Use of analytical method for calculating stiffnesses of straight waffle slabs

Introduction. The analysis of analytical and computer-assisted calculations of waffle slabs shows that, depending on the established finite-element model and structure geometry, the forces in beams can vary significantly. As a rule, the analytical model is used as a reference when comparing bending moments. Examples available in the literature show that regardless of the slab geometry, the stiffness of individual central orthogonal beams or conditionally selected beams is used in the calculations when determining structural loads.

Aim. In this work, the accuracy of resulting forces in the beams of straight waffle slabs was assessed using the stiffness of individual beams in the analytical calculation.

Materials and methods. The work was carried out by comparing the bending moments obtained analytically and in the SCAD software by the finite-element method for beams having various stiffnesses in the central zones of straight waffle slabs. 12.0 × 12.0 m slabs square in plan having different aspect ratios of waffle were considered, as well as slabs having square 1.5 × 1.5 m waffles and different aspect ratios of spans. A T-beam-and-girder construction was used in the computer model.

Results. The values of bending moments of slabs square in plan having square caissons calculated analytically and using the computer-assisted finite-element method coincide, being a particular case. The bending moments calculated analytically and using the finite-element method for rectangular slabs or slabs having rectangular caissons differ. As the ratio of the span or caisson sides increases, these deviations increase.

Conclusions. In the general calculation, using the stiffnesses of individual central orthogonal beams or conditionally selected beams for the analytical determination of forces in the beams of straight waffle slabs leads to erroneous results. 

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