This may be the author’s version of a work that was submitted/acceptedfor publication in the following source:

Sivakumar, Kesawan & Mahendran, Mahen(2016)Fire design rules for LSF walls made of hollow flange channel sections.Thin-Walled Structures, 107, pp. 300-314.

This file was downloaded from: https://eprints.qut.edu.au/96260/

c© Consult author(s) regarding copyright matters

This work is covered by copyright. Unless the document is being made available under aCreative Commons Licence, you must assume that re-use is limited to personal use andthat permission from the copyright owner must be obtained for all other uses. If the docu-ment is available under a Creative Commons License (or other specified license) then referto the Licence for details of permitted re-use. It is a condition of access that users recog-nise and abide by the legal requirements associated with these rights. If you believe thatthis work infringes copyright please provide details by email to qut.copyright@qut.edu.au

License: Creative Commons: Attribution-Noncommercial-No DerivativeWorks 2.5

Notice: Please note that this document may not be the Version of Record(i.e. published version) of the work. Author manuscript versions (as Sub-mitted for peer review or as Accepted for publication after peer review) canbe identified by an absence of publisher branding and/or typeset appear-ance. If there is any doubt, please refer to the published source.

https://doi.org/10.1016/j.tws.2016.05.022

1

Fire Design Rules for LSF Walls Made of Hollow Flange Channel Sections

Kesawan Sivakumar and Mahen Mahendran

Queensland University of Technology, Brisbane, QLD 4000, Australia

Abstract: Cold-formed Hollow Flange Channel (HFC) sections can be used in Light gauge

Steel Frame (LSF) wall systems due to their structural efficiency. Recent experimental and

finite element analysis based investigations conducted by the authors have demonstrated the

superior fire performance of LSF walls made of welded HFC sections. The authors have

developed a wide range of fire performance data of LSF walls through a finite element analysis

(FEA) based extensive parametric study. This paper investigates the applicability of the

available fire design rules to predict their structural capacities. Since fire design rules were not

available for HFC sections, the latest design rules for LCS studs subjected to non-uniform

temperature distributions were selected for evaluation from the pool of various design rules

given in standards and previous studies. Suitable modifications were then incorporated for

simplification and improved accuracy. Two improved design methods based on AS/NZS 4600

and Eurocode 3 were proposed. The structural capacity of HFC section stud found from the

design rule predictions was converted into load ratio which is the ratio between the structural

capacities under fire and ambient conditions, and the load ratio versus FRR curve were

produced for different LSF walls. These were then compared with the FEA results, to verify

the accuracy of the proposed design rules. This paper also presents suitable DSM based design

method proposed for HFC section studs subject to non-uniform temperature distributions in

LSF walls, and verifies its accuracy.

Keywords: Cold-formed steel structures, LSF walls, Hollow flange channel sections, Non-

uniform temperature distribution, Fire design, Effective width method, Direct strength method

Corresponding author’s email address: m.mahendran@qut.edu.au

2

1. Introduction

Typical load-bearing and fire resistant Light gauge Steel Frame (LSF) walls are made of cold-

formed steel frames and lined with gypsum plasterboards. Recent research studies have

focussed on using structurally more efficient cold-formed steel stud sections in these walls. An

example of this is Kesawan and Mahendran’s [1] proposed use of Hollow Flange Channel

(HFC) sections (Fig. 1) in LSF walls. These sections with rectangular hollow flanges can be

made by a combined cold-forming and rivet/screw fastening or welding process. A welded

hollow flange channel section known as LiteSteel Beam (LSB) is shown in Fig. 1. The

reduction in web depth and the presence of torsionally rigid hollow flanges increase their local

and distortional buckling capacities which are common problems in thin-walled members [2,3].

Kesawan and Mahendran [1] conducted full scale fire tests of LSF walls made of welded LSB

studs (Fig. 2), and subsequently developed finite element models to predict the thermal and

structural performances of LSF walls under standard fire conditions. These investigations

demonstrated the improved fire performance of LSF walls made of HFC stud sections in

comparison to those made of conventional Lipped Channel Sections (LCS). LSF floor systems

made of welded HFC joist sections also performed better under fire conditions [4, 5]. A brief

summary of experimental and numerical studies of LSF walls made of HFC stud sections is

presented in this paper.

Engineers adapt a prescriptive approach for the fire design of LSF walls where they use the

Fire Resistance Rating (FRR) given by the plasterboard manufacturers, obtained from

expensive and time consuming full scale fire tests. Although finite element modelling can be

used to surpass these barriers, most engineers do not have access to suitable finite element

analysis packages nor have the required expertise to use such advanced software packages.

Therefore developing suitable fire design methods to predict the structural fire performance of

load bearing LSF walls made of HFC section studs is the solution to overcome the above-

3

mentioned problems. For this purpose suitable design rules are needed to predict the structural

capacity of HFC sections subject to non-uniform temperature distributions.

The wall studs are subjected to non-uniform temperature distributions (Fig. 3) as LSF walls are

exposed to fire on one side, which makes their fire design a complex problem. At elevated

temperatures, the elastic modulus and yield strength of steel deteriorate rapidly. Hence with

the development of a non-uniform temperature distribution across the stud cross-section,

mechanical properties including elastic modulus and yield strength of steel also vary across the

cross-section, which shifts the neutral axis about both major and minor axes, and thus

generating a loading eccentricity. Further, the presence of a non-uniform temperature

distribution induces thermal bowing deflections, which also results in an eccentricity that is the

highest at the stud mid-height. It should be noted that this eccentricity is in the opposite

direction to that caused by the neutral axis shift (Fig. 3). These eccentricities develop an

induced bending action in the wall studs during a fire test in addition to the applied compression

action, which is further increased due to P-Δ effects. Other than these complex effects, the local

buckling, a common problem in thin-walled members, is likely to be complicated in wall studs

under non-uniform temperature distributions. All of these make the structural behaviour of LSF

wall studs subject to non-uniform temperature distribution complex as it has become a problem

of thin-walled beam-column subject to varying mechanical properties across its cross section.

Considering all the above mentioned complexities, many research studies have proposed

simplified design rules to predict the structural capacity of conventional open LCS studs subject

to non-uniform temperature distributions, but no design rules are available for HFC section

studs. This study reviews the available fire design rules and then selects the latest Gunalan and

Mahendran’s [6] design rules based on AS/NZS 4600 [7] and Eurocode 3 Part 1.3 [8], and

proposes suitable modifications to them for improved accuracy and simplifications. Two

4

separate design methods based on AS/NZS 4600 and Eurocode 3 Part 1.3 [7, 8] were proposed,

whose details are presented in this paper. The AS/NZS 4600 and AISI S100 [9] design rules

are the same and hence only AS/NZS 4600 is mentioned in this paper. The direct Strength

method (DSM) [10] is a simplified design approach for cold-formed and thin-walled steel

members subjected to various types of buckling. In this paper a DSM based design method is

also proposed to predict the structural capacity of HFC studs subject to non-uniform

temperature distributions.

Kesawan [11] produced load ratio versus failure time (FRR) curves for LSF walls with different

configurations and made of HFC studs with varying web depths and thicknesses using finite

element analyses (FEA), where the load ratio is the structural loading of HFC stud exposed to

non-uniform temperature distribution in a standard fire divided by that at ambient temperature.

