Shear deformation effect in plates stiffened by parallel beams |
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Authors: | E J Sapountzakis V G Mokos |
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Institution: | (1) Institute of Structural Analysis, School of Civil Engineering, National Technical University of Athens, Zografou Campus, 157 80 Athens, Greece |
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Abstract: | In this paper a general solution for the analysis of shear deformable stiffened plates subjected to arbitrary loading is presented.
According to the proposed model, the arbitrarily placed parallel stiffening beams of arbitrary doubly symmetric cross section
are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions
in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface
width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is
defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces.
The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear
forces and the nonuniform torsional response of the beams to be taken into account. The analysis of both the plate and the
beams is accomplished on their deformed shape taking into account second-order effects. The analysis of the plate is based
on Reissner’s theory, which may be considered as the standard thick plate theory with which all others are compared, while
the analysis of the beams is performed employing the linearized second order theory taking into account shear deformation
effect. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM based method.
The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical
methods. The adopted model permits the evaluation of the shear forces at the interfaces in both directions, the knowledge
of which is very important in the design of prefabricated ribbed plates. The effectiveness, the range of applications of the
proposed method and the influence of shear deformation effect are illustrated by working out numerical examples with great
practical interest. |
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Keywords: | Elastic stiffened plate Reinforced plate with beams Bending Nonuniform torsion Warping Ribbed plate Boundary element method Slab-and-beam structure Shear deformation Reissner’ s theory |
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