Aspect Ratio and Relative Beam-Slab Stiffness Effects on the Long-term Deflection of Slabs

This study investigates the deflection in reinforced concrete slabs aiming to have a better understanding for the effects of the aspect ratio and the relative beam-slab stiffness parameters and to assess the ACI318 provisions for slab deflection control. The investigations included both long-term deflection for the evaluation of the mentioned parameters and the short-term deflection for the assessment of the deflection calculation methods (Finite Element SAFE software, ANSYS software and the ACI crossing beam approach).

As ACI318-19 does not include the aspect ratio (long span/short span) within the span affecting the determination of the flat plate thickness; an evaluation for this variable, a parametric long-term deflection (LTD) analysis has been done using SAFE for variable long span length (5m, 7.5m, 10m) and different aspect ratio at different panel locations (interior, edge, and corner). The results showed there is a noticeable effect for the aspect on the LTD (long span) and that the ACI318-19 recommended thicknesses met partially the ℓ/240 LTD limit in panels of long spans up to 7.5 m with aspect ratio range 1 to 2, in panels of long spans up 10 m with aspect ratio 1. For the ℓ/480 deflection limit, apart from rectangular 5 m long spans panels, the provisions were inadequate to satisfy the ℓ/480 limit in all other cases. For larger aspect ratio of 3, the current research suggests the use of the same ACI318-19 two-way flat plate recommended thickness taking the long span as the active span for aspect ratio of 2 to 3.  For the non-satisfied cases, the current study proposed minimum thickness for corner, edge and interior flat plate slabs to satisfy both the deflection limit of ℓ/240 and ℓ/480.

For the effect of the relative beam-slab stiffness on the LTD of interior, edge and corner panel two-way beam-slabs system, the LDT deflection (both long span and mid panel deflection), the parametric study showed that the ACI318-19 provisions are adequate for interior slab panels; however, the provisions are inadequate for edge and corner panels of relative beam-slab equal to 0.2.

For the effects of the relative beam-slab stiffness of one-way slabs,  (10x4.9 m, 7.5x3.6 m and 6.1x3 m slab panels) with aspect ratio greater than 2, the current study showed that with using the ACI318-19 recommended slab thickness it is required to have  a minimum relative beam-slab stiffness of 5 to satisfy the LTD limit of ℓ /240, and 20 to satisfy the LTD limit of ℓ /480 along the supporting beams. For lower relative-beam stiffness, the current study proposes revised minimum thicknesses to ensure having the LTD under the long direction beam to be within the allowable deflection of ℓ /240 and ℓ /480.

Moreover, the Bondy’s approach has been evaluated considering the LTD of interior, edge and corner panel flat plates for different aspect ratios. In all cases studied, Bondy's approach has been shown to be adequate for the ℓ/240 deflection limits. With respect to the deflection limit of ℓ/480, Bondy's approach produced satisfactory results (deflections) at the interior panels only.

The current study also showed that the ACI crossing beam approach for long span deflection calculation in flat plate slabs at different panel locations (interior, edge, and corner) are not accurate even at the elastic short-term deflection in rectangular slab panels (aspect ratio of 2) when compared with the SAFE and ANSYS deflection results, which showed closer results between them.