In this study, these curves were obtained by using the proposed AS/NZS 4600 [7], Eurocode 3

[8] and DSM based design methods, where the same elevated temperature steel mechanical

properties, stud sizes and time-temperature profiles considered by Kesawan [11] were used.

This paper compares the design rule predictions with the FEA results to verify their accuracy

and applicability. Spread sheet based design tools were developed based on the proposed

design rules. The proposed fire design rules could facilitate and advance the use of HFC

sections in LSF walls, and this is a significant milestone in the process of establishing a

performance based approach to fire design.

2. Experimental and Numerical Studies

Kesawan and Mahendran [1] conducted full scale fire tests of LSF walls made of welded HFC

section/LiteSteel Beam (LSB) studs. They tested 2.4 m height LSF walls with three different

wall configurations (Fig. 4) subjected to varying load ratios from 0.2 to 0.6 under standard fire

conditions (ISO 834). In their test wall panels, four HFC section studs were spaced at 600 mm

5

and fire protected on both sides by gypsum plasterboards linings, and in one of the tests (Test

4), cavity insulation is used. The fire test details and the results are summarised in Table 1,

which confirms the superior fire performance of LSF walls made of HFC sections (> 2 hour

FRR).

Kesawan and Mahendran [12,13] then developed finite element models to predict the thermal

and structural performances of LSF walls using the well known finite element analysis

programs, SAFIR and ABAQUS, and validated them using full scale fire test results conducted

under standard fire conditions [1,14]. The structural finite element model development

procedure is discussed next. S4R shell elements with mesh sizes of 4 mm x 4 mm were used

to model the stud, and rigid plates made of R3D4 elements were attached to each end of the

studs (Fig. 5). Pinned boundary conditions were defined in the models (Fig. 5) at their

geometrical centroids on both ends while the lateral restraints provided by the plasterboards to

steel studs were simulated by restraining the stud movement along the minor axis/Z direction

at both the inner and outer flanges (Fig. 5) as the screws connecting the plasterboards and studs

penetrated through both flanges. The measured stud dimensions, time-temperature profiles

from the full scale fire tests and ambient temperature mechanical properties together with the

elevated temperature mechanical property reduction factor models proposed by Kesawan et al.

[15] were used. Both transient and steady state FEA were conducted and the FEA predictions

agreed well with the fire test results as seen in Table 1. Thereafter using the developed models,

a FEA based parametric study was performed to develop extensive fire performance data,

where three different wall configurations (Fig. 4) made of HFC sections of different depths and

thicknesses (150x45x15x1.6, 90x45x15x1.6, 60x45x15x1.6, 150x45x15x2.5 and

150x45x15x1.0 mm HFC sections) were considered. These studs were assumed to be made of

either G500 or G250 cold-formed steel sheet with Dolamune Kankanagme and Mahendran’s

[16] elevated temperature mechanical property reduction factors (Figs. 6(a) and (b)). Time-

6

temperature history of the three wall configurations exposed to the standard fire curve [14],

were obtained from SAFIR thermal analyses [12] (Fig. 7), and used as input to the structural

finite element models of HFC studs [11]. The temperature distribution model considered across

the HFC section is shown in Fig. 3(a), where a linear temperature distribution was taken across

the stud depth while it was considered uniform along the flanges. The load ratio versus FRR

curves were developed for different LSF walls using FEA, and are given in Kesawan [11]. In

this study these curves were used to verify the applicability of the proposed design equations

(Section 4). The available fire design rules for conventional LCS studs are discussed next.

3. Fire Design Rules

3.1. Review of Fire Design Rules

In the past, many researchers investigated the fire performance of LSF walls made of LCS

studs and proposed suitable fire design rules based on the design standards at that time, i.e.,

Klippstein’s [17] and Gerlich et al.’s [10] design rules were based on AISI design manuals

while Ranby’s [19], Kaitila’s [20], Feng and Wang’s [21] and Zhao et al.’s [22] design rules

were based on Eurocode 3 Part 1.3 [8]. Gunalan and Mahendran [23] evaluated the applicability

of these design rules using their FEA results, and identified a few drawbacks, which are

discussed next. Klippstein’s [17] method was not recommended as it needs the actual

experimentally measured deflections. Gerlich et al.’s [18] method of using the cold flange yield

strength to calculate the ultimate capacity of LSF wall studs at elevated temperatures resulted

in overestimation. Ranby’s [19] and Kaitila’s [20] methods of using the effective area at

ambient temperature to determine the ultimate capacity of LSF wall stud was not accurate, and

hence Gunalan and Mahendran [6] recommended the use of effective area at elevated

temperatures. Also, in Ranby’s [19] and Kaitila’s [20] methods, the section moment capacity

was determined using the effective area for pure compression, which was not accurate and

Gunalan and Mahendran [6] recommended calculating the effective area based on pure

7

bending. Feng and Wang’s [21] proposed design capacity calculations were accurate, but were

found to be complex, and based on the old Eurocode design rules.

Finally, Gunalan and Mahendran [6] concluded that the ambient temperature design rules given

in AS/NZS 4600 [7] and Eurocode 3 Part 1.3 [8] with some suitable modifications and

simplifications better predicted the FRRs of the load bearing LSF walls made of LCS studs.

Later Ariyanayagam and Mahendran [24] confirmed the applicability of their design rules to

LSF walls exposed to realistic design fire curves. Gunalan and Mahendran [6] and

Ariyanayagam and Mahendran [24] considered only LSF walls made of 90x40x15x1.15 mm

conventional LCS studs in their studies, and hence the applicability of these design rules has

to be verified for other section sizes, i.e., different stud depths. Also Feng and Wang’s [21] and

Gunalan and Mahendran’s [6] proposed design rules were validated soley for LSF walls made

of LCS studs. The adaptability of these design rules to predict the FRR of LSF walls made of

HFC sections has not been investigated yet. Gunalan and Mahendran’s [6] design rules are

summarised next.

3.2. Gunalan and Mahendran’s [6] Method based on Eurocode 3 Part 1.3 [8]

LSF wall stud subject to non-uniform temperature distributions behaves like a beam-column

with varying elevated temperature mechanical properties across its cross-section. Gunalan and

Mahendran [6] used the bending and compression interactive formula given in Eurocode 3 Part

1.3 [8] to solve this problem. They ignored the effects of minor axis bending in the combined

action equation based on Feng and Wang’s [21] findings, and further simplified it to the

following.

1,

*

,

*

effxRdb M

M

N

N

(1)

8

Where; *M is the total moment due to thermal bowing, neutral axis shift and their

magnifications. At the stud mid-height, the total moment due to thermal bowing, neutral axis

shift and their magnifications was considered while at the stud supports only the moment

induced by the neutral axis shift and its magnification was considered.

*N is the total axial force, RdbN , and Mx,eff are the member capacity under pure compression and

the section moment capacity under pure bending, which are calculated using the ambient

temperature design rules in Eurocode 3 Part 1.3 [8] together with the following guidelines.

