Vilnius Gediminas Technical University Lithuanian Academy of Sciences
Journal of Civil Engineering
and Management
2004, Vol X, Supplement 1
Vilnius Technika 2004
ISSN 1392-3730
EDITORIAL BOARD
Editor-in-Chief
Prof Edmundas K. ZAVADSKAS, Lithuanian Academy of Sciences,
Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania
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Assoc Prof Darius BAẩINSKAS, Vilnius Gediminas Technical University,
Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania
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Prof Michaự BOLTRYK, Biaựystok Technical University,
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Prof Patrick J. DOWLING, Felow Royal Society, University
of Surrey, Guildford GU25XH, UK
Prof Aleksandr A. GUSAKOV, Moscow State University of
Civil Engineering, Dorogomilevskaja, 5/114, 121059 Moscow,
Russia
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versity, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania
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University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania
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versity, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania
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cal University, Saulởtekio al. 11, LT-10223 Vilnius-40,
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University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania
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University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania
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Vilnius Gediminas Technical University, Saulởtekio al. 11,
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cal University, Saulởtekio al. 11, LT-10223 Vilnius-40,
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Construction, Tunelio g. 60, LT-3035 Kaunas, Lithuania
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University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania
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3

2004, Vol X, Suppl 1, 39
JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT
http:/www.vtu.lt/english/editions
ISSN 13923730
RESISTANCE OF MASONRY WALL PANELS TO IN-PLANE SHEAR AND
COMPRESSION
Piotr Aliawdin
1
, Valery Simbirkin
2
, Vassili Toropov
3
1
University of Zielona Góra, Poland. E-mail:
2
Belarussian Research Institute for Construction (BelNIIS), Minsk, Belarus. E-mail:
3
Altair Engineering, Coventry, UK. E-mail:
Received 30 Apr 2004; accepted 7 June 2004
Abstract. The paper presents results of large-scale tests carried out on masonry wall panels made of perforated bricks.
The specimens were subjected to in-plane: lateral loading combined with different levels of axial compression; concen-
trated compressive load applied to the wall top at different distances from the wall edge. Relationships between shear
strength and deformability of masonry and compressive stresses perpendicular to the shear plane have been found. An
evaluation of strength of masonry under local compression is given depending on the position of the concentrated load
relative to the wall edge. Analysis of test results and comparison of calculation techniques adopted in different design
codes is performed. Behaviour of the test specimens is modelled using the finite element method.
Keywords: masonry structures, full-scale tests, shear, compression, strength, deformations.
1. Introduction
By the present time, an extensive theoretical and
experimental research has been carried out on the

behaviour of masonry structures made of solid clay
bricks, for instance [15]. However, there are a few test
results for masonry structures made of perforated bricks
that are widely used in practice and have a number of
advantages.
This study presents an experimental and analytical
research into the behaviour of masonry wall panels made
of perforated clay bricks. The test specimens were sub-
jected to in-plane 1) local compressive force, and 2) rack-
ing shear force combined with vertical compression.
For each loading type, two test series have been
devised. In the local compression tests, position of the
applied force was changed. In the shear tests, lateral force
was combined with different levels of axial compression.
In the first case, vertical kinematic restraints were in-
stalled on the wall top to prevent in-plane rotation of the
walls. The vertical pressure arising in this case varied
during the loading process and had the minimum value.
In the second case, the lateral load was combined with
the given vertical compression.
The loading of the specimens was increased mono-
tonically up to the total failure of the specimens. The
resistance of the masonry walls to the predominant ac-
tion was evaluated with reference to the strength and
deformability.
2. Properties of masonry and masonry materials
The following materials were used for producing the
test specimens:
• Clay bricks (length 250 mm, width 120 mm, height
88 mm) with vertical holes. Each brick had 21 holes

whose cross-sections were square-shaped, 20x20 cm
(volume of holes is 28 % of the gross volume). Brick
grade M150.
• Dry pre-packed mortar mix, grade M100: Portland
cement of grade 500ÄÎ  180 kg/t, lime  50 kg/t,
sand  770 kg/t, water-retaining agent Valotsel
45000  0,3 κg/t.
The strength properties of the brick and mortar were
determined experimentally. Their mean values are pre-
sented in Table 1.
Table 1. Brick and mortar strengths
aPM,htgnertskcirB
hsitirByb(evisserpmoC
,]6[1293SBdradnatS
)Dxidneppa
skcirbgnitsetyb(elisneT
)gnidnebrof
6,133,2
aPM,htgnertsratroM
gnitsetyb(evisserpmoC
)mm7,07edisfosebuc
yrnosamagnitsetyb(raehS
)skcirbeerhtfotnemgarf
7,219,932,0
4
4
P. Aliawdin, et al
/ JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39
Strength and deformative properties of the masonry
under short-term compression were determined by tests

of five prismatic specimens having dimensions
lxhxt = 380×490×250 mm. On all four vertical sides of
each specimen, displacement transducers were installed
over a gauge length of 200 mm. They measured longitu-
dinal (vertical) and lateral (horizontal) deformations of
the masonry. The strains measured in this way were used
to calculate the deformation modulus and the Poissons
ratio of the masonry.
While testing the specimens, the mortar compres-
sive strength was checked. Its mean value was 9,9 MPa.
The tests showed that the masonry compressive
strength ranged between 8,4 and 11,1 MPa, and its value
averaged over strengths obtained for five specimens was
equal to σ
ult
= 9,3 MPa.
Averaged curves for strains, secant deformation
modulus, and Poissons ratio of the masonry are pre-
sented in Fig 1.
à)

0

0,2

0,4

0,6

0,8


1


50


25

0

25

50

75

100

125

ε
×10
5
s/s

ult

longitudinal strain


lateral strain

elongation

shortening

b)
0

0,1

0,2

0,3

0,4

0,5

0,6

7500

10000

12500

15000

17500


E

sec

,
MPa

s/s

ult

c)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,00


0,05

0,10

0,15

0,20

0,25

Poisson's ratio
s/s
ult

Fig 1. Dependences of strains
∑∑
∑∑
∑, secant deformation modu-
lus E
sec
, and Poissons ratio upon stress level for masonry
under axial short-term compression
The initial modulus of elasticity of the masonry is
computed according to [7] using the following logarith-
mic stress-strain relation proposed by L. I. Onistchik:









−−=
ult
ult
E
µσ
σ
µσ
ε
1ln
0
, (1)
where:
σ is the mean compressive stress in the test speci-
mens;
∑ is the mean experimental value of strains obtained
under stress σ;
µ is the plasticity coefficient depending on the ma-
sonry type.
The value of the masonry initial modulus of elastic-
ity computed in this way is equal to 11 290 MPa.
3. Response to shear
Shear tests were performed on six wall panels that
were produced of the masonry with the chain bond. The
overall dimensions of the specimens were as follows:
length 1500 mm, height 1500 mm, thickness 120 mm,
with the thickness of mortar joints of 10 to 12 mm. Af-
ter manufacture the specimens were stored under poly-

ethylene until the mortar has hardened (not less than 3
days). The tests were carried out at an age of the speci-
mens 19 to 25 days (after the mortar achieved the com-
pressive strength of 10 MPa).
The test specimens were divided into two series
(Fig 2). The specimens of the first series (series 1A) were
tested for incremental lateral load P, applied to the top
of the panel in its plane, combined with minimal vertical
pressure that was necessary to prevent in-plane rotation
of the wall. The vertical pressure was produced by spring
kinematic restraints on the wall top and varied during
loading so that detachment of the wall bottom from the
floor was not greater than 5 cm.
Displacement transducers (LVDTs) were installed
along the wall height to measure lateral deflections dur-
ing loading (Fig 2). In addition, displacement transduc-
ers were used to measure translation of the horizontal
support and detachment caused by a compliantly re-
strained rotation of the wall in its plane. Their readings
were taken into account for calculation of the clear
lateral deflections by correcting the values obtained by
LVDTs Th1Th5.
Unlike the first type specimens, specimens of the
series 1B were loaded, in addition to the lateral load P,
with a vertical uniformly distributed load q equal to
0,2F
k
= 225 kN/m, where F
k
is the ultimate failure load

in the pure compression case. This load did not vary
during the testing. The load P was applied to four top
rows of bricks, and displacements were measured only
at one level (at a height of 1450 mm from the wall bot-
tom).
The test showed that specimens of the series 1A
collapsed immediately after a zigzag crack has appeared
5
5
P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39
a) Test series 1A (three specimens)
b) Test series 1B (three specimens)
Fig 2. Shear test setup
along the wall diagonal connecting the lateral loading
point and the horizontal support (Fig 3, a). The failure
lateral load was equal to: 120,0 kN for the first speci-
men, 113,8 kN for the second specimen, and 80,0 kN
for the third one. Therefore, the failure lateral load aver-
aged over three these values was P
ult
= 104,6 kN. At the
ultimate stage, average total value of the compressive
load q was equal to 118 kN.
Experimental graphs showing the deforming process
of the series 1A specimens are presented in Fig 4.
The walls of the series 1B having been tested for
combined shear and compression failed also with an in-
clined crack connecting the lateral loading point and the
horizontal support. However, in this case some vertical
a) Series 1A (P

ult
=104,6 kN)
b) Series 1B (P
ult
=192,6 kN)
Fig 3. Crack patterns after testing (general views and
local failure at horizontal support)
cracks were observed, and a local failure at the horizon-
tal support was clearer (Fig 3, b). The ultimate failure
lateral load was equal to: 200,0 kN for the first speci-
men, 207,7 kN for the second specimen, and 170,0 kN
for the third one. The failure lateral load averaged over
three the values was P
ult
= 192,6 kN.
 LVDTs

6
6
a)
0
50
100
150
0 5 10 15 20 25
Lateral displacement, mm
Wall height, cm
P/Pult=0,10
P/Pult=0,29
P/Pult=0,48

P/Pult=0,67
b)
Fig 4. Lateral deflections for the series 1A specimens:
a) distribution of displacements along the wall height;
b) loaddisplacement relationships
The lateral load-displacement relationship averaged
over results of three tests of the series 1B is shown in
Fig 5.

