Higher-Order I-Section Beam Analysis Using Recursive Analysis

초록

To predict the responses of I-section beams (that is, displacements and stresses) under bending loads including end effects, a one-dimensional higher-order beam analysis requires numerous cross-sectional deformation modes. In this study, we establish a new recursive analysis method for I-section beams that can provide as many sectional deformation modes as required. In contrast to earlier studies that calculate the modes numerically by discretizing the cross-section using beam / shell elements, the proposed method derives the modes analytically. Hence, the shape functions of the resulting modes are written in closed form and are thus available irrespective of the cross-sectional dimensions of the I-section beams. Additionally, the resulting recursive relations between sectional shape functions allow us to establish explicit stress-generalized force relations applicable for higher-order I-section beam analysis. To check the validity of the proposed method, several examples of interpreting displacements and stresses of I-section beams are considered.

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