The effective area (Aeff) is calculated using the elevated temperature mechanical properties

for the individual plate elements

The member compression capacity RdbN , is calculated based on the weighted average

elevated temperature mechanical properties

In the section moment capacity ( effxM , ) calculations, flexural torsional buckling is not

considered as it is eliminated due to the lateral restraints provided by the plasterboards.

The section moment capacities are calculated separately at the stud mid-height and

supports, since at the stud supports hot flange elements are subjected to compressive

stresses while at the stud mid-height cold flange elements are subjected to compressive

stresses. Gunalan and Mahendran [6] considered partial plasticity at the mid-height where

the extreme fibre tension stress had reached yield and the maximum compression stress at

the extreme fibre was considered equal to the yield stress. Further at the stud supports they

considered the material yield on the tension side. These equations are given next,

9

Section moment capacity at stud mid-height

max

,

,y

IfM

teffyt

effx (2)

Section moment capacity at stud support

max

,,

,y

IfM

teffhfyt

effx (3)

Where; teffI , is the weighted average second moment of area, maxy is the distance from the

neutral axis to the extreme fibre, ytf__

is the weighted average yield strength and hfytf , is the hot

flange yield strength .

The bending moment (*

tM ) induced in the LSF wall stud by thermal bowing deflection caused

by the non-uniform temperature distribution and its magnification is given next.

cr

T

t

N

N

eNM

*

*

*

1

(4)

Where; crN is the critical buckling load

2

,,

2

L

IEN

igrit

cr

(5)

Where; L is the stud length, Et,i and Igr,i are the elastic modulus and the second moment

of area of element i at elevated temperature

Te is the thermal bowing deflection based on Cooke’s [24] equation, and is given next.

d

TLe T

8

2

(6)

10

Where; is the thermal expansion coefficient of the hot flange, L is the stud height, T

is the temperature difference between the hot and cold flanges, d is the section depth

The bending moment ( *

eM ) induced in the LSF wall studs about their major axis by the neutral

axis shift and its magnification is given next.

Exxe eNkM ** (7)

Where; kxx is the interaction factors calculated according to Annex A of Eurocode 3 Part 1.1

[26] and Ee is the neutral axis shift

The sum of *

tM and *

eM gives the total moment *M in Eq. 1.

3.3. Gunalan and Mahendran’s [6] Method based on AS/NZS 4600 [7]

Gunalan and Mahendran [6] adapted the same principles that they used in the Eurocode 3 based

design rules, in the AS/NZS 4600 based fire design rules. Their simplified interactive equation

to determine the structural capacity of LSF wall stud subject to combined compression and

bending actions is given by Eq. 8 while the equation to determine the total induced moment

(M*) in the LSF wall studs due to thermal bowing, neutral axis shift and their magnifications

is given by Eq. 9.

1,

**

effxc M

M

N

N (8)

cr

mxE

cr

T

N

N

Ce

N

N

eNM

**

**

11

(9)

where; Nc is the nominal member capacity in compression, Mx,eff is the section moment

capacity calculated using Eqs. 2 and 3, and Cmx is the coefficients for unequal end moments

11

It should be noted that Gunalan and Mahendran [6] limited the cold flange yield strength to be

less than 1.5 times the hot flange yield strength only in stud member capacity calculations

based on their Eurocode based design rules. However, they considered the actual yield

strengths corresponding to the hot and cold flange temperatures in AS/NZS 4600 [7] based

design rules, which has the same underlying principles. Moreover, they limited the cold flange

yield strength only in the section capacity calculations whereas they used the actual yield

strengths in the member slenderness calculations to determine the member compression and

bending capacities and effective area calculations. They used the calculated member

compression capacities of the stud at its mid-height and supports in the interactive formula (Eq.

1 or 8) of both AS/NZS 4600 [7] and Eurocode [8] based design rules. Their solution of limiting

the cold flange yield strength is not consistent within their design rules, and is only an interim

solution. In this study, the actual yield strengths of the hot and cold flanges were used in the

Eurocode 3 based design rules as used by Gunalan and Mahendran [6] with AS/NZS 4600 [7]

design rules.

4. Improved Design Methods Based on AS/NZS 4600 [7]

4.1. Improved Design Method 1

To evaluate the effects of various modifications on the accuracy of predictions, a spreadsheet

based design tool was developed based on Gunalan and Mahendran’s [6] equations following

each modification. The time-temperature profiles (Fig. 7), yield strength, elastic modulus and

stud dimensions were the input to the design tool, which assumed a linear temperature

distribution across the stud cross-section as shown in Fig. 3. The design tool was able to

produce the load ratio versus failure time (FRR) curves of LSF walls made of HFC sections.

After the HFC stud is exposed to a certain time during the standard fire time-temperature curve,

its compression capacity (N*) is calculated using the stud hot and cold flange temperatures

12

based on Fig. 7 and is non-dimensionalised using the compression capacity of stud at ambient

temperature to produce the load ratio versus failure time curves.

In Gunalan and Mahendran’s [6] design equations, the magnified bending action was included

in the structural capacity calculation at stud mid-height and supports. However, at stud supports

P-Δ effect is not present, and its inclusion may result in conservative design mainly for

members, which fail by yielding near their supports. FRR predictions of LSF walls made of

150x45x15x1.6 mm HFC section studs, which fail by section yielding near the supports were

investigated by including (mag) and excluding (no mag) the magnified bending action closer

to the support in the design capacity calculations by using Gunalan and Mahendran’s [6] design

rules. As expected FRR predictions without including the P-Δ effect are higher than those with

considering the P-Δ effect (Figs. 8(a) and (b)). Furthermore, they provide slightly better

agreement with the FEA results. Hence, the magnified bending action due to the P-Δ effect at

the stud supports is omitted in the improved method.

The modifications made to Gunalan and Mahendran’s [6] AS/NZS 4600 (SA, 2005) based

design rules are discussed next. Gunalan and Mahendran [6] calculated the thermal bowing

deflection using Eq. 10, while Baleshan and Mahendran [27] computed it using Eq. 11, which

is more accurate as it considers the thermal expansion co-efficients separately for hot and cold

flanges. These equations are based on Cooke [25]. Baleshan and Mahendran’s [27] equation

was used in this study as it is not too complex to use.

d

LOCFOHFe OHF

T8

)( 2

(10)

d

LOCFOHFe OCFOHF

T8

)( 2 (11)

13

In the bending capacity calculations, Gunalan and Mahendran [6] took ψ as -1 at stud mid-

height (ψ is the ratio between the end moments in an element). However, due to the neutral

axis shift and the difference between the hot and cold flange temperatures, ψ is generally higher

than -1. To investigate this problem, comparisons were made between the FRR predictions of

LSF walls made of 150x45x15x1.6 mm studs using Gunalan and Mahendran’s [6] design

equations considering the actual ψ value (Case 1) and assuming ψ as -1 (Case 2). As seen in

Figs. 9(a) and (b), the load ratio versus failure time (FRR) curve is similar in both cases. This

proves that the load bearing capacity of LSF wall studs is not significantly influenced by the

web buckling caused by bending. This is because the influence of bending action on the load

bearing capacity of LSF wall studs is not significant [6], and further the contribution to the

bending moment capacity by the web elements is also small. In the proposed Method 1, the

actual ψ value was used while it was taken as -1 in Method 2.

