Notional versus one-dimensional charring rates of timber
Jürgen KÖNIG
Tekn. dr
Trätek – Swedish Institute
for Wood Technology
Research
Box 5609
SE-114 86 Stockholm
Sweden
[email protected]
After civil engineering studies
at TU Berlin and some years of
consultancy, he worked at
Royal Institute of Technology
in Stockholm. Doctoral thesis
on lightweight steel structures
in 1978. From 1985 senior
researcher at Trätek. König is
Chairman of CEN/TC 250/SC 5
and co-ordinator of Eurocode 5.
Summary
In the Fire Part of Eurocode 5 one-dimensional and notional charring rates are given. In order to
simplify the determination of the load bearing capacity of cross sections, a notional charring rate is
given to be used on all fire exposed sides of the cross section. It is shown that these notional
charring rates can also be used for very small or narrow cross sections with a great influence of twodimensional heat transfer, for example very narrow timber joists exposed on three sides.
The use of the one-dimensional charring rate is only possible when zones with two-dimensional
heat flux, causing increased charring, are taken into account, that is roundings of the char line at
corners must be separately taken into account. A criterion is derived for the minimum width of
timber members permitting the use of the one-dimensional charring rate.
Key words: timber, structures, design, fire, charring rate, char depth, calculations, codes.
1.
Introduction
The Fire Part of Eurocode 5 (EN 1995-1-2) [1] makes a distinction between
· the charring rate for one-dimensional charring b0, which is valid for one-dimensional heat
transfer as in the case of a semi-infinite slab, or in parts of cross-sections where heat transfer is
predominantly one-dimensional;
· the notional charring rate bn which implicitly includes effects of two-dimensional heat transfer
in the vicinity of corners and large fissures, that is the corner roundings need not be taken into
account separately.
For softwood, the one-dimensional charring rate is given as 0,65 mm/min; the notional charring
rates for glued-laminated and solid timber are 0,7 and 0,8 mm/min respectively. For solid timber,
the relationship between the notional and one-dimensional value of charring rate is given by
bn
0,8
for solid timber
(1)
=
= 1, 23
b0 0, 65
bn
0, 7
for glued-laminated timber
(2)
=
= 1, 08
b0 0, 65
Performing heat transfer calculations, it has been shown [2] that this ratio is a reasonable
approximation when the real residual cross-section is replaced by a rectangular cross-section such
that the section modulus is the same. See figure 1. For small cross sections, e.g. a cross section of
size 45 mm ´ 120 mm, the figure shows that this approximation is safe during the first 9 to 10
minutes of fire exposure. For larger times the ratio of 1,23 would be non-conservative, however this
stage is normally not reached since the timber member would fail due to exhaustion of mechanical
resistance.
The values of figure 1 include that the char depth on the narrow side is greater than the char depth
on the wide side. For example, for the cross-section 45 mm ´ 120 mm, at 15 minutes the calculated
char depth is 10,4 mm while it is 14,7 mm on the narrow side, that is it is 41 % larger on the narrow
side. The reason is that heat flux is
pronouncedly two-dimensional.
In the following it is shown that
1,5
the simplified assumption of a
1,4
fixed value of bn/b0 can also be
applied for small narrow cross1,3
sections, where the charring rate of
1,2
the narrow side, after some time,
increases considerably compared
1,1
to the charring rate of the wide
side of the cross-section.
1
0
20
40
60
In EN 1995-1-2 [1] the concept of
Time [min]
notional charring rates is also
applied in annex C dealing with
Figure 1 — Charring rate ratios vs. time: Comparison of insulated timber frame assemblies,
calculated values with Eurocode 5 for solid (S) and glued- however with a notional charring
laminated (G) timber cross sections exposed on four sides [2] rate also being dependent on the
dimension of the cross-section, see
also [3]. In that case, the use of the real shape of the residual cross-section would imply
considerable difficulties for the designer.
EC 5 solid timber
EC 5 glulam
G 200 x 800; W
G 140 x 300; W
S 100 x 200; W
S 45 x 120; W
G 200 x 800; I
G 140 x 300; I
S 100 x 200; I
S 45 x 120; I
b n/b 0
1,6
2.
Test results by van de Haar
Van de Haar [4] made two fire tests on loaded floor assemblies consisting of two timber joists of
dimension 59 mm ´ 196 mm spaced at 650 mm and a decking consisting of 19 mm plywood and 10
mm calcium silicate board on top of it. The joists were initially unprotected and exposed to the fire
on three sides. Since the loading was different, the failure times were different: 25 minutes for floor
1 and 32 minutes for floor 2.
Figures 2 and 3 show some of the residual cross sections recorded after the fire tests. The graphs
were reproduced from the original report [4] by recording the co-ordinates of the border of the
residual cross-section using a digitizer. In order to illustrate the degree of charring the shapes of the
original cross-sections are also shown; their exact horizontal position in relation to the residual
cross-sections is, however, not known.
F1-1
F1-2
F1-3
F1-4
F2-1
F2-2
F2-3
F2-4
F2-5
Figure 2 — Recorded residual cross sections at four locations of floor 1 (left) at 24,7 minutes and
floor 2 at 32 minutes (their horizontal position in relation to the original cross-section is
approximate)
The residual cross-sections exhibit considerably larger char depths on the narrow sides than on the
wide sides. For a char depth on the wide side equal to b/4, the difference is between 45 and 85 %,
that is about the same order of magnitude as calculated for a cross-section of 45 mm ´ 120 mm with
a char depth equal to 23 % of the width.
