The simplified ACI 318-19 value, the factors that multiply it, and the lap it feeds
← Back to the calculatorDevelopment length is the length of bar that has to be buried in concrete before the bar can carry its yield force. Give a #8 ten inches of embedment and it pulls out; give it forty-eight and the concrete holds until the steel yields. It is not a rule of thumb, it is a formula, and every number on this page is arithmetic on that formula.
There is no rule of thumb hiding under the numbers: the table in section 03 is that one line of arithmetic, rounded up, and the lap a schedule quotes is 1.3 times it. Nothing on this page needs a second formula to be checked against the first.
A bar in tension does not carry the same force along its whole length. The force has to pass from steel into concrete through bond, and bond needs surface. ld is the length over which that transfer builds the bar up to its yield force, and it is checked where the bar is most heavily stressed — at the face of support in a simple beam, at a joint face, at the point where a bar is no longer needed for bending.
Two consequences that catch people out. First, ld is measured from the critical section, not from the end of the member, so a bar that turns up into a hook still has to develop on the straight side of the bend. Second, ld is a minimum and not a target: 40 in where 38 is required is fine, and 36 in is not, because the bar slips before it yields and the section behaves as if the steel were not there.
Where it decides the detail: the embedment of a column bar into a footing, a dowel into a slab on grade, the top steel of a cantilever, and every bar that ends at a construction joint. In all four the question is the same — is there enough length past this point — and this is the number that answers it.
ACI 318-19 25.4.2.3, simplified expression, US customary units:
That last line belongs to ld and to nothing else. A lap is not 1.3 times the floored ld: it is the greater of 1.3 times the expression and 12 in, then rounded up once. Two gates, not one — ld is floored at 12 in under 25.4.2.1, the lap is floored at 12 in under Table 25.5.2.1 — and the floor on ld is never carried into the 1.3.
| Symbol | What it is | Value on this page |
|---|---|---|
| fy | Yield strength of the bar, psi | 60,000 (Grade 60) |
| f'c | Specified compressive strength, psi | 3,000 to 5,000 |
| db | Nominal bar diameter, in | ASTM A615 |
| ψt | Location factor | 1.0 bottom, 1.3 top |
| ψe | Coating factor | 1.0 uncoated |
| ψg | Grade factor | 1.0 for Grade 60 |
| λ | Lightweight factor | 1.0 normal weight |
| C | The divisor in Table 25.4.2.3 | 25 (#6 and smaller), 20 (#7 and larger); 3/50 and 3/40, which is 1.5 times, when the spacing and cover limits are not met |
| 12 in | Floor on the result | 25.4.2.1 |
The divisor is not a safety factor and it is not one number. 60,000 ÷ (25 × 63.25) is 37.95, so a #5 develops in 23.7 in; a #8 at the same concrete is divided by 20, not 25, which is why it needs 47.4 in and not 37.9. Change either divisor and every row below changes with it, which is the test of whether a page like this can be checked at all.
Inches. Grade 60, uncoated, bottom bars, normal weight. Every value is the expression above, rounded up and floored at 12 in, and the rest of this page is built on this table.
| Bar | db (in) | C | 3,000 psi | 4,000 psi | 5,000 psi | 4,000 psi, ft-in |
|---|---|---|---|---|---|---|
| #3 | 0.375 | 25 | 17 | 15 | 13 | 1 ft 3 in |
| #4 | 0.500 | 25 | 22 | 19 | 17 | 1 ft 7 in |
| #5 | 0.625 | 25 | 28 | 24 | 22 | 2 ft 0 in |
| #6 | 0.750 | 25 | 33 | 29 | 26 | 2 ft 5 in |
| #7 | 0.875 | 20 | 48 | 42 | 38 | 3 ft 6 in |
| #8 | 1.000 | 20 | 55 | 48 | 43 | 4 ft 0 in |
| #9 | 1.128 | 20 | 62 | 54 | 48 | 4 ft 6 in |
| #10 | 1.270 | 20 | 70 | 61 | 54 | 5 ft 1 in |
| #11 | 1.410 | 20 | 78 | 67 | 60 | 5 ft 7 in |
Read the step between #6 and #7: 29 in to 42 in. The diameter grew by 17 per cent and the divisor fell from 25 to 20, so the length grew by 45 per cent. That single step is why a #7 lap looks disproportionately long next to a #6, and why swapping #6 for #7 to "use fewer bars" changes the splice schedule more than the bar count suggests.
