One-way slab
A solid nonprestressed one-way slab designed on a 12 in. strip to ACI 318-19 Chapter 7, with ASCE 7-22 load combinations (strength design). The moments and shears come from the ACI coefficients of 6.5 or from an elastic analysis of any support layout with the live-load patterns of 6.4.2.
Inputs of the one-way slab #
- Materials: f'c (at least 2,500 psi, 19.2.1.1), Grade 60 or 80 bars, normalweight or lightweight concrete (λ by Table 19.2.4.1(b), or from the equilibrium density wc by Table 19.2.4.1(a)), and the modulus Ec by 19.2.2.1(b) (57,000√f'c) or 19.2.2.1(a) (wc^1.5 × 33√f'c; always for lightweight concrete).
- Slab and reinforcement: thickness h, clear cover (3/4 in. prefilled, Table 20.5.1.3.1 for slabs not exposed to weather), bottom bars and spacing (positive moment), top bars and spacing (negative moment over the supports) and the shrinkage and temperature bars perpendicular to the span. The flexural bars are taken as the outer layer.
- Spans and analysis:
- ACI coefficients (6.5): the clear spans ℓn, the support width and how the exterior support is built (integral with a spandrel beam, integral with a column, or unrestrained). The conditions of 6.5.1 are checked: at least two spans, the longer of two adjacent spans at most 20 percent longer than the shorter, L ≤ 3D. Uniform loads and a prismatic slab hold by construction. Where all spans are 10 ft or less, wu ℓn²/12 may be used at the supports (Table 6.5.2 (a)); a check box turns this off.
- Elastic analysis: the slab length and any supports (pins or fixed), with the live load on all spans, on alternate spans and on each pair of adjacent spans (6.4.2) when the pattern box is ticked.
- The support width sets the span ℓ = ℓn + width used for Table 7.3.1.1, the face of support for the elastic moments (7.4.2.1) and the shear critical section at d from the face (7.4.3.2).
- Loads: uniform area loads per load type (D, L, Lr, S, R) and the self-weight from the unit weight entered (150 pcf prefilled). See Loads and combinations.
- Deflection: calculated when h is less than Table 7.3.1.1 (7.3.2.1), or always. The limits are span / n for the immediate live load deflection and for the part of the deflection after attachment of nonstructural elements (Table 24.2.2: 360 for floors, 180 for flat roofs; 480 or 240); the sustained load duration (ξ of Table 24.2.4.1.3) and the sustained fraction of the live load are the engineer's.
Auto-design (editor toolbar) varies the thickness (1/2-in. steps) and the bottom, top and shrinkage bars (size and spacing). Objectives: lowest cost index (concrete, reinforcement); thinnest slab, then cost; least reinforcement. Every other input is kept; see Auto-design.
Checks of the one-way slab #
| Check | Basis |
|---|---|
| Minimum thickness | Table 7.3.1.1 per span (simply supported ℓ/20, one end continuous ℓ/24, both ends continuous ℓ/28, cantilever ℓ/10), × (0.4 + fy/100,000) for fy ≠ 60 ksi (7.3.1.1.1), × max(1.65 − 0.005wc, 1.09) for lightweight concrete of 90 to 115 pcf (7.3.1.1.2). A thinner slab is not an error: the deflections are calculated instead |
| Positive and negative moment strength | φMn by strain compatibility (22.2) with φ from εt (Table 21.2.2), at the governing section: Table 6.5.2 coefficients, or the envelope of the combinations and live-load patterns |
| Tension-controlled section | εt ≥ εty + 0.003 (7.3.3.1 as printed in ACI 318-19) |
| Minimum flexural steel | As ≥ 0.0018Ag (7.6.1.1) |
| Bar spacing | ≤ min(3h, 18 in.) (7.7.2.3); crack control ≤ min(15(40,000/fs) − 2.5cc, 12(40,000/fs)) with fs = 2/3 fy (24.3.2, 24.3.2.1); clear spacing ≥ max(1 in., db) (25.2.1) |
| One-way shear | Vu ≤ φVc with Vc = 8λsλ(ρw)^(1/3)√f'c b d (Table 22.5.5.1(c), no shear reinforcement, 7.6.3.1), ρw of the top bars, Vu at d from the face (Table 6.5.4 shears less wu d, or the elastic shear at that section) |
| Shrinkage and temperature steel | ≥ 0.0018Ag (24.4.3.2), spacing ≤ min(5h, 18 in.) (24.4.3.3, 7.7.6.2.1) |
| Development length | ld by Eq. 25.4.2.4a (Ktr = 0), advisory |
| Immediate live load deflection | Δ(D + L) − Δ(D) with Ie of Table 24.2.3.5 at each load level (24.2.3.7), against ℓ/n |
| Long-term deflection | λΔ(ΔD + sustained part of ΔL) + ΔL with λΔ = ξ/(1 + 50ρ') (24.2.4.1), against ℓ/n |
The deflection model is the slab line itself: pinned at the support centrelines for the coefficient option, as entered for the elastic option. One Ie is used for the whole member: the value at the maximum positive service moment, or the smaller of that and the support value where the slab cantilevers.
