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 transv
erse
stiffeners
were only welded
to the web
element of LSB
.

Table 3

shows the shear capacities

of LSB
s

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

V
v
,
V
nl

and
V
nls
,
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 opening
s

(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 LSB
s

with
large
r

web openings

(127
mm)
.

Hence
the use of
transverse stiffeners
is not recommended
for
LSB
s

with large web openings.


12



5
.2
.

Sleeve Stiffener
s

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 edge
s
. This stiffener is
likely to
have a greater effect on

the buckling strength of LSBs than the ultimate shear strength.
How
ever, increasing the
shear
buckling capacity is
also
important.
The geometry and finite
element mesh of a typical LSB with

sleeve

stiffener
s

is shown in Figure 4

(c)
.
In comparison
with

other

stiffeners, the sleeve stiffener is less practical as it require
s the sleeve to be formed
during manuf
acturing or welded to the web. However, w
elding
thin
cold
-
formed steel
sections
is
to be
avoided as it
can be detrimental in terms of heat effects and r
esidual stresses.
Hence

the
use of
sleeve stiffener
s

may
complicate

the fabrication phase of LSB joists and bearers.


Th
e th
ickness and length of sleeve stiffener

that affects its
rigidity
were considered as
possible variables in FEA. T
he

sleeve
stiffener thickness
was considered
to be the
same as
the
LSB web
th
ickness
.
However, its
length
was varied (10, 20 and 25 mm) to determine its
effect
on

the

shear capacity of
200x45x1.6
LSB
s 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 signif
icant role on the shear capacity
of LSB with web opening
s
.
Table
5

show
s

the
shear capacities

of LSB
s with varying web opening sizes and 20 mm

sleeve stiffener
s
,
which

indicate

that
sleeve

stiffeners are

not adequate to restore the shear strengths of LSB with
large
r

web openings

(102 and 127 mm)
.

Hence
the use of
sleeve

stiffeners
is not
recommended
for LSB
s

with large web openings.

Figure 13

shows the failure mode of
200x45x1.6 LSB with
60 mm web opening
s

and
20 mm sleeve stiffener
s
.


5
.3
. LSB Stud Stiffener
s


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 T
ek 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).



13


E
ffect of LSB stud stiffeners on
the
shear cap
aci
ty 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.

He
nce
LSB stud stiffeners
are not
recommended
for LSB
s

with large
web openings.


5
.4
.

Plate Stiffener
s


Plate stiffeners are plates

with web opening
s

that are attached to the web

(see Figure
s

4

(
a
)
and 5
).
The
y are

attached to the web around the opening
s

by
fas
tening

with
No
.
12 Tek
screws
. In c
ontrast 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 stiffene
r
s were the best

stiffener for LSB
s

with
web openings.
However,
the number of shear tests was
limited
.

Hence in order to determine

the optimum

plate stiffener size
s
,
finite element models of LSBs
with web openings stiffened
with
plate stiffener
s

in shear were developed to simulate th
eir 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 s
tiffener dimensions and screw fastening arrangement were
adopted based on AISI

[9] (Arrangement 1)
. However, FEA and experimental results show
ed
that it

only reached
about
65% of t
he shear capacity of LSB

without web openings (
3
4.8 and
3
3.6
kN

vs 52 kN). H
ence FEA and test

results

showed that
the plate sti
ffeners
based on

AISI
[9]

recommendations
are not adequate to restore the shear st
rengths of LSBs
.



Test

Specimens

5 and 6

with 152x152x1.6
mm
plate stiffeners

were considered to investigate
the effect of
different
screw

spacing
s (Arrangements 1 and 2)
.
Both FEA and tests showed
that using

more screws (20 versus 8 screws) increased the

shear capacit
y

of LSBs

by
only

5%

as shown in Table 2
.

Test

Specimen
s 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 cap
acities increased considerably (Table 2).


14



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
).
T
est
and FEA
results

also showed that Arrangement 4 with reduced edge distance
s

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 pl
ate stiffeners

failed at
a higher load d
ue 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 incline
d
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 rec
ommended to avoid excessive heat an
d residual stress effects on

thin
-
walled cold
-
formed steel sections.


Test

Specimen
s 14 a
nd 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 c
apacity (
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 (d
wh
/d
1
)
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, h
owever, 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

an
d 50.5

vs

15


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 o
f 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 studi
es are given next
.


5
.
5
.

Parametric Study of LSB
s

with Stiffened Web Openings

(Plate Stiffener
s
)


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.
T
he ultimate shear capacities
obtained
for varying ratios of
d
wh
/d
1

are given in Tables 6 (a) to (
d
)
.


Figure 14 shows the FEA resu
lts 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

16


while Figure 17 shows the
se
results

fo
r 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 thickness
es

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 o
pening to the clear height of web ratio (d
wh
/d
1
) 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 (d
wh
/d
1
)
was limited
to 0.7 based o
n FEA results.