In summary, three modifications were proposed here: the magnified bending action due to the

P-Δ effect at the stud supports is omitted, the thermal bowing equation used in [27] was used

and the actual ψ value instead of -1 was used in the bending capacity calculations. The same

input parameters used in Kesawan [11] FEA based parametric study discussed in Section 2

were used as inputs in the proposed Method 1, and the load ratio versus FRR curves were

obtained and then compared with those obtained from FEA to verify the applicability of this

method for HFC sections. These comparisons are given in Figs. 10(a) to (e) for LSF walls with

different wall configurations and made of G500 HFC sections with varying stud sizes. The

design FRR predictions agreed reasonably well with FEA results. Further details are given in

Section 4.2.

14

The purpose of this study is not to verify the ambient temperature design rules to predict the

capacity of HFC members, but to verify the ability of the proposed fire design rules to predict

the reduction in the structural performance of LSF walls made of HFC sections under fire

conditions. Therefore the comparisons between the FEA and design predictions in the above

and the following discussions are based on the load ratio, which is the ratio of the compression

capacities of HFC studs in fire and ambient conditions.

4.2. Improved Design Method 2

In this method, P-Δ effect was not considered at the stud supports, the thermal bowing equation

in [27] was used and the ψ value was taken as -1 in the bending capacity calculations. In

addition, simplified equations were used to determine the bending capacities at stud supports

and mid-height, and are discussed next.

Baleshan and Mahendran [27] proposed simplified equations to predict the bending capacity

of LSF floor joists subject to non-uniform temperatures. One of his methods recommends the

calculation of the bending capacity by considering a uniform temperature distribution equal to

the mid-web temperature across its cross-section. This calculation procedure thus avoids the

neutral axis shift calculation, which is caused by the variation in elastic modulus across its

cross-section due to the non-uniform temperature distribution, and proposes the following

equations.

webmidytteffmideffx fZM ,,,, (12)

max

,

,y

IZ

teff

teff (13)

Where; webmidytf , is the mid-web yield strength, teffZ , and teffI , are the effective section

modulus and the effective second moment of area calculated by assuming uniform elevated

15

temperature equal to the mid-web temperature, and maxy is the maximum distance to either hot

or cold flange from the centroid of the effective cross-section

Baleshan and Mahendran’s [27] design equations are applicable to floor joists where the hot

flange is under tensile stresses while cold flanges are subject to compression stresses, which

are similar to that of LSF wall stud at mid-height. However, at the LSF wall stud supports the

hot flange elements are subjected to compressive stresses while the cold flange elements are

subjected to tensile stresses. Therefore, Baleshan and Mahendran’s [27] equations cannot be

used to calculate the bending capacity at the stud supports. In this study the following equation

is proposed to determine the bending capacity at the stud supports, which is very similar to

Gunalan and Mahendran’s [6] equation.

hfytteffeffx fZM ,,sup,, (14)

Where; hfytf , is the outer hot flange yield strength

The above mentioned equations are adapted in the proposed Method 2 for the bending capacity

calculations of LSF wall studs at their mid-height and supports. Thereafter load ratio versus

FRR curves were obtained using Method 2. These curves are compared with the FEA results

in Figs. 10(a) to (e), which depict a good agreement between them. The FRR predictions of

LSF walls made of 150x45x15x1.6 and 90x45x15x1.6 mm G500 HFC sections (Fig. 10(a) and

(b)), based on the design Methods 1 and 2 are conservative except in single layered and

uninsulated LSF walls, where they are marginally unconservative by 1 to 2 minutes for the load

ratios between 0.1 and 0.3. As seen in Fig. 10(c), FRR predicted using Method 2 for LSF walls

made of 60x45x15x1.6 mm G500 HFC sections also exhibited a similar behaviour, except in

insulated and dual plasterboard layered LSF walls, where the predicted values are slightly

16

unconservative below the load ratio levels of 0.2. In all other instances, the predicted FRRs

agree well with FEA results.

Furthermore, FRR predicted using Method 2 matches well with the FEA results than those

using Method 1, particularly in insulated LSF walls made of 150x45x15x1.6 and 90x45x15x1.6

mm G500 HFC sections, below the load ratios of 0.5. However, in LSF walls made of

60x45x15x1.6 mm studs, although it is the opposite below the load ratios of 0.2, the FRR

differences between these two predictions are low. FRR were also predicted for LSF walls

made of 150x45x15x2.5 and 150x45x15x1.0 mm G500 HFC sections, which agree reasonably

well with the FEA results (Figs. 10(d) and (e)).

Overall the improved design Methods 1 and 2 based on AS/NZS 4600 [7] predict the FRR of

LSF walls made of HFC section studs reasonably well. The good agreement observed for studs

with different section sizes demonstrates that these design methods can be used for HFC section

studs with varying member and element slendernesses. Method 2 was found to provide a better

agreement with the FEA results, and therefore it is recommended for the fire design of LSF

walls.

5. Improved Design Methods Based on Eurocode 3 Part 1.3 [7]

Following sections detail the suitable improvements made to Gunalan and Mahendran’s [6]

Eurocode 3 Part 1.3 [8] based design rules where two sets of improvements were proposed.

5.1. Improved Design Method 1

The improvements discussed in Section 4.1 for AS/NZS 4600 [7] based design rules were also

adapted in the Eurocode based improved fire design rules. FRRs of different LSF walls made

of G500 HFC sections were then predicted, and compared in Figs. 11(a) to (e) with the FEA

results, which depict a good agreement between them.

17

5.2. Improved Design Method 2

The improvements made for AS/NZS 4600 [7] based design rules as discussed in Section 4.2

were also adapted in the Eurocode based design rules. As seen in Figs. 11(a) to (c), the design

method predictions match well with the FEA results. Further, the accuracy of Method 2 was

better than Method 1 for LSF walls made of 150x45x15x1.6 mm studs for all the load ratios,

and for LSF walls made of 90x45x15x1.6 and 60x45x15x1.6 mm studs, below the load ratios

of 0.25. In insulated LSF walls made of 90x45x15x1.6 and 60x45x15x1.6 mm studs for load

ratios below 0.25, the differences between Method 2 and FEA predictions were slightly higher

than those between Method 1 and FEA predictions. FRRs were also predicted for LSF walls

made of 150x45x15x2.5 and 150x45x15x1.0 mm G500 HFC section studs, which agree well

with FEA predictions.

Overall, the agreements between the FEA and design method predictions demonstrate that both

Eurocode based improved design methods can be used to predict the FRR of LSF walls made

of HFC section studs. However, Method 2 is recommended due to its simplicity.

To demonstrate the applicability to LSF wall studs made of other steel grades, FRR of LSF

walls made of G250 (low strength) 150x45x15x1.6, 90x45x15x1.6 and 60x45x15x1.6 HFC

section studs were also predicted using Method 2 based on AS/NZS 4600 and Eurocode 3 Part

1.3, and the results are compared with the design rule predictions in Figs. 12 and 13, which

also show a reasonable agreement between them as for G500 studs. Spread sheet based design

tools were developed and used to predict the load ratio versus FRR curves in all cases.