0

0,2

0,4

0,6

0,8

1

0

0,5

1

1,5

2


2,5

Lateral displacement, mm (h=1450 mm)

P/P

ult

Fig 5. Lateral deflections for the series 1B specimens
Comparing the graphs presented in Figs 4 and 5 we
can notice that in-plane shear behaviour of the series 1B
specimens was more plastic than the behaviour of the
series 1A specimens which deformed almost elastically
up to the failure (excepting a displacement leap observed
at the second loading stage) and collapsed in a brittle
mode. Indeed, in the series 1A specimens the cracks were
not observed up to the failure, but cracks in the series
1B specimens appeared under the lateral load equal to
0,3 to 0,4 of the ultimate load. However, the specimens
of the series 1A had a much lower rigidity than those of
the other test series. Their failure occurred at lateral
deflections that were an order of magnitude higher than
ultimate deflections of the series 1B specimens. More-

0

0,2

0,4


0,6

0,8

0

5

10

15

20

25

Lateral displacement, mm

P/ P

ult

h=850 mm

h=1150 mm

h=1450 mm

over, the compressive action on the masonry walls re-

sulted in 84 % increase of the load-carrying capacity of
the walls under lateral loading.
Therefore, the effect of vertical compression leads
to a higher resistance of the masonry walls to shear loads,
making their rigidity and load-carrying capacity higher.
Behaviour of the test specimens is modelled on the
finite element basis using Software Stark_Es of the
MicroFE family. The wall panels are modelled with
highly accurate hybrid plane stress elements (mesh 30x30)
derived using a Reissner functional [8]. Second order
geometrical effects and unilateral elastic supports are
taken into account. As an example, Fig 6 shows some
analysis results for the specimens of series 1A.
a) Deformed scheme
b) Distribution of vertical normal stresses σ
z
along the wall
length at a level of a half of the wall height

Wall length, m
Fig 6. Finite element analysis results for wall panels of
series 1A (under P = 104,6 kN)
The test results presented above enable to draw an
experimental relationship between the shear strength and
compressive stress rate in masonry. This relationship is
presented in Fig 7.
As we can see in Fig 6, the masonry shear strength
depends almost linearly upon the compressive stress level.

ó

z
, MPa

0
-0,40
-0,80
-1,20
-1,60
-2,00
-2,40
-2,80
-3,20
-3,60
-4,00
0,00 0,15 0,30 0,45 0,60 0,75 0,90 1,05 1,20 1,35 1,50
P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39
7
7
0

0,2

0,4

0,6

0,8

1


1,2

1,4

0

0,5

1

1,5

2

2,5

3

Compressive stress, MPa

Shear strength, MPa

test

EC6, eq. 3.3a

EC6, eq. 3.3c

Ðÿä4


mortar strength

masonry strength

Fig 7. Relationships between masonry shear strength and
compressive stress level
Hence we can propose the following empirical formula
for approximate evaluation of the shear strength of ma-
sonry in a plane stress state for different levels of the
compressive stresses:
zultult
σττ
28,0
0,
+=
, (2)
where:
ult
τ
is the masonry shear strength;
z
σ
is the mean compressive stress perpendicular to
the shear plane;
0,ult
τ
is the initial masonry shear strength, under
zero compressive stress.
In equation (2), all magnitudes are in MPa.
Equation (2) is valid for only the cases where the

compressive stress ⌠ does not exceed 0,2 of the ultimate
compressive strength.
A similar relationship is given in Eurocode 6 [9] to
compute the masonry shear strength depending on the
compressive stress value. In our case, this strength should
be determined using equation 3.3a [9] but its value must
be not higher than a value computed by equation 3.3c
[9]. A graphical representation of the values calculated
by these equations for our cases is given in Fig 7. As
can be seen, equation 3.3a overestimates the shear
strength of masonry, but equation 3.3c provides a rather
high safety margin for the masonry shear strength.
4. Response to local compression
For local compression tests of masonry walls, six
specimens were produced and stored analogously as de-
scribed in the previous section.
The test specimens were tested to collapse for con-
centrated vertical load P applied incrementally at a dis-
tance 650 mm (series 2A) and 350 mm (series 2B) from
the wall edge, as shown in Fig 8. The bearing area was
10×12 = 120 cm
2
.
Along the loading line on both sides of the speci-
mens, displacement transducers (Tv, Fig 8) were installed
at the middle height over a gauge length of 800 mm to
measure mean vertical strains.
The tests showed that the specimens of both series
had the same failure mode  the failure was practically
brittle with formation of a local failure zone under the

bearing and a vertical crack along the loading line (Fig 9).
a) Test series 2A (three specimens)
b) Test series 2B (three specimens)
Fig 8. Local compression test setup
Fig 9. Failure pattern
P. Aliawdin, et al
/ JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39
8
8
Until the load reached the value P = 150 kN, the
mean vertical strains increased with loading almost iden-
tically for specimens of both series and had a slightly
non-linear kind (Fig 10). However, further loading caused
a deviation of the load-strain curve for series 2B from
the direct line and from the curve shown by the series
2A specimens. After that, under the load 188 to 200 kN
the failure of the series 2B specimens occurred. The mean
value of the failure load for these specimens was
192,7 kN. The series 2A specimens showed a higher load-
bearing capacity equal to 220 to 256 kN with the mean
value of 234,7 kN.
0
50
100
150
200
0 5 10 15 20 25 30
ε
x10
5

2 , kN
series 2A
series 2B
Fig 10. Experimental load-strain curves
At the failure moment, the mean value of the mid
height vertical strain was
5
1050
⋅
and
5
1035
⋅
for speci-
mens of the series 2A and 2B respectively. As can be
seen from Fig 1a, such strains correspond to compres-
sive stresses not exceeding a half of the ultimate strength
of masonry in pure axial compression. Thus the failure
of the specimens was local below the loaded area.
The results presented enable to evaluate the effect
of increase of the masonry resistance to concentrated
compressive loads as compared with overall axial com-
pression case. Table 2 presents values of the enhance-
ment factor for concentrated loads obtained experimen-
tally and calculated according to different building codes.
Table 2. Local compression effect
Enhancement factor for concentrated
compressive loads
Test series
test SNiP [10]

EC6 [9],
PN [11]
2A 2,1 1,5 1,45
2B 1,7 1,5 1,35
As we can see from Table 2, all design codes pro-
vide a rather high safety margin for the compressive
strength of masonry subjected to concentrated loads. In
addition, Russian code [10] defines the same enhance-
ment factor for both the test series and, in contrast to
Eurocode 6 [9] and Polish code [11], does not take into
account changes of the masonry local compressive
strength depending on the wall height.
The ultimate stage of the wall behaviour is mod-
elled on the basis of the finite element method using
Software Stark_Es. Results of the analysis are given in
Fig 11.
The analysis shows that for specimens of the differ-
ent series under the ultimate failure load the maximum
compressive stresses below the loaded area (ó
z
) have the
same ratio as the loads applied. However, calculated ten-
sile stresses in the orthogonal direction (ó
x
), which have
caused the vertical crack formation in the test specimens,
in the series 2B specimens are 1,25 times greater than in
the series 2A specimens even under a smaller load. This
indicates that in the series 2B specimens local compres-
sion (casing-type) effect is not so significant than in the

other series specimens. This fact is affirmed by the kind
of deformation distribution in the vicinity of the loaded
area  in the series 2A specimens the effective area is
greater than in the other specimens. From the deformed
shape presented in Fig 11 we can assume that the effec-
Fig 11. Results of finite element analysis (displacement
scale 200:1)
b) Series 2B
a) Series 2A
P. Aliawdin, et al
/ JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39
9
9
tive area includes wall parts of 250 mm length for the
series 2A specimens and 200 mm for the series 2B speci-
mens to both sides from the loaded area (but not 120
mm as adopted in code [10] for both our cases). In this
case, the enhancement factor calculated by Eq (19) given
in [10] would be equal to 1,82 and 1,71 for specimens
of the first and the second series respectively. These
values are much closer to the experimental ones than
those calculated according to [10]. Therefore, the ma-
sonry resistance to concentrated compressive loads can
be evaluated sufficiently accurate by the finite element
analysis.
5. Conclusions
1. Large-scale tests carried out on masonry wall
panels subjected to in-plane lateral (shear) loading com-
bined with different levels of axial compression show
that:

• Behaviour of masonry wall panels subjected to pure
shear is almost perfectly elastic, the failure occurs
in a brittle mode. Compressive load affects the shear
behaviour of the masonry making it plastic.
• Shear capacity of masonry walls increases by about
80 % due to the action of axial compressive load
equal to 20 % of the ultimate compressive strength;
the lateral rigidity of such walls can be of an order
of magnitude higher as compared with the walls un-
der pure shear.
2. Local compression tests of masonry walls show
that resistance of masonry to concentrated compressive
load depends significantly on the distance from the wall
edge to the load position even if this distance 2,5 times
greater than the wall thickness. This fact is not taken
into account in SNiP II-22-81 [10]. A finite element
analysis can be used for strength evaluation for masonry
subjected to concentrated loads.
Acknowledgement. The authors are pleased to acknowl-
edge the support of INTAS under international project
00-0600.
References
1. Bull, J. W. Computational modelling of masonry, brick-
work and blockwork structures. Saxee-Coburg Publications,
2001. 346 p.
2. Hendry, A. W. Structural masonry. London: Mac-Millan
Education Ltd, 1990. 284 p.
3. Majewski, S.; Szojda, L. Numerical analysis of a masonry
structure. Engineering and construction, 2002, No 10,
p. 578581 (in Polish).

