Q.: The specification for the floor of a maintenance building called for a 6-inch slab thickness and concrete with a design compressive strength of 3000 psi. The actual average cylinder strength for the floor concrete was 3630 psi. Four months after the floor was placed, 10 cores were drilled, measured, and tested in compression. The average core length was 5.62 inches, and the average strength was 5580 psi. Is the higher-than-specified strength enough to compensate for the lower-than-specified floor thickness?

A.: Most designers calculate the required thickness of a floor based on the flexural strength of the concrete. Flexural strength is estimated by the modulus of rupture, which is assumed to vary with the square root of the compressive strength. In the equation that relates design slab thickness and modulus of rupture, the thickness term is squared. Thus the thickness varies with the square root of the modulus of rupture. Because of the effect of taking a square root of a square root, a large increase in compressive strength results in only a small reduction in the required slab thickness.

You can estimate the expected change in floor load-carrying capacity that results from the higher average strength of 5580 psi (instead of the specfied strength of 3630 psi) as follows:

5580/3630 = 1.54
Square root of 1.54 = 1.24

Thus the compressive strength increase of 54 percent results in increased load-carrying capacity of 24 percent.

The load-carrying capacity of a floor varies as the square of the floor thickness. You can estimate the expected change in floor load-carrying capacity due to reducing the thickness from 6 inches to 5.62 inches instead of 6 inches as follows:

(5.62/6) squared = 0.88

Thus the reduction in thickness causes a 12 percent reduction in load-carrying capacity.

The increase in load-carrying capacity due to the higher-strength concrete is greater than the reduction in capacity due to the reduced thickness. We'ld give this information to the floor designer and let him decide what remedial action, if any, is needed.

### Reference

Boyd Ringo and Robert Anderson, Designing Floor Slabs on Grade, second edition, The Aberdeen Group, 1996, pp. 182-185.