18

6. Design Methods based on Direct Strength Method

6.1. Background

Direct Strength Method (DSM) is an alternative approach to effective width method for

designing cold-formed steel members. It is an extension of the use of column curves for global

buckling where application to local and distortional buckling instabilities with their interactions

and post-buckling reserve capacities are considered [10, 28]. At present DSM is increasingly

used due to its simplicity in addressing complex buckling problems of cold-formed steel

members. It does not require the effective width calculations and iterations. Moreover, gross

sectional properties of the sections and their local, distortional and global buckling loads are

adequate for design [10]. DSM is included in Appendix 1 of AISI S100 [9]. In the past,

Landesmann and Camotim [29, 30] and Shahbazian and Wang [31] investigated the

applicability of the DSM to predict the lipped channel studs subject to uniform elevated

temperature distributions.

Shahbazian and Wang [31, 32] proposed modified DSM equations for LCS studs subject to

non-uniform temperature distributions. Since the DSM method requires the squash load of

studs they introduced the concept of effective squash load, which is defined as the axial load

that causes the cross-sections subjected to non-uniform temperature distribution to reach their

stress limits under combined axial and bending actions. They used the plastic axial load-

bending moment interaction diagrams to calculate the effective squash load. Generally studs

subject to bending actions do not reach the yield stress at all the locations, and they tend to fail

when the compressive flange reaches its yield stress as in the case of Feng and Wang [21],

Baleshan and Mahendran [27] and Gunalan and Mahendran [6]. Therefore, the accuracy of

Shahbazian and Wang’s [31] DSM in determining the effective squash load needs to be further

investigated since plastic state is not attained in cold-formed columns subject to non-uniform

19

temperature distributions. Also their method is complex as it needs the plastic axial force

moment interaction curve for each temperature distribution. Shahbazian and Wang [31, 32] did

not consider the magnified moment due to the thermal bowing at the mid-stud height. This

magnified moment is considered by Gunalan and Mahendran [6], Ranby [19], Kaitila [20],

Feng and Wang [21], Zhao et al. [22] and Alfawakhiri [33], in their proposed effective width

method design rules as it is significant. Since the agreement between the FEA results and DSM

predictions was not good, Shahbazian and Wang [31] modified the DSM equations given by

Schafer [10] to improve their accuracy. They considered three different temperature ratios

between the exposed and unexposed flanges (3.0, 2.0 and 1.5) in their FEA and DSM

calculations. Shahbazian and Wang [31] stated that for each temperature profile (temperature

ratio), the FEA results are within a narrow band, however, the overall comparison between the

FEA results and the DSM predictions show large discrepancies in some cases.

Batista-Abreu and Schafer [34] evaluated the use of DSM method to determine the LCS stud

capacity using the compression capacity DSM equations. They computed the elastic buckling

capacities using their finite strip analysis program CUFSM with temperature dependent

mechanical properties. They calculated the squash load based on the weighted average (fyt) and

minimum (fymin) yield strengths. The predictions using the weighted average yield strength were

found to be unconservative while those using the minimum yield strength were found to be

conservative, and hence it was recommended for design. The method using the minimum yield

strength was also found to be unconservative in some cases, and further there are large

differences between the FEA and the DSM predictions. They have also not considered the

effects of thermal bowing and neutral axis shift, and their magnifications separately since they

used a uniform temperature distribution by assuming the whole section to have either weighted

average or minimum yield strength.

20

It is noteworthy to mention that acceptable DSM guidelines are still not developed for beam-

column members. Members subjected to non-uniform temperature distributions should be

treated as an advanced beam-column problem since they are subjected to compression and

bending actions while their mechanical properties vary across their cross-section. Therefore

developing DSM based equations for LSF wall studs subject to non-uniform temperature

distributions without developing equations for general beam-column members is not desirable.

This might not give accurate results as shown in [31,34]. Furthermore, it is not essential to

develop new DSM based equations for beam-column members as compression and bending

capacities could be found separately and then checked for combined bending and compression

actions using AISI S100 [9] or AS/NZS 4600 [7] equations. This is also considered much easier

than the other available design methods. The proposed DSM based design method built on the

above concept is discussed next.

6.2. DSM Based Design Method

The compression and bending capacities of LSF wall studs were calculated separately and then

the overall capacity was checked for combined bending and compression interactions. The

basic DSM equations were used to calculate the compression and bending capacities. However,

suitable guidelines have been given on the parameters such as global buckling load, local

buckling load and gross section yielding capacity/squash load to be used in these equations.

The DSM based equations are given next.

Member capacity of a column

tsetce NN ,,

2

658.0 if 5.1c (15a)

tsetce NN ,2,

877.0

if 5.1c (15b)

where

21

tclx

tse

N

N

,,

, (16)

tseN , is the squash load, tclxN ,, is the buckling capacity and is given next,

2

,,

2

,,L

IEN

igrit

tclx

(17)

Where; L is the stud length, Et,i and Igr,i are the elastic modulus and the second moment

of area of element i at elevated temperature

Local buckling capacity of a column

tcetx NN ,, if 5.1c (18a)

tcetx NN ,

4.0

tce,

tol,

4.0

tce,

tol,

,N

N

N

N15.01

if 5.1c (18b)

where

tol

tce

N

N

,

, (19)

txN , is the section capacity at elevated temperature, tolN , is the local buckling load at elevated

temperature and is given as,

20

,

20,,E

ENN

webmidt

oltol

(20)

Where; 20,olN is the local buckling load at ambient temperature found from buckling

analysis by using finite element/strip analysis software application, webmidtE , and 20E

are the elastic modulus values at the mid-web elevated temperature and the ambient

temperature, respectively.

22

Bending capacity calculations

At the stud mid-height

webmidyttmidcetmidx fZMM ,,,,, if 776.0 (21a)

tmidcetmidx MM ,,

4.0

tmid,ce,

tol,

4.0

tmid,ce,

tol,

,,M

M

M

M15.01

if 776.0 (21b)

At the stud support

HFyttcetx fZMM ,sup,,sup,, if 776.0 (22a)

tcetx MM sup,,

4.0

tsup,ce,

tol,

4.0

tsup,ce,

tol,

sup,,M

M

M

M15.01

if 776.0 (22b)

where

tol,

tmid,ce,

M

Mmid (23a)

tol,

tsup,ce,

supM

M (23b)

tZ is the section modulus, HFytf , is the outer hot flange temperature, tmidxM ,, and txM sup,, are the

section capacities at stud mid-height and support, respectively, tolM , is the local buckling

moment at elevated temperature and is given as,

20

20,,E

EMM t

oltol (24)

20,olM is the local buckling moment at ambient temperature found from buckling

analysis

After calculating the ultimate bending and compression capacities separately, the structural

capacity of the LSF wall studs at their mid-height and supports subject to combined bending

and compression actions can be obtained by using the simplified bending-compression

23

interaction formula given by Gunalan and Mahendran [6] based on AS/NZS 4600 (Eqs. 25(a)

and (b)), and they are given next.

At the stud mid-height

1,,

*

,

*

tmidx

mid

tx M

M

N

N (25a)

At the stud support

1sup,,

*

sup

,

*

txtx M

M

N

N (25b)

txN , is the compression capacity of the LSF wall stud, tmidxM ,, and txM sup,, are the section

moment capacities at the stud mid-height and support, *

midM is the total bending moment

induced in the LSF wall stud due to thermal bowing, neutral axis shift and their magnifications

(refer Eq. 9).

