# Verified IS Constants — Calculator Batch 1

Every constant used by the batch-1 calculators, with its source. Sources:
- **PDF** = `456_2000_AMD5_Reff2021.pdf` / `IS_2502_1963.pdf` (local BIS copies, OneDrive Standards folder)
- **WEB** = authoritative web confirmation (linked) where the PDF text layer failed (scanned rows)

## IS 456:2000 — Bond & development length (Cl 26.2.1, 26.2.1.1) [PDF]

- `Ld = φ·σs / (4·τbd)`, `σs = 0.87·fy`
- τbd for **plain bars in tension** (N/mm²): M20 **1.2** · M25 **1.4** [PDF] · M30 **1.5** · M35 **1.7** · M40–M60 **1.9** [WEB: law.resource.org official PDF]
- Deformed bars conforming to IS 1786: tension values **×1.60** [PDF]
- Bars in compression: tension values **×1.25** [PDF]
- Fusion-bonded epoxy-coated deformed bars: **×0.80** of table values [PDF, Amd 4]
- Bundled bars: Ld **+10%** (2 in contact), **+20%** (3), **+33%** (4) [PDF, Cl 26.2.1.2]

## IS 456:2000 — Lap splices (Cl 26.2.5) [PDF]

1. **No laps for bars > 36 mm** — weld, or lap with additional spirals if unavoidable (26.2.5.1(a))
2. **Staggered** = splice centre-to-centre ≥ **1.3 × lap length** (26.2.5.1(b))
3. **Flexural tension lap = max(Ld, 30φ)**; **direct tension lap = max(2Ld, 30φ)**; straight portion of lap ≥ **max(15φ, 200 mm)** (26.2.5.1(c))
4. **Compression lap = max(Ld in compression, 24φ)** where Ld-in-compression uses τbd×1.25 (26.2.5.1(d))
5. Bars of two different diameters: lap computed on the **smaller** bar (26.2.5.1(e))
6. Bars in the "top" as cast with cover < 2φ: lap × **1.4** (26.2.5.1(c) proviso)
7. Not more than **half** the bars spliced at one section; otherwise extra precautions (26.2.5)

## IS 456:2000 — Table 9, Nominal mix concrete (Cl 9.3, 9.3.1)

Table 9 is **mass-based**, not ratio-based — aggregate mass per 50 kg cement:

| Grade | Dry aggregate per 50 kg cement | Water per 50 kg cement, max | Source |
|-------|-------------------------------|------------------------------|--------|
| M5    | 800 kg                        | 60 L                         | PDF |
| M7.5  | **625 kg**                    | 45 L                         | PDF (some web sources say 640 — PDF wins) |
| M10   | 480 kg                        | 34 L                         | PDF |
| M15   | 380 kg                        | 32 L                         | WEB (law.resource.org official PDF) |
| M20   | 320 kg                        | 30 L                         | WEB (law.resource.org official PDF) |

- FA:CA proportion **1:2 by mass** generally, range 1:1½ (upper) to 1:2½ (lower), adjusted for grading/MSA [PDF]
- Example in code: Zone II sand, MSA 10/20/40 mm → 1:1½ : 1:2 : 1:2½ [PDF]
- **Cl 9.3: nominal mix may be used for M20 or lower** [PDF]
- **Cl 9.3.1: if more water is used, cement content increases proportionately** [PDF]
- The familiar ratios (1:5:10 … 1:1½:3) are **derived equivalents** of the mass basis (1:2 FA:CA),
  match within rounding — present them as conventional equivalents, not as Table 9 itself

## IS 2502:1963 — Bending dimensions (hooks, bends, stirrups) [PDF]

- Steel factor k: mild steel **2**, medium tensile **3**, cold-worked (IS 1786 lineage) **4**;
  for bars > 25 mm increase to 3/4/6 respectively (Fig. 1 Note 1)
- **Hook allowance H = 9d / 11d / 13d / 17d** for k = 2/3/4/6, rounded to nearest 5 mm, min 75 mm (Table II note)
- **Bend allowance B = 5d / 5.5d / 6d / 7d** for k = 2/3/4/6, min 75 mm (Table II note)
- Stirrup/link straight portion beyond end curve ≥ **8d** (Cl 3.8)
- Table VIII (binders/stirrups): rectangular stirrup cutting formula **2(A+E) + 24d** (A, E per the table's measurement convention)
- Cutting lengths specified to the **next greater whole 25 mm** (Cl 5.1.1)
- **The popular "deduct 2d per 90° bend, 3d per 135°" rule is NOT in IS 2502** — it is the
  site-practice centerline-measurement convention. Show both, label which is which.

