2. Scope
The main purpose of this research is to investigate the
behavior of a T-stub connection, having various bolt
layouts, bolt materials for different plate thicknesses in
order to establish the most suitable choice for such a
connection;
Analytic calculations are to be carried out according to
the current design norms, EC3-1-8.
A connection between an IPE240 beam and a HE160A
column is to be analyzed via numerical and analytic
calculations.
For this study it is relevant to observe the behaviour of
the tension part of the connection since plastic
deformations and yielding occurs in that part.
3. T-stubs in connections
According to EC3-1-8 an equivalent T-stub in tension
may be used to model the design resistance of some of
the basic components of the connection.
4. T-stubs in connections
The T-stub in tension method of
calculation can be applied for various
connection types.
5. Vulnerability of T-stubs
There are 3 modes of failure recognized
by the current design code, which are
1. complete yielding of the flange;
2. bolt failure with yielding of the flange;
3. bolt failure.
6. Analytic calculation
The rotational capacity of a connection
is obtained in function of the moment
resistance Mj,Rd, rotational stiffness Sj
and rotational capacity .ϕ
7. Analytic calculation
In order to calculate the elements which
compose the design moment-rotation
characteristic of the connection, it is
important to identify and calculate the
basic joint components using the
component method.
The equivalent T-stub in tension is a
versatile tool which helps in the
calculation of these components.
8. Analytic calculation
A connection may be regarded as a set of components
which together make up the load paths by which
internal forces are transmitted;
Mainly, the strength of the connection is that of its
weakest component, and the flexibility of the
connection is the sum of the flexibilities of the
components.
9. Analytic calculation
Basic joint components
Column web panel in shear
Column web in transverse compression
Column web in transverse tension
Column flange in bending
End plate in bending
Flange cleat in bending
Beam or column flange and web in compression
Beam web in tension
Plate in tension or compression
Bolts in tension
Bolts in shear
Bolts in bearing
10. Analytic calculation
Design resistance of components
Column web panel in shear
Column web in transverse compression
Column web in transverse tension
Column flange in bending
End plate in bending
Flange cleat in bending
Beam or column flange and web in compression
Beam web in tension
Plate in tension or compression
Bolts in tension
Bolts in shear
Bolts in bearing
0
,
,
3
**9.0
M
wcwcy
Rdwp
Af
V
γ
=
0
,,,
,,
M
wcywcwcceffwc
Rdwcc
ftbk
F
γ
ω
=
0
,,,
,,
M
wcywcwcteff
Rdwct
ftb
F
γ
ω
=
m
M
F
Rdpl
RdT
,1,
,1,
4
=
nm
FnM
F
RdtRdpl
RdT
+
+
=
∑ ,,2,
,2,
2
∑= RdtRdT FF ,,3,
)(
,
,,
fb
Rdc
Rdfbc
th
M
F
−
=
0
,,
*
M
yd
Rdpt
fA
F
γ
=
0
,,,
,,
M
wbywbwbteff
Rdwbt
ftb
F
γ
=
2
2
,
**
M
sub
Rdt
Afk
F
γ
=
2
,
**
M
ubv
Rdv
Af
F
γ
α
=
2
1
,
****
M
ub
Rdb
tdfk
F
γ
α
=
11. Analytic calculation
Stiffness coefficients of components
Column web panel in shear
Column web in transverse compression
Column web in transverse tension
Column flange in bending
End plate in bending
Flange cleat in bending
Beam or column flange and web in compression
Beam web in tension
Plate in tension or compression
Bolts in tension
Bolts in shear
Bolts in bearing
z
A
k vc
*
*38.0
1
β
=
c
wcwcceff
d
tb
k
,,
2
*7.0
=
c
wcwcteff
d
tb
k
,,
3
*7.0
=
3
3
4
*9.0
m
tl
k
fceff
=
3
3
5
*9.0
m
tl
k
peff
=
3
3
6
*9.0
m
tl
k
aeff
=
b
s
L
A
k
*6.1
10 =
16
2
11
*16
M
ubb
Ed
fdn
k =
E
dfkkn
k utbb*24
12 =
∞
12. Analytic calculation
Tension resistance of bolts
Shear resistance of bolts
Bearing resistance of bolts
Design moment resistance
∑=
r
RdtrrRdj FhM ,, *
2
2
,
**
M
sub
Rdt
Afk
F
γ
=
2
,
**
M
ubv
Rdv
Af
F
γ
α
=
2
1
,
****
M
ub
Rdb
tdfk
F
γ
α
=
14. Analytic VS numeric
The behaviour of the T-stub element
was analyzed and compared with
numerical results, for high strength bolts
and mild steel bolts.
15. State of the art
Studies carried out by Bursi &
Jaspart focused on studying the
semi-rigid behaviour of bolted steel
connections.
16. State of the art
A quarter of the T-stub was modeled, with correct
boundary conditions;
The “spin” model was introduced for the bolt with a
shank of 20mm calculated with Agerskov’s formula;
Contact elements were introduced in order to
simulate the contact between the bottom of the T-
stub flange and the other T-profile in tension;
The evolution of d was measured with respect to the
applied force F.
17. State of the art
T-stub models can be modeled in 2D
and 3D space;
The positioning of the bolt and the
bolt length influences the behaviour
of the T-stub in a 3D manner.
