Two-way slab
One panel of a flat plate, a flat slab with drop panels or a slab with beams on all sides, by the direct design method, with the minimum thickness, the reinforcement of each column and middle strip and the punching shear at a column (ACI 318-19 Chapter 8 and 22.6, ASCE 7-22 gravity combinations, strength design).
ACI 318-19 permits the direct design method for gravity loads (6.2.4.1) but no longer prints it: the commentary R6.2.4.1 refers to the method of the 2014 Code. The moment coefficients, strip fractions and unbalanced moments used here are therefore those of ACI 318-14 Section 8.10; everything else is ACI 318-19.
Inputs of the two-way slab #
- Materials: as for the other concrete calculations (f'c, Grade 60 or 80, λ, Ec).
- Slab system and panel: the system, the centre-to-centre spans ℓx and ℓy, whether the panel is an interior or an end span in each direction, the adjacent spans and the number of spans (for the limits of 8.10.2 and the unbalanced moment of 8.10.7.2), the largest column offset, and the exterior edge (on columns, an unrestrained bearing wall or a fully restrained concrete wall: the column of Table 8.10.4.2), with or without edge beams.
- Columns: rectangular c1 × c2 (c1 along x), or circular, taken as a square of equal area (22.6.4.1.2).
- Slab and reinforcement: thickness h, clear cover, the bar size in each direction and which layer is outermost (it sets d in each direction; punching uses the average d, 22.6.2.1). For a flat slab: the drop panel projection below the slab and its plan size (8.2.4: at least h/4 and ℓ/6 each side of the column). For beams (or edge beams): the beam width and overall depth, used for αf (with the slab portion of 8.4.1.8) and βt.
- Loads: uniform gravity area loads per load type and the self-weight (the drop panel weight is averaged over the panel). Wind and earthquake are outside the direct design method.
- Punching shear: the column checked (interior, edge or corner; the slab edge is across the end-span direction) and the distance from the slab edge to the column face. Vu and the unbalanced moments come from the panel loads (tributary area; 8.10.7.2 at interior columns, 0.3Mo at edge and corner columns, 8.10.7.3) or are entered. The stresses of the two moment directions are added when the box is ticked (always at corner columns).
Auto-design (editor toolbar) varies the thickness (1/2-in. steps) and bar size in each direction (the strips' spacings follow). Objectives: thinnest slab (least concrete), then smaller bars. Every other input is kept; see Auto-design.
Checks of the two-way slab #
| Check | Basis |
|---|---|
| Limits of the direct design method | ACI 318-14 8.10.2: three spans each way, successive spans within 1/3 of the longer, ℓlong/ℓshort ≤ 2, offsets ≤ 10 %, gravity load, L ≤ 2D, 0.2 ≤ αf1ℓ2²/(αf2ℓ1²) ≤ 5.0 with beams. Outside them the calculation is not feasible |
| Minimum thickness | Table 8.3.1.1 (interpolated for fy; edge beams count with αf ≥ 0.8; at least 5 in., 4 in. with drop panels) or Table 8.3.1.2 with αfm and β (+10 % at a discontinuous edge without an αf ≥ 0.80 edge beam, 8.3.1.2.1). A thinner slab fails: calculated two-way slab deflections (8.3.2) are not covered |
| Strip moments | Mo = qu ℓ2 ℓn²/8 (ℓn face to face of columns, ≥ 0.65ℓ1); 0.65 / 0.35 in an interior span, Table 8.10.4.2 in an end span; column-strip fractions of Tables 8.10.5.1, 8.10.5.2 (βt) and 8.10.5.5 with αf1ℓ2/ℓ1; beams take 0.85 of the column strip when αf1ℓ2/ℓ1 ≥ 1 (8.10.5.7); the middle strips the rest |
| Reinforcement of each strip | The bar spacing is designed: As for Mu (rectangular stress block), at least 0.0018Ag (8.6.1.1), at most min(2h, 18 in.) (8.7.2.2); then φMn by strain compatibility (22.2). A strip that cannot be reinforced at a clear spacing of max(1 in., db) is not feasible |
| Tension-controlled strips | εt ≥ εty + 0.003 (8.3.3.1 as printed) |
| Punching shear | vu = Vu/(bo d) + γv Msc c/Jc (8.4.4.2, Jc of the straight-sided critical section at d/2, R8.4.4.2.3) against φvc, vc = least of 4λsλ√f'c, (2 + 4/β)λsλ√f'c, (2 + αs d/bo)λsλ√f'c (Table 22.6.5.2, √f'c ≤ 100 psi); for flat slabs also at d/2 outside the drop panel |
| Moment transfer by flexure | γf Msc (Eq. 8.4.2.2.2) resisted by top bars within bslab = column width + 1.5h each side (Table 8.4.2.2.3); the number of bars to concentrate there is given |
| As,min near the column | 5vuv bslab bo/(φ αs fy) when vuv > φ2λsλ√f'c (8.6.1.2) |
For gravity loads the moment-transfer stress adds at the face of the critical section towards the span; for entered moments the larger distance to a face is used (the moment may reverse).
