--- title: "IS method mix design for fck 30 N/mm2 (numerical)" subject: "Concrete Technology and Masonry Structure" chapter: 3 key: "semester_5/concrete_technology_and_masonry_structure:is-mix-design-fck30-numerical" source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/is-mix-design-fck30-numerical site: BCT Engineering --- # IS method mix design for fck 30 N/mm2 (numerical) Concrete Technology and Masonry Structure · Chapter 3: Mix design of concrete and property of green concrete - Asked in: 2072 Kartik, 8 marks - Video: [Concrete Mix Design of M30 Grade of Concrete as Per IS - 10262:2019| Solved Problem](https://www.youtube.com/watch?v=qFbOfW97_Tw) — Master Civil Engineering - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/is-mix-design-fck30-numerical - Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-3 ## Question Design the mix proportion for concrete with the help of the following particulars using the IS method. Design parameters: characteristic strength $f_{ck}$ = 30 N/mm$^2$; maximum size of aggregate = 20 mm; shape of CA = angular; degree of workability = 0.85; degree of quality control = fair; degree of exposure = severe. (Assume all necessary relevant data) ## Short answer IS 10262 method, target strength39.9 MPa, w/c 0.42, water 186 kg/m³. Result: cement 443 kg/m³, fine aggregate 630 kg/m³, coarse aggregate 1139 kg/m³. Mix ratio 1:1.42:2.57. ## Answer **Method: IS 10262 with IS 456:2000.** **Data:** M30; 20 mm angular aggregate; compaction factor 0.85 (low-medium workability, about 50 mm slump); fair quality control; severe exposure. **Assumptions:** OPC 43 grade ($G = 3.15$); sand Zone II, $G_{FA} = 2.65$; $G_{CA} = 2.74$; no admixture; aggregates in SSD condition; entrapped air 2%. **Step 1: Target strength.** IS 10262 Table 1 (and IS 456 Table 8) gives $s = 5.0$ N/mm$^2$ for M30 with good site control; for **fair** control the value is increased by 1 N/mm$^2$, so $s = 6.0$ N/mm$^2$. $$ f'_{ck} = 30 + 1.65 \times 6 = 39.9\ \text{N/mm}^2 $$ (this is higher than $f_{ck} + X = 30 + 6.5 = 36.5$ required by the 2019 revision). **Step 2: w/c ratio.** The strength-w/c curve for OPC 43 (IS 10262:2019 Fig 1) gives about 0.42 for 39.9 N/mm$^2$. For severe exposure (IS 456 Table 5, RCC): maximum w/c = 0.45, minimum cement 320 kg/m$^3$. Adopt the lower value, **w/c = 0.42**. **Step 3: Water** (IS 10262 Table 2): for 20 mm angular aggregate at 50 mm slump, no correction needed. Water = **186 kg/m$^3$**. **Step 4: Cement** = $186/0.42 = 443$ kg/m$^3$; this is $> 320$ (minimum) and $< 450$ (maximum). **Step 5: Coarse aggregate volume** (Table 3: 20 mm, Zone II, w/c 0.50 gives 0.62). For w/c 0.42 (0.08 lower): $+0.016$, so the volume of CA = **0.636** and FA = 0.364 of the total aggregate. **Step 6: Mix calculation per m$^3$** (absolute volume) | Item | Volume (m$^3$) | |---|---| | Cement: 443/(3.15 × 1000) | 0.1406 | | Water: 186/1000 | 0.1860 | | Air | 0.0200 | | **Aggregates** = 1 - 0.3466 | **0.6534** | $$ \begin{aligned} CA &= 0.6534 \times 0.636 \times 2.74 \times 1000 = 1139\ \text{kg} \\ FA &= 0.6534 \times 0.364 \times 2.65 \times 1000 = 630\ \text{kg} \end{aligned} $$ **Answer (per m$^3$): cement 443 kg, water 186 kg, FA 630 kg, CA 1139 kg; w/c = 0.42; ratio 1 : 1.42 : 2.57** (about 2398 kg/m$^3$). Corrections for moisture and absorption, and trial mixes, follow. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For M30 with fair control s = 5, the target strength is A. 30 + 6.5 = 36.5 B. 30 + 5 C. 30 D. 30 + 1.65 x 5 = 38.25 N/mm2 Answer: D. It is the higher of 38.25 and fck + X = 36.5. (Key point: Target strength) 2. Fig 1 gives about 0.45; severe exposure max is 0.45. Adopt A. 0.45 B. 0.55 C. 0.50 D. 0.40 Answer: A. Both agree on 0.45. (Key point: w/c adopted) 3. Table 3 gives 0.62 at w/c 0.50; for w/c 0.45 the CA volume fraction is A. 0.61 B. 0.63 C. 0.62 D. 0.65 Answer: B. Each 0.05 decrease adds 0.01, giving 0.63. (Key point: CA fraction) 4. With cement 0.1312, water 0.1860 and air 0.0200 m3, volume available for aggregate is A. 0.3372 m3 B. 1.0 m3 C. 0.6628 m3 D. 0.7 m3 Answer: C. 1 - 0.3372 = 0.6628 m3. (Key point: Aggregate volume) ## Related in Concrete Technology and Masonry Structure - [DoE mix design for fck 35 MPa (numerical)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Adoe-mix-design-fck35-numerical) — Concrete Technology and Masonry Structure, chapter 3 - [ACI mix design for fck 30 MPa (numerical)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Aaci-mix-design-fck30-numerical) — Concrete Technology and Masonry Structure, chapter 3 - [Effect of shape and size of aggregate on workability](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Aaggregate-shape-size-workability) — Concrete Technology and Masonry Structure, chapter 1, asked 2× - [DOE mix design for M25 concrete (numerical)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Adoe-mix-design-m25-numerical) — Concrete Technology and Masonry Structure, chapter 3 - [Aggregate shape and texture: strength, workability](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Aaggregate-shape-texture-strength) — Concrete Technology and Masonry Structure, chapter 1, asked 2× - [ACI mix design for M25 concrete (numerical)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Aaci-mix-design-m25-numerical) — Concrete Technology and Masonry Structure, chapter 3, asked 2× ## Related in other subjects - [Characteristic and design strength and loads](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Acharacteristic-strength-loads) — Design of Steel and Timber Structure, chapter 3