TY - CHAP

T1 - Sectional Shape Functions for a Box Beam Under Torsion

T2 - Wall-Bending Field

AU - Kim, Yoon Young

AU - Jang, Gang Won

AU - Choi, Soomin

N1 - Publisher Copyright:
© 2023, Springer Nature Singapore Pte Ltd.

PY - 2023

Y1 - 2023

N2 - In Chap. 4, the sectional shape functions (ψzW, ψsχ) for a box beam under torsion, which correspond to the wall-membrane field, were derived. This section is devoted to the derivation of the sectional shape functions (ψnχ, ψnη¯, ψnη^) corresponding to the wall-bending field. (See Ferradi and Cespedes (2014), Bebiano et al. (2015), and Choi et al. (2017) for earlier developments.) To argue for the co-existence of ψnχ with ψsχ, we observe that if the distortion mode χ has a non-zero ψsχ (the s-directional displacement component) only (see Fig. 5.1a) without its n-directional counterpart, ψnχ, two adjacent sectional edges cannot remain connected at the corners. Therefore, ψnχ cannot be zero. It was shown in Chap. 2 that the zeroth-order distortion mode χ0 has a non-zero ψnχ0, as given by Eq. (2.50). If ψnχ(z,s) does not vanish, it will induce a non-zero u~s(z, n, s) for n≠ 0, as expressed by Eq. (3.3c) and thus causes the bending of cross-sectional walls. The sectional shape functions ψnχk for k≥ 1 will be derived in Sect. 5.3 identically to how ψsχk was derived in Chap. 4; ψnχk can be obtained as the secondary deformation of the axial stress through Poisson’s effect.

AB - In Chap. 4, the sectional shape functions (ψzW, ψsχ) for a box beam under torsion, which correspond to the wall-membrane field, were derived. This section is devoted to the derivation of the sectional shape functions (ψnχ, ψnη¯, ψnη^) corresponding to the wall-bending field. (See Ferradi and Cespedes (2014), Bebiano et al. (2015), and Choi et al. (2017) for earlier developments.) To argue for the co-existence of ψnχ with ψsχ, we observe that if the distortion mode χ has a non-zero ψsχ (the s-directional displacement component) only (see Fig. 5.1a) without its n-directional counterpart, ψnχ, two adjacent sectional edges cannot remain connected at the corners. Therefore, ψnχ cannot be zero. It was shown in Chap. 2 that the zeroth-order distortion mode χ0 has a non-zero ψnχ0, as given by Eq. (2.50). If ψnχ(z,s) does not vanish, it will induce a non-zero u~s(z, n, s) for n≠ 0, as expressed by Eq. (3.3c) and thus causes the bending of cross-sectional walls. The sectional shape functions ψnχk for k≥ 1 will be derived in Sect. 5.3 identically to how ψsχk was derived in Chap. 4; ψnχk can be obtained as the secondary deformation of the axial stress through Poisson’s effect.

UR - http://www.scopus.com/inward/record.url?scp=85159855466&partnerID=8YFLogxK

U2 - 10.1007/978-981-19-7772-5_5

DO - 10.1007/978-981-19-7772-5_5

M3 - Chapter

AN - SCOPUS:85159855466

T3 - Solid Mechanics and its Applications

SP - 115

EP - 164

BT - Solid Mechanics and its Applications

PB - Springer Science and Business Media B.V.

ER -