MD10 BS/Test 3: ABAQUS model using beam general sections

25 Pages·2001·1.38 MB·English

PIT Project
Behaviour of steel framed structures under fire conditions
British Steel Fire Test3:
Reference ABAQUS model using grillage representation for
slab
Research Report
Report R00-MD10
Abdel Moniem Sanad
The University of Edinburgh
School of Civil & Environmental Engineering
Edinburgh, UK
June, 2000
TABLE OF CONTENTS
1. GEOMETRIC DESCRIPTION 5
1.1. Layout 5
1.2. Finite element mesh 6
2. MATERIAL BEHAVIOUR 8
2.1. Section behaviour for steel members 9
2.2. Slab modelling 9
3. CONNECTIONS BETWEEN MEMBERS 12
4. BOUNDARY CONDITIONS 13
5. LOADING 13
5.1. Distributed load 13
5.2. Thermal load 13
6. COMPARISON WITH TEST DATA 16
6.1. Deflection of primary beams 16
6.2. Deflection of secondary beams 18
6.3. Deflection of edge protected beams 19
6.4. Horizontal displacement of columns 21
7. CONCLUSION 23
8. REFERENCES 24
9. LIST OF ABAQUS INPUT FILES 17
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LIST OF FIGURES :
Figure 1: Layout of Test3
Figure 2: Model of fire test3
Figure 3: Typical cross section of the steel beams
Figure 4: Cross section of the composite slab
Figure 5: Steel stress-strain relationship at high temperature
Figure 6: Concrete stress-strain relationship at high temperature
Figure 7: Axial Force- Axial Strain relationship at high temperature in the longitudinal direction
Figure 8: Moment-Curvature relationship at high temperature in the longitudinal direction
Figure 9: Axial Force- Axial Strain relationship at high temperature in the lateral direction
Figure 10: Moment-Curvature relationship at high temperature in the lateral direction
Error! Reference source not found.: Error! Reference source not found.
Figure 11: Temperatures in the joists and the slab
Figure 12 : Deflection of the heated primary beam at mid span
Figure 13 : Deflection of the heated primary beam at Y/H=25%
Figure 14 : Mid span deflection of the heated secondary beam on grid line 2
Figure 15 :Mid span deflection of the heated secondary beam between grid 1 and 2
Figure 16 :Mid span deflection of edge protected secondary beam on grid 1
Figure 17 : Mid span deflection of edge protected primary beam on grid F
Figure 18 :Horizontal displacement of column E1 in Y direction
Figure 19 :Horizontal displacement of column F1 in Y direction
Figure 20 :Horizontal displacement of column F2 in X direction
Table 1: Dimensions of the steel members
Table 2: Dimensions of slab sections
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NOTES:
1. In the description of the numerical model below we use the following terms :
2. “the plane” to define the plane of the floor.
3. “joist” means a steel beam, and the “test joist” means the heated joist during the fire test.
4. “vertical” means vertical to the slab plane.
5. “in-plane” means in the plane of the slab.
6. “joist longitudinal direction” or “longitudinal direction” to mean parallel to the joist length
coordinate.
7. “transverse direction” to mean at right angle to the joist longitudinal direction (i.e. in the
direction of the longitudinal axis of the ribs).
8. “Reference vertical coordinate” is the interface between the slab and joist.
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1. GEOMETRIC DESCRIPTION
1.1. Layout
The test was performed on the second floor of the building to study the behaviour of a complete
floor system and in particular the membrane action. The compartment of approximately 80m2 was
built on the first floor in one corner of the structure. To achieve the required level of thermal loading
(around 1000°C), a real fire was created, with a fire loading of 45 kg of wood/m2 and the ventilation
was provided by a an adjustable 7m wide opening. The tested floor contains 4 unprotected beams
and 2 protected edge beams. All secondary beams are equally spaced and have 9m span connected
semi-rigidly to columns or to primary beams. The heated primary beam has a length of 6m. All
columns were protected along their full height. The composite profiled deck slab has a span of 3m
between secondary beams. Figure 1 shows the layout of the test and the location of the deflections
measurements.
