Target Mean Strength in Concrete Mix Design (IS 10262:2019) with Example
Target mean strength is the average strength a concrete mix is designed for, so that almost all cubes still pass the characteristic strength fck. IS 10262:2019 takes it as the higher of f'ck = fck + 1.65 s and f'ck = fck + X, where s is the standard deviation and X is a margin that depends on the grade. For M25 with the assumed s = 4.0 N/mm², the target is 25 + 1.65 × 4 = 31.6 N/mm².
Why the mix is designed above fck
Cube strengths from the same mix scatter around their mean, roughly following a normal curve. IS 456 defines fck as the strength below which not more than 5% of results are expected to fall. On a normal curve, 5% of results lie more than 1.65 standard deviations below the mean. So the mean has to sit 1.65 s above fck. The poorer the site control, the larger s, and the richer (and costlier) the mix must be.
The two formulas in IS 10262:2019
| Formula | What it protects against |
|---|---|
f'ck = fck + 1.65 s | The statistical 5% failure limit |
f'ck = fck + X | A minimum margin when s is small (for example, very good plant data) |
The larger of the two is adopted. The second formula was added in the 2019 revision; the 2009 edition used only fck + 1.65 s.
Assumed standard deviation and X
When fewer than 30 test results are available from the site, the code gives assumed values of s. These are replaced by the site value once enough results are in.
| Grade | Assumed s (N/mm²) | X (N/mm²) | Target for lowest grade in group |
|---|---|---|---|
| M10, M15 | 3.5 | 5.0 | M10: 15.8 |
| M20, M25 | 4.0 | 5.5 | M20: 26.6 |
| M30 to M60 | 5.0 | 6.5 | M30: 38.25 |
Exam tip: With the assumed s values, fck + 1.65 s is always the higher one (for M25: 31.6 vs 30.5). The X formula takes over only when a site has a low measured s. A common MCQ: "target mean strength of M20 with s = 4" → 20 + 1.65 × 4 = 26.6 N/mm².
The next steps after target strength
Target strength is step one. The following steps fix the mix proportions:
| Step | What you decide | Where the value comes from |
|---|---|---|
| 1 | Target mean strength f'ck | IS 10262 clause 4.2 (above) |
| 2 | Water-cement ratio | Strength curves of IS 10262 for the cement used, then capped by the IS 456 Table 5 maximum for the exposure |
| 3 | Water content | IS 10262 Table 4: 208 kg (10 mm), 186 kg (20 mm), 165 kg (40 mm) for 50 mm slump; add about 3% per extra 25 mm slump |
| 4 | Cement content | Water ÷ w/c; check against the IS 456 Table 5 minimum and the 450 kg/m³ maximum |
| 5 | Coarse and fine aggregate | Volume of coarse aggregate from IS 10262 (depends on aggregate size, sand zone and w/c), then absolute volume method |
| 6 | Trial mixes | Cast cubes, adjust and confirm |
IS 456 durability limits (RCC)
| Exposure | Min cement (kg/m³) | Max free w/c | Min grade |
|---|---|---|---|
| Mild | 300 | 0.55 | M20 |
| Moderate | 300 | 0.50 | M25 |
| Severe | 320 | 0.45 | M30 |
| Very severe | 340 | 0.45 | M35 |
| Extreme | 360 | 0.40 | M40 |
Worked example: M25 for moderate exposure
Design data: M25 RCC, moderate exposure, 20 mm crushed coarse aggregate, slump 100 mm, no admixture, no site data for s.
- Assumed s for M25 = 4.0 N/mm²; X = 5.5 N/mm².
- fck + 1.65 s = 25 + 6.6 = 31.6 N/mm²; fck + X = 25 + 5.5 = 30.5 N/mm². Adopt the higher: f'ck = 31.6 N/mm².
- Water-cement ratio: say the strength curve for the cement in use gives about 0.45 for 31.6 N/mm² (assumed for this example). The IS 456 limit for moderate exposure is 0.50, so adopt 0.45.
- Water content: 186 kg for 50 mm slump; for 100 mm slump add 2 × 3% = 6%: 186 × 1.06 = 197 kg/m³.
- Cement content: 197.2 / 0.45 = 438 kg/m³. This is above the 300 kg/m³ minimum and below the 450 kg/m³ maximum. ✔
- Next: find the coarse aggregate volume from IS 10262 for 20 mm aggregate and the sand zone, then the aggregate masses by absolute volume, and confirm with trial cubes. If cement looks high, a plasticiser lets you cut water (and so cement) at the same w/c.
Common mistakes
- Designing the mix for fck itself instead of f'ck.
- Forgetting the 2019 "fck + X" check when site s is low.
- Picking w/c from strength alone and not checking the durability limit for the exposure.
- Ignoring the 450 kg/m³ cement cap, which IS 456 sets to limit shrinkage and heat.
Frequently asked questions
What is the formula for target mean strength?
As per IS 10262:2019, f'ck is the higher of fck + 1.65 s and fck + X, where s is the standard deviation and X depends on the grade.
What is the target mean strength of M25 concrete?
With the assumed standard deviation of 4.0 N/mm², it is 25 + 1.65 × 4 = 31.6 N/mm², which is higher than 25 + 5.5 = 30.5 N/mm².
Why is 1.65 used in target mean strength?
Because only 5% of results on a normal distribution fall more than 1.65 standard deviations below the mean, matching the IS 456 definition of characteristic strength.
What is the water content for 20 mm aggregate in IS 10262?
186 kg per cubic metre for 50 mm slump, increased by about 3% for every additional 25 mm of slump.
Concrete technology is in every AE/JE paper. Revise mix design, admixtures and tests free in the Advanced Civil Engineering Handbook (Building Materials & Concrete Technology chapter).
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