A new analysis is presented for plates reinforced with an orthogonal system of eccentric ribs of rectangular section, which enables the accurate determination of elastic rigidities in flexure and torsion. The new expression for torsional rigidity resulting from this analysis is found to correlate well with experimental values obtained from tests on asbestos-cement ribbed plates.
THE RIBBED plate is a common structural form in buildings, bridges, ships and aircraft. The distribution of elastic stresses and deformations in the plate is dependent upon its rigidity in torsion and flexure. It is of importance for the structural engineer to have accurate means of assessing the flexural and torsional rigidities. For example, the draft unified code of practice for concrete calls for checks of deflection of floors; the T-beam floor and the coffered slab floor are both forms of ribbed plate. A second example of particular interest to the authors is the beam and slab bridge deck; in the field of bridge deck analysis it sometimes seems inappropriate to employ computer-based analyses with input data which include ill-defined rigidities.
In this paper the stress distribution is analysed in a plate reinforced eccentrically with an orthogonal system of intersecting ribs of rectangular cross-section. The ribbed plate is treated as an orthotropic plate with flexural rigidities Dx, Dy and torsional rigidities Dxy, Dr~ in the longitudinal and transverse directions respectively. The bending moments in the x and y directions are expressed as