FIRE DESIGN OF BOLTED BEAM-TO

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FIRE DESIGN OF BOLTED STEEL BEAM-TO-COLUMN JOINTS
Aldina Santiago; Luís Simões da Silva
ISISE - Department of Civil Engineering, University of Coimbra, Portugal
[email protected]; [email protected]
Paulo Vila Real
LABEST - Department of Civil Engineering, University of Aveiro, Portugal
[email protected]
ABSTRACT
In this paper, the main approaches used for developing a practical consistent
methodology to predict the behaviour of bolted steel beam-to-column joints under a
natural fire are presented and discussed. This methodology incorporates the influence of the transient temperature variation on the time-varying forces that act on the
joint and gives design guidance on how to avoid the failure of the joint throughout
the fire event (heating and cooling phase). Validation of the proposed model is carried out by comparison against the available results obtained from an experimental
programme of steel sub-frames under a natural fire undertaken at the University of
Coimbra, Portugal (Santiago et al., 2008).
1. INTRODUCTION
Under a natural fire conditions, the behaviour of steel joints within a structure
highly depends on the redistribution of internal forces with time as a result of the
global behaviour of the structure. In this situation, the actual behaviour clearly deviates from the results of isolated joint tests, being subjected to a full 3D stress state
(N, My, Mz, Mt, Vz and Vy), resulting from local, distortional or global instability of the
connected members that could lead to the failure of the tensile components (such as
bolts or end-plates).
This paper gives a brief description of a consistent methodology to predict the
behaviour of bolted steel beam-to-column joints under a natural fire. This methodology incorporates the influence of the transient temperature variation on the timevarying forces that act on the joint and gives design guidance on how to avoid the
failure of the joint throughout the fire event. Validation of the proposed model is carried out by comparison against experimental results (Santiago et al., 2008).
2. BEHAVIOUR OF JOINTS IN FIRE
Based on the studies previously described, it is confirmed that it was in the last fifteen years that the subject of steel joints under fire conditions suffered its main developments. Several experimental tests were performed in different typologies of
joints and under different boundary and loading conditions, and analytical and numerical models were developed, which tried to reproduce adequately the behaviour
of such tested joints. However, some of these experimental tests were concentrated
on predicting the behaviour of isolated joints at high temperatures under monotonic
bending loading, while other tests used this known bending-rotational behaviour as
HEA 300
HEA 300
300
1129
boundary conditions, in order to study the behaviour of the heated connected
beams. Despite the evident importance of modelling the behaviour of beam-tocolumn joints under a natural fire, as part of a frame structure, low experimental
studies concerned with this matter have yet been published in the open literature.
In a research projected developed at the University of Coimbra (Santiago et
al., 2008; Santiago, 2008), some fire tests on a sub-frame beam-to column were carried out (Figure 1). The structural definition consisted of two thermally insulated
HEA300 cross-section columns (S355) and an unprotected IPE300 cross-section
beam (S355) with 5.7 m free span, supporting a steel-concrete composite slab. The
mechanical loading applied at room temperature corresponded to the self-weight
and the concentrated loads equal to 20 kN at 700 mm from the mid-span crosssection; the thermal loading corresponded to a heating-cooling curve applied to the
beam and joints.The parametric study is focused on the beam-to-column joint configuration (Table 1).
IPE 300
1210
5700
Z
Y
X
Figure 1. Structural model (mm).
Table 1. Beam-to-column joint configuration.
Test ID
FJ01
FJ02
FJ03
EJ01
HJ01
WJ01
Joint typology
Flush end-plate
Extended end-plate
Header plate
Welded
End-plate dimensions (mm)
and steel grade
(320×200×10); S275
(320×200×16); S275
(320×200×16); S275
(385×200×16); S275
(260×150×8); S275
-------------
Bolts / Weld
2 bolt row M20, 8.8
2 bolt row M20, 10.9
2 bolt row M20, 8.8
3 bolt row M20, 8.8
4 bolt row M20, 8.8
af = aw = 10 mm
3. COMPONENT METHOD IN FIRE
3.1
Overview
Over the past three decades, a considerable effort was undertaken to give
consistent predictions of the steel joints at room temperature using the component
method (Jaspart, 2002); however due to the large number of parameters that need
to be taken into account when modelling the joint's response in fire, very little research work has been conducted in fire situation; exception should be mentioned to
the work developed by the University of Coimbra (Simões da Silva et al., 2001), the
University of Sheffield (Block et al., 2007) and the Imperial College London (Ramli
Sulong et al., 2007). From the available methods(Simões da Silva et al., 2005), the
component-based approach is also chosen in this work to model the connection behaviour because of its computational efficiency and capacity to provide a reasonable
representation of the full range of response starting from the actual geometrical and
mechanical properties.