The important techniques/assumptions adapted in these DSM based design rules are discussed

next.

The squash load (Nse,t) of the stud is the summation of the multiplication of the area of an

element (i) of the stud by its elevated temperature yield strength.

Local buckling load (Nol,t) of the LSF wall stud subject to non-uniform temperature

distributions under pure compression is calculated by multiplying the ambient temperature

local buckling load obtained from THIN-WALL or CUFSM elastic buckling analysis by the

elevated temperature elastic modulus reduction factor corresponding to the mid-web

temperature. The same principle is applied to determine the local buckling load (Mol,t) of

studs subjected to pure bending.

24

Euler buckling equation (Eq. 17) is used to determine the global buckling load (Nx,cl,t), but

the differences in elastic modulus between the different elements of studs are considered.

Further the lateral torsional buckling stress and the flexural buckling stress about the minor

axis of the stud need not be calculated as they are eliminated by the lateral restraints

provided by the plasterboards.

Further, unlike the improved design Methods 1 and 2 proposed in Sections 4 and 5 based on

AS/NZS 4600 [7] and Eurocode 3 Part 1.3 [8], the effects of neutral axis shift due to the

difference in the effective widths of hot and cold flange elements caused by local buckling

are not considered in the DSM based design method as effective width is not used in DSM.

However, neutral axis shift due to thermal bowing and elastic modulus variation across the

section were considered.

Bending moment capacity of LSF wall stud at its mid-height is calculated by multiplying

the weighted average section modulus of the stud by the web yield strength. Bending

moment capacity of LSF wall stud at its support is calculated by multiplying the weighted

average section modulus of the stud by the hot flange yield strength. In bending capacity

calculations, it is assumed that the lateral torsional buckling is completely eliminated due to

the provision of lateral restraints to the studs by the plasterboards.

A spread sheet based design tool was developed based on the proposed DSM based design

rules. It was used to produce the load ratio versus FRR curves for different LSF walls made of

HFC section studs. These predictions were then compared with the FEA results. As seen in

Figs. 14(a) to (c), the predicted FRRs of LSF walls made of 150x45x15x1.6, 90x45x15x1.6

and 60x45x15x1.6 mm HFC studs agree well with those obtained from FEA, and importantly

the predicted FRRs fall on the conservative side. The load ratio versus FRR curves of LSF wall

made of 150x45x15x2.5 mm HFC studs also show similar behaviour (Fig. 14(d)). Although

the FRR predictions of LSF walls made of 150x45x15x1.0 mm studs agree well with FEA

25

results, the predicted FRR values are slightly unconservative (Fig. 14(e)). Overall, the closer

agreement between the FRR predicted by using the proposed DSM based design method and

the FEA confirms the applicability of the proposed DSM based design rules to determine the

FRR of LSF walls made of HFC section studs.

As part of this research study, fire tests of LSF walls made of welded HFC sections and finite

element analyses were also conducted [1], and their FRR results are given in Table 1. The FRR

of tested wall panels were predicted using the proposed design rules in this paper using the

measured time-temperature profiles [1,13] and elevated temperature mechanical properties

[15]. Comparison of FRR in Table 2 show that both fire test and FEA results show a reasonable

agreement with the design rule predictions. Inclusion of fire test results in this comparison

provides further confirmation of the accuracy of the proposed design rules in this paper.

The applicabilty of the improved effective width design methods based on AS/NZS 4600 [7]

and Eurocode 3 Part 1.3 [8], and DSM method [7,9] to predict the capacity/FRR of LSF walls

made of G250 and G500 HFC sections of different depths (60-150 mm) and thicknesses (1.0-

2.5 mm) has been verified in this study. These design rules can be applied to any other HFC

sections if the accurate mechanical property reduction factors and time-temperature profiles

are known. The effective width method has been verified for lipped channel sections [6].

However, the DSM method should be verified for lipped channel sections..

7. Conclusions

This paper has presented the details of improved design rules to predict the structural capacity

of the new hollow flange channel (HFC) stud sections subject to non-uniform temperature

distributions in order to determine the FRR of LSF walls. Since none of the previous research

studies had proposed design guidelines for LSF walls made of HFC sections in fire, Gunalan

26

and Mahendran’s [6] design rules for lipped channel section studs in fire were selected to verify

their accuracy for HFC studs. Suitable modifications were made to Gunalan and Mahendran’s

[6] design rules based on AS/NZS 4600 [7] and Eurocode 3 Part 1.3 [8] for improved accuracy

and simplifications. Two improved methods were proposed based on each of the design

standards considered. Furthermore, design rules based on the direct strength method were also

proposed to determine the structural capacity of HFC sections subject to non-uniform

temperature distributions and thus the FRR of LSF walls made of HFC section studs. Spread

sheet based design tools were developed based on all the proposed design methods where the

time-temperature profiles, stud dimensions and the elevated temperature mechanical properties

were the input, and the load versus FRR curves of LSF walls were the output. These design

tools were then used to produce the load ratio versus FRR curves of insulated and uninsulated

LSF walls made of HFC sections with varying sizes and lined with single or dual plasterboard

layers. These curves were compared with those found from FEA. The FRR predictions using

the proposed design methods agreed reasonably well with the FEA results, thus confirming the

applicability of all the proposed design rules to predict the structural capacity of HFC studs

subjected to non-uniform temperature distributions. Design Method 2 based on AS/NZS 4600

and Eurocode 3 Part 1.3 design rules, and the DSM based design method were recommended

based on their simplicity and accuracy. The proposed design methods would facilitate and

advance the use of HFC sections in LSF wall systems, and further enable a performance based

approach to structural fire design of LSF walls made of HFC section studs. They can also be

used for LSF walls made of studs with other cross-sections.

Acknowledgements

The authors would like to thank QUT for providing all the necessary support with the full scale

fire tests and for providing the high performing computing facilities, and QUT and Australian

Research Council for providing the financial support to conduct this research project.

27

References

1. Kesawan S, Mahendran M. (2015), Fire Tests of Load-Bearing LSF Walls Made of Hollow

Flange Channel Sections, Journal of Construction Steel Research, J Constr Steel Res,

http://dx.doi.org/10.1016/j.jcsr.2015.07.020.

2. Anapayan, T., and Mahendran, M. Mahaarachchi D. (2011), Section Moment Capacity

Tests of LiteSteel Beams, Thin-Walled Structures, Vol. 49(4), pp. 502-512.

3. Keerthan, P., and Mahendran, M. (2010), Experimental studies of Hollow Flange Channel

Beams Subject to Combined Bending and Shear Actions, Engineering Structures, Vol. 77,

pp. 129-40.

4. Jatheeshan, V. and Mahendran M. (2015), Experimental Study of LSF Floors Made of

Hollow Flange Channel Section Joists under Fire Conditions, Journal of Structural

Engineering, ASCE, Vol. 142 (2), pp. 04015134-1-14 (submitted).

5. Jatheeshan, V. and Mahendran M. (2015), Numerical Study of LSF Floors Made of Hollow

Flange Channels in Fire, Journal of Constructional Steel Research, ASCE, Vol. 115, pp.

