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Research Papers

Exact Matching Condition at a Joint of Thin-Walled Box Beams Under Out-of-Plane Bending and Torsion

[+] Author and Article Information
Soomin Choi

School of Mechanical and Aerospace Engineering,  Seoul National University, Shinlim-Dong, San 56-1, Kwanak-Gu, Seoul 151-742, Koreasoomin0603@snu.ac.kr

Gang-Won Jang

Faculty of Mechanical and Aerospace Engineering,  Sejong University, 98 Gunja-Dong, Gwangjin-Gu Seoul 143-747, Koreagwjang@sejong.ac.kr

Yoon Young Kim1

WCU Multiscale Mechanical Design Division, School of Mechanical and Aerospace Engineering,  Seoul National University, Shinlim-Dong, San 56-1, Kwanak-Gu, Seoul 151-742, Koreayykim@snu.ac.kr

1

Corresponding author.

J. Appl. Mech 79(5), 051018 (Jun 29, 2012) (11 pages) doi:10.1115/1.4006383 History: Received August 30, 2011; Revised January 21, 2012; Posted March 15, 2012; Published June 28, 2012; Online June 29, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Thin-walled box beams connected at an angled joint

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Figure 2

(a) Coordinate system and (b)–(f) displacements/deformations of the beam section corresponding to the field variables (V, β, θ, U, χ)

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Figure 3

(a) The top view of the beam centerlines in the x-z plane with an indication of the assumed common intersection point A and (b) beam cross sections passing though the common intersection points A and B. (The generalized force quantities having nonzero resultants are shown.)

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Figure 4

Description of the procedure to obtain T(−φ): (a) T(φ) relation for a positive φ and (b) T(−φ) defined for a negative φ, which can be derived from T(φ) defined in a different coordinate system

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Figure 5

Numerical results for the two-beam structure in Fig. 1 with b = 50 mm, h = 100 mm, φ = 60 deg: (a) vertical bending deflection V, (b) bending/shear rotation β, (c) torsional rotation θ, (d) warping U, and (e) distortion χ

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Figure 6

Numerical results for the two-beam structure in Fig. 1 with b = 50 mm, h = 100 mm, φ = 30 deg: (a) vertical bending deflection V, (b) bending/shear rotation β, (c) torsional rotation θ, (d) warping U, and (e) distortion χ

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Figure 7

Numerical results for the two-beam structure in Fig. 1 with b = 50 mm, h = 100 mm, φ = 90 deg: (a) vertical bending deflection V, (b) bending/shear rotation β, (c) torsional rotation θ, (d) warping U, and (e) distortion χ

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Figure 8

Numerical results for the two-beam structure in Fig. 1 with b = 50 mm, h = 150 mm, φ = 60 deg: (a) vertical bending deflection V, (b) bending/shear rotation β, (c) torsional rotation θ, (d) warping U, and (e) distortion χ

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Figure 9

A thin-walled beam structure having three angled joints under a bending moment M (L1  = L2  = L3  = L4  = 1000 mm, φ1  =  − 45 deg, φ2  = 20 deg, M =  − 100 Nm)

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Figure 10

Numerical results for the beam structure shown in Fig. 9: (a) vertical bending deflection V, (b) bending/shear rotation β, (c) torsional rotation θ, (d) warping U, and (e) distortion χ

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