3.2
Proposed component method
Considering the evidences reached from the experimental tests and the numerical simulations (Santiago et al., 2008 and Santiago, 2008), some important aspects were identified as relevant for the formulation of any component methodology
to analyse steel joints under fire: i) components characterization; ii) material properties dependency with temperature; iii) variable combination of bending moment and
axial force; iv); non-conservation of linear cross-sections; v) loading-unloadingreloading that characterise the changing temperatures; vi) effective length of the
components.
The spring model chosen in this work corresponds to the one developed by
Cerfontaine (Cerfontaine, 2004) to analyse joints under bending moment and axial
force at room temperature. Figure 2 depicts the proposed model to a flush end-plate
joint; the number and location of each component depends on the joint typology. For
a bolted joint, the compression components (beam flange in compression and column web in compression) are located at the level of the beam flanges axis and the
tension components (column web in tension, column flange in bending, end-plate in
bending, bolts in tension and beam web in tension) are located at the level of the
bolt rows axis. Additionally, the shear column components are located independently
of the tension-compression system, as suggested by Cerfontaine. However an important difference should be highlighted; in the Cerfontaine model, the axial force
and bending moment is monotonic increased and proportional throughout the analysis; but under a natural fire, the axial force changes from compression to tension
and the bending moment from hogging to sagging.
tension components (1st bolt row)
co
lum
n
we
b
in
sh
ea
r
compression components (beam top flange)
tension components (2nd bolt row)
compression components (beam bottom flange)
Figure 2. Proposed model to a flush end plate joint.
For the performed experimental tests, the columns were maintained at low
temperatures, and its deformability, compared with the global deformability of the
joint, was much reduced (Santiago, 2008). So, on the application of the proposed
model, the column web components could be disregarded: column web in shear,
compression and tension.
The application of the proposed model is feasible when the component response is introduced as a force – displacement curve. Due to the reduced number of
studies on the component characterization at high temperatures, a bilinear law was
assumed in this study: the plastic resistance and initial stiffness at room temperature
were calculated according the EN 1993-1-8-2005; once the component was loaded
beyond its yield capacity, post-limit stiffness defined on literature was adopted (San-
tiago, 2008). For each step, the degradation of the strength and stiffness of each
component material with temperature was considered using the reduction factors
proposed by EN 1993-1-2-2005, and the component temperatures corresponded to
the experimental measurements (Figure 3). The effective length of each component
remains constant throughout the analysis and corresponds to the value calculated
by the EN 1993-1-8-2005 at room temperature.
7 50
6 00
b o t t o m flan g e (jo in t )
w e b (jo in t )
900
t o p flan g e (jo in t )
b o t t o m flan g e (b e am ) 750
w e b (b e am )
600
t o p flan g e (b e am )
temp. (ºC)
b e am
b e am
b e am
b e am
b e am
b e am
tem p . (º C)
9 00
bolts
end-plate
450
4 50
300
3 00
150
1 50
t im e (m in )
0
0
20
40
60
80
1 00
1 20
14 0 1 60
time (min)
0
0
20
40
60
80
100 120 140 160 180
18 0
Figure 3. Temperature applied to the FJ03 model.
The variable combination of bending moment and axial force, derived from
the finite element models, was introduced in the spring model as axial forces at the
level of each component (Santiago, 2008).
