Joist and waffle slab
A ribbed (pan-joist) slab by ACI 318-19 9.8, or a two-way joist (waffle) slab by 8.8, designed per rib as a T-beam: the dimensional limits of joist construction, the slab thickness over the pans, the rib's flexure at midspan and at the support, shear with the 10 % increase of 9.8.1.5, minimum steel and deflection.
Inputs of the joist slab #
- Forming: the pan (or dome) width at the top of the rib, the pan depth, the rib width at the bottom and the side taper of the forms, and the top slab thickness. The section is the tapered rib (in slices) under a flange one rib spacing wide. Standard sizes (20 and 30 in. pans, 8 to 20 in. deep; 19 and 30 in. waffle domes) are from the CRSI handbook, which is not on file: the forming dimensions are yours, from the form supplier.
- Cover (3/4 in. for joists not exposed, Table 20.5.1.3.1), aggregate size, materials.
- Loads: superimposed dead and live load per ft² (times the rib spacing) and the computed self-weight.
- Moments and shears: the coefficients of 6.5 (end or interior span, the discontinuous end, two or more spans; 6.5.1(c) is checked, (d) and (e) are yours to confirm), a simple span, or entered per rib. Two-way joists take entered moments: they come from the two-way slab analysis.
- Reinforcement per rib: bottom bars, top bars over the support (placed in the slab), optional stirrups.
- Deflection: the minimum depth of Table 9.3.1.1, or computed with Ie (24.2.3) against your limits.
Auto-design varies the pan depth (standard depths and your value) and the bottom and top bars per rib; the pan width, rib width, taper, slab, loads and spans stay yours.
Checks performed #
| Check | Basis |
|---|---|
| Joist limits | Rib width ≥ 4 in., depth ≤ 3.5 × minimum rib width, clear spacing ≤ 30 in. (9.8.1.2 to 9.8.1.4; 8.8.1.2 to 8.8.1.4); outside them: designed as slabs and beams (9.8.1.8), NOT FEASIBLE |
| Slab thickness | ≥ max(clear spacing / 12, 2 in.) over removable forms (9.8.3.1) |
| Demands | Tables 6.5.2 and 6.5.4 with 6.5.1, simple span, or entered |
| Flexure | Strain compatibility (22.2), φ by εt, tension-controlled (9.3.3.1), As,min (9.6.1.2) at midspan and at the support |
| Shear | 1.1 Vc of Table 22.5.5.1 at the minimum rib width (9.8.1.5); Av,min not required where Vu ≤ φVc (Table 9.6.3.1) |
| Deflection | Table 9.3.1.1 (with 9.3.1.1.1, 9.3.1.1.2), or Ie (Table 24.2.3.5) and λΔ (24.2.4) |
| Detailing | Integrity bar (9.8.1.6) and slab steel across the ribs (9.8.1.7) stated |
The drawing is a section across two ribs with the bars and the forming dimensions.
Limitations #
- One typical rib. The coefficients take equal adjacent spans for the negative moment (Table 6.5.2 note [1] uses their average). Concentrated loads, distribution ribs, solid heads at columns of a waffle slab and the slab reinforcement across the ribs are not designed.
- The computed deflection uses the elastic formula of the idealized end condition (simple 5/384, one end continuous 1/185, both ends 1/384) with Ie at midspan: an approximation; the code permits any method in reasonable agreement with tests (24.2.3).
- Wide-module joists (pans over 30 in.) are beams and slabs (9.8.1.8): use the continuous beam calculation.
Verification examples #
Verification status: 16 values compared in 4 examples (0 published, 4 hand calculations from the cited equations): 16 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: the provisions it uses were read in the target edition.
No published ACI 318-19 joist example is on file. The values are hand calculations (closed form): the rib geometry and self-weight, the coefficients of Tables 6.5.2 and 6.5.4 for end and interior spans, the 1.1 Vc of 9.8.1.5 with Table 22.5.5.1(c), the minimum depths of Table 9.3.1.1 and the slab thickness of 9.8.3.1.