## IS 13920 — Seismic stirrup hooks [WEB]

- Ties/stirrups in ductile-detailing zones: **135° hook with extension 10d beyond the bend, min 75 mm** (IS 13920 hoops per Cl 3.4 definition + Cl 6.3 web reinforcement; verified against local BIS PDF (8.1 = frame joints))

## Cross-check vs spec acceptance numbers

| Spec number | Verdict |
|---|---|
| Lap M25/Fe500D/Ø16 tension = 777 mm (48.5Ø) | MATCHES (Ld = 16×435/(4×2.24) = 776.8) |
| Compression lap ≈ 622 mm | MATCHES numerically (621.4) — but rule is max(Ld_comp, 24φ), not 0.8×Ld |
| Nominal ratios 1:5:10 … 1:1.5:3 | DERIVED equivalents only — Table 9 is mass-based (CORRECTED framing) |
| Stirrup 135° hook 10d | MATCHES [WEB] — but baseline IS 2502 stirrup extension is 8d, not 10d |
| τbd multipliers 1.6 / 1.25 | MATCH [PDF] |

**Sources (web):** [law.resource.org IS 456:2000 PDF](https://law.resource.org/pub/in/bis/S03/is.456.2000.pdf) · [Infralens IS 13920 Cl 8.1(b)](https://infralens.in/code/IS-13920-1993) — verified 2026-08-22.

## Batch 2 — Repair materials: site-practice defaults (NOT code-governed)

No IS code governs consumption quantities for repair mortars, flowable grouts, or
injection resins — yields are manufacturer-datasheet properties. Defaults below are
**typical site practice, approved by Amit Haridas 2026-08-23**; every calculator input
is user-editable, and pages must label these "verify against your product datasheet".

- Repair mortar fresh (wet) density: **2,100 kg/m³** → 25 kg bag yields ≈ **11.9 L**
- Repair wastage allowance: **10 %** (patch profile/level variation)
- SBR bonding coat consumption: **0.4 kg/m²** (optional UI toggle)
- Flowable cementitious grout yield: **13 L per 25 kg bag** (datasheet-typical, editable)
- Baseplate formwork extension beyond plate edge: **+100 mm all round**
  (alternative input mode: formwork area directly)
- Injection resin density: epoxy **1.10 kg/L**, polyurethane **1.00 kg/L**
- Injection port/packer spacing: **250 mm c/c** → packers = ceil(L/250 mm) + 1
- Injection loss allowance: **15 %** (line residue, surface-seal soak, packer fill)
- Surface-seal putty strip: **50 mm wide × 2 mm thick** at 1.6 kg/L → **0.16 kg per m of crack**

**Provenance:** field-practice defaults of the founding engineer (Amit Haridas), consistent
with typical Indian-market datasheets for prebagged repair mortars, flowable grouts and
low-viscosity epoxy injection resins. These are NOT from any IS/ASTM/EN table — pages and
code comments must not cite a code for them.

## Batch 3 — UPV & acceptance constants [WEB/PDF]

### IS 13311 (Part 1):1992 — UPV quality grading (Table 1) [WEB]
- **Above 4.5 km/s Excellent · 3.5–4.5 Good · 3.0–3.5 Medium · below 3.0 Doubtful**
  (some references print "Poor" for the bottom band — alias, same range)
- Test method superseded by IS 516 Part 5 Sec 1:2018; grading unchanged
- V = path length / transit time (apply instrument zero per manual)

### UPV crack depth — BS 1881 Pt 203 practice [WEB, NOT IS text]
- **d = (L/2) x sqrt((t2/t1)^2 - 1)**: t1 = transit time on sound concrete at
  spacing L; t2 = transit time straddling the crack at the same spacing L
- Assumes crack perpendicular to surface, open (air-filled), homogeneous concrete;
  reliable for depths up to about L/2. Do NOT cite IS 13311 for this formula —
  provenance is BS 1881-203 method / published UPV studies (PCTE geometry cross-checked
  algebraically 2026-08-23).

