Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections
Предложена конечноэлементная методика расчета деформирования и относительного проскальзывания креплений стальной колонны кжелезобетонному основанию. Рассмотрены два случая крепления: пластина приваривается к торцу колонны и крепится двумя или четырьмя анкерными болтами к железобетонному основанию....
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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| Zitieren: | Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections / M. Hamizi, H. Ait-Aider, A. Alliche // Проблемы прочности. — 2011. — № 6. — С. 104-116. — Бібліогр.: 27 назв. — англ. |
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irk-123456789-952742016-03-11T17:48:00Z Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections Hamizi, M. Ait-Aider, H. Alliche, A. Научно-технический раздел Предложена конечноэлементная методика расчета деформирования и относительного проскальзывания креплений стальной колонны кжелезобетонному основанию. Рассмотрены два случая крепления: пластина приваривается к торцу колонны и крепится двумя или четырьмя анкерными болтами к железобетонному основанию. В конечноэлементной модели с использованием модифицированного метода Лагранжа учитывается растрескивание бетонного основания и эффекты трения. Деформирование бетонного основания описывается с помощью упругопластической модели сжатия материала. По результатам расчетов построены диаграммы перемещений элементов крепления. Запропоновано скінченноелементну методику розрахунку деформування і відносного проковзування кріплень стальної колони до залізобетонної основи. Розглянуто два випадки кріплення: пластина приварюється до торця колони і кріпиться двома або чотирма анкерними болтами до залізобетонної основи. У скінченноелементній моделі з використанням модифікованого методу Лагранжа враховується розтріскування бетонної основи й ефекти тертя. Деформування бетонної основи описується за допомогоюпружно-пластичної моделі стиску матеріалу. За результатами розрахунків побудовано діаграми переміщень елементів кріплення. 2011 Article Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections / M. Hamizi, H. Ait-Aider, A. Alliche // Проблемы прочности. — 2011. — № 6. — С. 104-116. — Бібліогр.: 27 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/95274 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Hamizi, M. Ait-Aider, H. Alliche, A. Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections Проблемы прочности |
| description |
Предложена конечноэлементная методика расчета деформирования и относительного проскальзывания креплений стальной колонны кжелезобетонному основанию. Рассмотрены два случая крепления: пластина приваривается к торцу колонны и крепится двумя или четырьмя
анкерными болтами к железобетонному основанию. В конечноэлементной модели с использованием модифицированного метода Лагранжа учитывается растрескивание бетонного основания и эффекты трения. Деформирование бетонного основания описывается с помощью упругопластической модели сжатия материала. По результатам расчетов построены диаграммы перемещений элементов крепления. |
| format |
Article |
| author |
Hamizi, M. Ait-Aider, H. Alliche, A. |
| author_facet |
Hamizi, M. Ait-Aider, H. Alliche, A. |
| author_sort |
Hamizi, M. |
| title |
Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections |
| title_short |
Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections |
| title_full |
Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections |
| title_fullStr |
Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections |
| title_full_unstemmed |
Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections |
| title_sort |
finite element method for evaluating rising and slip of column–base plate for usual connections |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2011 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/95274 |
| citation_txt |
Finite Element Method for Evaluating Rising and Slip of Column–Base Plate for Usual Connections / M. Hamizi, H. Ait-Aider, A. Alliche // Проблемы прочности. — 2011. — № 6. — С. 104-116. — Бібліогр.: 27 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT hamizim finiteelementmethodforevaluatingrisingandslipofcolumnbaseplateforusualconnections AT aitaiderh finiteelementmethodforevaluatingrisingandslipofcolumnbaseplateforusualconnections AT allichea finiteelementmethodforevaluatingrisingandslipofcolumnbaseplateforusualconnections |
| first_indexed |
2025-07-07T02:04:08Z |
| last_indexed |
2025-07-07T02:04:08Z |
| _version_ |
1836951902482333696 |
| fulltext |
UDC 539.4
Finite Element Method for Evaluating Rising and Slip of Column–Base
Plate for Usual Connections
M. Hamizi,
a,1
H. Ait-Aider,
a,2
and A. Alliche
b,3
a Université Mouloud Mammeri de Tizi Ouzou, Algérie
b Université Pierre et Marie Curie Paris VI, Paris, France
1 chamizi@yahoo.fr
2 h_aitaider@yahoo.fr
3 abdenour.alliche@upmc.fr
ÓÄÊ 539.4
Êîíå÷íîýëåìåíòíûé ìåòîä îöåíêè äåôîðìèðîâàíèÿ è ïðîñêàëüçû-
âàíèÿ êðåïëåíèé ñòàëüíîé êîëîííû ê îñíîâàíèþ
Ì. Õàìèçè
à
, Õ. Ýéò-Ýéäåð
à
, À. Àëëèø
á
à Óíèâåðñèòåò èì. Ìóëóäà Ìàììåðè, Òèçè-Óçó, Àëæèð
á Óíèâåðñèòåò èì. Ïüåðà è Ìàðè Êþðè, Ïàðèæ, Ôðàíöèÿ
Ïðåäëîæåíà êîíå÷íîýëåìåíòíàÿ ìåòîäèêà ðàñ÷åòà äåôîðìèðîâàíèÿ è îòíîñèòåëüíîãî ïðî-
ñêàëüçûâàíèÿ êðåïëåíèé ñòàëüíîé êîëîííû ê æåëåçîáåòîííîìó îñíîâàíèþ. Ðàññìîòðåíû äâà
ñëó÷àÿ êðåïëåíèÿ: ïëàñòèíà ïðèâàðèâàåòñÿ ê òîðöó êîëîííû è êðåïèòñÿ äâóìÿ èëè ÷åòûðüìÿ
àíêåðíûìè áîëòàìè ê æåëåçîáåòîííîìó îñíîâàíèþ.  êîíå÷íîýëåìåíòíîé ìîäåëè ñ èñïîëü-
çîâàíèåì ìîäèôèöèðîâàííîãî ìåòîäà Ëàãðàíæà ó÷èòûâàåòñÿ ðàñòðåñêèâàíèå áåòîííîãî
îñíîâàíèÿ è ýôôåêòû òðåíèÿ. Äåôîðìèðîâàíèå áåòîííîãî îñíîâàíèÿ îïèñûâàåòñÿ ñ ïîìî-
ùüþ óïðóãîïëàñòè÷åñêîé ìîäåëè ñæàòèÿ ìàòåðèàëà. Ïî ðåçóëüòàòàì ðàñ÷åòîâ ïîñòðîåíû
äèàãðàììû ïåðåìåùåíèé ýëåìåíòîâ êðåïëåíèÿ.
Êëþ÷åâûå ñëîâà: ñîåäèíåíèÿ, îñíîâàíèå, ìåòîä êîíå÷íûõ ýëåìåíòîâ, ïðî-
ñêàëüçûâàíèå, áåòîííîå îñíîâàíèå, óïðóãîïëàñòè÷åñêàÿ ìîäåëü.
Introduction. In column-beam connections, the base plate is necessary to
transmit the effort acting in the column to the reinforced concrete foundation. The
dimensions of the base plate (b d� ) are given by considering the pressure
transmitted to the subjacent concrete, which must resist without rupture. The
thickness of the base plate t p is given by considering the pressure transmitted by
the concrete. The number of anchor bolts, the space between bolts just as the
welding connecting the column to the base plate are other factors which can
influence the choice of dimensions of the base plate. The dimensioning of the base
plate is a relatively simple work if one has tables and scheme solvers like those
proposed by Stockwell [1], Sandhu [2], Bird [3], C.M. 66 [4], Eurocode [5]. The
recent studies, both experimental and numerical, have shown that other parameters
like rising and slip could affect the base plate behavior. The rising and slip are
generated by the contact between the base and the reinforced concrete foundation.