236-51.

6. Gunalan, S. and Mahendran, M. (2013), Development of Improved Fire Design Rules for

Cold-formed Steel Wall Systems, Journal of Constructional Steel Research, Vol. 88, pp.

339-362.

7. Standards Australia (SA) (2005), Cold-formed Steel Structures, AS 4600, Sydney,

Australia.

8. EN 1993-1-3 (2006), Eurocode 3: Design of Steel Structures, Part 1-3: General Rules -

Supplementary Rules for Cold-formed Members and Sheeting, European Committee for

Standardization, Brussels.

9. AISI S100 (2012), North American Specification for the Design of Cold-formed Steel

Structural Members, American Iron and Steel Institute, U.S.A.

28

10. Schafer, B.W. (2008), The Direct Strength Method of Cold-formed Steel Member Design,

Journal of Constructional Steel Research, Vol. 64(7-8), pp. 766–778.

11. Kesawan S. Fire performance and design of light gauge steel frame wall systems made of

hollow flange sections. PhD Thesis, School of Civil Engineering and Built Environment,

Queensland University of Technology, Brisbane, Australia; 2015.

12. Kesawan, S. and Mahendran, M. (2015), Thermal performance of Load-bearing Walls

Made of Cold-formed Hollow Flange Channel Sections in Fire, Fire and Materials, 2015,

DOI: 10.1002/fam.2337.

13. Kesawan S, Mahendran M. (2015), Predicting the Performance of LSF Walls Made of

Hollow Flange Sections in Fire. Thin-Walled Struct, Vol. 98(A), pp. 111-26.

14. ISO 834 -1, (1999), Fire Resistance Tests - Elements of Building Construction, Part 1:

General Requirements, International Organization for Standardization, Geneva,

Switzerland.

15. Kesawan S, Jatheeshan, V, Mahendran M. Elevated temperature mechanical properties of

welded and cold-formed hollow flange sections. Constr and Build Materials 2015;87:86-

99.

16. Dolamune Kankanamge, N. and Mahendran, M. (2012), Mechanical Properties of Cold-

formed Steels at Elevated Temperatures, Thin-Walled Structures, Vol. 49, pp. 26-44.

17. Klippstein, K.H. (1980), Strength of Cold-Formed Studs Exposed to Fire, American Iron

and Steel Institute. Washington, DC.

18. Gerlich, J.T, Collier, P.C.R., and Buchanan, A. H. (1996), Design of Light Steel-Framed

Walls for Fire Resistance, Fire and Materials, Vol. 20(2), pp. 79-96.

29

19. Ranby, A. (1999), Structural Fire Design of Thin Walled Steel Sections, Licentiate Thesis,

Department of Civil and Mining Engineering, Lulea University of Technology,

Stockholm, Sweden.

20. Kaitila, O. (2002), Finite Element Modelling of Cold-formed Steel Members at High

Temperatures, Master’s Thesis, HUT, Otakaari, Finland.

21. Feng, M. and Wang, Y.C. (2005), An Analysis of the Structural Behaviour of Axially

Loaded Full-scale Cold-formed Thin-Walled Steel Structural Panels Tested under Fire

Conditions, Thin-Walled Structures, Vol. 43, pp. 291-332.

22. Zhao, B., Kruppa, J., Renaud, C., O’Connor, M., Mecozzi, E., Apiazu, W., Demarco, T.,

Karlstrom, P., Jumppanen, U., Kaitila, O., Oksanen, T. and Salmi, P. (2005), Calculation

rules of lightweight steel sections in fire situations, Technical Steel Research, European

Union.

23. Gunalan, S. and Mahendran, M. (2013), Review of Current Fire Design Rules for Cold-

formed Steel Wall Systems, Journal of Fire Sciences, Vol. 32(1), pp. 3-34.

24. Ariyanayagam, A.D. and Mahendran, M. (2014), Fire Performance and Design of Load

Bearing Light Gauge Steel Frame Wall Systems Exposed to Realistic Design Fires,

Proceedings of the Conference of Structural Engineering in Australasia, Auckland, New

Zealand.

25. Cooke, G.M.E. (1987), Thermal Bowing and How it Affects the Design of Fire Separating

Construction, Fire Research Station, Building Research Establishment, Herts.

26. EN 1993-1-1 (2005), Eurocode 3: Design of Steel Structures, Part 1-1: General Rules,

European Committee for Standardization, Brussels.

27. Baleshan, B. and Mahendran, M. (2016), Fire Design Rules to Predict the Moment

Capacities of Thin-walled Floor Joists Subject to Non-uniform Temperature Distributions,

Vol 105, pp. 29-43.

30

28. Yu, C. and Schafer, B.W. (2007), Simulation of Cold-formed Steel Beams in Local and

Distortional Buckling with Applications to the Direct Strength Method, Vol. 63(5), pp.

581-590.

29. Landesmann, A., and Camotim, D. (2011), On the Distortional Buckling, Post-buckling

and Strength of Cold-formed Steel Lipped Channel Columns under Fire Conditions,

Journal of Structural Fire Engineering, Vol. 2(1), pp.1–19.

30. Landesmann, A., and Camotim, D. (2016), Distortional Failure and DSM Design of Cold-

formed Steel Lipped Channel Beams under Elevated Temperature, Thin-walled Structures,

Vol. 98, pp.75-93.

31. Shahbazian, A. and Wang, Y.C. (2011). Application of the Direct Strength Method to

Local Buckling Resistance of Thin-walled Steel Members with Non-Uniform Elevated

Temperatures Under Axial Compression, Thin-Walled Structures, Vol. 49(12), pp. 1573-

1583.

32. Shahbazian, A. and Wang, Y.C. (2011), Calculating the Global Buckling Resistance of

Thin-walled Steel Members with Uniform and Non-uniform Elevated Temperatures Under

Axial Compression, Thin-Walled Structures, Vol. 49(11), pp. 1415-1428.

33. Alfawakhiri, F., Sultan, M.A., and MacKinnon, D.H. (1999), Fire Resistance of Load

Bearing Steel-Stud Walls Protected with Gypsum Board, Journal of Fire Technology, Vol.

35, pp. 308-335.

34. Batista-Abreu, J.C. and Schafer, B.W. (2014), Stability and Load-Carrying Capacity of

Cold-formed Steel Compression Members at Elevated Temperatures, Proceedings of the

Annual Stability Conference Structural Stability Research Council Toronto, Canada.