4. Orùowicz, R.; Maùyszko, L. Masonry structures. Cracks and
their elimination. Olsztyn: Wydawnictwo Uniwersytetu
Warmiñsko-Mazurskiego, 2000. 152 p. (in Polish).
5. Kubica, J.; Drobiec, Ù.; Jasiñski, R. Study of secant de-
formation modulus of masonry. In: Proceedings of XLV
Scientific Conference KILiW PAN i KN PZITB. Wrocùaw-
Krynica, 1999, p. 133140 (in Polish).
6. BRITISH STANDARD BS 3921: Specifications for clay
bricks. London: British Standards Institution, 2001. 22 p.
7. Sementsov, S. A. On the method of selection of logarith-
mic stress-strain relation using test data. In: Strength and
stability of large-panel structures, Vol 15. Moscow:
Gosstroyizdat, 1962, p. 303309 (in Russian).
8. Semenov, V. A.; Semenov, P. J. Highly accurate finite el-
ements and their use in software MicroFE. Residential
Construction, 1998, No 8, p. 1822 (in Russian).
9. prEN 1996-1-1: Redraft 9A. Eurocode 6: Design of ma-
sonry structures  Part 1-1: Common rules for reinforced
and unreinforced masonry structures.  European Commit-
tee for Standardization, 2001. 123 p.
10. SNiP II-22-81. Masonry and reinforced masonry structures.
Design Code. (ÑÍèÏ II-22-81. Moscow: Gosstroi USSR,
1983. 39 p. (in Russian).
11. PN-B-03002:1999. Masonry structures. Design and analy-
sis. PKN, 1999. 67 p. (in Polish).
P. Aliawdin, et al
/ JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39
11
11
2004, Vol X, Suppl 1, 1118

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT
http:/www.vtu.lt/english/editions
ISSN 13923730
FE SOFTWARE ATENA APPLICATIONS TO NON-LINEAR ANALYSIS OF RC
BEAMS SUBJECTED TO HIGH TEMPERATURES
Darius Bacinskas
1
, Gintaris Kaklauskas
2
, Edgaras Geda
3
Dept of Bridges and Special Structures, Vilnius Gediminas Technical University, Saulëtekio al 11, LT-10233
Vilnius-40, Lithuania. E-mail:
1
,
2
,
3

Received 15 Apr 2004; accepted 23 Feb 2004
Abstract. Reinforced concrete structures subjected to fire will generally experience complex behaviour. This paper
presents a strategy of numerical simulation of reinforced concrete members exposed to high temperatures and subjected
to external loading. Finite element modelling of full load  deflection behaviour of experimental reinforced concrete
beams reported in the literature has been carried out by the FE software ATENA. A constitutive model based on Eurocode
2 specifications has been used in the analysis. Comparison of numerical simulation and test results have shown reason-
able accuracy.
Keywords: reinforced concrete fire design, non-linear finite element analysis, fire tests, fire resistance, constitutive
models of concrete and steel.
1. Introduction
There are many buildings and civil engineering struc-

tures (tunnels, high-rise buildings, bridges and viaducts,
containment shells, offshore platforms, airport runways
etc.) under construction which are at risk of fire. A few
dramatic accidents in recent years have prompted inves-
tigations in the field of safety of reinforced concrete struc-
tures subjected to fire. Fires in railway Channel Tunnel
(autumn 1996), in the road tunnels of Mont Blanc
(France/Italy 1999), in the television tower of Ostankino
(Moscow, 2000), in the Twin Towers (New York, 2001)
should be mentioned [1]. In all cases, the load-bearing
capacity of structure in the actual fire conditions is of
primary importance for evacuation of persons and things,
as well as for safety of rescue teams.
The analysis of the behaviour of load-bearing mem-
bers under high temperature conditions is very compli-
cated [2, 3]. Various factors influencing the behaviour
of members need to be taken into account, including:
variation of member temperature with time, variation of
temperature over the cross-section and along the mem-
ber, temperature effects on material properties (expan-
sion, creep, reduction in strength and stiffness, spalling,
etc), material non-linearity, external restrains, section
shape, etc. A parametric study of the influence of differ-
ent factors on the behaviour of RC beams and frames is
presented in [4].
Because of the no-linear nature of the problem,
closed-form solutions usually cannot be found and an
iterative approach is required [5]. The non-linear
behaviour of a member under elevated temperature con-
ditions can be simulated using the finite element method

[6, 7]. Because of increasing interest in the field of struc-
tural fire protection, the number of existing software
capable to analysing the thermal response of materials
under transient heating conditions is quite large [8, 9].
The majority of these programmes was developed in
professional software houses, such as DIANA [10],
ATENA [11], ABAQUS, MSC.MARC, etc. Such
programmes have many advantages including documen-
tation, sophisticated non-linear material models, pre/post-
processing facilities, etc.
This paper presents a strategy of numerical simula-
tion of reinforced concrete members exposed to high
temperatures and subjected to external loading. Finite
element modelling of full load  deflection behaviour of
experimental reinforced concrete beams reported in [12]
has been carried out by the FE software ATENA. A con-
stitutive model based on Eurocode 2 specifications for
fire design [13] has been used in the analysis. Compari-
son of numerical simulation and test results has been
carried out.
2. Reported fire tests of RC beams employed in the
numerical analysis
The present analysis employs experimental data [12]
of reinforced concrete beams subjected to external load-
ing and elevated temperatures. A total of 13 specimens
were cast and tested. Except for TSB2-1, the other speci-
mens were heated on three surfaces (the bottom and two
12
12
lateral surfaces) according to the same heating curve.

Specimens TSB1-(0-6) were tested in the FT (force-tem-
perature) path to obtain failure temperatures under dif-
ferent applied load levels. These specimens were first
loaded to a predetermined value, and then heated until
the specimens failed. Specimens TSB2-(1-6) were tested
in the TF (temperature-force) path to obtain ultimate
bending moment resistances. These specimens were first
heated up to a predetermined temperature, and then
loaded at a quicker rate until the specimens failed. As
the loading time was very short compared to its heating
time, the thermal duration effect during loading can be
neglected. Thus, the duration of thermal exposure be-
tween the FT and TF paths can be considered to be the
same.
The specimens were 1300 mm long, 100 mm wide,
and 180 mm deep, with a 10 mm concrete cover all round
the section.
The specimens were cast in two batches of normal
Portland cement (Standard grade China cement), natural
river sand and crushed limestone with 15 mm maximum
size. The mean compressive cube strength of TSB2 se-
ries is 29,45 MPa.
Low-carbon plain steel bars with diameter 10 mm
and yield stress 270 MPa at room temperature were used
as tensile and compressive reinforcement, while those
with diameter 3,5 mm and yield stress 289 MPa at room
temperature were used as stirrups. The specimen tensile
steel ratio was 0,95% and the stirrup spacing was 80
mm. The specimen dimensions, detailing and loading po-
sitions are shown in Fig 1.

The specimens were compacted using a vibrating
rod and cured in a moist environment at 20°C and 100%
relative humidity for a period of 7 days after casting,
and then placed in a natural environment. To reduce the
difference of the water content between specimens aris-
ing from a long test period, all specimens were tested
after 60 days.
Fig 1. Dimensions, cross-section and loading of test speci-
mens
The present report includes results of modelling three
beams of the TF series, namely TSB2-1, TSB2-4 and
TSB2-6, first exposed to temperatures of 20°, 400° and
600°C, respectively, and then subjected to external load-
ing. The experimental temperature distribution through-
out the section of the beams TSB2-4 and TSB2-6 is
shown in Fig 2. The experimental load-deflection dia-
grams are presented in Fig 3 with the failure load speci-
fied in Table 1.
0
30
60
90
120
150
180
0 100 200 300 400 500 600 700
Temperature, C
Depth of section, mm
400 C temperature
600 C temperature

Fig 2. Experimental temperature distribution within the
section depth
400 ºC
600 ºC
D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1118
Table 1. Failure loads of test beams
Beam Temperature,
o
C Failure load, kN
TSB2-1 20 19,46
TSB2-4 400 14,99
TSB2-6 600 5,49
Fig 3. Experimental load-deflection diagrams of beams
TSB2-1, TSB2-4 and TSB2-6

0

0.004

0.008

0.012

0.016

0.02

0.024

0


0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

f, m

P
, MN
20 °C

400 °C

600 °C


1300 mm
D3,5@80
D10
D10
1
1
1-1
100
10 10
D3,5@80
10
180
10
D10
D10
1200
400400400
13
13
3. A Constitutive model applied in the analysis
The reliability of a fire analysis results is strongly
affected by the choice of the constitutive laws of materi-
als and the values of theirs parameters. In the present FE
model the material properties are considered to be tem-
perature-dependent. This section describes constitutive
models for concrete and steel assumed in the numerical
analysis. The constitutive relationships are based on
Eurocode 2 specifications [13, 14].
3.1. Concrete

