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2023 | OriginalPaper | Chapter

8. Bridging Between Rectangular Cross-Sections and Generally Shaped Cross-Sections

Authors : Yoon Young Kim, Gang-Won Jang, Soomin Choi

Published in: Analysis of Thin-Walled Beams

Publisher: Springer Nature Singapore

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Abstract

Chapters 4, 5, 6, 7 presented procedures for deriving the shape functions of higher-order section-deformable modes of thin-walled rectangular cross-sections (or box beam cross-sections) recursively and hierarchically. To extend the procedure to thin-walled beams of generally shaped cross-sections, including open, closed, or open–closed sections, it is important to summarize the types of higher-order modes of a rectangular cross-section and the recursive relationships of their sectional shape functions. This summary will guide us to develop recursive relationships for the sectional shape functions of generally shaped cross-sections.

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previous chapter Sectional Shape Functions for a Box Beam Under Flexure
next chapter Sectional Shape Functions of Thin-Walled Beams with General Cross-Section Shapes
Footnotes
1
We can have multiple unconstrained and constrained distortion modes for each mode set for a cross-section of a general shape. Therefore, different notations will be used to denote the mode number and the mode set number, correspondingly indicated by subscript and superscript, respectively (details are given in Chap. 9.) If this rule applies, we should have denoted the mode set number N as the superscript of \(\chi\) in the left side of Eq. (8.4). However, the rule was not applied here to avoid unnecessary complications.
 
2
For a box beam, the torsional distortion mode in Chap. 2 corresponds to the fundamental distortion mode.
 
Metadata
Title
Bridging Between Rectangular Cross-Sections and Generally Shaped Cross-Sections
Authors
Yoon Young Kim
Gang-Won Jang
Soomin Choi
Copyright Year
2023
Publisher
Springer Nature Singapore
Book
Analysis of Thin-Walled Beams

Print ISBN: 978-981-19-7771-8

Electronic ISBN: 978-981-19-7772-5

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-981-19-7772-5_8

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