1

Figure 1: 150x45x15x1.6 mm HFC Sections

Figure 2: Full Scale Fire Test Set-up

LSB t = 1.6 mm

Furnace

Test Wall Specimen

Support Frame

2

Figure 3: Non-uniform Temperature Distribution in LSF Wall Studs and

Neutral Axis Shift

Note; X is the initial centroid of the stud, Y is the position of centroid after only

considering thermal bowing, Z is the position of centroid after considering thermal

bowing and neutral axis shift, e∆T is the centroidal shift due to thermal bowing and

e∆E is the centroidal shift due to neutral axis shift and e is the effective eccentricity

Figure 4: LSF Wall Configurations

e∆E

Z

Ambient side

Y

X

e∆T

e

Fire side

+

- Uniform

temperature

distribution

Linear

temperature

distribution

Linear

temperature

distribution Ambient side

Fire side

(a) Non-insulated LSF walls lined with dual plasterboard layers

Pb 1-Outer Fire Side

Layer

Pb 3-Inner Ambient

Side Layer Pb 4-Outer Ambient Side Layer

Pb 3-Ambient Side Layer (b) Non-insulated LSF walls lined with single plasterboard layer

Stud A Stud B Stud C Stud D Pb 2-Inner Fire Side

Layer Outer Fire Side

Fire Side

(FS)

Ambient Side

(AS)

Outer Hot Flange (OHF)

Inner Hot Flange (IHF)

Mid-web

Inner Cold Flange (ICF) Outer Cold Flange (OCF)

Vertical Plasterboard

Joint Location

Stud A Stud B Stud C Stud D

Pb 2-Fire Side

Layer

(c) Insulated LSF walls lined with dual plasterboard layers

50 mm thick insulation Stud A Stud B Stud C Stud D

Pb 2-Inner Fire Side

Layer Outer Fire Side Pb 3-Inner Ambient

Side Layer Pb 4-Outer Ambient Side Layer

Pb 1-Outer Fire Side

Layer

3

Figure 5: Loading and Boundary Conditions Used in FEA [13]

(a) Yield Strength Reduction Factors of G250 and G500 Steels

Restrained

DOF ‘234’

Restrained

DOF ‘1234’

Restrained

DOF ‘3’

Restrained

DOF ‘3’

Restrained DOF ‘3’ at 300 mm spacing

(Lateral restraints provided by the plasterboards)

300 mm

Y

Z

X

Load

G250 G500

4

(b) Elastic Modulus Reduction Factors of G250 and G500 Steels

Figure 6: Mechanical Property Reduction Factors in Dolamune Kankanamge

and Mahendran (2011)

(a) Outer Hot Flange - Uninsulated LSF Walls Lined with Single Plasterboard Layer

5

(b) Outer Cold Flange - Uninsulated LSF Walls Lined with Single Plasterboard

Layer

(c) Outer Hot Flange - Uninsulated LSF Walls Lined with Dual Plasterboard Layers

6

(d) Outer Cold Flange - Uninsulated LSF Walls Lined with Dual Plasterboard Layers

(e) Outer Hot Flange - Insulated LSF Walls Lined with Dual Plasterboard Layers

7

(f) Outer Cold Flange - Insulated LSF Walls Lined with Dual Plasterboard Layers

Figure 7: Time-Temperature Profiles of HFC Studs of Varying Thicknesses

Used in Three LSF Wall Configurations

Note: The above time-temperature profiles are valid for LSF walls made of studs of

different web depths, and 45 and 15 mm flange width and lip length, respectively.

(a) AS/NZS 4600 Based Design Rules

8

(b) Eurocode 3 Based Design Rules

Figure 8: FRR Predictions with and without the Effect of Magnified Moment at

the Stud Supports Using Eurocode 3 and AS/NZS 4600 Based Design Rules

FEA: FEA results; Des: Design rule predictions

Unins-Sing: Uninsulated LSF wall system lined with single plasterboard layer on both sides

Unins-Dual: Uninsulated LSF wall system lined with Dual plasterboard layer on both sides

Ins-Dual: Insulated LSF wall system lined with dual plasterboard layers on both sides

(a) AS/NZS 4600 Based Design Rules

9

(b) Eurocode 3 Based Design Rules

Figure 9: FRR Predictions Using Eurocode 3 and AS/NZS 4600 Based Design

Rules Considering Different Buckling Factors in Bending Capacity Calculations

(a) 150x45x15x1.6 mm HFC Sections

10

(b) 90x45x15x1.6 mm HFC Sections

(c) 60x45x15x1.6 mm HFC Sections

11

(d) 150x45x15x2.5 mm HFC Sections

(e) 150x45x15x1.0 mm HFC Sections

Figure 10: FRR of LSF Walls Made of G500 HFC Section Studs Using AS/NZS

4600 Based Improved Design Methods 1 and 2, and FEA

FEA: FEA results; Des: Design rule predictions

Unins-Sing: Uninsulated LSF wall system lined with single plasterboard layer on both sides

Unins-Dual: Uninsulated LSF wall system lined with Dual plasterboard layer on both sides

Ins-Dual: Insulated LSF wall system lined with dual plasterboard layers on both sides

M1: Method 1, M2: Method 2

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 20 40 60 80 100 120 140 160 180 200 220 240

Load

Rat

io

Time (minutes)

FEA - Unins-Dual Des - Unins-Dual-M1 Des - Unins-Dual-M2

FEA - Unins-Sing Des - Unins-Sing-M1 Des - Unins-Sing-M2

FEA - Ins-Dual Des- Ins-Dual-M1 Des - Ins-Dual-M2

12

(a) 150x45x15x1.6 mm HFC Sections

(b) 90x45x15x1.6 mm HFC Sections

13

(c) 60x45x15x1.6 mm HFC Sections

(d) 150x45x15x2.5 mm HFC Sections

14

(e) 150x45x15x1.0 mm HFC Sections

Figure 11: FRR of LSF Walls Made of G500 HFC Section Studs Using

Eurocode Based Improved Design Methods 1 and 2, and FEA

(a) 150x45x15x1.6 mm HFC Sections

15

(b) 90x45x15x1.6 mm HFC Sections

(c) 60x45x15x1.6 mm HFC Sections

Figure 12: FRR of LSF Walls Made of G250 HFC Section Studs Using AS/NZS

4600 Based Improved Design Method 2 and FEA

16

(a) 150x45x15x1.6 mm HFC Sections

(b) 90x45x15x1.6 mm HFC Sections

17

(c) 60x45x15x1.6 mm HFC Sections

Figure 13: FRR of LSF Walls Made of G250 HFC Section Studs Using

Eurocode Based Improved Design Method 2 and FEA

(a) 150x45x15x1.6 mm HFC Sections

18

(b) 90x45x15x1.6 mm HFC Sections

(c) 60x45x15x1.6 mm HFC Sections

19

(d) 150x45x15x2.5 mm HFC Sections

(e) 150x45x15x1.0 mm HFC Sections

Figure 14: FRR of LSF Walls Made of G500 HFC Section Studs Using DSM

Based Improved Design Method and FEA

3

Table 1: Fire Test and FEA Results [1, 8]

Note: * - based on stability criterion, FRR – Fire Resistant Rating, FEA – Finite

Element Analysis

Wall Configurations Load

Ratio

Fire Tests-

FRR*(mins.)

FEA –

FRR*(mins.)

Transient

State

Steady

State

Test 1

0.4 180 183 184

Test 2

0.2 205 208 209

Test 3

0.2 136 125 127

Test 4

0.2 182 180 180

Test 5

0.6 138 136 137

3

Table 2: FRR from Fire Tests, FEA and Design Rule Predictions

Test

Number

FRR*(mins.)

Fire Test FEA

AS/NZS

4600 -

Design

Method 2

Eurocode -

Design

Method 2

DSM

Method

1 180 183 178 181 192

2 205 208 199 201 205

3 136 125 103 109 113

4 182 180 176 179 175

5 138 136 128 133 135

Note: * - based on stability criterion