The drawings (on screen, in the report and on the DXF / PDF drawing sheet) show the panel plan with the column lines, the columns, the exterior slab edges of an end span, the column and middle strips of both directions (tagged CS-X, MS-X, CS-Y, MS-Y), the drop panels or beams and the punching critical section at the checked column; a strip reinforcement schedule with the designed bar size and spacing of every strip at each moment location and the transfer bars of 8.4.2.2; and a typical section at a column through the column strip (slab, drop panel or beam, top and bottom layers with the outer layer as entered, cover). Bar lengths, cut-offs and the column, beam and drop panel reinforcement are not part of the calculation and are not drawn.
Limitations of the two-way slab #
- Direct design method only (no equivalent frame or finite elements), gravity loads only, one panel and the column checked; the frame width is taken as the panel's transverse span ℓ2 (equal adjacent transverse spans).
- The direct design method text is that of ACI 318-14 8.10 [verify: against the ACI 318-14 text, not on disk], including the uniform distribution of the exterior negative moment at wall supports (8.10.5.4), the 0.3Mo edge moment and the tributary-area column shear.
- The optional 10 % modification of 8.10.4.3 (318-14) and the increased γf of Table 8.4.2.2.4 are not used (conservative).
- Column strip negative bars use the slab d even over a drop panel (conservative for flexure).
- No shear reinforcement (stirrups or headed studs) for punching; no openings near the column.
- Edge beams of the flat-plate systems are counted for Table 8.3.1.1 and βt but are not designed; the beams of a slab with beams are reported (moment share) for design with the Concrete beam calculation. Their stiffness αf uses a slab width of ℓ2 (interior) and ℓ2/2 (edge) [verify: edge-beam slab width].
- Corner reinforcement 8.7.3 and integrity reinforcement 8.7.4.2 are the engineer's detailing.
Verification of the two-way slab #
The two-way slab is verified against the free StructurePoint examples (ACI 318-14, from PCA Notes on ACI 318-11 Examples 20.1 and 20.2), the ACI Design Handbook (MNL-17(21)) Two-way Slab Example 1 as tabulated in the free Tekla Tedds verification example, and hand calculations. The direct design method coefficients of the published flat plate match the module's ACI 318-14 8.10 tables exactly.
| Example | Source | What it checks | Published | ILX Calcs |
|---|---|---|---|---|
| SP-TWFP | StructurePoint, Two-Way Flat Plate (ACI 318-14), pp. 5–13 | 18 × 14 ft end panel, h = 7 in., DDM | hmin = 6.67 in., Mo = 93.82, 0.26/0.52/0.70Mo = 24.39/48.79/65.67 kip-ft, column strip 24.39/29.27/49.25, middle strip 19.52/16.42 kip-ft (per 7 ft), As,min, interior punching Vu = 48.00 kips, bo = 87 in., vc = 252.98 psi, φvc = 189.74 psi | equal within 0.1 % |
| SP-TWDP | StructurePoint, Two-Way Flat Slab with Drop Panels (ACI 318-14), pp. 12–18 | 30 × 30 ft, h = 10 in., 10 × 10 ft drops | hmin = 10.30 in., d = 12.75 in., bo = 131 and 514 in.; vc = 282.8 psi at the column and at the drop | 10.30, 12.75, 131, 514; 265.2 (λs, deviation ACI318-19-LS) and 188.2 psi (Table 22.6.5.2(c) governs, deviation SP-TWDP-VC) |
| SP-TWB | StructurePoint, Two-Way Slab with Beams (ACI 318-14), pp. 5–9 | 22 × 17.5 ft, beams 14 × 20 in., h = 6 in. | αfm = 3.57, β = 1.28, hmin = 5.69 in. | 3.56, 1.28, 5.79 (ℓn face to face of beams, deviation SP-TWB-LN) |
| ACI-HB-TW1 | ACI MNL-17(21) Two-way Slab Ex. 1 via Tekla Tedds | 18 × 14 ft interior panel, h = 7 in., 24 in. columns | hmin = 5.8 in., Mo = 127, 0.65Mo = 83 kip-ft, Vu = 70 kips, φVc = 137.4 kips | 5.82, 126.8, 82.4, 69.6, 137.8 |
Hand calculations:
| Example | What it checks | Hand calculation | ILX Calcs |
|---|---|---|---|
| TW-1 | Flat plate 20 × 20 ft end panel, h = 8 in., 16 in. columns: ℓn/30, Mo, column and middle strip moments, interior column punching (vuv + γvMsc c/Jc against 4λsλ√f'c), γf Msc | 7.47 in., Mo = 195.1 kip-ft, 10.24 / 5.07 / 4.06 kip-ft per ft, vu = 168.4 psi, φvc = 189.7 psi, 11.7 kip-ft | equal within 0.1 % |
The behaviour tests also check the Table 8.10.5.1, 8.10.5.2 and 8.10.5.5 fractions, the commentary Jc of an interior section, and an edge-column section derived by hand.