The constitutive model (material model) describes
the behaviour of heated and loaded concrete in math-
ematical terms. It is based on the stress-strain relation-
ships of heated concrete. The strain components can be
modelled using the superposition theory whereby the to-
tal strain is considered to be the sum of various strain
components [3]:
( ) ( ) ( ) ( )
θσεθσεθεθσσεε
σ
,,,,,
trcrthtot
t
+++=
, (1)
where
tot
ε
is the total strain,
σ
ε
the stress-related strain,
th
ε
the thermal strain,
cr
ε
the creep strain,
tr
ε

the tran-
sient strain,
θ
the temperature,
t
the time,
σ
a stress,
σ
the stress history.
The superposition theory has been particularly use-
ful in the analysis of the strain components at high tem-
perature and has been found to be applicable experimen-
tally [3]. Each of the terms of Eq 1 is briefly described
below.
The EC2 model implicitly takes account of the ef-
fect of high-temperature creep. Both the physical loss of
moisture and shrinkage at high temperature cause a de-
crease in the coefficient of expansion, but these effects
have not been considered in the present model. The model
also does not attempt to model spalling, the concrete
cross-section being assumed to remain intact.
3.1.1. Stress-strain relationships in compression and
tension
The stress-strain relationships of compressed con-
crete for different temperature levels are shown in Fig 4.
The theoretical model of these relationships is given in
Fig 5. On the compression side, the curve consists of a
parabolic branch followed by a descending curve until
crushing occurs. On the tension side, the curve consists

of a bilinear diagram. An initial stiffness of concrete in
tension is equal to that in compression. At tensile strains
greater than this value of
cr
ε
the concrete is assumed to
follow the descending branch of the stress-strain curve.
Once tensile strains exceed
cu
ε
, the concrete in tension
is ignored, although it is still assumed to be capable of
carrying compression. Once the concrete has crushed, it
is assumed to have no residual strength in either com-
pression or tension.
Stress-strain behaviour of compressive concrete un-
der normal conditions (
C20
o
=
θ
) in ATENA is mod-
elled by the EC2 [14] relationship the ascending branch
of which has the form
( ) ( )
( )
η
ηη
σ
21

C20C20
2
−+
−
=
k
k
f
cc
oo
(2)
where
( )
C20
o
c
σ
is the stress of concrete at room
temperature,
( ) ( )
C20C20
0
oo
cc
εεη
=
,
( )
C20
o

c
ε
is the
strain of concrete at room temperature,
( )
C20
0
o
c
ε
is the
concrete strain at peak stress at the same condition,
( )
C20
o
c
f
is the characteristic value of compressive
strength of concrete at
C20
o
=
t
,
( ) ( ) ( )
C20/C20C201,1
0
ooo
ccc
fEk

ε
=
,
( )
C20
o
c
E
is the
elastic modulus of concrete.
It should be noted that the stress-strain relationship
for compressive concrete presented in Eurocode 2 for
fire design of concrete structures [13] is different from
formula 2. The former relationship is not available on
Fig 4. Stress-strain relationship of concrete at different
temperatures
ε
c
(θ)
f
ct
(θ)
ε
cr
(θ) ε
cu
(θ)
ε
c0
(θ)ε

cu
(θ)
f
c
(θ)
E
c
(θ)
Fig 5. Theoretical model of the stress-strain relationship
of concrete
D. Bacinskas, et al
/ JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1118
14
14
the ATENA 2D user interface. However, the shape of
the stress-strain relationship of the compressive concrete
does not have significant influence on the results of the
analysis. Therefore, Eq (2) has been modified in order
to model temperature effects. Thus the parameters
( )
C20
o
c
σ
,
( )
C20
o
c
f

,
( )
C20
o
c
ε
,
( )
C20
0
o
c
ε
and
( )
C20
o
c
E
from formula (2) corresponding to normal con-
ditions (
C20
o
=θ
) were replaced by respective param-
eters
( )
θσ
c
,

( )
θ
c
f
,
( )
θε
c
,
( )
θε
0c
and
( )
θ
c
E
taken
for given temperature
θ
. Further the relationships for
( )
θ
c
f
,
( )
θε
0c
and

( )
θ
c
E
are briefly discussed.
The variation of the relative compressive strength
( )
( )
C20
o
cc
ff
θ
of concrete with siliceous and calcare-
ous aggregates under increasing temperatures is shown
in Fig 6. Similar relationship for strain
( )
θε
0c
is pre-
sented in Fig 7.
0

0.2

0.4

0.6

0.8


1

0

200

400

600

800

1000

1200

1400

Temperature, °C

Siliceous
t
Calcareous
t
Fig 6. Relative compressive strength of concrete with sili-
ceous and calcareous aggregates at elevated temperatures
0

0.005


0.01

0.015

0.02

0.025

0.03

0

200

400

600

800

1000

1200

Temperature, °C


Fig 7. Variation of strain
( )

θε
0c
corresponding to maxi-
mum stress
( )
θ
c
f
under increasing temperature
A relationship for
( )
θ
c
E
is absent in Eurocode 2,
therefore it was taken from [15]:
( )
θε
0c
( ) ( ) ( )
Cº20
ccc
EE
θβθ
=
, (5)
where
( )
θβ
c

is an empirical factor, for normal strength
concrete taken as:
( )
θθβ
0017,01
−=
c
. (6)
The behaviour of concrete in tension under fire con-
ditions is not fully investigated. So far few investiga-
tions have been carried out, mainly aimed at the overall
and stress-strain behaviour of structures.
As mentioned above, the behaviour of tensile con-
crete was modelled by a bilinear diagram. The current
model of tensile concrete is characterised by two main
factors: tensile strength and the ultimate cracking strain.
The reduction of tensile strength of concrete at high
temperatures is accounted for by the coefficient
)(θ
t
k
,
taken as [13]:
( ) ( ) ( )
Cº20
cttct
fkf
θθ
=
. (7)

In absence of a more accurate information the following
( )
θ
t
k
values should be used [13]:
( )
( )
( )







<=
≤<
−
−=
≤≤=
θθ
θ
θ
θ
θθ
Cº6000
Cº600Cº100
500
100

1
Cº100Cº200,1
fork
fork
fork
t
t
t
(8)
To the authors' knowledge, investigations regarding
the limit strain
( )
θε
cu
of tensile concrete are practically
absent. In reference [16] it is taken as
( )
θε
cr
15
, where
( ) ( ) ( )
θθθε
cctcr
Ef
/
=
is the cracking strain of concrete.
The same source also notes that the analysis of RC beams
at ambient temperature is very sensitive to the assumed

tensile behaviour of concrete.
In ATENA 2D post-peak behaviour of tensile con-
crete is modelled using principles of fracture mechanics
[17]. Fracture energy
f
G
was assumed by modifying a
formula from [11] given for
Cº20
=θ
:
( ) ( )
θθ
tf
fG
000025,0
=
, [MN/m]. (9)
It should be noted that a sudden drop in tensile
strength with increasing temperatures takes place, lead-
ing to degradation of tension softening.
3.1.2. Thermal strain
Thermal strain of concrete during heating is a simple
function of temperature and its theoretical curve is plot-
ted in Fig 8. The theoretical curve also includes drying
shrinkage, but despite this, the curve is justified for rapid
heating during fire.
3.1.3. Creep strain
The creep strain depends on concrete, the load, the
temperature and the time. The following expression

is used to describe the creep of ordinary concrete:
D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1118
( )
( )
C20
o
cc
ff
θ
15
15
( )
( )
( )
( )
1000
2004,3
6
3
10530,,
−
−
×××⋅−=
θ
∆
θσ
θσ
θσε
e
t

t
cu
cr
(10)
where
( )
t
cr
,,
θσε
is the creep strain,
( )
θσ
a stress of
concrete,
( )
θσ
cu
the ultimate compressive stress of con-
crete (Fig 5),
θ
is the temperature of concrete,
t∆
the
time interval.
3.1.4. Transient strain
Transient stress is the hindered part of thermal
expansion for loaded concrete structures exposed to heat-
ing. It is an irreversible process and occurs only during
the first heating. The transient stress is found to be pro-

portional to the thermal expansion and to the ratio
between the compressive stress and strength at 20 °C:
( )
( )
( )
th
c
tr
Cf
ε
θσ
θσε
××−=
o
20
35,2,
(11)
where
( )
θσε
,
tr
is the transient strain,
( )
( )
C20
o
c
f
θσ

is the ratio between the compressive stress and compres-
sive strength of the concrete at 20 °C,
th
ε
the thermal
expansion.
3.2. Reinforcement
The constitutive model describes the behaviour of
heated and loaded steel in mathematical terms. Since tran-
sient strain does not exist for steel, the model is simpler
than for concrete and is described as the sum of three
terms [13]:
( ) ( ) ( )
t
crthcrtot
,,,
θσεθεθσεε
++=
(12)
where
tot
ε
is total strain,
( )
θσε
,
cr
the stress related
strain,
( )

θε
th
the thermal strain,
tot
ε
the total strain.
The strength and deformation properties of reinforc-
ing steel at elevated temperatures shall be obtained from
the stress-strain relationships [13] specified in Fig 9 and
Table 2.
D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1118
Fig 8. Thermal strain of concrete
Table 2. Stress-strain relationships for steel under a high temperature
Descending branch
Failure
Parameters
Functions
Elastic
Non-linear
Plastic
Range Stress Tangent modulus