© M. HAMIZI, H. AIT-AIDER, A. ALLICHE, 2011
104 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6
In the last decades, a significant work dealing with the problem of rising and slip
between base plate and reinforced concrete foundation has been carried out by
many researches. Several approaches were used: experimental, analytical and
numerical ones. The laboratory tests have confirmed that separation of the connection
always occurred at the level surface of contact between the base plate and reinforced
concrete foundation which is treated as fully rigid connection [6–8]. Other
experimental studies under concentrated loads and offset loads describing and
evaluating the response of the column base connections were carried out [9–12].
The analytical approach, on the other hand, based on a variable distribution of the
reaction of the reinforced concrete foundation on the base plate under a low
concentrated load applied in the top of the column gave a significant surface of
contact [13, 14]. Another approach, by the finite element method, to evaluate the
rising and the slip of the base plate compared to the reinforced concrete foundation
has been implemented recently [15, 16]. Several models were used. The
unidimensional model based on the theory of Bernoulli with spring simulation of
the anchor bolt yielded somewhat mitigated results [17]. On the other hand, models
with two (2D) and three dimensions (3D) have been used, which had the following
advantages:
(i) visualization of normal and tangential displacement;
(ii) precise numerical results;
(iii) minimal costs of data processing.
The results obtained by the above models have provided adequate assessment
of rising and slip between the base plate and the reinforced concrete foundation
[18–25].
1. Development of the Finite Element Model. Taking into account studies
enumerated above and various recommendations, a three-dimensional finite element
model based on the nonlinear analysis of the structure to simulate the behavior of
column–base plate connection is proposed in this study. The model takes into
account nonlinearity of materials and nonlinearity of contact between the foundation
and the base plate, where it simulates the rising and the slip of the base plate and
where friction at the interface concrete foundation–base plate is ensured by
four-nodal quadratic elements [26]. The model has been elaborated in CASTEM3M
computer code. The aim of this study is the analysis of the behavior of the most
frequently used column–base plate connections. For this purpose, the curves of
rising versus rotations and normal displacement versus tangential displacement are
plotted.
2. Unilateral Contact (the Signorini Problem). In numerous simulations, the
law of unilateral contact used is illustrated by the Signorini problem. Consider a
deformable body in contact with a rigid body (Fig. 1), the conditions of unilateral
contact of the Signorini problem have to be satisfied in all points of the deformable
bodies located in the contact �C [27]:
h�0, (1)
Rn
� �0, (2)
h Rn� �� 0, (3)
Finite Element Method for Evaluating Rising ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6 105
where h is the displacement of a point of contact in the normal direction to the
contact,
�
n, while Rn
� are the normal effort components. Equation (1) represents the
condition of impenetrability; Eq. (2) – the fact that the normal force of contact is
compression, and Eq. (3) represents the condition of complementarity (if the point
is in contact, then h�0 and Rn
� �0; if the point leaves the contact then h � 0 and
Rn
� �0) [27].
3. Coulomb Law. The force at the point of contact can be split into the
normal force Rn
� and the tangential force Rt
� ( ).
� � �
� �R R n R tn t� � � � The model of
Coulomb friction is written as follows [27]:
| | | | ,R Rt n
� �� � (4)
| | | |R R vt n t
� � �� � �0 (adherence), (5)
R R
v
vt n
t
t
� �
�
�
�
� | |
| |
(slip) (6)
where v t
� is tangential relative speed between the two bodies and � is the
Coulomb friction coefficient (see Fig. 2,) which includes all the local parameters,
such as roughness of surface between the two bodies.
M. Hamizi, H. Ait-Aider, and A. Alliche
106 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6
Fig. 1. Contact between a deformable body and a rigid body (the Signorini problem).
Fig. 2. Coulomb law.
4. Equilibrium without Friction. The deformable body is designated by �1
and the rigid body- by �2 , while combination of the two bodies is � � �� �1 2 .
