Visnyk LNAU: Architecture and Farm Building 2018 №19: 19-27
THE METHOD OF SOLVING OF THIN RIBBED PLATES AS CARRIER PART OF BRIDGED STRUCTURES
M. Delyavskyy, Doctor of Technical Sciences
University of Technology and Life Sciences in Bydgoszcz
D. Buchaniec, Candidate of Technical Sciences
University of Economy in Bydgoszcz
Yu. Famulak, Candidate of Technical Sciences
Lviv National Agrarian University
The design method for ribbed plate as carrier part of bridged construction is suggested in this paper. The method is named as construction element method. The thin isotropic plate reinforced at the lower surface with series of parallel thin ribs having rectangular cross-sections and uniformly placed with respect to the symmetry of longitudinal axis of the plate is considered.
The plate is loaded on the upper surface with uniformly distributed loading. It is free supported at the lateral sides and their longitudinal edges are free.
The reinforced plate is divided into separate parts containing element of the plate and one rib. Such parts are called plate ribs construction elements. Each of them contains a part of plate and one rib.
Three kinds of construction elements: left-side ribbed, central ribbed and right-side ribbed are considered in this paper.
The the mathematical model of construction plate rib element was built. For that it is separated into smaller parts (plate and rib) which are called microele-ments.
Cartesian coordinate system originated in geometrical center of the plate is introduced. It is oriented so that normal axe is directed into down and tangent axis lied in middle plane of the plate creating right hand side coordinate system. Similarly Cartesian coordinate system originated in geometrical center of the rib is taken so that directions of corresponded axis of the plate and rib be coincided. Interaction of the plate and rib is replaced by unknown normal and tangent forces applied simultaneous to bottom surface of the plate and to the upper surface of the rib. On the bottom surface interactive forces are applied only at the contact plac-es of late and ribs and they are equal to zero whenever. Plate is considered in the frames of Kirchoff’s model but rib is treated as Euler’s beam.
Equilibrium equation for each construction element was obtained. Next with help of aggregation of microelements mathematical model of construction element has been gotten. In mathematical sense it is reduced to satisfaction of continuity conditions for displacements, moments, normal and shearing forces.
According to suggested method the ribbed plate is replaced into homogene-ous plate loaded by unknown normal and shear forces applied at the common surface of plate and rib.
ribbed plate, method of calculation, construction elements, microelements, interaction, effective modulus
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