()
θε<ε
sp

() ()
sss
E

εθ=θσ
,
()
θ
s
E


() ()
θε≤ε≤θε
syssp

() () ( ) () ()
()
2
2
θε−θε−+−θ=θσ
ssysps
aa/bcf

()
() ()
()
() ()
()
2
2
θε−θε−
θε−θε
=θ

sps
ssy
s
aa
b
E

() ()
θε≤ε≤θε
stssy

() ()
θ=θσ
sys
f

()
0
=θ
s
E


() ()
θε≤ε≤θε
susst

() ()
() ()
() ()







θε−θε
θε−θε
−θ=θσ
stu
sts
sys
f
1



()
θε=ε
sus

0 

() () ()
θθ=θε
sspsp
E/f
,
( )
02,0

=θε
sy
,
( )
15,0
=θε
st
,
( )
2,0
=θε
sy


() ()
()
() () ()
()
θ+θε−θεθε−θε=
sspsyspsy
E/ca
2
,
() ()
()
()
22
cEcb
sspsy
+θθε−θε=

,
() ()
()
() ()
()
() () ()
()
θ−θ−θθε−θε
θ−θ
=
spsysspsy
spsy
ffE
ff
c
2
2

16
16
Fig 9. Stress-strain relationship of steel
For a given steel temperature, the stress-strain curves
in Fig 9 are defined by three parameters:
 the slope of the linear elastic range
( )
θ
s
E
for
reinforcement,

 the proportional limit
)(
θ
sp
f
,
 the maximum stress level
( )
θ
sy
f
.
Values for each of the three parameters for hot rolled
and cold worked steel are given in Fig 1012 [13].
0

0.2

0.4

0.6

0.8

1

1.2

0


200

400

600

800

1000

1200

1400

Temperature, °C
hot rolled

cold worked

Fig 10. Relative maximum stress of hot-rolled and cold-
worked steel at elevated temperatures
0

0.2

0.4

0.6

0.8


1

1.2

0

200

400

600

800

1000

1200

1400

Temperature, °C
hot rolled

cold worked

Fig 11. Relative proportional limit of hot-rolled and cold-
worked steel at elevated temperatures
4. Numerical modelling of experimental beams
4.1. FE package ATENA

ATENA is a commercial finite element software
package developed for non-linear simulation of concrete
and reinforced concrete structures. Based on advanced
material models it can be used for realistic modelling
the structural response and behaviour.
ATENA programme consists of solution core and the
user interface. The solution core has got capabilities for
the 2D and 3D analysis of continuum structures. It has
libraries of finite elements, material models and solution
methods. ATENA User Graphic Interface for 2D analysis
is a programme, which enables access to the ATENA
solution core. It is limited to 2D graphical modelling
and covers the state of plane stress, plain strain and ra-
tional symmetry.
A smeared approach is used to model the material
properties, such as cracks. This means that material prop-
erties defined for a material point are valid within a cer-
tain material volume, which is in this case associated
with the entire finite element. The constitutive model is
based on the stiffness and is described by the equation
of equilibrium in a material point. The concrete models
can include the following effects of concrete behaviour:
non-linear behaviour in compression including harden-
ing and softening, fracture of concrete in tension based
on the non-linear fracture mechanics, biaxial strength
failure criterion, reduction of compressive strength after
cracking, tension stiffening effect, reduction of the shear
stiffness after cracking (variable shear retention), fixed
direction crack model. The discrete reinforcement is in
the uniaxial stress state and its constitutive law is a bi-

linear stress-strain diagram. The material matrix is de-
rived using the non-linear elastic approach. In this ap-
proach the elastic constants are derived from a
stress-strain function.
ATENA enables loading of the structure with vari-
ous actions: body forces, nodal or linear forces, supports,
prescribed deformations, temperature, shrinkage, pre-
D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1118
Fig 12. Relative elastic modulus of hot-rolled and cold-
worked steel at elevated temperatures
( ) ( )
Cº20/
ss
EE
θ
( ) ( )
Cº20/
yksy
ff
θ
( ) ( )
Cº20/
yksp
ff
θ

0

0.2


0.4

0.6

0.8

1

0

200

400

600

800

1000

1200

1400

Temperature, °C
hot rolled

cold worked

17

17
stressing. These loading cases are combined into load
steps, which are solved utilising advanced solution meth-
ods: NewtonRaphson, modified NewtonRaphson or arc-
length. Secant, tangential or elastic material stiffness can
be employed in particular models. Line-search method
with optional parameters accelerates the convergence of
solution, which is controlled by residual-based and en-
ergy-based criteria. This is only a concise survey of
ATENA features. All the described features support the
user by engineering analysis of connections between steel
and concrete and computer simulation of its behaviour.
4.2. FE model of experimental beams
Load-deflection behaviour of the experimental beams
described in Section 2 have been analysed by the finite
element package ATENA. The present report includes
results of modelling the three beams of the TF series, ie
TSB2-1, TSB2-4 and TSB2-6, first exposed to tempera-
tures 20, 400 and 600°C, respectively, and then sub-
jected to external loading till failure.
SBETA material model with parameters given in
Section 3 was applied for simulating the concrete
behaviour. Reinforcement is modelled by a single straight
line in a discrete way (bar reinforcement). Material of
reinforcement is represented by the bilinear model.
The experimental temperature distribution through-
out the section of the beams TSB2-4 and TSB2-6 is
shown in Fig 2. In order to assess degrading material
properties due to high temperature effects, the beams
within the depth were divided into six macroelements.

These macroelements were discretised by CCIsoQuad
type quadraliteral elements with rigid connections be-
tween the macroelements. The temperatures and respec-
tive material properties in different macroelements were
assessed according to the experimental temperature dia-
grams from Fig 2. Standard Newton-Raphson solution
method was applied for non-linear analysis of experi-
mental beams. FE model of TSB2 series experimental
beams is presented in Fig 13.
Fig 13. FE model of TSB2 series experimental beams
4.3. Analysis results
In this section, comparison of numerical modelling
with test data has been carried out. The modelled load-
deflection diagrams are presented in Fig 8 along with
the experimental curves. The modelling has included all
the stages of temperature and loading. First, the beams
TSB2-4 and TSB2-6 were subjected to temperature of
400 and 600 °C, respectively. As the temperatures were
increasing from the bottom to the top, the beams have
deflected downwards. The calculated deflections due to
temperature effects only (no loading) are in a good agree-
ment with the tests for the beam TSB2-6, but some dis-
crepancies can be noted for the beam TSB2-4. With in-
creasing load the experimental load-deflection diagrams
(Figs 2, 14) can be roughly approximated by a bilinear
diagram consisting of two lines: the first one describing
pre-yielding and the second post-yielding behaviour. It
can be seen from Fig 14 that the shape of experimental
load-deflection diagrams has been qualitatively captured
in the finite element analysis. Pre-yielding deflections

were accurately modelled for the beam TSB2-1
(t =20ºC), but were underestimated for the beam TSB2-
4 and overestimated for the beam TSB2-6. Agreement
of the ultimate load is within reasonable limits. Deflec-
tion fields and cracking pattern of TSB2-4 beam at load
P = 16 kN are shown in Fig 15.
0
0,005
0,01
0,015
0,02
0,025
0 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0,04 0,045 0,05
f , m
P , MN
20 C temperature 400 C temperature 600 C temperature
20 C Atena 400 C Atena 600 C Atena
Fig 14. Calculated and experimental load-deflection dia-
grams
Fig 15. Deflection fields and cracking pattern of TSB2-4
beam at load P=16 kN
5. Concluding remarks
Load-deflection behaviour of reinforced concrete
beams subjected to high temperatures (up to 600°C) has
been modelled by the finite element package ATENA.
D. Bacinskas, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1118
20 ºC
400 ºC 600 ºC
18
18

A constitutive model based on specifications of Eurocode
2 has been used in the analysis. Comparison of the ex-
perimental and modelling results has shown that ATENA
has satisfactorily captured the load-deflection behaviour
of the beams.
6. Acknowledgment
The financial support under Framework 5 project
Cost-effective, sustainable and innovative upgrading
methods for fire safety in existing tunnels (UPTUN,
project No GRD1-2001-40739/UPTUN) provided by the
European Community is gratefully acknowledged.
References
1. Felicetti, R.; Gambarova, P. G. and Meda, A. Expertise
and Assesment of Structures after Fire. In: Report in the
Meeting of fib Task Group 4.3.2 Guidelines for the Struc-
tural Design of Concrete Buildings Exposed to Fire, Brus-
sels, Nov 2002. 15 p.
2. Khoury, G. A.; Anderberg, Y.; Both, K.; Felinger, J.;
Majorana, C. E. and Hoj, N. P. Fire Design of Concrete:
Materials, Structures and Modelling. In: Proc. of the 1st
fib Congress Concrete Structures in 21
st
Century, Osaka,
2002, p. 99118.
3. Khoury G. A., Majorana C. E., Pesavento F. and Schrefler
B. A. Modelling of Heated Concrete. Magazine of Con-
crete Research, Vol 54, No 2, 2002, p. 77101.
4. Riva, P. Parametric Study on the Behaviour of RC Beams
and Frames under Fire Conditions. In: Report in the Meet-
ing of fib Task Group 4.3.2 Guidelines for the Structural

