PCA Thickness Design
Inputs
This tool runs the PCA EB075.04, "Concrete Floors on Ground" (2008) Chapter 5 thickness methods for lift trucks, rack posts and distributed loads on one slab, and reports which load governs. The post charts are unchanged from the 2001 edition (EB075.03), so its post examples solve the same way here; the 2008 edition redrew the lift truck chart (see PCA's worked examples below the results). Each concentrated load is read two ways: PCA's interior chart with a joint factor, and PCA's edge chart, which needs none. The equivalent joint factor is the JF the interior chart would need to match the edge chart.
"Because the three commonly used slab thickness design methods (PCA, WRI, and COE) all are based on Westergaard's work and the assumption that slabs are always fully supported by the subgrade, they give erroneous results for slab thickness where the slab is not in contact with the subgrade. This is called the cantilever effect."
This is why we built SLABS™.
Read more about our why or see our workshops and demos.
Governing thickness by joint type
Design thickness of the governing load (largest of the included loads) for each joint type, read three ways. Only the middle group uses the joint factors entered at left; the outer groups are PCA's two bounds, full load transfer and zero load transfer, so their three bars match.
Solving...
Detailed results for
Lift truck
Interior, JF 1.0-
Interior, JF 1.60-
Free edge (Fig 5-5b)-
Equivalent JF-interior JF that matches the free-edge required thickness
Lift truck readings
Rack posts
Interior, JF 1.0-
Interior, JF 1.60-
Edge chart-
Equivalent JF-post JF on Fig 5-9 that matches Fig 5-13
Bearing and shear under the post
| Check | Computed | Allowable | Result |
|---|
How the charts are read
Figs 5-4b and 5-5b were digitized from the chart images. Every other chart and table (Figs 5-6b, 5-7b, 5-9a to c, 5-13a to d, 5-15a and b, and Tables 5-3b and 5-4b) was taken directly from the vector artwork and text of the 2008 PDF. Between printed curves the tool interpolates spacing, contact area and k on a log scale and thickness linearly. All charts are the inch-pound versions; metric values are converted at the input and output. PCA wrote its metric examples as separate problems (Lift Truck A uses k = 20 MPa/m, about 74 psi/in., against 150 psi/in. in the inch-pound version), so they are not conversions of the inch-pound examples; LOAD in the worked examples sets each one up as printed.
Lift trucks. Working stress is MR × SR / JF on Fig 5-4b and MR × SR on Fig 5-5b, where SR is the stress ratio (1 / safety factor). Duals become an equivalent single-wheel axle, F × axle load (Fig 5-6b). Figs 5-6b and 5-7b need a thickness, so each case is iterated until the thickness used in them matches the thickness read.
Rack posts. The interior route is Fig 5-9 (k = 50, 100 and 200 psi/in. charts, interpolated) with working stress MR × SR / JF and the plate area corrected by Fig 5-7b, iterated the same way. The edge route is Okamoto's Fig 5-13 (y = 20, 40, 60 and 100 in., interpolated), entered with MR × SR and no JF because the edge effect is built into the charts. Plates other than 10 sq in. are converted with Fig 5-15; PCA gives one chart for bottom tension and one for top tension, and the tool uses whichever gives the lower design stress (the thicker slab). Bearing and shear use PCA's limits: 4.2 MR interior, 2.1 MR at edges, and 0.27 MR in shear.
Distributed loads. Variable layouts use PCA's Table 5-3 equation, W = 0.123 fₜ √(h k), which reproduces the table. Fixed layouts use Table 5-4 at the critical aisle width or a specified aisle. Both use the subgrade k without subbase, as PCA directs. The narrow strip-load charts (Figs 5-18 and 5-19) are not included; PCA notes the allowable load changes little with load width.
Governing. Each load gets a required thickness, rounded up to the next 1/2 in. (5 mm in metric), and the largest governs. The summary does this for each joint type on three bases: the interior charts at JF 1.0, the interior charts at that joint type's JF, and the edge charts (Fig 5-5b for trucks, Fig 5-13 for posts), which take no JF. The tabs switch the detailed results, including the bearing and shear checks, between joint types.
PCA states that the interior chart at JF 1.6 matches the free-edge chart for lift trucks. Across 450 single-wheel combinations inside the chart ranges, the equivalent JF read here runs from 1.56 to 1.89 (mean 1.71), higher on soft subgrades. For rack posts, the equivalent JF depends strongly on post spacing because Okamoto's edge charts get thicker as y grows from 20 to 60 in.
Several printed values in Table 5-4b are typos (for example 9.5 psf and 2,615 psf); those cells were dropped and the neighboring working-stress rows used instead. The second page of Table 5-4b is labeled k = 50 but is the k = 200 data.
The metric edge post charts (Figs 5-12b, 5-12c and 5-12d) are the same drawing repeated three times, so they cannot all be right; the tool uses the inch-pound Figs 5-13a to 5-13d, which differ from one another, and converts. In those charts the required thickness is lowest at y = 20 in. and highest at y = 60 in. at the same stress, so results between 40 and 100 in. depend heavily on which charts bracket the spacing. Within 3% of a printed spacing the tool reads that chart alone.
PCA's worked examples, 2008 and 2001 editions
LOAD fills the inputs with that example, sets the units it was printed in and the joint factors it used, and returns you to the results with the matching card outlined. Compare PCA's value with the "required" line under the big number on that card; the big number is rounded up to the next 1/2 in. or 5 mm. The governing bars take the largest of every included load and chart route, so they can read higher than the one value an example checks.
| Edition | Example and inputs | PCA printed | This tool | Where to read it |
|---|
All six 2008 examples solve to within chart-reading precision except the inch-pound Lift Truck A at zero load transfer. There PCA prints 9.25 in. for both JF 1.6 and the free-edge chart; this tool reads about 8.4 and 8.8 in. at k = 150 psi/in. The metric version of the same truck, at k = 20 MPa/m, matches PCA's 235 mm free-edge result, and 235 mm is 9.25 in., so the inch-pound answer appears to have been carried over from the metric problem rather than read at k = 150.
The 2001 edition (EB075.03) already used joint factors for both lift trucks and posts, including 1.6 for undoweled joints. Its post charts (2001 Figs 5-8 and 5-11 to 5-12) are the same as 2008 Figs 5-9 and 5-13 to 5-15, and its post example is the same problem with the same answer, so results here match either edition for posts. Its lift truck chart (2001 Fig 5-4, contact areas 25 to 200 sq in., k = 50 to 200 psi/in.) is an older drawing that the 2008 Fig 5-4b replaced. On the 2008 chart the two 2001 lift truck examples come out 1/2 to 3/4 in. thicker than PCA printed in 2001 (the 2001 Lift Truck A tire, 114 sq in., is also past the 100 sq in. top curve of the 2008 chart). The dual-wheel and effective contact area charts are the same in both editions.
Single-chart checks
- Fig 5-4b example (18.5 psi, 12.5 sq in., 30 in., k 400): chart 7 in.; tool 7.17 in.
- Fig 5-5b example (39.5 psi, 25 sq in., 30 in., k 300): chart about 6 in.; tool 5.99 in.
- Fig 5-6b, Lift Truck B (Sd 18 in., 100 sq in.): PCA reads F = 0.775 at 10 in. and 0.78 at 11 in.; tool 0.776 and 0.781.
- Fig 5-7b, Lift Truck A (21 sq in. tire at 7 in.): PCA reads 30 sq in.; tool 28.6 sq in.
- Table 5-3b: the equation reproduces the printed values (5 in., k 50, MR 550: 535 psf; tool 535).