Layout of Test3
Figure 1
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1.2. Finite element mesh
Figure 2 shows the finite element model of the test. The area affected by the fire is indicated by
dashed lines. In the direction of the secondary beams (longitudinal), the model starts from the corner
of the structure, covers the heated compartment and extends to the end of the span beyond the
compartment to include the membrane forces expected to develop during the fire. In the transverse
direction (direction parallel to the slab ribs), the model starts from the edge of the building, cover
the heated compartment and extends to the centreline of the building for the same reason. In the
model, each structural steel member is idealised by an appropriate beam element.
Figure 3 shows the typical cross-section of the steel members, Table 1 gives the dimensions of the
primary and secondary joists respectively. The centroid of the secondary joists is located 152.5mm
below the reference vertical co-ordinate of the joist’s top flange. The centroid of the primary and
edge joists is located 178mm below the reference level. The column is modelled using a similar
beam elements.
Model of fire test3
Figure 2
The slab behaviour is modelled by a grillage type idealisation using beam elements to represent the
slab behaviour in both the longitudinal and transverse directions. In the longitudinal direction (X),
the slab element has a rectangular section with 70mm depth and an effective width equal to
2250mm, calculated according to the Eurocode 4 (ENV1994) for a simply supported beam case. In
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the transverse direction (Y), slab elements have a trapezoidal shape and the geometry of the
concrete section in this direction is shown in Figure 4. The thickness of the steel deck used is 9mm.
Reinforcement of one layer of A142 mesh was provided. Table 2 gives the dimensions of the
sections in both directions.
y
x
tf
hj
tw
wj
Typical cross section of the steel beams
Figure 3
hj (mm) wj (mm) tf (mm) tw (mm)
Primary & Edge beams (H) 355.6 171.5 11.5 7.3
Secondary beams (L) 303.8 151.9 10.2 6.1
Table 1
Dimensions of the steel members
y
wc
as
ddss
hc
hc
hcb a
x
wcb
Cross section of the composite slab
Figure 4
Wc Wcb hct hcb a ((cid:176) ) as ds
mm mm mm mm mm2 mm
Slab in transverse direction 300 136 70 60 65 42.6 55
Slab in longitudinal direction 2250 - 70 - - 319.5 55
Table 2
Dimensions of slab sections
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2. MATERIAL BEHAVIOUR
For steel structures under high temperature the relationship between stress and strain changes
considerably. At increased temperature, the material properties degrade and its capacity to deform
increases which is measured by the reduction of the Young’s modulus. In the finite element model,
the relation between the stress and the strain under high temperature is defined according to the
Eurocode 3 (ENV1993). The relation is elastic-perfect plastic at ambient temperature, and the
reduction of the material properties starts at a temperature higher than 100C as shown in Figure 5.
Identical material behaviour is assumed for both tension and compression.
Properties of steel at high temperature
(cid:0) (cid:1) (cid:2) (cid:3) (cid:4) (cid:4) (cid:5) (cid:6) (cid:3) (cid:6) (cid:7) (cid:8) (cid:3) (cid:4) (cid:4) (cid:9)
450
20 ºC
400
100 ºC
200 ºC
350
300 ºC
) 300 400 ºC
a
P 500 ºC
M 250 600 ºC
(

s 700 ºC
s 200
e 800 ºC
r
St 150 900 ºC
1000 ºC
100
50
0
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Strain (%)
Figure 5
Steel stress-strain relationship at high temperature
Similarly, the behaviour of concrete is characterised by material property degradation with increased
temperature. The stress-strain relationship is then defined according to the Eurocode 2 (ENV1992)
as shown in Figure 6. Here, the initial elastic behaviour is followed by a plastic-hardening curve up
to the ultimate stress, after which, a decaying zone represents the post-crushing behaviour for
concrete. This relationship has the advantage of allowing the definition of a stress level for large
plastic deformations, usually reached during fire conditions. It may be noted that no tension is
considered in the model for the concrete at both ambient and elevated temperature, however the
tensile resistance of the reinforcement and the steel deck is considered.