The section moduli Wtest of the recorded residual cross-sections were calculated using the recorded
co-ordinates of the border and a computer program for the determination of cross-sectional of
arbitrary cross-sections, see table 1. These section moduli were compared with section moduli WEC5,
obtained by assuming a notional char depth equal to 1,23 times the experimental char depth on the
wide sides of the joists according to equation (1). The ratios Wtest/ WEC5 are shown in table 1 and
illustrated in figure 3. The average value of the ratio is slightly conservative. It can be seen that the
relationship (1), derived from EN 1995-1-2 [1], takes reasonably well into account the effect of
increased charring of the narrow sides of small timber cross-sections.
Table 1 – Relative section moduli – comparison
of test results and values calculated according
to EN 1995-1-2
3.
0,4
0,2
F2-5
F2-4
F2-3
0,0
F2-2
1,020
1,091
0,860
0,940
0,861
1,302
1,077
1,110
1,073
1,037
F2-1
0,414
0,346
0,35
0,452
0,310
0,259
0,265
0,312
0,338
0,8
0,6
F1-4
0,406
0,317
0,407
0,481
0,360
0,199
0,246
0,281
0,315
1,0
F1-3
Wtest/WEC5
F1-2
WEC5
F1-1
Wtest
1,2
W test/W EC5
Crosssection
F1-1
F1-2
F1-3
F1-4
F2-1
F2-2
F2-3
F2-4
F2-5
Average
1,4
Test
Figure 3 – Comparison of section moduli
When should the one-dimensional charring rate be used?
Temperature [°C]
We can expect that some designers may wish to use the concept of one-dimensional char depths,
which implies that the corner roundings must be separately taken into account, in order to obtain
more favourable results. Since rectangular cross-sections may exhibit an extensive degree of twodimensional heat transfer in the vicinity of the narrow sides, an application limit is needed in order
to prevent non-conservative results.
Performing a heat transfer analysis using the thermal
300
properties given in EN 1995-1-2 [1], for a cross250
section of 100 mm ´ 200 mm, at 30 minutes the
5 min
calculated char depth is 20,3 mm on the wide side
200
10 min
and 21,8 mm on the narrow side, that is it is 7,3 %
150
20 min
greater on the narrow side. The conditions on the
narrow side are influenced by two-dimensional heat
100
flux, since the width of residual cross-section of
50
about 60 mm is less than twice the heat affected
zone in the case of one-dimensional heat transfer in
0
timber exposed on one side only. A stable
0
10
20
30
40
temperature profile is developed after 20 minutes,
Distance from char line [mm]
e.g. see figure 4 with temperature profiles of three
specimens after 5, 10 and 20 minutes according to
Figure 4 — Temperature profiles for onetests results reported in [5]. After 20 minutes, the
dimensional heat transfer at 5, 10 and 20
depth dQ of the zone below the char layer which is
minutes fire exposure
affected by increased temperature is about 40 mm
and does not increase significantly after that time.
For application to rectangular cross-sections of beams and columns, a minimum width of the crosssection, bmin, can be derived for the transition of one-dimensional to two-dimensional heat transfer
taking place in the middle of the narrow side, see figure 5. Therefore
bmin = 2 ( d char,0 + d Q )
(3)
With b0 = 0,65 mm/min, giving a char depth dchar,0 of 13 mm at 20 minutes, and assuming a
temperature affected depth dĬ of 40 mm, expression (3) becomes (see also figure 6)
1003
b min [mm]
bmin = 2 d char,0 + 80 [mm]
for dchar,0 ³ 13 mm
(4)
For simplicity, it is assumed that dĬ increases linearly during the first twenty minutes (from 0 to 40
mm), although the increase is somewhat greater in the beginning as can be seen from figure 4.
Therefore, for the first twenty minutes of fire exposure, expression (3) becomes
bmin = 8,15 dchar,0
for dchar,0 < 13 mm
(5)
Since EN 1995-1-2 [1] gives the corner radius as r = dchar,0, for dchar,0 > 40 mm, expression (4)
should be replaced by
bmin = 4 d char,0
(6)
300
250
200
150
100
50
0
Equ. (6)
Equ. (4)
Equ. (5)
0
10
20
30
40
50
60
d char,0 [mm]
Figure 6 — Minimum width of cross section for
use of one-dimensional charring rate as a
function of one-dimensional char depth dchar,0
Figure 5 — Definition of minimum width for
use of one-dimensional charring rate
4.
Other applications
It has been shown [6], [7] that the concept of notional charring rates also can be applied to naillaminated timber plates, where, due to drying gaps between the laminations, increased charring
takes place near the gaps. Here the one-dimensional charring rate would give non-conservative
results. For normal gap widths, expression (1) will give conservative results [7].
5.
References
[1]
EN 1995-1-2:2004, Eurocode 5 – Design of timber structures – Part 1-2: General – Structural
fire design
König, J. and Källsner, B., “Cross section properties of fire exposed rectangular timber
members”. Proceedings of CIB W18, Meeting 34, Paper 34-16-2, 2001
König J. and Winter S., “The Eurocode 5 Fire Part – EN 1995-1-2”. Proceedings of WCTE
2004. Lahti, Finland
Van de Haar, P. W., “Onderzoek naar de invloed van de grootte van de veranderlijke
belastning op de brandwerendheid op bezwijken van HSB-vloeren”. TNO, Rijswijk,
Netherlands, 1983
König, J. and Walleij, L., “One-dimensional charring of timber exposed to standard and
parametric fires in initially unprotected and post-protection situations”. Swedish Institute for
Wood Technology Research. Report I 9908029, Stockholm, 1999
König, J, and Rydholm, D., “Small-scale fire tests of heavy timber components”. Swedish
Institute for Wood Technology Research. Report P 0310036, Stockholm, 2003
König, J., “Basic and notional charring rates”. Proceedings of CIB W18, Meeting 35, Paper
35-16-1, 2002
[2]
[3]
[4]
[5]
[6]
[7]