To take into account the flexibility resulting from sectional deformations of a thin-walled box beam, higher-order beam theories considering warping and distortional degrees of freedom (DOF) in addition to the Timoshenko kinematic degrees have been developed. The objective of this study is to derive the exact matching condition consistent with a 5-DOF higher-order beam theory at a joint of thin-walled box beams under out-of-plane bending and torsion. Here we use bending deflection, bending/shear rotation, torsional rotation, warping, and distortion as the kinematic variables. Because the theory involves warping and distortion that do not produce any force/moment resultant, the joint matching condition cannot be obtained just by using the typical three equilibrium conditions. This difficulty poses considerable challenges because all elements of the 5×5 transformation matrix relating the field variables of one beam to those in another beam should be determined. The main contributions of the investigation are to propose additional necessary conditions to determine the matrix and to derive it exactly. The validity of the derived joint matching transformation matrix is demonstrated by showing good agreement between the shell finite element results and those obtained by the present box beam analysis in various angle box beams.

References

References
1.
Vlasov
,
V. Z.
, 1961,
Thin Walled Elastic Beams
,
Israel Program for Scientific Translations
,
Jerusalem
.
2.
Bazant
,
Z.
, and
El Nimeiri
,
M.
, 1974, “
Stiffness Method for Curved Box Girders at Initial Stress
,”
ASCE J. Struct. Div.
,
100
(
10
), pp.
2071
2090
. Available at: http://cedb.asce.org/cgi/WWWdisplay.cgi?22132
3.
Mikkola
,
M. J.
, and
Paavola
,
J.
, 1980, “
Finite Element Analysis of Box Girders
,”
ASCE J. Struct. Div.
,
106
(
6
), pp.
1343
1357
. Available at: http://cedb.asce.org/cgi/WWWdisplay.cgi?5015498
4.
Boswell
,
L. F.
, and
Zhang
,
S. H.
, 1983, “
A Box Beam Finite Element for the Elastic Analysis of Thin-Walled Structures
,”
Thin-Walled Struct.
,
1
(
4
), pp.
353
383
.
5.
Maisel
,
B. I.
, 1982,
Analysis of Concrete Box Beams Using Small-Computer Capacity
,
Cement and Concrete Association
,
London
.
6.
Zhang
,
S. H.
, and
Lyons
,
L. P. R.
, 1984, “
A Thin-Walled Box Beam Finite Element for Curved Bridge Analysis
,”
Comput. Struct.
,
18
(
6
), pp.
1035
1046
.
7.
Balch
,
C. D.
, and
Steele
,
C. R.
, 1987, “
Asymptotic Solutions for Warping and Distortion of Thin-Walled Box Beams
,”
J. Appl. Mech.
,
54
(
1
), pp.
165
173
.
8.
Razaqpur
,
A. G.
, and
Li
,
H. G.
, 1991, “
A Finite Element with Exact Shape Functions for Shear Lag Analysis in Multi-Cell Box Girders
,”
Comput. Struct.
,
39
(
1-2
), pp.
155
163
.
9.
Boswell
,
L. F.
, and
Li
,
Q.
, 1995, “
Consideration of the Relationships Between Torsion, Distortion and Warping of Thin-Walled Beams
,”
Thin-Walled Struct.
,
21
(
2
), pp.
147
161
.
10.
Kim
,
J. H.
, and
Kim
,
Y. Y.
, 1999, “
Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections
,”
J. Appl. Mech.
,
66
(
4
), pp.
904
912
.
11.
Kim
,
J. H.
, and
Kim
,
Y. Y.
, 2001, “
Thin-Walled Multicell Beam Analysis for Coupled Torsion, Distortion, and Warping Deformations
,”
J. Appl. Mech.
,
68
(
2
), pp.
260
269
.
12.
Sumami
,
Y.
,
Yugawa
,
T.
, and
Yoshida
,
Y.
, 1988, “
Analysis of Joint Rigidity of In-Plane Bending of Plane-Joint Structures
,”
JSAE Rev.
,
9
(
2
), pp.
44
51
.
13.
Sunami
,
Y.
,
Yugawa
,
T.
, and
Yoshida
,
Y.
, 1990, “
Analysis of the Joint Rigidity of the Automotive Body Structure-Out-of-Plane Bending of Plane-Joint Structures
,”
JSAE Rev.
,
11
(
3
), pp.
59
66
. Available at: http://www.bookpark.ne.jp/cm/jsae/search_e.asp?page=3&table=JSAQ&bk_title=&bk_author=&bk_comment=&bk_company=&keyword=Sunami+Y&condition=and&bk_dateS= &bk_dateE=&option1=&option2=&option3=&content_id=&category=
14.
Lee
,
K.
, and
Nikolaidis
,
E.
, 1992, “
A Two-Dimensional Model for Joints in Vehicle Structures
,”
Comput. Struct.
,
45
(
4
), pp.
775
784
.
15.
Garro
,
L.
, and
Vullo
,
V.
, 1986, “
Deformations Car Body Joints Under Operating Conditions
,”
SAE
, pp.
5403
5420
.
16.
El-Sayed
,
M. E. M.
, 1989, “
Calculation of Joint Spring Rates Using Finite Element Formulation
,”
Comput. Struct.
,
33
(
4
), pp.
977
981
.
17.
Jang
,
G. W.
,
Kim
,
K. J.
, and
Kim
,
Y. Y.
, 2008, “
Higher Order Beam Analysis of Box Beams Connected at Angled Joints Subject to Out of Plane Bending and Torsion
,”
Int. J. Numer. Methods Eng.
,
75
(
11
), pp.
1361
1384
.
18.
Jang
,
G. W.
, and
Kim
,
Y. Y.
, 2009, “
Higher-Order In-Plane Bending Analysis of Box Beams Connected at an Angled Joint Considering Cross-Sectional Bending Warping and Distortion
,”
Thin-Walled Struct.
,
47
(
12
), pp.
1478
1489
.
19.
Jang
,
G. W.
, and
Kim
,
Y. Y.
, 2009, “
Vibration Analysis of Piecewise Straight Thin-Walled Box Beams Without Using Artificial Joint Springs
,”
J. Sound Vib.
,
326
(
3-5
), pp.
647
670
.
20.
ANSYS, 2007, ANSYS Structural Analysis Guide.
You do not currently have access to this content.