The deformable body is subjected to action of the imposed displacements
�
ud in
zone �u , the imposed efforts
�
f S in zone �
, and bulk forces
�
f V acting in the
field (Fig. 1):
div
� �
� �f v 0 in �, (7)
� �
u ud� on �u , (8)
[ ]
� �
� �
n f S on �
, (9)
[ ]
� �
� �
n R on �C . (10)
5. Equilibrium with Friction. Equilibrium of deformable body with frictional
contact is written:
W dV f udV f udS Wsolid V S cont
VV C
�
�
�
���
1
2
[ ]:{ } .
�
� � � �
�
(11)
The work of contact forces in the deformable body is written as follows:
W R n u R u dScont n n t t
C
� � � ��� ( )
� � � �
�
(12)
where
� � � � �
u u u u nt n�
�( ) .2 1
The action of rigid body �2 on body �1 is written as
� � �
f R n R dScont n t
C
� � ��� ( ) .
�
(13)
6. Finite Element Modeling.
Behavior law:
��C : .
Interpolation of deformations: �� �[ ] .B u
Interpolation of displacements: u N u k� �[ ] .
In matrix form, Eq. (11) is written as
W u K u u Fsolid
T T� �
�
�
�
�
�
�
1
2
[ ] { } (14)
with rigidity matrix
[ ] [ ]K B C BdVT
V
��
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6 107
Finite Element Method for Evaluating Rising ...
and external efforts’ vector
{ } [ ] [ ] [ ] { }.F N f dV N f dS N f dS FT
V
T
S
T
cont
V CC
� � � ���
� � �
��
The system equilibrium with frictional contact aims to minimize the energy
equation under the following constraint:
div
�� �
�
� � �
�
�
�
W
h u u n G u
solid
T
n
0
02 1
,
(( ) [ ] .
� � � (15)
7. Method of Resolution (Modified Lagrangian):
W u u K u G u u G G usolid
T T T T T( , ) [ ] [ ] [ ][ ] ,� �
�
� � � �
1
2 2
0 (16)
� �
�
�
�
��
�
W u
W
u
W
K GG u G
solid
T K
( , )
,
,
[ ] [
�
�
�
�
�
��
�
�
�
� �
0
0
0
] ,
[ ] .
�
� � �
K
K K T K
F
G u
�
� �
�
�
�
��
�1
(17)
8. Behavior Laws. For the adopted finite elements model of the column, the
base plate and anchor bolts obey the laws depicted in Figs. 3 and 4.
For the foundation concrete, the material is considered which operates in the
elasto-plastic field with the Young modulus EC �29 GPa, Poisson’s ratio �C � 0.18,
the tensile strength f t �3 0. MPa, and the compressive strength f c �38 MPa.
9. Numerical Analysis. Three types of connections are studied, the first one
consisting of a base plate (t p �11 mm) welded to the end of column and attached
to the reinforced concrete foundation with two anchor bolts. These bolts are placed
on the major axis of the I-shaped column cross section, one anchor bolt on each
108 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6
M. Hamizi, H. Ait-Aider, and A. Alliche
Fig. 3. Adopted stress–strain relations for the steel column and base plate connection.
Fig. 4. Adopted stress–strain relations for the anchor bolts.
Fig. 3 Fig. 4
side of the web (Fig. 5). In the second configuration, the connection comprises a
base plate (t p �30 mm) and four anchor bolts placed outside the flanges of the
I-shaped section (Fig. 6). In the third configuration, the connection comprises a
base plate (t p �19 mm), a column with a hollow cross section and four anchor
bolts (Fig. 7). Two loading types are used. Initially, the connections were subjected
to shear force and bending moment only, and then the connections were loaded by
shear force, bending moment and axial compressive force (Fig. 8). In this case,
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6 109
Finite Element Method for Evaluating Rising ...
Fig. 5. Detail of two anchor bolts connection.
