Rebar development and splices
Development and lap splice lengths of one deformed bar size to ACI 318-19 Chapter 25: straight bars, standard hooks and headed bars in tension, bars in compression, and tension and compression lap splices. Every length is listed in the results with every modification factor shown as a step; the anchorage you pick is checked against the length you provide. Development lengths take no strength reduction factor (25.4.1.3), so the method switch is hidden.
Inputs of the bar and anchorage #
- Bar and concrete: bar size #3 to #18; Grade 40, 60, 80 or 100 (ψg = 1.0, 1.0, 1.15, 1.3, Table 25.4.2.5); f'c (√f'c is limited to 100 psi, 25.4.1.4); normalweight or lightweight concrete (λ = 0.75 for any lightweight concrete in Chapter 25); uncoated / galvanized or epoxy-coated bars; top bar when more than 12 in. of fresh concrete is placed below it (ψt = 1.3).
- Anchorage checked and length provided: straight bar in tension (ℓd), standard hook (ℓdh, measured to the outside of the hook), headed bar (ℓdt, to the bearing face of the head), straight bar in compression (ℓdc), tension lap (ℓst) or compression lap (ℓsc). The length provided is measured from the critical section, which is yours to locate.
- Cover and spacing: clear cover (top or bottom; in the plane of a hook), clear side cover (normal to the plane of a hook) and the center-to-center spacing of the bars developed or spliced. cb is the least of the two covers plus db/2 and half the spacing (R25.4.2.4).
- Straight bars and laps: the method is your choice (25.4.2.1): the general Eq. 25.4.2.4a or the simplified Table 25.4.2.3, with the other shown for comparison. The table's first row needs clear cover ≥ db and either clear spacing ≥ 2db or clear spacing ≥ db with stirrups or ties throughout ℓd at least the Code minimum (a box you tick). Ktr is 0 (permitted as a simplification, 25.4.2.4) unless you include the transverse reinforcement Atr at spacing s crossing the splitting plane of n bars (Eq. 25.4.2.4b); the same bars show 25.4.2.2 / 25.5.1.5 (Ktr ≥ 0.5db for fy ≥ 80 ksi bars closer than 6 in.). The excess reinforcement reduction of 25.4.10.1 (As,required / As,provided) applies to ℓd and ℓdc only when you state that none of the exclusions of 25.4.10.2 applies; it never applies to hooks, heads or laps. For a tension lap, As,provided / As,required at the splice and the percent of the bars spliced within the lap set Class A or B (Table 25.5.2.1).
- Hooks and heads: 90- or 180-degree hook; the number of bars developed at the section (Ahs = n Ab); the ties confining the hooks Ath (25.4.3.3); whether the hook or head ends inside a column core; whether the hook is at a discontinuous end (25.4.3.4); the net bearing area of the head Abrg and whether it meets ASTM A970 Class HA; whether headed bars are in a beam-column joint, with the parallel ties Att (25.4.4.4; elsewhere Att is not counted, 25.4.4.5); compression bars enclosed in a spiral or ties / hoops at 4 in. or less (ψr = 0.75).
