Concrete diaphragm
Checks one direction of a rectangular concrete floor or roof diaphragm by ACI 318-19 Chapter 12, as a beam spanning between two lines of vertical elements: in-plane shear, the chord, a collector, the transfer into the vertical element, and one opening. Strength design. Enter the factored in-plane force yourself; Diaphragm forces gives Fpx.
Inputs of the diaphragm #
- Span, depth, force: L between the lines of vertical elements, B along the force, and the factored force on the span. Run one calculation per direction.
- Reaction factor: the reaction over w L / 2 where torsion or stiffness gives a line more. Yours; 1.0 for a flexible, symmetric plan.
- φ: 0.75 by 12.5.3.2. Enter less where 21.2.4 requires it, for example 0.60 for many shear-controlled diaphragms in SDC D to F.
- Construction: cast-in-place; a composite topping on precast (Acv on the combined thickness, the lesser f'c); a noncomposite topping (Acv on the topping). A topping also checks shear friction at the joints.
- Field reinforcement: area per foot crossing the shear, bars or welded wire. You can leave it out of Vn, as SP-17(14) does.
- Chord: bars at each edge, the lever arm as B less your offset, and the distance from the tension edge to the bars.
- Collector: the depth it drags, a force factor (1.0 or your overstrength from ASCE 7-22 12.10.2.1), and its bars. 0 means no collector.
- Transfer: the length of the vertical element, the dowels and the surface there.
- Opening: its center, size, the depth of the strip on one side, and the share of shear in that strip. By default the share is by depth; SP-17(14) Example 2 uses mass.
Auto-design varies the slab thickness, field reinforcement, chord bars, collector bars and dowels. The plan, forces and surfaces stay yours.
Checks performed #
| Check | Basis |
|---|---|
| In-plane shear | Eq. 12.5.3.3: Vn = Acv (2λ√f'c + ρt fy); √f'c at most 100 psi |
| Section limit | Eq. 12.5.3.4: Vu ≤ φ 8√f'c Acv |
| Precast joints | 12.5.3.5(b), 22.9: μ Avf fy with the topping's steel, fy at most 60 ksi |
| Chord | R12.5.2.1: T = M / lever arm, As = T / (0.90 fy); 12.5.2.3, within h/4 |
| Collector | R12.5.4.2, 12.5.4.2: T = v × depth dragged × factor, As = T / (0.90 fy); 12.5.4.3, the bars' ℓd along the element |
| Transfer | 12.5.3.7, 22.9: dowels into the vertical element, with Table 22.9.4.4 |
| Opening | 12.2.2: net section shear; chord force plus the strip's local moment |
| Notes | 12.6.3 what may be shared; with the SDC switch, what 18.12 adds |
Limitations #
- A rectangle, a simple span and a uniform force. A trapezoidal force, an overhang, a stepped plan: use your own analysis and check sections by hand.
- Precast without a topping, mechanical connectors (12.5.3.6), stress fields and distributed chords are not covered.
- 18.12 is not checked. The SDC switch only says what it adds. Enter φ yourself, and check the thickness and details by hand.
- One opening. The strip's local moment assumes each strip acts fixed at both ends of the opening: a simple assumption, and yours to replace. Trim bars around the opening are not detailed.
- Concrete cover, slab flexure, and combining these bars with those for gravity are yours (12.6.3).
- The collector length here is ℓd as a floor. The transfer length by shear friction (12.5.4.3(b)) is what the transfer check is about.
Verification examples #
Verification status: 37 values compared in 7 examples (5 published, 2 hand calculations from the cited equations): 37 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
| Example | Source | Published |
|---|---|---|
| East-west | ACI SP-17(14), Rigid Diaphragm Example 1, pp. 298, 305, 306 (318-14) | w 1.94 kip/ft; V 70, Vn 2,590, φVn 1,940 kips; M 1,260 kip-ft; As 0.1 in² |
| North-south | Same, pp. 298 to 304 | V 52.2, φVn 513 kips (φ = 0.60); M 2,595 kip-ft; T 37.6 kips; As 0.70 in²; collector 15.8 kips |
| Noncomposite topping | FEMA P-1051 (2015), 11.1.2, p. 539 (318-14) | φVn at the joint 264 kips (3.67 kip/ft) |
The example's moment takes a trapezoidal force and differs from the uniform one here by under 0.3 %. The rest is hand checked from the equations: opening, section limit, transfer. Example 2 of SP-17(14), with its opening shares by mass, was not run, and no published example is to ACI 318-19. ACI MNL-17(21) comes after wave 7 and would confirm these.