To respond to the changing loading-unloading-reloading characteristic, a
modified Masing rule has also been implemented into the model. Masing rule assumes that a material like steel unloads with a stiffness equal to the initial stiffness
of the loading curve, and then follows a hysteresis curve meeting the mirror image of
the point at which unloading started in the opposite quadrant. However, if the temperature changes between loading and unloading, this process becomes more complicated because the components response is temperature dependent. In this case,
the assumption that the plastic strain is not affected by the temperature distribution
should be employed (Franssen, 1990). The main underline of this assumption it that
each force-displacement curves at different temperature unloads to the same plastic
deformation, p (Figure 4).
One of the main problems of this approach originates from the fact that the
tensile and compressive forces in the connection do not share the same line of action. So, it was assumed that the compression springs are plastically deformed and
unload until the end-plate loses contact with the column flange, the compression
springs are deactivated and the tension springs start taking load from this deformed
position. However, if the tension springs are deformed plastically and unload to initial
position, it is assumed that all subsequent compression forces in the tension spring
is taken by the compression spring row adjacent to the unloading tension spring row.
Another problem inherent to a fire situation is the large deformations developed on the beam. After large deformations, the well known Bernoulli’s hypothesis,
according to which plane cross-sections remain plane in the deformed state of the
beam, is not valid, as observed in the experimental tests (Santiago et al., 2008). The
component method presented in the EN 1993-1-8 assumes that the cross-section
remains always plane, even at large deformations. Here, the same simplifying assumption was adopted.
0
Force, F
F Ed , 0
A
A'
F Rd , 0
F Rd , 1
F Ed , 1
1
 1 >  0)
B
Deformation ,
O
p 0
O'
Figure 4. Force-displacement paths for loading with increasing temperature.
3.3
Application to a bolted end-plate beam-to-column joints
The connection element has been validated against the experimental results
(Santiago et al., 2008). The active components were chosen according the variation
of the axial stresses integrated in a beam cross section near the connection and the
axial stresses of the bolts; Figure 5 illustrates it for the flush end-plate joint FJ03:
The active beam components were divided in five periods: t < 12 min - compression
in the lower zone and tension in the upper zone; 12 ≤ t < 27 min - compression in
the lower and upper zones; 27 ≤ t < 90 min - compression in the lower and tension in
the upper zone; t ≥ 90 min - tension in the lower and upper zones.
400
160
200
t (min.)
0
-200
-400
-600
0
Fx (kN)
200
Fx (kN)
600
25
50
75
100
125
150
175
compression in the upper zone
tension in the upper zone
tension in the lower zone
compression in the lower zone
200
tension in the 2nd bolt-row
120
tension in the 1st bolt-row
80
40
t (min.)
0
0
25
50
75
100
125
150
175
200
Figure 5. Forces introduced in the component model (joint FJ03).
Applying the axial forces and the bilinear force-displacement response of the
active components at each temperature (Figure 6), the main quantities relevant for
the FJ03 joint, for some representative times, are set out in Tables 2 and 3. For t <
27 min; no active component reached its capacity. Between 27 ≤ t < 90 min. the
beam bottom flange exhibits a decrease of the compressive force and the upper
connection zone changes from compression to tension. This change of forces is
shown in the active components during this period: the components reached their
highest temperature leading to a relevant decrease of their resistances and to the
yielding of the beam bottom flange in compression and beam web in tension (top).
F (kN)
900
end-plate in bending
bolts in tension
beam flange in compression
beam web in tension
column flange in bending
750
600
450
300
150
dx (mm)
0
0.0
0.2
0.4
0.6
0.8
1.0
Figure 6. Force-displacement response of each component at room temperature.
Table 2. Proposed model applied to the bolted joint FJ03 (27 ≤ t < 90 min).