Everything in this table multiplies the value from section 03. They stack, which is where the surprises come from.
| Factor | Symbol | Value | When it applies |
|---|---|---|---|
| Location | ψt | 1.0 | Bottom bar: 12 in or less of fresh concrete below |
| 1.3 | Top bar: more than 12 in of fresh concrete below | ||
| Coating | ψe | 1.0 | Uncoated |
| 1.5 | Epoxy, cover under 3db or clear spacing under 6db | ||
| 1.2 | Epoxy, all other cases | ||
| Grade | ψg | 1.0 | Grade 60 and below |
| 1.15 | Grade 80 | ||
| 1.3 | Grade 100 | ||
| Lightweight | λ | 1.0 | Normal weight concrete |
| 0.75 | Lightweight (sand-lightweight 0.85) | ||
| Combined | ψt × ψe | ≤ 1.7 | Cap on the top bar and coating factors together |
Two of those are worth carrying in your head. A top bar that is also epoxy coated would compute to 1.95 times the bottom uncoated length, but ψt × ψe is capped at 1.7, so on a #5 the answer is 41 in and not 47 — the cap takes 6 in off a detail that nobody would have checked. And on the small bars the lightweight factor still lands just above the floor: a #4 in lightweight computes to 14.2 in and is built as 15.
A lap splice is two bars doing one bar's job side by side, so the lap is a multiple of ld: 1.0 for Class A and 1.3 for Class B, applied to the tabulated ld and rounded up. Same basis as section 03, 4,000 psi:
| Bar | ld (in) | Class A lap (in) | Class B lap (in) | Class B, ft-in |
|---|---|---|---|---|
| #3 | 15 | 15 | 19 | 1 ft 7 in |
| #4 | 19 | 19 | 25 | 2 ft 1 in |
| #5 | 24 | 24 | 31 | 2 ft 7 in |
| #6 | 29 | 29 | 37 | 3 ft 1 in |
| #7 | 42 | 42 | 54 | 4 ft 6 in |
| #8 | 48 | 48 | 62 | 5 ft 2 in |
| #9 | 54 | 54 | 70 | 5 ft 10 in |
| #10 | 61 | 61 | 79 | 6 ft 7 in |
| #11 | 67 | 67 | 87 | 7 ft 3 in |
The field rule of thumb of 40 × bar diameter is supposed to be a Class B lap for Grade 60 bar in 4,000 psi concrete, and it is short at every size. For a #4, 40db is 20 in against a 25 in lap. For a #8, 40db is 40 in against 62 in — because ld grows faster than db once the divisor drops from 25 to 20 at #7.
Use ACI 318-19 Table 25.4.2.3. The simplified expression is ld = (fy ÷ (C × λ × √f'c)) × ψt × ψe × ψg × db, with C = 25 for #6 and smaller and 20 for #7 and larger, and a 12 in minimum. For a #4 Grade 60 bar in 4,000 psi concrete: 60,000 ÷ (25 × 63.25) = 37.95, × 0.500 = 18.97, rounded up to 19 in.
19 in for a Grade 60 bottom bar in 4,000 psi concrete, uncoated, normal weight. A top bar is 25 in, an epoxy-coated bar with tight cover is 29 in, and a top bar that is also epoxy coated is 33 in — 1.3 × 1.5 would give 37, but ψt × ψe is capped at 1.7.
12 in, ACI 318-19 25.4.2.1, whatever the formula returns. With Grade 60 and f'c between 3,000 and 5,000 psi the arithmetic never gets that low — the shortest value in the table, a #3 at 5,000 psi, computes to 12.7 in — but the floor is there for the cases that do reach it.
Yes, through ψe: 1.5 when cover is under 3db or clear spacing is under 6db, 1.2 in every other case. On a #5 in 4,000 psi concrete that turns 24 in into 36 in at 1.5, and into 29 in at 1.2. The coating reduces bond, so more length is needed to develop the same force.
This page does not adjust for cover. The expression printed here takes fy, f'c, db and the four factors, and there is no cover term in it, so nothing in the table moves when the chair height changes. A detail where cover decides the answer is a different calculation, and this page does not print it.
Development length is what one bar needs to embed in concrete to reach yield. A lap splice is two bars doing that job side by side, so it is a multiple of ld: 1.0 for Class A and 1.3 for Class B. The lap is not a longer bar, it is the length over which the second bar takes over, which is why the class factor multiplies ld instead of adding to it.
Two things step at once. The diameter goes from 0.750 in to 0.875 in, a factor of 1.167, and the divisor falls from 25 to 20, a factor of 1.25. Together that is 1.46, so 29 in becomes 42 in. Nothing about the concrete or the cover changed.
Not on the numbers here. There is no cover term in the expression printed here, so there is nothing for extra cover to shorten: the 48 in for a #8 and the 24 in for a #5 are the same whatever the cover. A detail where cover decides the answer is a calculation this page does not reproduce.