Fig. 6. Detail of four anchor bolts connection.
Fig. 7. Detail of four anchor bolts connection with a hollow cross section.
bending moment is induced by the offset compressive load. Different eccentricities
and variable axial loadings (P �100 to 600 kN) are chosen, in order to show the
influence of these parameters on the degree of fixity of the column base connections.
In this study, the following assumptions were made, in order to obtain essential
response features:
1) An interaction between the holes in the base plate and the anchor bolts is
ensured by considering a unilateral contact between these two bodies.
2) In order to simplify the mesh, the anchor bolts that are of circular sections
are simulated in this study by bolts of square sections of equivalent surface.
3) The displacement of the anchor bolts is postulated so that the nodes
coincide with the nodes of the holes of the base plate.
4) To take into account the contact friction between the base plate and the
foundation, the nodes, as well as the degrees of freedom of the two bodies, are
selected in a such way that they coincide.
5). The same precaution is also taken with regard to the nodes and the degrees
of freedom of the anchor bolts and the concrete foundation.
6). Traction in the concrete develops only in the upper part of bolt (on the one
third of LP ).
7). The loadings are introduced in the forms of increments (ensured well by
CASTEM3M code).
10. Results. For the column–base plate connection with only two anchor bolts
without compressive load rising of the base plate side of traction occurs. The anchor
bolts undergo elongation and bending. The columns manifest no deformation; all
rotation occurs at the level of connection.
For the same connection with two anchor bolts in the presence of compressive
load (P � 100–400 kN), the rising of the base plate side of traction is still quite
pronounced, but less critical (reduction from 6 to 16%). We observe that a contact
zone is established under the right edge of the base plate. The remaining part of the
110 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6
M. Hamizi, H. Ait-Aider, and A. Alliche
Fig. 8. Finite element mesh of the 3D model.
plate starts to separate from concrete foundation, overstressing the left bolt. The
deformation of the base plate, as well as the plastic strains, decreases as axial load
increases.
For the column–base plate connection with four anchor bolts without a
compressive load: rupture of two anchor bolts in traction occurs. The base plate is
raised considerably before the rupture of the anchor bolts. Rising maxima are 36,
32, and 29 mm, respectively, for the base plate thickness t p �11 mm (Figs. 9 and
10), 19 mm (Fig. 11), and 30 mm (Fig. 12). Comparing the results obtained with
the model for base plate thickness t p �30 mm to those with base plate thickness
t p �11 mm, the highest uplift is slightly smaller, as well as the separation length.
These results are natural, since the stiffness of the base plate increases for thickness
t p �30 mm, permitting smaller deformability and reducing its final plastic strain.
On the compression side, there is friction of the base plate over 80 mm
distance from the base plate edge. The columns remained practically rectilinear.
The results obtained for the same connections (HEB 160 with four anchor
bolts) in the presence of compressive load (P � 100–600 kN) are as follows.
The rising of base plate is less visible than when there is no compressive load.
The contact area increases along with the axial loading from 0 to 600 kN.
We observe that the bending of the base plate is reduced in comparison with
the connection without compressive load. This proves that the increase of the
stiffness of the base plate significantly affects its response under applied axial
loading and bending moment combination.
The rising of base plate side of traction becomes less critical when the
compressive load increases. The reduction of the maximum rising is of the order of
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6 111
Finite Element Method for Evaluating Rising ...
Fig. 9. Maximum rising-rotation diagrams for base plate thickness tp �11 mm under various axial
loadings. Base plate connections with HEB 100 column.
magnitude (6 to 70%) while passing from compressive load of P �100 kN to
P �600 kN.
Local warping of the wing in compression is observed.
Traction at the base of column is located at the same side as the wing in
compression at the top of column. This is an indication that a moment is developed
in the connection and the column works in double curve.
112 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6
M. Hamizi, H. Ait-Aider, and A. Alliche
Fig. 10. Maximum rising-rotation diagrams for base plate thickness tp �11 mm under various axial
loadings. Base plate connections with HEB 160 column.