The drawings (on screen, in the report and on the DXF / PDF drawing sheet) show the slab elevation of the strip with its supports and spans (centre to centre, and the clear spans between the support faces for the coefficient method), a typical section across the span with the bottom and top bars at their spacing, the shrinkage and temperature bars, the thickness and the cover, and for the elastic analysis the shear and moment envelopes per strip under the elevation. Bar lengths, cut-offs, laps and the extent of the top bars are not part of the calculation and are not drawn.
Limitations of the one-way slab #
- Solid nonprestressed slabs of constant thickness with uniform area loads; no point or line loads, openings, joists or composite deck.
- No shear reinforcement: a slab that needs it (Vu > φVc) fails the shear check; thicken the slab.
- Moments by the coefficients are not redistributed (6.5.3). The elastic option does not redistribute either.
- The wu ℓn²/12 option is applied at the interior supports and at integral exterior supports [verify: whether Table 6.5.2 (a) also replaces the exterior-support values].
- Deflections: no compression steel is counted in ρ' (λΔ is conservative), no deduction for the deflection before the nonstructural elements are attached, and one Ie for the member (24.2.3.7).
- The top bars are assumed to be top bars for development (ψt) only where more than 12 in. of concrete lies below them.
Verification of the one-way slab #
The one-way slab is verified against the free StructurePoint one-way slab example (ACI 318-14, Wight Ex. 5-7), the ACI Reinforced Concrete Design Handbook (MNL-17(21), ACI 318-19) One-way Slab Example 1 as tabulated in the free Tekla Tedds verification example, and hand calculations. ACI 318-19 changed Vc of slabs without shear reinforcement (Table 22.5.5.1(c), with λs and ρw); the 318-14 value is a deviation (ACI318-14-VC).
| Example | Source | What it checks | Published | ILX Calcs |
|---|---|---|---|---|
| SP-OWS | StructurePoint, One-Way Slab (ACI 318-14), pp. 4–12, 39 | 4 spans, h = 7 in., #4 @ 12 in., ACI coefficients | hmin = 7.17 in., Mu+ = 3.14, Mu− = 4.65 kip-ft/ft, As,min = 0.151 in²/ft, s ≤ 18 in., crack spacing 12 in., S&T 0.151 in²/ft, ≤ 18 in. | 7.13, 3.14, 4.65, 0.151, 18, 12, 0.151, 18 |
| SP-OWS | same | φVc (318-14, deviation) | 6.83 kips/ft | 3.84 (Table 22.5.5.1(c)) |
| ACI-HB-OW1 | ACI MNL-17(21) One-way Slab Ex. 1 via Tekla Tedds | 14 ft span + 6 ft cantilever, h = 7 in., f'c = 5 ksi | hmin 7.0 / 7.2 in., As,min = S&T = 0.15 in²/ft, φVc = 4.9 kips/ft | 7.0, 7.2, 0.151, 0.151, 4.93 |
Hand calculations:
| Example | What it checks | Hand calculation | ILX Calcs |
|---|---|---|---|
| OW-1 | 3 spans of 12 ft, h = 7 in., #4 at 12 in.: ℓ/24, wu ℓn²/14 and /10, φMn, 1.15wu ℓn/2 − wu d, φVc (Table 22.5.5.1(c)), crack-control spacing | 6.50 in., 2.97 and 4.16 kip-ft, 5.27 kip-ft, 1.85 kips, 3.84 kips, 12 in. | equal within 0.1 % |
| OW-2 | Simple span 12 ft, h = 5 in.: immediate live load and long-term deflection with Ie of Table 24.2.3.5 | 5wℓ⁴/(384 Ec Ie) | equal within 0.1 % |