Design of Concrete Buildings Exposed to Fire, Brussels,
Nov 2002. 61 p.
5. Bazant, Z. P and Kaplan, M. F. Concrete at High Tem-
peratures: Material Properties and Mathematical Models.
Longman Group Lt., 1996. 412 p.
6. Mutoh, A. and Yamazaki, N. Non-linear Analysis of Rein-
forced Concrete Members under High Temperature. In:
Proc. of Conf. DIANA Computational Mechanics94.
Kluwer Academic Publishers, 1994, p. 4555.
7. Bratina, S.; Planinc, I.; Saje, M. and Turk, G. Non-Linear
Fire-Resistance Analysis of Reinforced Concrete Beams.
Structural Engineering and Mechanics, Vol 16, No 6, 2003,
p. 695712.
8. Sullivan, P. J. E.; Terro, M. J. and Morris, W. A. Critical
Review of Fire-Dedicated Thermal Structural Computer
Programs. In: Applied Fire Science in Transition Series,
Vol III Computer Applications in Fire Protection Engineer-
ing. Paul R. DeCicco ed Baywood Publishing Company,
Inc., 2001. p. 527.
9. Wang, Y. C. Steel and Composite Structures. Behaviour
and Design for Fire Safety. EF&N Spon, 2002. 264 p.
10. de Witte, F. C. and Wijtze, P. K. DIANA Finite Element
Analysis. Users Manual Release 8.1. Analysis Procedures.
TNO Building and Construction Research, Delft, 2002.
580 p.
11. Cervenka, V. and Cervenka, J. ATENA Program Documen-
tation. Part 2. ATENA 2D User Manual. Prague, 2002.
138 p.
12. Shi, X.; Tan T H.; Tan, K H. and Guo, Z. Effect of Force
Temperature Paths on Behaviour of Reinforced Concrete

Flexural Members. Journal of Structural Engineering,
Vol 128, No 3, March 2002, p. 365373.
13. prEN 1992-1-2. Eurocode2: Design of Concrete Structures
- Part 1.2: General Rules Structural Fire Design. Euro-
pean Committee for Standartisation, Brussels, July 2001.
102 p.
14. prEN 1992-1. Eurocode2: Design of Concrete Structures -
Part 1: General Rules and Rules for Buildings. European
Committee for Standartisation, Brussels, Oct 2001. 230 p.
15.
Iljin, N. A. Outcomes of fire effect on reinforced
concrete structures (ẽợủởồọủũõố ợóớồõợóợ õợỗọồộủũ-
õố ớ ổồởồỗợỏồũợớớỷồ ờợớủũúờửốố). Moscow:
Stroizdat, 1979. 128 p. (in Russian).
16. Cai, J.; Burgess, I. and Plank, R. A Generalised Steel/Re-
inforced Concrete Beam-Column Element Model for Fire
Conditions. Engineering Structures, Vol 25, No 6, 2003,
p. 817833.
17. Karihaloo, B. L. Fracture Mechanics and Structural Con-
crete. Longman Scientific and Technical, England, 1995.
330 p.
D. Bacinskas, et al
/ JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 2004, Vol X, Suppl 1, 1118
19
19
ANALYSIS OF THERMAL STRAIN OF STRUCTURAL STEELS IN VARIABLE
THERMAL FIELD
Zoja Bednarek, Renata Kamocka
The Main School of Fire Service (MSFS) in Warsaw, Str. J. Sùowackiego 52/54, 01-629 Warsaw, Poland.
E-mail: sgsp@ sgsp.edu.pl

Received 3 Nov 2003; accepted 8 Apr 2004
2004, Vol X, Suppl 1,1922
JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT
http:/www.vtu.lt/english/editions
ISSN 13923730
Abstract. The strain analysis of steels subjected to a thermal field with a high temperature increase rate is presented.
The results of tests of thermal strain caused by thermal expansion and the coefficient of linear thermal expansion are
presented for the structural steel, class AIII, grade 34GS, tested in a linearly variable temperature field at various heating
rates. The impact of heating rate on thermal strain ε
T
= α(T) · ∆T and coefficient of linear thermal expansion α(T) is
discussed.
Keywords: thermal expansion, thermal strain, coefficient of linear thermal expansion, structual steel.
1. Introduction
The impact of elevated temperatures on structural
materials (including structural steels) results in a change
of their elastic and plastic behaviour. The intensity of
such phenomena as creep and relaxation also increases
with temperature. As results of our previous studies, such
phenomena have a considerable impact on structural
strength at fire temperatures.
Furthermore, not only an absolute value of tempera-
ture is essential but also temperature distribution with
time and rate of temperature increase are of vital impor-
tance.
Our previous studies [1] concerning the impact of
rapid-heating conditions, like fire, on the properties of
reinforcing steel, also including its thermal strain, have
shown that:
• Such properties and the type of rupture are influ-

enced by temperature distribution during the test,
and in particular, by temperature increase rate
dT/dτ, what was found while testing steels at both
relatively slight and significant temperature increase
rates;
• Different grades of steels (including structural steels)
show some kind of inertia, which consists in a par-
tial or full inhibition of some processes leading to
the material rupture due to heating at a significant
rate as compared to the same processes at constant
temperatures or at a slight rate of temperature in-
crease;
• Thermal fields characterised by higher temperature
increase rates undoubtedly produce more favourable
effects in terms of the material strength, eg result
in higher critical temperatures (causing rupture).
Structural strength under fire conditions and fire
resistance are calculated on the basis of well established
mechanical and strength characteristics of building ma-
terials.
The nature of structural steels strain, being a result
of simultaneous impact of stresses and time-dependent
thermal field during a fire, is still under examination.
According to a proposal made by RILEM-
COMMITEE 44-PHT, an international committee, total
strain at elevated temperatures can be described by the
following constitutive equation for the material (steel):
( ) ( ) ( )
τσεσεεε
τ

,,, TTT
peT
++=
−
, (1)
where
T
ε
is thermal strain
( )
TT
T
∆αε
⋅=
caused by
thermal expansion of steel,
pe
−
ε
mechanical strain computed ignoring creep
strain as described by Ramberg-Osgood equation as fol-
lows:
σσ
σ
σ
εεε
µ
µ
1)(
)(

]
)(
1
[002,0
)(
−
−
+=+=
T
T
y
pepe
TTE
,(2)
τ
ε
is creep strain (dependent on time τ) as described by
Dorns theory and Harmothys studies; also being the
subject of our earlier studies conducted at the Applied
Mechanics Department (MSFS) under Z. Bednareks
guidance.
The total strain of steel at elevated temperatures can
be calculated by summing up the thermal strain, the strain
calculated from the Ramberg-Osgood equation and the
creep strain.
This paper presents the results of studies of the first
component of the steel strain model based on equation (1),
ie the thermal strain caused by linear expansion of steel.
20
20

2. Model of thermal expansion of solid bodies
According to the microscopic description, the ther-
mal expansion of solid bodies can account for an
increase of the crystal lattice parameter (interatomic dis-
tances in a crystal). Some of these phenomena can also
account for defects in the crystal lattice  mainly vacan-
cies (the lack of atom in the place, which is assigned to
such atom).
As temperature rises, the amplitude of atoms oscil-
lations from their average equilibrium positions increases
(Fig 1).
H

H

H
o

H
o

H
o

H
1

H
2


-
1

-
2

6
2
>6
1

.

7(H)

Fig 1. Relation between force, potential energy and inter-
atomic distance r: r
0
, r
1
, r
2
 average interatomic dis-
tances at increasingly elevated temperatures
The interatomic distance at temperature 0°K is con-
stant and equal to r
0
.
As temperature rises up to T
1

, the energy of atoms
in the crystal lattice increases resulting in their oscilla-
tions from their average equilibrium position r
1
[2].
It can be shown that the average displacement of
the equilibrium position can be expressed as
2
K
Tkb
x
⋅⋅
>=<
, (3)
where <x>  average distance from r
0
, eg <x> = r
1
 r
0
;
b  anharmonicity coefficient (determines the de-
viation of atom oscillations from harmonicity);
K  coefficient of quasi-elastic force acting between
atoms in the crystal lattice
(Fx = K
x
+ bx
2
);

T  temperature; k  Boltzman constant.
Thus, as temperature rises, the average interatomic
distance increases and the solid body expands.
There is the following relation between the linear
expansion coefficient α and the anharmonicity coefficient:
0
2
0
1
r
K
kb
Tr
x
⋅
⋅
=
⋅
><
=
α
. (4)
The higher the curve asymmetry, the greater the
thermal expansion coefficient.
3. Testing the impact of temperature on steel strain
due to linear thermal expansion
Steel is a homogenous and isotropic continuous
medium, which is subject to thermally activated strain.
A body length at a given temperature can be deter-
mined by means of the following formula:

l(T) = l
0
(1 + αT + βT
2
). (5)
For isotropic changes (a steel specimen), when ap-
proximating linearity of changes in length, we can write:
∆l = l(T)  l
0
= α(T) l T
or (6)
ε = ∆l/l = α(T) × T.
According to Harmothy [36] (ENV 1993-1-2), the
strain of heated steel with temperature can be expressed
by the following formulae:
l
l∆
= 1,2 · 10
5
T +0,4·10
8
T
2
 2,416 · 10
4
20 °C < T <750°C, (7a)
l
l∆
= 1,1 · 10
2