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Properties of concrete at high temperature
(cid:10) (cid:11) (cid:12) (cid:13) (cid:14) (cid:14) (cid:15) (cid:16) (cid:13) (cid:16) (cid:15) (cid:17) (cid:13) (cid:14) (cid:14) (cid:18)
50
20 ºC
45
100 ºC
200 ºC
40
300 ºC
35 400 ºC
a) 500 ºC
P 30 600 ºC
M
700 ºC
(
s 25 800 ºC
s
e 900 ºC
tr 20 1000 ºC
S
15
10
5
0
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Strain (%)
Figure 6
Concrete stress-strain relationship at high temperature
2.1. Section behaviour for steel members
For all steel members, the classic linear beam element applying the hypotheses of plane surface
remains plane is used. Each point on the cross section, along each member, follows the stress-strain
relationship (Figure 5) as a function of the point’s temperature. This takes into consideration the
variable temperature profile applied across the section and the corresponding material properties
during different stages of the fire. The connections between different steel members (beam to
column connection and beam to beam connection) are modelled by pin connections where boundary
conditions are imposed on the relative displacement of the joining elements.
2.2. Slab modelling
In a reinforced concrete slab, more complex behaviour has to be modelled. The different behaviour
of concrete in tension and compression, the orthotropic behaviour of concrete due to the reinforcing
mesh and the decking steel and the development of membrane action need to be considered in order
to provide a realistic representation of the slab behaviour. In the numerical model developed in this
paper, the concrete modelling is based on the global behaviour of the concrete section, with the
above factors taking into consideration. The slab is modelled by two sets of beam elements running
parallel and perpendicular to the secondary beams. In each direction, the beam elements have a pre-
defined force-strain and moment-curvature relationship. These relationships are calculated based on
the geometry and the material properties of the section in each direction and taking into account the
variable temperature over the same section and the corresponding material properties (O’Connor
and al. 1995).
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The behaviour of the slab in the longitudinal direction (direction of the secondary joists axis) is
modelled by beam elements, using bilinear moment/curvature and force/strain relationships which
are uncoupled (Figure 7,8). The yield points for the force relationship in each sense are given by the
section's plastic resistance for normal force (with different values for tension and compression).
The yield points for the bending relationship are given by the section's plastic resistance for bending
(with different values for sagging and hogging). The post-yield behaviour is modelled by a linear
relationship (moment/curvature and force/strain), decreasing from the yield point to the ultimate
section resistance based on the steel reaching the limiting strain for yield strength.
The behaviour of the slab in the direction of the primary joist axis (transverse) is modelled by beam
elements. The transverse bending and transverse membrane action of the slab is modelled by beam
elements with their longitudinal axis in the transverse direction, using bilinear moment/curvature
and force/strain relationships which are uncoupled (Figure 9,10). The yield points for the force
relationship in each sense are given by the section's plastic resistance for normal force (with
different values for tension and compression). The yield points for the bending relationship are
given by the section's plastic resistance for bending (with different values for sagging and hogging).
These beam ribs have a very high bending stiffness about the vertical axis (i.e. relating to bending
deformations in the horizontal plane) this is modelled by a increasing this bending stiffness to 100
times the bending stiffness of an individual rib. Also to overcome convergence problems in the
numerical solutions, the slab tension and hogging moment included hardening beyond the first yield
point. The beam used in modelling the slab are 3D beam element which has linear elastic behaviour
for the torsional
.
Behaviour of the slab section in the longitudinal direction
1.E+06
0.E+00
-2.00E-02 -1.50E-02 -1.00E-02 -5.00E-03 0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02
-1.E+06
-2.E+06
20°C
e (N) -3.E+06 100°C
c 200°C
or
al f 300°C
m -4.E+06 400°C
Nor 500°C
600°C
-5.E+06
700°C
800°C
-6.E+06
900°C
1000°C
-7.E+06
-8.E+06
Axial strain (mm/mm)
Figure 7
Axial Force- Axial Strain relationship at high temperature in the longitudinal direction
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