Hollow-core plank
One simply supported precast, pretensioned hollow-core unit, untopped or with a composite topping, by ACI 318-19: stresses at transfer and at service, flexural strength with fps of Eq. 20.3.2.3.1, the 1.2 Mcr minimum, strand development, shear by Vci and Vcw without shear reinforcement, horizontal shear at the topping and the camber at release. The section comes from the producer (or a Dynaspan section of the PCI Design Handbook 8th Ed. Table 3.7).
Inputs of the hollow-core plank #
- Section: depth, area, centroid, moment of inertia and weight of the untopped unit, the unit width, the total web width (for shear) and the top flange above the cores (for the stress block), f'c and f'ci.
- Strands: count, size, height of their centroid, jacking stress and the losses at transfer and in total (lump sums: the producer's or a loss calculation).
- Topping: thickness and f'c; it is transformed by √(f'c,top / f'c), as the PCI table does.
- Span and loads: design span, bearing length, superimposed dead and live load and the sustained part.
Auto-design varies the strand size and count; the section, concretes, topping, span, loads and losses are kept.
Checks performed #
| Check | Basis |
|---|---|
| Transfer stresses at the end of ℓtr = 50db and at midspan | 0.70 / 0.60 f'ci, 6√f'ci / 3√f'ci (24.5.3, 22.5.9.1) |
| Service stresses | Class U / T by the bottom tension (Table 24.5.2.1); top compression 0.45 / 0.60 f'c (Table 24.5.4.1) |
| Flexural strength | fps (Eq. 20.3.2.3.1, γp = 0.28), stress block in the topping, flange and webs; φ by εt (21.2.2) |
| Minimum strength | φMn ≥ 1.2 Mcr (7.6.2.1) |
| Strand development | ℓd (Eq. 25.4.8.1) within half the span |
| Shear at h/2 | Vc = least of Vci and Vcw with the prestress over ℓtr (22.5.6.3); no stirrups: Vu ≤ φVc |
| Horizontal shear (topped) | 80 bv d, roughened surface without ties (Table 16.4.4.2 (d)) |
| Camber (note) | Release camber from Pi and the self-weight; PCI long-time multipliers (to confirm against the code text) |
The drawings show the plank elevation with its loads and the section with the topping, the strands and schematic cores.
Limitations #
- Simple spans with uniform loads only; continuity, cantilevers, openings, point and line loads, diaphragm action and fire ratings are not covered.
- Losses are entered; the camber multipliers of the PCI Design Handbook are from knowledge (to confirm against the code text). The hollow-core rows of Table 9.6.3.1 are not readable in the text copy: the deep-unit advisory is to confirm.
- The stress block uses strength-equivalent widths where it passes from the topping into the precast.
Verification examples #
Verification status: 12 values compared in 5 examples (4 published, 1 hand calculations from the cited equations): 12 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| PCI Table 3.7, Dynaspan 4, 6, 8, 10 in. with 2 in. topping | Composite ycb and Ic from the untopped values | e.g. 8 in.: 5.15 in., 3,205 in.⁴ | same |
The 12 in. row of the table is not compared: it matches the topping at its full width, unlike the other rows. Hand calculations check fps, fse, ℓd and the depth of the stress block.