beam bottom
flange in compression
1st bolt-row in
tension
end-plate in
bending (top)
column flange
in bending
(top)
Beam web in
tension (top)
t (min)
27.0
42.0
89.0
27.0
42.0
89.0
27.0
42.0
89.0
27.0
42.0
89.0
27.0
42.0
89.0
temp. (ºC)
700.0
849.5
686.5
206.4
378.7
414.5
291.1
518.2
502.5
95.4
302.7
404.9
636.0
790.9
572.6
FRd,t (kN)
188.4
69.8
215.0
370.4
318.5
294.8
336.2
243.2
259.7
390.7
390.7
390.7
250.8
79.1
362.9
FEd,t (kN) t (mm)
189.0
0.396
51.1
0.396
27.2
0.396
41.2
0.027
110.8
0.090
77.8
0.067
33.0
0.015
87.1
0.057
113.9
0.069
41.2
0.008
110.8
0.028
77.8
0.023
33.0
0.000
87.1
0.423
113.9
1.609
note
yield
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
yield
elastic
From Figure 5 it is observed that between 90 ≤ t < 165 min, only the tension
components are active. According the proposed methodology, there was one component that reached its plastic resistance: end-plate in bending (bottom) at t = 131
min, FRd,t = 336.2 kN and FEd,t = 358.2 kN, with a corresponding displacement of t =
0.93 mm (Table 3). The last active component that reached its maximum capacity
was the 2nd bolt-row in tension at t = 165 min, FRd,t = 376.7 kN and FSd,t = 377.1 kN,
with a corresponding displacement of t = 13.6 mm. It should be referred that on the
experimental test, this component failed at t = 190 min. For each bolted end-plate
beam-to-column joints, Table 4 summarizes the components that reached their plastic capacity.
4. RECOMMENDATIONS FOR DESIGN RULES
In the previous section, a methodology for the evaluation of the response of
steel joints under fire loading based on the component method was developed and
applied. It was able to reproduce with sufficient accuracy the transient response of
the steel joints throughout the fire development and to identify the failure modes of
the joint. This procedure provides an adequate basis for incorporation in advanced
Table 3. Proposed model applied to the bolted joint FJ03 (90 ≤ t < 165 min).
t (min)
temp. (ºC)
FRd,t (kN) FEd,t (kN)
t (mm)
note
1st bolt-row in
tension
end-plate in
bending (top)
column flange in
bending (top)
Beam web in
tension (top)
2nd bolt-row in
tension
end-plate in
bending
(bottom)
column flange in
bending
(bottom)
Beam web in
tension (bottom)
90.0
131.0
165.0
90.0
131.0
165.0
90.0
131.0
165.0
90.0
131.0
165.0
90.0
131.0
165.0
90.0
131.0
165.0
90.0
131.0
165.0
90.0
131.0
165.0
389.1
256.5
159.3
467.1
300.9
192.9
379.2
241.3
161.2
515.8
292.3
153.2
389.1
256.5
159.3
455.0
314.1
196.6
379.2
241.3
161.2
515.8
292.3
153.2
313.2
364.0
376.7
286.6
336.2
336.2
390.7
390.7
390.7
478.0
653.7
653.7
313.2
364.0
376.7
276.7
336.2
336.2
390.7
390.7
390.7
653.7
653.7
653.7
86.4
183.8
275.6
118.9
186.5
234.9
86.4
183.8
275.6
118.9
186.5
234.9
35.9
299.2
377.1
0.0
358.2
497.9
35.9
299.2
377.1
0.0
358.2
497.9
0.072
0.128
0.173
0.067
0.083
0.093
0.024
0.043
0.059
1.609
1.609
1.609
0.030
0.209
13.60
0.000
0.930
5.105
0.010
0.070
0.081
0.000
0.000
0.000
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
elastic
yield
elastic
yield
plastic
elastic
elastic
elastic
elastic
elastic
elastic
Table 4. Sequence of yield or failure (bolts) of the components to each bolted endplate beam-to-column joints.
acting Top – T
forces Bottom - C
-----FJ01
FJ02
------
FJ03
------
EJ01
------
Top – C
Bottom - C
Heating
t = 22 (beam bottom flange in
compression)
t = 22 (beam bottom flange in
compression)
Top – T
Bottom - C
t = 32 (end plate
in bending - top)
Top – T
Bottom - T
Cooling
t = 99 (end plate in bending - bottom)
t = 44 (beam web t = 123 (column flange in bending in tension - top)
bottom)
t = 141 (column flange in bending top)
t = 170 (failure of the 2nd bolt-row
in tension is imminent: FEd,t = 0.99
FRd,t)
t = 27 (beam bot- t = 42 (beam web t = 131 (end-plate in bending - bottom flange in
in tension - top)
tom).
compression)
t = 165 (2nd bolt-row in tension)
t = 34 (beam
t = 110 (end-plate in bending – 3rd
web in tension bolt-row)
bottom)
-----t = 141 (beam web in tension - 3rd
bolt-row)
t = 190 (3rd bolt-row in tension)
calculation methods through the development of specialized joint finite elements.