Bolt length calculated with the help
of the Agerskov’s formula:
)2( 41 KK
A
A
L
b
s
eff +=
nts lllK 71.043.11 ++=
24 2.01.0 llK n +=
18. Numeric calculation
Numerical investigations were
performed in 2D with the help of Cast3M
software;
3D investigations were carried out with
the help of Abaqus finite element
software.
19. Numeric calculation
Analysis of the T-stub was facilitated by the
symmetry, modeling only a quarter of the element,
with appropriate boundary conditions.
20. Numeric calculation
A calibration of the 2D model was
performed in comparison with the results
obtained in state of the art research.
22. Numeric calculation
Accuracy of 2D model versus analytic
calculation.
25% difference acceptable?
=> 3D investigation
23. Numeric calculation
Calibration of the 3D model, according
to state of the art research.
2/3 Mj,Rd [kNm] Φj,ini [rad] Sj,ini [kNm] Difference
Experimental 43.5 0.00433 10046
8.62%
Numeric - Abaqus 39.8 0.00362 10994
24. Numeric calculation
Parametric study – 48 test models:
Positioning of the bolt (e=30mm, 35mm, 40mm);
Bolt dimension (M14, M16, M20);
Bolt grade (gr. 5.8, gr. 10.9);
Thickness of T-stub flange
(10mm, 12.5mm, 15mm).
Investigated parameters:
Force-displacement curve;
Evolution of prying force;
Bolt reaction.
Bolts
M14 M16 M20
Thickness of plate
15 mm
T15H1-14 T15H1-16 T15H1-20
T15M1-14 T15M1-16 T15M1-20
T15H2-14 T15H2-16 T15H2-20
T15M2-14 T15M2-16 T15M2-20
T15H3-14 T15H3-16 -
T15M3-14 T15M3-16 -
12.5 mm
T12H1-14 T12H1-16 T12H1-20
T12M1-14 T12M1-16 T12M1-20
T12H2-14 T12H2-16 T12H2-20
T12M2-14 T12M2-16 T12M2-20
T12H3-14 T12H3-16 -
T12M3-14 T12M3-16 -
10 mm
T10H1-14 T10H1-16 T10H1-20
T10M1-14 T10M1-16 T10M1-20
T10H2-14 T10H2-16 T10H2-20
T10M2-14 T10M2-16 T10M2-20
T10H3-14 T10H3-16 -
T10M3-14 T10M3-16 -
25. Numeric calculation
Position of the bolt
Bolt dimension
Bolt grade
Thickness of plate
10mm / 12.5mm / 15mm
M14 M16 M20
46. Conclusions
High strength bolts boost the performance in terms of
ultimate force, in comparison with mild steel bolts.
Using high strength bolts, the value of the prying force is
increased.
Placing the bolts closer to the T-stub web increases the
chance of developing plastic hinges in the bolt.
In order to achieve proper ductility of a connection, placing
the bolts at a reasonable distance from the edge of the T-
stub flange, could represent an ideal solution.
A higher value of stiffness can be obtained by increasing the
thickness of the T-stub flange and by placing the bolts further
from the edge of the T-stub flange.
47. Acknowledgements
The research work leading to the findings
in this paper were performed under the
coordination of:
Prof. Dr. Ing. Hamid BOUCHAIR
Conf. Dr. Ing. Adrian CIUTINA
Special thanks to Dr. Sébastien DURIF for
his help in developing this research
paper.
48. References
Eurocode 3: Design of steel structures – Part 1-8: Design of joints, European Committee for
Standardization, December 1993;
Abaqus – Analysis User’s Manual, Volume I: Introduction, Spatial Modeling, Execution & Output,
version 6.10
Cast3M finite element software, www-cast3m.cea.fr
Bursi OS & Jaspart JP Calibration of a Finite Element Model for Isolated Bolted End-Plate Steel
Connections, J. Construct. Steel Res. Vol. 44, No. 3, pp. 225-262, 1997
Agerskov H, High strength bolted connections subjected to prying, J Struct Div 1976; 102(1), pp. 161-
175.
Charis J. Gantes & Minas E. Lemonis, Influence of equivalent bolt length in finite element modeling of
T-stub steel connections, Computers and Structures 81, pp. 595-604, 2003
Gioncu V, Mateescu D, Petcu D, Anastasiadis A, Prediction of available ductility by means of local
plastic mechanism method: DUCTROT computer programme, “Moment resistant connections of steel
frames in seismic areas: Design and reliability, Ed. F.M. Mazzolani, E&FN Spon, London, pp. 95-146,
2000
Ana M. Girão Coelho, Luís Simões da Silva and Frans S. K. Bijlaard, Finite-Element Modeling of the
Nonlinear Behavior of Bolted T-stub Connections, Journal of Structural engineering, ASCE, pp. 918-
928, 2006
Arcelor Sections Commercial Catalogue, Beams, Channels and Merchant Bars, 2005
Eurocode 1: Actions on structures – Part 1-2: General actions – Densities, self-weight, imposed loads
for buildings, European Committee for Standardization, 2002
Design of Structural Connections to Eurocode 3 – Frequenvtly Asked Questions, Watford, September
2003, Building Research Establishment, Ltd.