750 °C < T < 860 °C, (7b)
l
l∆
= 2 ⋅ 10
–5
T + 6,2 ⋅ 10
–3
860°C < T < 1200 °C. (7c)
The linear expansion coefficient can be precisely
defined as:
p
dT
Tpdl
l
)
),(
(
1
0
=
α
, (8)
where p  constant pressure.
At constant pressure, coefficient α is a temperature-
dependant function.
For practical purposes of making structural analy-
sis, the average based on the reference value of
1,2 · 10
5
(1/deg) for low-carbon steels is frequently as-

sumed instead of an actual value of linear expansion
coefficient α at a given temperature. There is no avail-
able precise data on the linear expansion coefficient for
structural steels for the needs of a more detailed steel
strain analysis at elevated temperatures, including fire
conditions characterised by a rapid increase in tempera-
ture. When searching through the publications available
to us we have only found the data on American steel
ASTM A36 [7], austenitic steels S350GD, S355 and
S460 [8] and formulae describing the relation between
coefficient α and temperature as follows:
Z. Bednarek, R. Kamocka / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1922
21
21
α = (0,004T + 12) · 10
6
(1/K) [9, 6], (9)
α = (6,1 + 0,0019T)·10
6
inch/inch per degree [10].(10)
For the needs of further studies on individual com-
ponents of formula (1), which describes the strain of
structural steels at fire temperatures, the behaviour of
linear expansion coefficient for the steel, class AIII, grade
34GS, was examined in a linearly variable temperature
field at different heating rates.
The tests were conducted under anisothermic con-
ditions (T ≠ const) for 4 different temperature increase
rates. Fig 2 shows temperature-time distributions. Under
fire conditions, the rate of temperature increase is

5 °C/min for a steel element covered by a good quality
fire insulation. For uncovered structures, the rate of tem-
perature increase can reach 50 °C/min. The results of tests
are shown on Figs 3 and 4, below.
Fig 2. Relation between temperature and time for speci-
mens heated at various temperature increase rates
Fig 3. Relation between strain and temperature for speci-
mens heated at various temperature increase rates
Below, we present a comparison of the curve taken
from ENV 1992-1-2/1995/ (curve a) with our curves
(curves b, c, d, e in Fig 3) describing the relation
between strain and temperature that we obtained from
experiments:
a 
l
l∆
= 1,2 · 10
5
T +0,4·10
8
T
2
 2,416 · 10
4
,
(formula 7a)
b 
l
l∆
=1,32·10

5
T + 0,256 · 10
8
T
2
5,95·10
4
,
(11a)
c 
l
l∆
= 1,27 · 10
5
T + 0,322 · 10
8
T
2
 6,65 · 10
4
,
(11b)
d 
l
l∆
= 1,28·10
5
T + 0,298 · 10
8
T

2
 7,79 · 10
4
,
(11c)
e 
l
l∆
= 1,28 · 10
5
T + 0,244 · 10
8
T
2
 7,85 · 10
4
.
(11d)
The points marked in Fig 3 to determine curves "b,
c, d and e" are measuring points obtained by the authors
from their own tests, whereas points on curve "a" were
calculated according to the formula 7a taken from the
references.
Below, we present a comparison of the curve taken
from the references (curve a) with our curves (curves
b, c, d, e in Fig 4) describing the relation between

0,0E+00

2,0E-06


4,0E-06

6,0E-06

8,0E-06

1,0E-05

1,2E-05

1,4E-05

1,6E-05

0

100

200

300

400

500

600

Temperature [°C]


Thermal ex
p
ansion coefficient á
[
1/de
g]


b


c


a


d


e


a  wg Lie,T.T. [3]

b  dT/d
τ
= 5
°

C/min

c  dT/d
τ
= 10
°
C/min


d  dT/d
τ
= 15
°
C/min


e  dT/d
τ
= 20
°
C/min

Fig 4. Relation between thermal expansion coefficient and
temperature for specimens heated at various temperature
increase rates
thermal expansion coefficient a and temperature that we
obtained by experiments:
a  α = 4·10
9
T + 1,2·10

5
, (formula 9)
b  α =  2,51 · 10
11
T
2
+ 2,78 · 10
8
T + 5,87 · 10
6
,
(12a)
c  α =  2,81 · 10
11
T
2
+ 3,04·10
8
T + 5,3·10
6
,
(12b)
d  α =  3,08·10
11
T
2
+ 3,39 · 10
8
T + 3,9·10
6

,
(12c)
e  α =  3,89 · 10
11
T
2
+ 4,09·10
8
T + 1,95 · 10
6
.
(12d)
The points marked in Fig 4 to determine curves b,
c, d and e are measuring points obtained by the authors
in their own tests, whereas points on curve a were
calculated according to formula (9) taken from the refer-
ences.
Z. Bednarek, R. Kamocka / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1922
22
22
4. Conclusions
The objective of investigations was to determine and
conduct a comparative analysis of thermal strain and ther-
mal expansion coefficient for structural steels at differ-
ent temperature increase rates. As the results of the tests
conducted at different heating rates on specimens made
of structural steel, class AIII, grade 34GS show, the ther-
mal strain of specimens is affected by the temperature
increase rate. The higher the temperature increase rate,
the lower the thermal strain of specimen. The thermal

expansion coefficient also changes in a similar way. The
reason for such a behaviour of steel is its material iner-
tia which consists in a partial or full inhibition of some
processes leading to the material rupture and taking place
in steel due to a significant heating rate, as we have also
shown in our papers [1] and [11].
Linear expansion coefficient α(T) rises with tem-
perature. As the regression analysis of the results, ob-
tained by the tests on linear expansion coefficient α at a
given heating rate shows, the best correlation degree was
obtained when approximating experimental data with
quadratic polynomials. This paper includes the functions
that describe the relation between coefficient a and tem-
perature at different heating rates (formulae 12a, b, c,
and d).
References
1. Bednarek, Z. Influence of thermal conditions on strength
parameters of reinforcing steel exposed to fire. Inýynieria
i Budownictwo, 12/93, p. 526528.
2. Staub, F. Metal Science, WNT Katowice 1994.
3. Lewis, K. R. Fire design of steel members, fire engineer-
ing research report 2000/07 ISSN 11735996.
4. Böðvar, T. High performance concrete. Design guide lines,
Department of fire safety engineering, Report 5008, Lund,
1998.
5. Burgon, B. Elevated temperature and high strain rate prop-
erties of offshore steels, Steel Construction Institute, Off-
shore Technology Report 2001, 020, Norwich.
6. Alfawakhiri, F.; Sultan, M. A.; MacKinnon, D. H. Fire
Resistance of Loadbearing Steel-Stud Walls Protected with

Gypsum Board: A Review, Fire Technology, Vol 35, No 4,
1999.
7. Skowroñski, W. Theory of fire safety of steel structures,
PWN 2001.
8. Outinen, J.; Kaitila, O.; Mäkeläinen, P. High-temperature
testing of structural steel and modelling of structures at
fire temperatures. Research report TKK-TER-23. Helsinki
University of Technology, 2001.
9. Guy C. Gosselin. Structural fire protection- predictive
methods, Building science inside 1987, Institute for Re-
search in Construction, National Research Council Canada.
10. R.H.R. Tide: Integrity of structural steel after exposure to
fire, Engineering Journal /First Quarter, 1998.
11. Bednarek, Z. Effects of increase of temperature on struc-
tural steel strength parameters as applied to the estimation
of fire safety of concrete construction. Doctor Habilitatis
thesis. Vilnius: Technika, 1996, p. 1208.
Z. Bednarek, R. Kamocka
/ JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 1922
23
23
2004, Vol X, Suppl 1, 2329
JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT
http:/www.vtu.lt/english/editions
ISSN 13923730
SLIP OF BULLDOG-TYPE TOOTHED-PLATE CONNECTORS IN STEEL-TIMBER
JOINTS OF OPEN-WEB GIRDERS
Rimantas Èechavièius
Dept of Metal and Timber Structures, Vilnius Gediminas Technical University,
Saulëtekio al. 11, LT-10223 Vilnius-40, Lithuania. E-mail:

Received 4 June 2003; accepted 3 May 2004
1. Introduction
Toothed Bulldog-type plate connectors (DS Bull-
dog) are means of mechanical ties used in timber struc-
tures. The main purpose of them is to increase the tim-
ber bearing area in structural joints and to diminish the
slip of feathered joints. They could also allow to increase
considerably the bearing capacity of such joints and to
tie light steel-timber open-web girders (trusses) and
frames. This is characteristic of OPEN-WEB trusses
having been produced since 1960 by the joint-stock com-
pany MacMillan; these trusses can be used for span-
ning both small openings (l≈4,59m) and large (12
120m) ones (Fig 1).
The main advantages of such trusses are their small
weight and rational joint work of timber chords and the
network of metal tubes. The main research on the bear-
ing capacity of toothed Bulldog-type connectors was
performed at Stevin-Laboratorium (Delft University of
Techology, Netherlands), Dannish Construction Research
Institute, Otto-Graf Institute (Stuttgart University, Ger-
many) [15]. During these investigations the strength of
joints was analysed by J.H. Blass, etc [67]. The model
of calculating such joints presented in his work is rec-
ommended by the project of new Eurocode standards [8].
The slip of Bulldog-type plate connectors was investi-
gated by Y. Hirashima [9]. The results are presented in
Fig 2, where slipping of different joining means is com-
pared.
Abstract. Composite steel-timber open-web girders invented by Truss Joint MacMillan company (Canada) provide

some technological and structural advantages. Timber chords and steel diagonals of triangular open-web are connected
by "Bulldog" type single-sided toothed-plate connectors. The article presents the results of research on four real-size
(span  3 m) open-web trussed purlin with "Bulldog"-type connectors. From carried out tests next parameters are
determined: resistance of "Bulldog"-type connectors, slip modulus and statical slip values depending on the angle
between the force and wood fibres directions. It is also received numerical values of the slip modulus and statical slip,
which are substantically greater than given in experimental Eurocode 5. The tests also let to find that redistribution of
forces in steel diagonals of the trussed purlin starts when slip of "Bulldog"-type connectors in steel-to-timber joints
approaches to the limit (2 mm) value.
Keywords: composite structure, steel-timber joint "Bulldog"-type connector, slip, resistance test.
The majority of these results is obtained by investi-
gating separate joints. But there is a lack of data con-
cerning the slip of such joints in real steel-timber struc-
tures where the redestribution of stresses among
individual truss elements becomes clear.
The article presents the results of research on four
open-web trusses with Bulldog-type connectors [10
12]. Not only the strength of such joints and their slip
but also the stress redestribution among elements of the
truss were determined.
Fig 1. Composite steel-timber open-web truss of Truss
Joist MacMillan
24
24
2. The structure of trusses and test scheme
Four steel-timber (3 m span) trusses SN-1-1, SN-1-
2, SN-1-3, SN-1-4 have been tested and some joints of
them strengthened by DS Bulldog [13]: all joints in
SN-1 and SN-2; mostly loaded were the joints M1, M5,
M6, M7, M10 and M11 in trusses SN-1-3, SN-4. In the
latter trusses, the less loaded joints M2, M3, M4, M8,