Fig. 11. Curves of the rising of the 19 mm thickness base plate under various axial loadings. Base
plate connections with HEB 160 column.
For the connections with a hollow cross section, the rising of base plate is
even less pronounced (Fig. 13).
Increasing the base plate thickness, the respective stiffness ensures limited
deformation which manifests itself only slightly (Figs. 14–16).
Conclusions. To study the rising of the base plate, an approach treating
problems of contact friction between the base plate and the foundation has been
developed. The numerical solution is obtaiined by the modified Lagrangian method.
For the account of the concrete foundation behavior, the developed model is based
on the compressive elasto-plastic model.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6 113
Finite Element Method for Evaluating Rising ...
Fig. 12. Curves of the rising of the 30 mm thickness base plate under various axial loadings.
Fig. 13. Curves of the rising of the 19 mm thickness base plate under various axial loadings. Base
plate connections with a hollow cross section.
114 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6
M. Hamizi, H. Ait-Aider, and A. Alliche
Fig. 14. Curves of the normal and tangential displacement of the 11 mm thickness base plate.
Fig. 15. Curves of the normal and tangential displacement of the 19 mm thickness base plate.
Fig. 16. Curves of the normal and tangential displacement of the 30 mm thickness base plate.
Ð å ç þ ì å
Çàïðîïîíîâàíî ñê³í÷åííîåëåìåíòíó ìåòîäèêó ðîçðàõóíêó äåôîðìóâàííÿ ³
â³äíîñíîãî ïðîêîâçóâàííÿ êð³ïëåíü ñòàëüíî¿ êîëîíè äî çàë³çîáåòîííî¿ îñíî-
âè. Ðîçãëÿíóòî äâà âèïàäêè êð³ïëåííÿ: ïëàñòèíà ïðèâàðþºòüñÿ äî òîðöÿ
êîëîíè ³ êð³ïèòüñÿ äâîìà àáî ÷îòèðìà àíêåðíèìè áîëòàìè äî çàë³çîáåòîííî¿
îñíîâè. Ó ñê³í÷åííîåëåìåíòí³é ìîäåë³ ç âèêîðèñòàííÿì ìîäèô³êîâàíîãî ìå-
òîäó Ëàãðàíæà âðàõîâóºòüñÿ ðîçòð³ñêóâàííÿ áåòîííî¿ îñíîâè é åôåêòè òåðòÿ.
Äåôîðìóâàííÿ áåòîííî¿ îñíîâè îïèñóºòüñÿ çà äîïîìîãîþ ïðóæíî-ïëàñòè÷íî¿
ìîäåë³ ñòèñêó ìàòåð³àëó. Çà ðåçóëüòàòàìè ðîçðàõóíê³â ïîáóäîâàíî ä³àãðàìè
ïåðåì³ùåíü åëåìåíò³â êð³ïëåííÿ.
1. F. W. Stockwell, Jr., “Preliminary base plate selection,” Eng. J. AISC, 12,
No. 3, 92–99 (1975).
2. B. S. Sandhu, “Steel column base plate design,” Ibid, 10, No. 4, 131–133
(1973).
3. W. R. Bird, “Rapid selection of column base plate,” Ibid, 13, No. 2, 43–47
(1976).
4. Regles de Calcul des Constructions en Acier et Additive 80, 12éme edition
(1988).
5. Eurocode 3. Design of Steel Structures. 1.1. General Rules for Building, Env
1993-1-1 (1992).
6. A. Picard et J. Dion, Etude Expérimentale des Assemblages Poteau–Fondation
dans les Charpentes d’Acier, Report GCT-81-04, Department of Civil
Engineering, Laval University, Quebec (1981).
7. G. Samson et D. Beaulieu, Etude de la Stabilité d’Un Poteau avec Attache
Semi-Rigide à la Fondation, Report GCT-83-01, Department of Civil
Engineering, Laval University, Quebec (1982).