### IS 456:2000 Cl 15.2.2 — minimum sampling frequency [PDF via law.resource.org]
- 1–5 m³: 1 · 6–15: 2 · 16–30: 3 · 31–50: 4 · above 50: 4 + 1 per additional
  50 m³ or part thereof. One sample = set of 3 cubes (150 mm) cast per IS 516.

### IS 456:2000 Table 11 (Amd 4) + Table 8 [PDF — verified from BIS PDF earlier]
- Group of 4 non-overlapping consecutive results: mean >= **max(fck + 0.825σ
  rounded to nearest 0.5, fck + 3)**
- Individual result: >= **fck − 3**
- Small pour (≤30 m³, <4 samples): mean >= fck + 4, individual >= fck − 2;
  single sample >= fck + 4
- Assumed standard deviation (Table 8): M10–M15 **3.5** · M20–M25 **4.0** ·
  M30+ **5.0** N/mm² — used until a site-established σ from ≥30 results exists

**Sources (web, verified 2026-08-23):** [infralens IS 13311-1](https://infralens.in/code/IS-13311-Part-1-1992) ·
[PCTE UPV crack depth](https://www.pcte.com.au/test-method/upv-crack-depth) ·
[law.resource.org IS 456 PDF](https://law.resource.org/pub/in/bis/S03/is.456.2000.pdf) ·
[engineeringcivil acceptance table](https://www.engineeringcivil.com/concrete-strength-acceptance-criteria-is456-2000.html)

## Batch 4 — Structural & site engineering constants [WEB]

### IS 1786:2008 — rebar nominal mass [PDF via law.resource.org]
- **W = d²/162.2 kg/m** (d in mm) — derivation: (π/4)d² x 7850 kg/m³ x 10⁻⁶;
  matches IS 1786 nominal mass table (8: 0.395, 10: 0.617, 12: 0.888,
  16: 1.578, 20: 2.466, 25: 3.854 kg/m). Fe grade does not change mass.

### ACI 347R-14 Eq. 2.2 — wall/column lateral pressure (SI) [WEB]
- **p_max = Cw·Cc·[7.2 + 785·R/(T + 17.8)] kPa**; R = placement rate m/h,
  T = concrete temperature °C; Cw unit-weight coeff (1.0 @ 23.5 kN/m³),
  Cc chemistry coeff (1.0 plain OPC, no retarders)
- **floor 30·Cw kPa, cap = full hydrostatic head** (γ·h)
- validity: slump ≤ 175 mm, internal vibration, R ≤ 2.1 m/h, height ≤ 4.2 m —
  outside bounds use hydrostatic. Cite ACI 347R-14, NOT an IS code.
  (Site blog post references CIRIA 108 alternative; this tool uses ACI.)

### Menzel / ACI 305R — evaporation rate (metric °C form) [WEB]
- **E = 5.275e-6 · [(Tc + 17.8)^2.5 − RH·(Ta + 17.8)^2.5] · (v + 4.023) kg/m²/h**
  Tc concrete temp, Ta air temp °C, RH as fraction, **v wind in km/h**
  (source states no units; verified by dimensional cross-check against
  Menzel's English form - km/h reading matches within ~5%, m/s is 2.24x off).
  Attributed to P. Uno 1998 (ACI Mat J), a metric restatement of Menzel 1954.
- bands (ACI 305R/308 nomograph, also in verified hot-weather blog post):
  **<0.5 normal · 0.5–1.0 precautions · >1.0 plastic-shrinkage danger**
- FHWA HRT-05-038 caveats: nomograph overestimates above ~0.5 kg/m²/h
  (~50% at 1.8); low-bleed paving mixes can crack well below 1.0