M9 were connected only by bolts M16. All the network
Fig 2. Experimental load-slip curves for joints in tension
parallel to the grain: a  glued joints (12, 5·10³ mm²), b 
split ring (100 mm), c  double-sided toothed plate (¸ 62
mm) [15], d  dowel (¸ 14 mm), e  bolt (¸ 14 mm), f 
punched plate (0,1E5 mm²), nail (¸ 4,4 mm)
Fig 4. Truss testing scheme: a  general view of truss
testing (SN-1-3); b  truss SN-1-1 testing diagram: 1 
truss SN-1-1; 2  traverse; 3  hinge; 4  stiff support;
5  jack; 6  dynamometer; 7 steel spreader; 8  timber
pad; X  traverse braces; T1-T16  electric strain resis-
tance gauges; II.1  II.7  0,01 mm accuracy dial gauges
(deflection indicators); In.1In. 6  displacement of ends
of pipe indicators with precision of 0,01 mm
Fig3. Structure of SN-1 trusses: adiagram for analysis;
bstructure of M6 joint; cstructure of M1 joint
=
3. A
3. B
3. C
4. B
4. A
Joint M6
Joint M1
R. Èechavièius / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 2329
25
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Table 1. Schedule of materials for a SN-1 truss
No Materials and details Characteristic Remarks, standards
1 Wooden element (upper chord) 50×120 Fig 4. Test of girder

diagram:mm, 1 = 3280 mm
Pinewood, 2
nd
sort W = 12%+/-2%
2 Wooden element (lower chord) 50×120 mm, 1 = 2680 mm Pinewood, 2
nd
sort W = 12%+/-2%
3 Tube (truss network) d = 45,0 mm, t = 4,0 mm, 1 = 680 mm C235, GOST 10704-76
4 Toothed connector E75M16 DIN 1052 Bulldog [19]
5 Pin M16,1 = 200 mm C235, GOST 1759-70
6 Plate (insertion) a = 68 mm, t = 8 mm, hole 16,5 mm C235, GOST 27772-88
7 Washer a = 68 mm, t = 6 mm, hole 16,5 mm C235, GOST 27772-88
8 Nut M16 C235, GOST 1759-70
elements of metal tubes are connected at 60° angle with
the upper and lower chords. The tubes at connecting
points are flattened and a hole of 16,2 mm was drilled.
In joints with one network element (M6 and M11), an
insertion was put. The structure of these trusses and the
testing scheme are shown in Figs 3, 4 and Table 1.
The trusses were tested at the laboratory of build-
ing structures of the VGTU. The source of loading was
a hydraulic jack based on a rigid metal frame. The
scheme of truss testing is shown in Fig 4. Strain gauges
(20 mm on metal and 50 mm on wooden basis) were
used only when testing SN-1-1 truss. The vertical strains
of truss supports and lower chords joints as well as slip
strains of joints M1, M5, M6, M11 were measured by
indicators of 0,01 mm precision.
For stability of experimental equipment in the plane
of bending moment, hinge supported horizontal wooden

squared beam connections were provided. It was observed
during testing that the horizontal ties are free and they
do not hinder transferring vertical forces.
3. Test results
It has been determined by testing steel-timber con-
nections [14, 15] that the characteristic value R
ck
 of truss
chord timber compressive strength along fibres is equal
to 38,61 MPa and characteristic volume weight r
k
= 434
kg/m². Testing trusses lasted for 23 h. During this time
span the strains of on average 21 devices were deter-
mined at every stage of 15 loadings. Loading duration
in separate stages was in the interval of 1020 min de-
pending on the necessity to rearrange either the devices
(when strains were larger than the size of limit strains)
or the equipment of horizontal braces. Testing trusses is
shown in Fig 5.
The unit deformations of the truss SN-1-1 are shown
in Fig 6. The average strains in compressive truss bars
17 and 510 under the loading of 80 kN (σ
c
= 86,64
MPa) and in the members in tension 16 and 511 un-
der the loading of 110 kN (σ
c
= 121,46 MPa) were close
to those calculated theoretically according to the experi-

mentally defined pipe compressive (E
t
) and tensioned
bars elasticity models: E
c
=2,10·10
5
MPa, and
E
t
=2,12·10
5
MPa. But from F=8590kN loading the
growth of strains of compressed pipes and from F=110
kN the strains of tensioned pipes decreased considerably
and later have stopped almost entirely. Thus at the in-
crease of loading the stresses in these bars have not
changed, ie the stresses were redestributed among the
truss elements. This phenomenon can be explained by
the data of Table 2: exactly at this time M-11 ir M-6
joints slip deformations were larger than the allowable 2
Fig 5. General view of testing the open-web truss: atest of truss SN-1-2; b  arrangement of test
devices in the truss SN 14
R. Èechavièius / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 2329
26
26
Table 2. Characteristics for serviceability limit state of Bulldog-type connectors in steel-to-timber joints
Impact kN
Slip modulus according to LST EN 26891 [19],
kN/mm

Slip according [14]

No of girder
connections
No of joint
connections
α
°,
F
max
F
2
K
s
K
0,6
K
0,7
K
0,8
K
e
u
K
e
ser

K
e
ser

K
t
ser

K
e
u

K
t
u

U
y
,
mm
U
u
,
mm
µ
s

M1 90 36,2 23,0 21,0 12,0 11,0  2,8 11,5 1,18 0,43 1,07 13,0 12,15
M2 90 32,2 21,6 22,9 13,8 9,6  3,9 10,8 1,11 0,60 0,85 8,2 9,65
M3 90 31,8 21,0 20,3 11,8 9,2  5,8 10,5 1,08 0,89 0,85 5,5 6,47


Connections
B-2


Vid.: 90 33,4 21,9 21,4 12,6 10,0 4,2 10,9 1,12 0,64 0,92 8,9 9,42
M4 0 34,0 26,2 24,0 18,6 15,3  5,7 13,1 1,34 0,93 0,97 6,0 6,19
M5 0 38,0 30,0 24,6 21,6 17,9  5,4 15,0 1,54 0,83 1,17 7,1 6,07
M6 0 39,5 25,7 25,9 16,2   4,4 12,8 1,31 0,68 0,92 9,0 9,80

Connections
B-1

Vid.: 0 37,1 27,3 24,8 18,8 16,6 5,2 13,6 1,40 0,81 1,02 7,4 7,35
M6 60 36,4 29,3 41,8 21,7  16,0 7,7 14,7 1,51 1,18 0,7 4,7 6,7
SN-1-1
M11 60 36,4 24,5 38,4 15,3  9,6 6,6 12,2 1,25 1,01 0,5 5,5 11,0
M6 60 34,2 29,2 39,2 19,4  15,4 11,8 14,6 1,50 1,81 0,4 2,9 7,3
SN-1-2
M11 60 34,2 20,7 17,7 10,7  7,3 5,4 10,4 1,07 0,83 1,1 6,3 5,7
M6 60 37,0 19,2 14,2 7,6  5,7 6,2 9,6 0,98 0,95 1,0 6,0 6,0
SN-1-3
M11 60 37,0 19,5 10,2 9,2  8,5 2,8 9,8 1,00 0,43 0,4 5,3 13,2
M6 60 37,0 26,2 44,0 19,1  11,2 2,5 13,1 1,34 0,38 0,4 5,9 14,8
SN-1-4
M11 60 37,0 29,2 48,3 19,3  15,7 9,7 14,6 1,50 1,49 0,4 3,8 9,5

Average 60 36,2 24,7 31,7 15,3 11,2 6,6 12,4 1,27 1,01 0,6 4,9 7,4
Fig6. Kinetics of strain in steel web members of SN-1-1
(Figs3, 4). Tension members: 16 (T-9, T-10) and 511
(T-15, T-16); compression members: 17 (T-11, T-12)
and 510 (T-13, T-14); 1, 2  strain of compression and
tension members, respectively
Fig7. End displacements of web members of SN-1-2 truss

(Figs3, 4): dial gauges In.1 and In.4 for tensile member
16; In.2 and In.5for tensile member 511; In.3 and
In.6for compressive struts 17 and 510, respectively
Fig8. Views of joints M6 (In.1) (a) and M1 (In.3 and In.4) (b) of SN-1-4 truss after failure
R. Èechavièius
/ JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 2329