### Abstract

Warping due to transverse shear in multilayered elastic beams is studied in this paper. The Bernoulli-Kirchhoff hypothesis that plane sections remain plane after deformations, with independent rotations, is assumed for each lamina to account for the out-of-plane deformation of the composite cross section. The effects of shear are included by taking the rotations independent of the transverse deflection, as in Timoshenko beam theory. The result is a simple piecewise linear warping theory for layered composite beams. The solution to the governing equations is presented in terms of the eigenvalues and eigenvectors of a generalized matrix eigenvalue problem associated with the coefficient matrices that appear in the governing equations. The problem of a two-layered cantilever beam subjected to a uniformly distributed loading is solved in detail to show the effects of different elastic moduli on the interfacial shear stress. Compared with a finite-element solution, the current theory yields significant improvement over elementary beam theory (excluding warping) in predicting the interface shear stress.

Original language | English (US) |
---|---|

Pages (from-to) | 377-384 |

Number of pages | 8 |

Journal | Journal of Engineering Mechanics |

Volume | 124 |

Issue number | 4 |

State | Published - Apr 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Journal of Engineering Mechanics*,

*124*(4), 377-384.

**Piecewise linear warping theory for multilayered elastic beams.** / Zuo, Q. H.; Hjelmstad, Keith.

Research output: Contribution to journal › Article

*Journal of Engineering Mechanics*, vol. 124, no. 4, pp. 377-384.

}

TY - JOUR

T1 - Piecewise linear warping theory for multilayered elastic beams

AU - Zuo, Q. H.

AU - Hjelmstad, Keith

PY - 1998/4

Y1 - 1998/4

N2 - Warping due to transverse shear in multilayered elastic beams is studied in this paper. The Bernoulli-Kirchhoff hypothesis that plane sections remain plane after deformations, with independent rotations, is assumed for each lamina to account for the out-of-plane deformation of the composite cross section. The effects of shear are included by taking the rotations independent of the transverse deflection, as in Timoshenko beam theory. The result is a simple piecewise linear warping theory for layered composite beams. The solution to the governing equations is presented in terms of the eigenvalues and eigenvectors of a generalized matrix eigenvalue problem associated with the coefficient matrices that appear in the governing equations. The problem of a two-layered cantilever beam subjected to a uniformly distributed loading is solved in detail to show the effects of different elastic moduli on the interfacial shear stress. Compared with a finite-element solution, the current theory yields significant improvement over elementary beam theory (excluding warping) in predicting the interface shear stress.

AB - Warping due to transverse shear in multilayered elastic beams is studied in this paper. The Bernoulli-Kirchhoff hypothesis that plane sections remain plane after deformations, with independent rotations, is assumed for each lamina to account for the out-of-plane deformation of the composite cross section. The effects of shear are included by taking the rotations independent of the transverse deflection, as in Timoshenko beam theory. The result is a simple piecewise linear warping theory for layered composite beams. The solution to the governing equations is presented in terms of the eigenvalues and eigenvectors of a generalized matrix eigenvalue problem associated with the coefficient matrices that appear in the governing equations. The problem of a two-layered cantilever beam subjected to a uniformly distributed loading is solved in detail to show the effects of different elastic moduli on the interfacial shear stress. Compared with a finite-element solution, the current theory yields significant improvement over elementary beam theory (excluding warping) in predicting the interface shear stress.

UR - http://www.scopus.com/inward/record.url?scp=11344287029&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11344287029&partnerID=8YFLogxK

M3 - Article

VL - 124

SP - 377

EP - 384

JO - Journal of Engineering Mechanics - ASCE

JF - Journal of Engineering Mechanics - ASCE

SN - 0733-9399

IS - 4

ER -