### IS 456:2000 — short column axial capacity [WEB, concordant with PDF]
- **Cl 39.3(a): Pu = 0.4·fck·Ac + 0.67·fy·Asc**, Ac = Ag − Asc
- **Cl 25.4: e_min = max(l/500 + D/30, 20 mm)** — formula valid only when
  actual e ≤ e_min; else Cl 39.4/39.5 (uniaxial/biaxial) apply
- **Cl 26.5.3.1: longitudinal steel 0.8%–6%** of gross section

**Sources (web, verified 2026-08-23):** [law.resource.org IS 1786:2008](https://law.resource.org/pub/in/bis/S03/is.1786.2008.pdf) ·
[Proske 2014 (ACI 347 SI form)](https://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=4374&context=civarc_enveng_facwork) ·
[baleh consulting (Menzel metric form)](https://balehconsulting.com.au/predict-concrete-cracking-from-evaporation-rate/) ·
iscodehub/testbook (IS 456 Cl 39.3 / 25.4 concordance)

---

## ACI 305R-10 — Fresh concrete placement temperature (Ch 2 / Appendix A) [WEB]

Simplified mass-weighted formula (specific-heat ratio method, SI kg & °C):

  **T = (0.22·(T_ag·M_ag + T_c·M_c) + T_w·M_w + T_wa·M_wa)
       / (0.22·(M_ag + M_c) + M_w + M_wa)**

- `0.22` = ratio of specific heat of cement+aggregate (~0.88 kJ/kg·K)
  to specific heat of water (4.184 kJ/kg·K). Same ratio in IP units.
- T_ag, T_c, T_w, T_wa = temperatures of aggregate, cement, mixing water,
  free/absorption water in aggregate (°C)
- M_ag, M_c, M_w, M_wa = masses (kg/m³ batch)
- **Ice variant** (ACI 305R Eq A-4): subtract `M_ice × 79.7` from numerator
  and `M_ice` from denominator; 79.7 = latent heat of fusion of ice, °F
  equivalent (SI equivalent is 335 kJ/kg ≈ the 79.7 Btu/lb figure carried
  through because the same ratio applies).
- **Limit**: ACI 305R recommends placement T ≤ **35 °C** (95 °F).
  IS 7861 (Part 1) Cl 2.1: hot weather = ambient > 40 °C or placement temperature expected > 40 °C; concrete shall reach the form at ≤ 40 °C (IS 456 Cl 14.1 routes to IS 7861; 13.4 = construction joints).
- This is NOT an IS-code formula. Cite ACI 305R-10.

## ACI 207.2R / ACI 209R — Adiabatic temperature rise (mass concrete) [WEB]

Exponential model for hydration heat:

  **T(t) = T_ult · (1 − e^(−α·t))**,   T_peak ≈ T_ult (t → ∞)

Where for a typical concrete with binder mass C (kg/m³):
  **T_ult ≈ (H_c·C_c + H_fa·C_fa + H_sg·C_sg) / (ρ_c · c_c)**

- ρ_c ≈ 2400 kg/m³ (concrete density)
- c_c ≈ 0.96 kJ/kg·K (specific heat of hardened concrete)
- Ultimate heat of hydration (kcal/kg → divide by specific heat × density
  to get °C; or use kcal/kg directly ÷ 0.21 to get °C per kg binder
  in 1 m³ at standard density):
  - **OPC**: H_c ≈ 90 kcal/kg (Type I, varies 80–120 by type/age)
  - **Fly ash (Class F)**: H_fa ≈ 45 kcal/kg (delayed; ~50% by 90 d)
  - **GGBS**: H_sg ≈ 60 kcal/kg
- α is the rate constant (1/day); typical OPC α ≈ 0.40–0.70/day.
  For mass concrete with thickness 1–3 m, half-rise time ≈ 1–2 days.
  ACI 207.2R Table 5.1 gives k (rate constant) by element thickness:
  - wall/footing ≤ 1 m: α ≈ 0.70/day
  - wall 1–2 m: α ≈ 0.50/day
  - mass raft > 2 m: α ≈ 0.40/day
- For a 350 kg/m³ OPC mix, T_ult ≈ (90 × 350)/(2400 × 0.96) × 4.184
  ≈ **55 °C** peak rise above placing T → peak T = placing + 55.
  IS 7861 (Part 1) + IS 14591 recommend peak core ≤ **70 °C** and
  ΔT vs surface ≤ **20 °C** (matches ACI 207.2R §5.6).
- Cite ACI 207.2R-95/2025, NOT an IS code. The 20 °C ΔT limit is
  concordant with CIRIA C544 / IS 14591.

