Concrete – Complete Study Notes for GATE, ESE & SSC JE

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Concrete — Complete Study Notes

10 chapters · GATE, ESE (IES), SSC JE, State PSC, RRB JE

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Concrete Technology is one of the highest-weightage topics in GATE Civil, ESE (IES) and SSC JE. This chapter covers every stage — from constituents and fresh-concrete workability through mix design, hardened properties, durability, testing (destructive and non-destructive), production/placing and special concretes — with all formulae, tables, diagrams and exam-pattern analysis.

Learning Objectives

After studying this chapter you will be able to:

Describe the role of each constituent of concrete and compute bulking of sand from moisture content
Select the right workability test (slump, compaction factor, Vee-Bee, flow table) for a given mix and interpret the result
Apply Abrams' w/c law and the IS 456 exposure-condition w/c limits to predict strength and durability
Carry out the IS 10262:2019 design-mix procedure step by step, including target mean strength and water/cement content
Compute modulus of elasticity, split tensile strength, creep coefficient and shrinkage strain for hardened concrete
Explain durability mechanisms (sulphate attack, carbonation, ASR, chloride corrosion, freeze-thaw) and their IS 456 defences
Distinguish destructive tests from NDT methods (rebound hammer, UPV, core test) and interpret their acceptance criteria
Identify the correct special concrete (SCC, HPC, FRC, LWC, RCC, etc.) for a given site requirement

Exam Relevance

ESE★★★★★

GATE★★★★★

SSC JE★★★★★

State PSC★★★★☆

💡 Concrete Technology is the single highest-weightage Building Materials topic in GATE Civil — target mean strength, modulus of elasticity, w/c-vs-strength and mix design numericals appear almost every year.

Concept Map

Constituents (Cement + Aggregates + Water + Admixtures)

↓

Fresh Concrete → Workability (Slump, CF, Vee-Bee)

↓

W/C Ratio → governs Strength (Abrams' Law)

↓

Mix Design (IS 10262) → Trial Mixes

↓

Hardened Properties — strength, E, creep, shrinkage

Durability — permeability, sulphate/ASR/chloride/freeze-thaw

↓

Testing (Destructive + NDT) → Production, Placing, Compaction

↓

Special Concretes (SCC, HPC, FRC, LWC, RCC, …)

Where This Fits

Prerequisite: Cement — concrete strength and durability are governed directly by cement chemistry and hydration covered there.

Leads into: Design of RCC/PCC Structures, which uses the material properties from this chapter ($f_{ck}$, $E_c$, creep, shrinkage) directly in design equations.

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Ch 1 · Constituents of Concrete

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Overview of Ingredients

Constituent	Typical Proportion by Volume	Function
Cement paste (cement + water)	25–40%	Binds all ingredients; fills voids; provides workability
Fine Aggregate (sand)	25–35%	Fills voids in CA; reduces cost; improves workability
Coarse Aggregate	35–45%	Main load-bearing skeleton; reduces shrinkage
Entrapped air	1–3%	Unavoidable; reduced by good compaction
Admixtures (if used)	< 1%	Modify fresh or hardened properties

Fine Aggregate (Sand) — IS 383:2016

Passes 4.75 mm IS sieve; retained on 75 µm sieve
Types: natural (river sand, pit sand, sea sand), crushed stone sand, manufactured sand (M-sand)
Sea sand: contains chlorides and shells → not recommended for RCC unless washed
Pit sand: angular particles; good bond; may contain clay / organic matter
River sand: rounded particles; better workability but slightly lower strength

Grading Zones of Fine Aggregate (IS 383)

Zone	Fineness Modulus (approx.)	Nature	Suitability
Zone I	3.5–4.5 (coarser range)	Coarse	Harsh mix; use only with low w/c
Zone II	2.9–3.5	Medium-coarse	Best for RCC — recommended
Zone III	2.4–2.9	Medium-fine	Acceptable; increase sand proportion slightly
Zone IV	1.6–2.4	Fine	Avoid in structural concrete; high water demand

Bulking of Sand

Surface tension of the moisture film around fine sand particles causes them to push apart, increasing the apparent volume (bulking). Coarse sand bulks less than fine sand.

⚠ Bulking is zero for both bone-dry sand AND fully saturated (submerged) sand — maximum bulking occurs at ~4–8% moisture content. Always correct for bulking when measuring sand by volume.

Coarse Aggregate — IS 383:2016

Retained on 4.75 mm sieve; maximum size typically 10, 20 or 40 mm
Angular, rough-textured aggregate → better bond with paste → higher strength
Rounded aggregate → better workability but lower bond strength
Specific gravity: 2.6–2.8; Water absorption ≤ 2%

Maximum Size of Aggregate (MSA)

Structural Element	Max Aggregate Size
Mass concrete (unreinforced)	Up to 80 mm
Lightly reinforced slabs, pavements	40 mm
Beams, columns, slabs (normal RCC)	20 mm
Thin slabs, heavily reinforced sections	10 mm
General limit	MSA ≤ 1/4 minimum member dimension
IS 456 bar-spacing limit	MSA ≤ 3/4 × clear spacing between bars
IS 456 cover limit	MSA ≤ cover to reinforcement

💡 GATE Tip: Larger MSA → less surface area → less cement paste needed → lower w/c possible → higher strength. BUT larger MSA → reduced workability and risk of segregation in thin sections.