Auto-design (editor toolbar) varies the length provided (whole inches) and keeps the bar, the anchorage, cover, spacing and confinement. Objective: shortest length provided. Every other input is kept; see Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Straight bar in tension ℓd | 25.4.2.1, Table 25.4.2.3 or Eq. 25.4.2.4a with Table 25.4.2.5 (λ, ψg, ψe 1.5 below 3db cover or 6db clear spacing else 1.2, ψs, ψt, ψtψe ≤ 1.7), (cb + Ktr)/db ≤ 2.5, at least 12 in. |
| Standard hook ℓdh | 25.4.3.1 with Table 25.4.3.2 (λ, ψe, ψr 1.0 for No. 11 and smaller with Ath ≥ 0.4Ahs or s ≥ 6db else 1.6, ψo 1.0 inside a column core with 2.5 in. side cover or with 6db side cover else 1.25, ψc), at least 8db and 6 in.; hook geometry Table 25.3.1 |
| Hook at a discontinuous end | 25.4.3.4 (advisory: ties at 3db or less when side and top cover are both under 2.5 in.) |
| Headed bar ℓdt | 25.4.4.2 with Table 25.4.4.3 (ψe, ψp, ψo, ψc), at least 8db and 6 in.; conditions 25.4.4.1(a) to (f) each as a check; 25.4.4.6 note in joints |
| Compression ℓdc | 25.4.9.1, 25.4.9.2 (a) and (b) with Table 25.4.9.3 ψr, at least 8 in. |
| Tension lap ℓst | Table 25.5.2.1 (Class A 1.0ℓd, Class B 1.3ℓd, at least 12 in.), ℓd per 25.4.2.1(a) without the excess reduction (25.5.1.4); 25.5.1.3 noncontact spacing note |
| Compression lap ℓsc | 25.5.5.1 (a), (b) or (c) by fy, × 4/3 below 3,000 psi |
| Lap of bars larger than No. 11 | 25.5.1.1, 25.5.5.2: not feasible |
| Ktr for high-strength bars | 25.4.2.2, 25.5.1.5 |
| Length provided | The anchorage checked: provided ≥ required |
Drawings #
The sheet shows the anchorage checked in elevation from the critical section (straight bar, standard hook drawn to its Table 25.3.1 bend diameter and extension, headed bar, or the two lapped bars), the length provided and the length required, and a section through the bars with the cover and spacing used. The member, the location of the critical section, the head dimensions (drawn schematically from Abrg) and the transverse reinforcement are not part of the calculation.
Limitations #
- One bar size per calculation; laps of bars of different sizes (25.5.2.2, 25.5.5.4) and bundled bars (25.6) are not covered.
- Welded wire reinforcement (25.4.6, 25.4.7, 25.5.3, 25.5.4), mechanical anchorage (25.4.5), mechanical and welded splices (25.5.7) and end-bearing splices (25.5.6) are not covered.
- The column lap splice provisions of 10.7.5 and the seismic provisions of Chapter 18 (for example 18.8.5 in special moment frame joints) are not applied.
- Grade 100 bars: where they may be used is limited by Table 20.2.2.4(a); that is the engineer's check.
- The hooked-bar confinement Ath (25.4.3.3) and the headed-bar ties Att (25.4.4.4) are taken as entered.
Verification examples #
Verification status: 151 values compared in 88 examples (78 published, 10 hand calculations from the cited equations): 147 within tolerance, 4 recorded deviations. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| CRSI ACI 318-19 Tables A1 to A3 (30 bar, cover and position cases, 58 values) | Tension ℓd (Class A) and Class B laps, #3 to #18, f'c = 3,000 / 4,000 / 5,000 psi, covers 0.75 to 3 in., bottom and top bars | e.g. #8, 4,000 psi, 1.5 in.: 36 / 47 in. bottom, 47 / 61 in. top | same (rounded up to the inch as CRSI tabulates) |
| CRSI ACI 318-19 Table C1 (32 values) | Standard hooks #5, #8, #11, #18 at f'c = 3,000 to 10,000 psi | e.g. #8 at 4,000 psi: 30 in. | same |
| Simpson Strong-Tie SE Blog example 1 | #5 dowel lap, f'c = 3,000 psi, (cb + Ktr)/db capped at 2.5 | ℓd = 16.4 in., Class B 21.3 in. | 16.4, 21.4 |
| VCmaster template (ACI 318-11 simplified method) | #7 lightweight, epoxy-coated top bar, other cases, ψtψe = 1.7 | ℓd = 142 in., Class B 184 in. | 141.1, 183.5 (the template takes db = 0.88 in.) |
Hand calculations in closed form cover what no free published example shows: headed bars (outside and inside a beam-column joint), compression development with confining ties, compression laps (Grade 60, Grade 80 below 3,000 psi), Ktr from transverse reinforcement, Grade 80 and 100 bars, the excess reinforcement reduction and a confined hook. Published examples for these (CRSI Reinforcing Bars: Anchorages and Splices, ACI MNL-17(21)) are listed in research/DOCUMENTS_NEEDED.md.