However, for conceptual and pre-design, the proposal of simple design recommendations is a desirable goal. Although the number of tests carried out in this research
work is clearly insufficient to validate wide-ranging simplified rules, it is nevertheless
enough to propose a framework and a methodology for future simplified rules.
600
105
80
55
350
t (min.)
100
-150 0
-400
-650
-900
M (kNm)
850
Fx (kN)
Focussing on bolted end-plate beam-to-column joints, simplified design rules
should take into account two distinct design points (on top of the fulfilment of the
cold-design criteria): (i) design period A that corresponds to the critical period during
the heating phase; and (ii) design period B that corresponds to the critical cooling
time. Based on the times when the active components yield or fail (bolts in tension):
period A is in the range 20 ≤ t ≤ 40 min and period B in the range t ≥ 100 min. Naturally, the choice of these two design periods depends on the fire scenario that must
be considered as a relevant parameter in the simplified design recommendations. To
propose these periods, only the fire scenario adopted in this research work was considered.
The second step in the proposed simplified procedure consists on the evaluation of approximate levels of bending moment and axial force corresponding at the
two design periods A and B (Figure 7).
25
50
75
100
125
FJ02 - beam
FJ03 - beam
EJ01 - beam
FJ01 - beam
150
175
30
t (min.)
5
200 -20 0
25
50
75
100
125
-45
FJ03 - beam
-70
EJ01 - beam
FJ02 - beam
-95
-120
150
175
200
FJ01 - beam
Figure 7. Numerical curves of the axial force and bending moments on the joints
during the fire.
Finally, the tensile capacity of the main brittle component, which could lead to
the structural failure, should be compared with the active forces. In this case, special
reference will be made to the bolts in tension during the cooling phase:
Ften ,t ,Ed  F ten ,t ,Rd  0.9f ub As k b ,θ
(1)
where Ften,t,Ed is the tensile force in the bolt; Ften,t,Rd is the design tension resistance
of a single bolt in fire; fub is the ultimate stress of the bolts; As is the tensile stress area of the bolt and kb, is the reduction factor for bolt resistance at temperature 
This comparison is made in Figure 8. The tensile bolt forces are represented by
thick lines, the bolt resistances are drawn using dashed lines and the failure of the
bolts is represented by a circle. This approximation allows the identification of the
bolt failure.
Of course, the tensile forces in the bolts were obtained performing an exhaustive numerical model. The identification of the degree of lateral and rotational restraint of the beam and the evaluation of approximate levels of bending moment and
axial force at the two design periods A and B could be an alternative to obtain these
tensile forces. As example, expressions proposed by Yin and Wang could be used
to approximate these values (Yin and Wang, 2005). Although appropriate calculation
and benchmarking would be mandatory.
500
Fx (kN)
400
300
200
FJ02 - 2nd bolt-row
FJ03 - 2nd bolt-row
EJ01 - 3rd bolt-row
FJ01 - 2nd bolt-row
t (min.)
100
0
0
25
50
75
100
125
150
175
200
Figure 8. Bolts in tension.
Moreover, to avoid failure of the joint throughout the fire development, it was
shown that a crucial factor is the ability of the connection to redistribute the applied
internal forces. In particular, the deformability of the end-plate vis a vis the forces in
the bolts plays a most relevant role. In EN 1993-1-8-2005 it is stated that a bolted
end plate joint may be assumed to have sufficient rotation capacity for plastic analysis, provided that both of the following conditions are satisfied: (i) the moment resistance of the joint is governed by the resistance of either the column flange in
bending or the end plate in bending and (ii) the thickness t of either the column
flange or the end plate (not necessarily the same basic component as in (i)) satisfies:
t  0.36
f ub
fy
(2)
where  is the bolt diameter, fu.b is the tensile strength of the bolt and fy is the yield
strength of the relevant basic component. The application of this expression to the
tested joints, results in the following bolt requirements (Table 5). It is observed that
only the joint FJ01 meets the ductility criteria.