8. B. Pérusse et D. Beaulieu, Etude Expérimentale de la Rigidité d’Un Assemblage
Poteau–Fondation de Type Standard, Report GCT-85-07, Department of
Civil Engineering, Laval University, Quebec (1985).
9. J. T. Dewolfe, “Axially loaded column base plates,” J. Struct. Div. ASCE,
104, 781–794 (1978).
10. J. T. Dewolfe and E. F. Sansely, “Columnbase plates with axial loads and
moments,” Ibid, 106, 2167–2184 (1983).
11. D. P. Thambiratnam and P. Paramasivan, “Base plates under axial loads and
moments,” Ibid, 112, 1166–1181 (1986).
12. R. A. Cook and R. E. Klinger, “Ductile multiple-anchor steel-to-concrete
connections,” Ibid, 118, 1645–1665 (1992).
13. R. S. Fling, “Design of steel bearing plates,” Eng. J. AISC, 7, 37–40 (1970).
14. T. M. Murray, “Design of lightly loaded steel column base plates,” Ibid, 20,
92–99, 143–152 (1983).
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6 115
Finite Element Method for Evaluating Rising ...
15. N. Krishnnamurthy and D. D. Graddy, “Correlation between 2- and 3-
dimensional finite element analysis of steel bolted end-plate connections,”
Comput. Struct., 6, 381–389 (1976).
16. M. Hamizi et N. E. Hannachi, “Evaluation par la méthode des éléments finis
du facteur de flexibilité et du degré de fixité des pieds de poteaux les plus
couramment utilisés,” Annales du Batiment et des Travaux Publics, No. 2-3
(2007).
17. N. Krishnnamurthy, “A fresh look at bolted steel end-plate behavior and
design,” Eng. J. AISC, 15, 39–49 (1978).
18. B. Kato and W McGuire, “Analysis of T stub flange to column connection,” J.
Struct. Div. ASCE, 99, 865–888 (1973).
19. S. A. Paker and L. J. Morris, “A limit state design method for tension of
bolted column connections,” Struct. Eng., 55, 876–889 (1977).
20. A. R. Kukreti, T. M. Muray, and A. Abolmaali, “Endplate connection
moment-rotation relationship,” Struct. Steel Res., 8, 137–157 (1987).
21. W. F. Chen and K. V. Patel, “Static behaviour of beam-to-column moment,”
J. Struct. Div. ASCE, 197, 1815–1838 (1981).
22. W. F. Chen and E. M. Lui, “Steel beam-to-column moment connections. Pt. 1.
Flange moment connections,” S. M. Arch., 11, 257–316 (1986).
23. J. Bortmann and B. A. Szabo, “Nonlinear models for fastened structural
connections,” Comput. Struct., 43, 909–1023 (1992).
24. D. P. Thambiratnam and N. Krishnnamurthy, “Computer analysis of column
base plates,” Ibid, 33, 839–850 (1989).
25. C. C. Baniotopoulos, G. Karoumbas, and P. D. Panagiotopoulos, “A
contribution to the analysis of steel connections by means of quadratic
programming techniques,” in: Proc. of 1st Eur. Conf. on Numerical Methods
in Engineering, Elsevier, Amsterdam (1992), pp. 519–525.
26. M. Hamizi et D. Beaulieu, Etudes Expérimentale et Numérique des Pontages
Métalliques, Report GCT-87-05, Department of Civil Engineering, Laval
University, Quebec (1987).
27. L. Champaney, Contact Unilatéral entre Solides Élastiques. Notes de Cours
‘Eléments Finis’ du DESS Dynamique des Structures Modernes dans leur
Environnement.
Received 25. 05. 2010
116 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 6
M. Hamizi, H. Ait-Aider, and A. Alliche
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/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /NoConversion
/DestinationProfileName ()
/DestinationProfileSelector /NA
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure true
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /NA
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|