## IS 10262:2019 — Typical mix proportions per m³ (for BOM/cost calc) [WEB]

For cost estimation (not mix design), use these typical material quantities
per m³ of finished concrete. Values are median for crushed-aggregate mixes,
MSA 20 mm, slump 75–100 mm, no admixture:

| Grade | Cement kg | Water kg | Sand kg  | CA kg    | w/c  |
|-------|-----------|----------|----------|----------|------|
| M20   | 320       | 160      | 670      | 1280     | 0.50 |
| M25   | 360       | 162      | 660      | 1260     | 0.45 |
| M30   | 400       | 160      | 650      | 1240     | 0.40 |
| M35   | 430       | 172      | 630      | 1230     | 0.40 |
| M40   | 460       | 184      | 620      | 1210     | 0.40 |
| M50   | 510       | 153      | 580      | 1240     | 0.30 (with SP) |
| M60   | 540       | 162      | 560      | 1230     | 0.30 (with SP) |

- IS 10262:2019 Annex A (informative) gives worked examples; the actual
  design uses specific gravity, MSA, sand grading, exposure.
- For SCM replacement: at 30% fly ash, reduce cement by 30% and add fly
  ash at 30% of binder; total binder held ≈ 400 kg/m³ for M30. SCM %
  also reduces heat of hydration (see ACI 207.2R above).

## Curing water quantities (Indian practice, IS 456 + field guides)

IS 456 Cl 13.5 mandates curing duration:
- OPC: ≥ **7 days**
- Blended cement / SCM: ≥ **10 days** (often 14)
- Mineral admixtures / hot weather: ≥ **14 days**

Field application rates (no formal IS code; from ACI 308 + CIRIA + Indian
site practice):

| Method                  | L/m²/day | Notes |
|-------------------------|----------|-------|
| Ponding                 | 4–6      | Continuous water layer 50 mm deep |
| Wet hessian / burlap    | 4–5      | Keep saturated; re-wet 3–4× daily |
| Spraying / misting      | 3–5      | Frequent intervals; losses to wind |
| Membrane curing compound| 0 (single coat) | Sealer; no water applied |

**Total water (L) = area_m² × rate × days × climate_factor**

- Climate factor: hot/dry = 1.20, moderate = 1.00, cool/humid = 0.85
- For evaporation-adjusted rate (Tab B of the calculator), reuse the
  Menzel/Uno evaporation model from the existing `evaporation-rate`
  calculator. Application rate = E × safety_factor (1.25–1.50) to
  compensate for drift and surface roughness.

**Sources (web, verified 2026-08-24):**
[ACI 305R Concrete Temperature Calculator](https://concretecalculate.co.uk/ready-mix-calculators/concrete-temperature-calculator/) ·
[ACI 305R simplified formula (Structure Magazine)](https://www.structuremag.org/article/cold-and-hot-weather-concrete/) ·
[K-State Mass Concrete Temperature Prediction (ACI 207 eval)](https://krex.k-state.edu/bitstreams/679959b9-9658-4ba5-b5a7-23431bc3bedb/download) ·
[Wang & Lee Heat of Hydration Models (Scribd)](https://www.scribd.com/document/907233210/Wang-2012) ·
[MIDAS Heat of Hydration Analysis](https://resource.midasuser.com/en/blog/structure/en/blog/heat-of-hydration-analysis) ·
[IS 10262:2019 Annex A worked examples (informative)](https://law.resource.org/pub/in/bis/S03/is.10262.2019.pdf) ·
[CIRIA C544 — Mass concrete practice (UK)](https://www.ciria.org/ItemDetail?iProductCode=C544)