Fire performance of cold-formed steel sections Dr Shanshan Cheng, Professor Long-yuan Li & Dr Boksun Kim

School of Engineering, Plymouth University

Aim: Provide a better understanding of buckling behaviour of CFS members in fire

Introduction

Background

Design availability?

Temperature distribution?

Stress distribution? Change of

buckling modes?

Cold-formed steel (CFS) has been widely used in buildings and bridges due to advantages of high strength-to-weight ratio, ease of fabrication and flexibility of sectional profiles, which lead to cost-effective designs and waste reduction.

Methodology

Linear buckling analysis

MethodLongitudinal

stress distribution

Pre-buckling analysis

Non-uniformlongitudinal stress by thermal bowing

CUFSM [3]

Yes, but thermal expansion and

variation of elastic modulus due to

non-uniform sectional

distribution of temperature are not considered

no

Modified FSM Yes Yes

Conclusions & future work

References[1] http://fairdealindustries.com/c-z-purlins.html [2] A. Shahbazian & Y.C. Wang. Thin-walled Structures 2011, 49(11), 1415-

1428. [3] Z. Li, & B.W. Schafer. 20th CCFSS, Nov 3&4, 2010, USA. [4] X.T. Chu, Z.M. Ye, R. Kettle & L.Y. Li. Thin-Walled Structures 2005,

43(4), 531-542.[5] N.D. Kankanamge & M. Mahendran. Thin-Walled Structures 2012,

61, 213-228.

• Thermal bowing can significantly affect the global buckling behaviour but has almost no effect on the local buckling behaviour of columns.

• There is no remarkable difference in critical moment of local buckling between pure bending and UDL regardless the temperature distribution. However, considerable difference was found in critical moment of lateral-torsional buckling between pure bending and UDL.

• Fire expose surface has significant effect on the buckling of beams. The lowest critical buckling moment occurs when the fire is exposed on the compression side of the beam.

• Shift of buckling mode happens in beams when fire is exposed on the compressive side.

Further FE analysis will be carried out on the failures of beams caused due to local and distortional buckling.

Fig.1 Examples of application of CFS members[1].

xzxy zyx κκεε +−= 0)( )(),()( TTx thεσεε σ +=

( )thxzxyTT zyEE εκκεεσ σσ −+−== 0

+++

=

−

3

2

1

1

332313

232212

1312110

FMFMFN

kkkkkkkkk

y

z

x

xz

xy

κκε

Fig.2 Examples of CFS channels in fire[2].

Fire resistance of CFS has been a key factor impeding its application. The buckling behaviour of CFS exposed to fire on one side is still not fully understood. The availability of current design methods for CFS under non-uniform temperatures should be further examined.

Nonlinear finite element analysis

Application of direct strength method

Pre-buckling analysis

Modified Finite strip method (Modified FSM)Table 1 Comparison between CUFSM and modified FSM

Finite element method

Bernoulli beam theory is used to conduct pre-buckling stress analysis on CFS channels under non-uniform temperatures.

Fig.5 Axial stress distribution in a column/beam(L=6000mm, h=200mm, b=75mm, c=20mm, t=2mm, T=600oC).

(a) Column without thermal bowing effect, (b) column with thermal bowing effect, (c) beam.

(a) (b) (c)

Objective: Develop MATLAB programme to investigate the fire behaviour of CFS.Carry out numerical studies to examine current design methods.

Global buckling failure of simply supported CFS channel members under non-uniform temperatures were investigated. The failure modes were shown in consistence with the linear buckling modes given by modified FSM (Fig. 6 and Fig. 7).

Fig.8 Failure modes of CFS channel members under non-uniform temperatures (h=200mm, b=75mm, c=20mm, t=2mm).

(a) Column (L=4m) and (b) beam (L=3m).

(a)

(b)

The DSM design formulas are examined using nonlinear FEA results. It was found that: • For columns the DSM design curve proposed by Shahbazian

and Wang[2] is applicable for slender members but would be unsafe for intermediate members.

• For beams the DSM design curve proposed by Kankanamgeand Mahendran[5] for CFSs under uniform temperatures would be unsafe when applied to the case of non-uniform temperatures.

Direct strength method (DSM)),,,,( ycrdcrlcren PPPPfP = ),,,( ycrdcrlcren MMMMfM =

Fig.3 Finite element model of CFS

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

λc=(Py/Pcre)0.5

Pne

/Py o

r PFE

/Py

FEM resultsDSM by AISIDSM by Shahbazian (2011)

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

λc=(My/Mcre)0.5

Mne

/My o

r MFE

/My

FEM resultsDSM by AISIDSM by Kankanamge (2012)

Fig.9 Comparison of FEA results with different DSM design curves. (a) Column and (b) beam.

(b)(a)

The non-uniform stress distribution and reduced material properties at elevated temperatures are input in the modified FSM to carry out linear buckling analysis.

Local buckling is dominant buckling mode until the column becomes very long.

Thermal bowing has almost no influence on the local buckling. The effect of thermal bowing on lateral-torsional buckling

depends on the column length.

• Columns

The critical bending moment is higher in UDL than in PB. The worst critical moment is when the fire is applied on the

compression side of the section The effect of temperature is much greater on the critical

moments of distortional and lateral-torsional buckling than that of local buckling.

• Beams

Fig.4 DSM design curves for columns using AISI

Fig.7 Buckling curves of channel-section beams (h=200mm, b=75mm, c=20mm, t=2mm). (a) PB under uniformly distributed temperature, (b) PB

with fire on tensile side, (c) PB with fire on compression side, and (d) comparisons between PB and UDL (PB stands for Pure bending and UDL

stands for uniformly distributed transverse loading).

(a)

(c) (d)

(b)

0.3 0.6 0.9 3 6 9

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Member length, m

Mcr

/My,

20o C

T=20oC

T=600oC, uniform temperature

T=600oC, fire on tension side

T=600oC, fire on compression side

T=20oC

T=600oC, uniform temperature

T=600oC, fire on tension side

T=600oC, fire on compression side

Pure bendingUniformly distributed loading

Fig.6 Buckling curves of channel-section columns under axial compression (h=200mm, b=75mm, c=20mm, t=2mm). (a) Uniformly

distributed temperature and (b) non-uniformly distributed temperature.

(a) (b)