6
. Optimum Stiffener System
s

for LSB with Web Openings

Subject
ed

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 t
he width of the
optimum plate stiffener is d
wh
+100 mm and
its
height is
lesser

of clear web height (d
1
) and
d
wh
+100 mm. These dimensions have been chosen for practicality and allow a distan
ce of 50
mm between the
free edge
s 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 LSB
s using

optimum plate stiffener arrangement

(Arrangement 3 with No.12 screws)
. It shows

that
LSBs were able to restore the original
s
hear s
trength 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 (V
v
)
. 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 c
ompleteness.


Figure 19 shows the plot of optimum plate stiffener t
hickness to
web thickness ratio (t
Siff
/t
w
)
versus depth of web opening to clear height of w
eb

(d
wh
/d
1
).
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
(t
Stiff
)
conservatively
and thus
ensure a safe design of LSBs with stiffened web openings.


17



w
wh
Stiff
t
d
d
t
















035
.
0
52
.
3
1

70
.
0
24
.
0
1


d
d
wh

(1)




(2
)


Stiff
h

Lesser of
1
d
and
100

wh
d


(3)



w
her
e


w
stiff

x h
stiff

= 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 th
e shear strengths of
LSB
s

with web openings.

New
plate
stiffener
systems

with optimum sizes and screw
-
fastening arrangements have been proposed

to restore the shear capacity of LSB
s

with web
openings

based on both experimental and
numerical

parametric study results.

It was found
that
t
he width of the optimum plate stiffener is d
wh
+100 mm and
its
height is
lesser

of
the
clear web height (d
1
) and d
wh
+100 mm

while the associated screw fastening is to be based on
Arrangement 3 with

12 screws.
S
uitable predictive equations have been proposed for LSB
designers to determine the optimum plate stiffener thickness

as a function of d
wh
/d
1
.


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 Sc
ott
-
Toms
for their
valuable
assistance in
performing the
shear tests of stiffened LSBs
.

The

authors

would also like to thank Mr Ross
100


wh
Stiff
d
w

18


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, <
www.litesteelbeam.com.au
>.


[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]
K
eert
han, P. and Mahendran, M. (2010
), Experimental Studies on the Shear Behaviour
and Stre
ngth of LiteSteel Beams, Engineering Structures, Vol.
32, pp. 3235
-
3247.


[5] Keerthan, P. and Mahendran, M. (2012), Shear Behaviour and Strength of LiteSteel
Beams w
ith 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 E
ngineering, ASCE, In Pres
s.



[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 I
ron and Steel Institute, Washington, DC
, USA
.


19



[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, Brisban
e, Australia.


[11]
Hibbitt, Karlsson and Sorensen, Inc. (HKS)

(2007)
, ABAQUS User’
s Manual
, New
York, U
SA
.


[12]

Keerthan, P. and Mahendran, M. (2010), Elastic Sh
ear Buckling Characteristics of
LiteSteel Beams, Journal of Constructional Steel Research, Vo
l
.

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 5
th

I
nternational

Conference
on Thin
-
Walled Struc
tures, Brisbane, Australia
,
pp. 451
-
460.


[14]
Keerthan, P. and Mahendran, M.

(2011)
, New
Design Rules for the S
he
ar Strength of
LiteSteel Beams,
Journal of Con
structional 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.















20


Appendix A:
Proposed Design Equations for the Shear Strength of LSBs

[14]


yw
v




for
yw
LSB
w
f
Ek
t
d

1


(Shear yielding)

(A
-
1
)


i
yw
i
v







25
.
0

for
yw
LSB
w
yw
LSB
f
Ek
t
d
f
Ek
508
.
1
1





(Inelastic shear buckling)



(A
-
2
)


for
yw
LSB
w
f
Ek
t
d
508
.
1
1


(Elastic shear buckling)


(A
-
3
)

where

where
yw
yw
f
6
.
0









For LSBs
)
(
87
.
0
ss
sf
ss
LSB
k
k
k
k








(A
-
4)



2
1
34
.
5
4
d
a
k
ss



for
1
1

d
a

(A
-
5)



2
1
4
34
.
5
d
a
k
ss



for
1
1

d
a


(A
-
6)







1
1
2
1
39
.
8
44
.
3
31
.
2
34
.
5
d
a
d
a
d
a
k
sf





for
1
1

d
a


(A
-
7)





3
1
2
1
99
.
1
61
.
5
98
.
8
d
a
d
a
k
sf




for
1
1

d
a

(A
-
8)

where k
ss
, k
sf

= shear buckling coefficients of plates with simple
-
simple and simple
-
fixed
boundary conditions.





2
1
905
.
0







w
LSB
e
t
d
Ek



e
yw
e
v







25
.
0







w
yw
LSB
i
t
d
f
Ek
1
6
.
0


21


Direct Strength Method (DSM)


1

yw
v





≤ 0.815


(A
-
9
)














815
.
0
1
25
.
0
815
.
0
yw
v

0.815<


≤ 1.23

(A
-
10
)










2
2
1
1
25
.
0
1




yw
v


> 1
.23

(A
-
11
)


where

yw
yw
f
6
.
0




(A
-
12
)



2
1
2
2
1
12










d
t
E
k
w
LSB
cr





(A
-
13
)



























LSB
yw
w
cr
yw
Ek
f
t
d
1
815
.
0





(A
-
14
)