Table 5. Ductility criteria (EN 1993-1-8-2005).
fub (MPa) fyp (MPa)  (mm) tp (mm)
joint failure mode
FJ01
FJ02
FJ03
EJ01
810
1076
810
810
275
275
275
275
M20
M20
M20
M20
10
16
16
16
end-plate deformation
stripping-off of the
threads of the bolts
bolt required
M20 √
M24 χ
M24 χ
M27 χ
5. CONCLUSIONS AND GENERAL RECOMMENDATIONS
In this paper, a component method and a design verification to analyse
beam-to-column joints under a fire were proposed and compared with experimental
tests. Based on the results and considerations achieved during this research work,
some design suggestions were proposed:
i) The application of a thin end-plate demonstrated to be a good option to reduce the large bolt strain and consequently the bolt failure (FJ01). However, even no
bolt failure was observed, large deformations on the end-plate were developed and
bearing failure around the bolts could be happen.
ii) Special attention should me made when it is intended to increase the joint
resistance. The application of a bolt class with higher resistance reduces the bolt deformations and reveals to be a good choice to increase the joint resistance. Howev-
er, a joint typology with a higher resistance at room temperature only increases the
resistance to the hogging moment, but not to sagging moment that controls the cooling phase. Additional bolt rows in the lower zone of the connections should be considered in order to increase the joint resistance during the cooling phase.
ACKNOWLEDGMENTS
Financial support from the Portuguese Ministry of Science and Higher Education
(Ministério da Ciência e Ensino Superior) under contract grant POCI/ECM/55783/2004
is gratefully acknowledged
REFERENCES
Block, F., Burgess, I. Davison, B. and Plank, R.J. (2007), “The development of a
component-based connection element for end-plate connections in fire”. Fire
Safety Journal, vol. 42(6-7) (pp. 498-506).
Cerfontaine, F. (2004), “Etude de l’interaction entre moment de flexion et effort normal dans les assemblages boulonnés” (in french), Thèse de Docteur en Sciences Appliquées, Faculté des Sciences Appliquées, University of Liège, Belgium.
EN 1993-1-2-2005.European Committee for Standardization – CEN. Eurocode 3:
Design of Steel Structures. Part 1.2: General Rules – Structural Fire Design,
Brussels.
EN 1993-1-8-2005. European Committee for Standardization – CEN. Eurocode 3:
Design of steel structures. Part 1.8: Design of joints, Brussels.
Franssen, J-M (1990) “The unloading of building materials submitted to fire”. Fire
Safety Journal, vol.16, (pp. 213-227).
Jaspart, J.P. (2002) “Design of structural joints in building frames” Progress in Structural Engineering and Materials, vol. 4 (pp. 18-34).
Ramli Sulong, N.H., Elghazouli, A.Y. and Izzuddin, B.A. (2007), “Behaviour and design of beam-to-column connections under fire conditions”. Fire Safety Journal, 42 (6-7), (pp.437-451).
Santiago, A., Simões da Silva L., Vila Real P., Gameiro Lopes A. and Vaz G. (2008),
“Experimental evaluation of the influence of connection typology on the behaviour of steel structures under fire”, Engineering Journal, AISC (submitted).
Santiago, A. (2008), “Behaviour of beam-to-column steel joints under natural fire”.
Doctoral Thesis, Department of Civil Engineering, University of Coimbra.
Simões da Silva L., Santiago A. and Vila Real P. (2001), “A component model for
the behaviour of steel joint at high temperatures”. Journal Constructional
Steel Research, vol. 57(11) (pp. 1169-1195).
Simões da Silva, L., Santiago, A., Vila Real, P. and Moore, D. (2005), ‘Behaviour of
steel joints and fire loading’. International Journal of Steel and Composite
Structures vol. 5(6) (pp. 485-513).
Yin, Y.Z. and Wang, Y.C. (2005), “Analysis of catenary action in steel beams using a
simplified hand calculation method, Part 1: theory and validation for uniform
temperature distribution”. Journal of Constructional Steel Research, vol. 61
(pp. 183-211).
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