Water for Concrete (IS 456:2000, Clause 5.4)

Should be fit for drinking (potable) or tested against IS 456 limits
pH: 6–8.5
Sulphates (as $SO_3$): ≤ 400 mg/L
Chlorides (as $Cl^-$): ≤ 500 mg/L (PCC); ≤ 250 mg/L (RCC)
Organic matter: ≤ 200 mg/L
Suspended matter: ≤ 2000 mg/L
Seawater: may be used for PCC in non-aggressive environments; not for RCC

Aggregate Tests Relevant to Concrete Quality

Test	IS Code	Limiting Value	Importance
Aggregate Crushing Value (ACV)	IS 2386 Pt IV	≤ 30% (pavement); ≤ 45% (concrete)	Structural strength
Aggregate Impact Value (AIV)	IS 2386 Pt IV	≤ 30% (pavement); ≤ 45% (concrete)	Impact toughness
Los Angeles Abrasion Value	IS 2386 Pt IV	≤ 30% (pavement); ≤ 50% (concrete)	Wear resistance
Flakiness Index (FI)	IS 2386 Pt I	≤ 15% preferred (≤ 35% max)	Workability & strength
Elongation Index (EI)	IS 2386 Pt I	≤ 15% preferred (≤ 35% max)	Strength & compaction
Specific Gravity	IS 2386 Pt III	2.6–2.8 (normal weight)	Mix design calculations
Water Absorption	IS 2386 Pt III	≤ 2% (CA); ≤ 3% (FA)	Effective w/c adjustment
Soundness ($Na_2SO_4/MgSO_4$)	IS 2386 Pt V	≤ 10–12% loss	Weathering resistance
Alkali-Reactivity (ASR)	IS 2386 Pt VII	Non-reactive preferred	Prevents gel expansion

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Ch 1 · Formulas

Bulking of Sand

$$ Bulking(\%) = \frac{V_{bulked} - V_{dry}}{V_{dry}}\times100 $$

Max ~25–30% for fine sand, ~15–20% for coarse sand, at 4–8% moisture

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Ch 1 · Solved Examples

GATE CE / ESE level

A site engineer measures 1 m³ of dry sand by volume box, then finds the same mass of moist sand occupies 1.22 m³. Find the bulking percentage.

Approach hint

Use $Bulking\% = (V_{bulked}-V_{dry})/V_{dry}\times100$ with $V_{dry}=1$, $V_{bulked}=1.22$.

$Bulking = \dfrac{1.22-1}{1}\times100 = 22\%$
22% is within the typical fine-sand bulking range (25–30% max) — plausible for a moderately fine sand

✓ Bulking ≈ 22% — the site must add ~22% extra volume of sand (by loose volume) to get the same dry mass, or better, batch by weight

A heavily reinforced beam has a minimum bar clear spacing of 24 mm and a member minimum dimension of 200 mm. What is the maximum aggregate size (MSA) permitted, applying both IS 456 rules?

Approach hint

Apply MSA ≤ 1/4 × min dimension AND MSA ≤ 3/4 × clear bar spacing; the governing (smaller) value controls.

From member dimension: $MSA \leq 200/4 = 50$ mm
From bar spacing: $MSA \leq 0.75 \times 24 = 18$ mm
The smaller governs

✓ MSA ≤ 18 mm — round down to the next standard size, 10 mm, since 20 mm would violate the bar-spacing rule

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Ch 1 · Diagrams

Click any diagram to zoom

Fig 1 – Bulking of Sand: zero at 0% (bone dry) and ~12%+ (submerged); peak at 4–8% MC. Fine sand bulks more than coarse sand.

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Ch 1 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

Bulking of sand is zero at which two moisture conditions?

Bulking vanishes at 0% moisture (no water film) and at full saturation (water fills all voids, no surface-tension separation) ✓

Question 2

Which fine-aggregate grading zone is recommended as "best for RCC" in IS 383?

Zone II (FM 2.9–3.5) is the medium-coarse grading recommended as the best general-purpose zone for RCC ✓

Question 3

A larger maximum size of aggregate (MSA), for the same workability, generally allows:

Larger MSA reduces total aggregate surface area, needing less cement paste to coat it, which allows a lower w/c ratio and higher strength for the same workability ✓

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Ch 2 · Fresh Concrete — Workability, Segregation & Bleeding

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Definition of Workability

Workability is the property of freshly mixed concrete that determines the ease and homogeneity with which it can be mixed, transported, placed, compacted and finished with minimum loss of homogeneity. (Defined by Glanville and Collins.)

Factors Affecting Workability

Factor	Effect on Workability
Water content (w/c ratio)	Single most important factor; ↑ water → ↑ workability
Cement content	↑ cement → finer paste → ↑ workability (at fixed w/c)
Aggregate size (MSA)	↑ MSA → less surface area → ↑ workability
Aggregate shape	Rounded > angular for workability (less friction)
Aggregate texture	Smooth > rough for workability
Aggregate grading	Well-graded → fewer voids → less paste needed → ↑ workability
Air entrainment	Air bubbles act as ball bearings → ↑ workability
Admixtures	Plasticizers / superplasticizers → ↑ workability without extra water
Temperature	↑ temperature → faster hydration → ↓ workability (slump loss)
Time after mixing	Workability reduces with time (slump loss)
Cement type / fineness	Finer cement → faster hydration → faster slump loss

Workability Tests — Complete Comparison

Test	IS Code	Range	Best For	Principle
Slump Test	IS 7320; IS 1199 Pt 2	0–175 mm	Medium workability (25–175 mm)	Subsidence of concrete after removing Abrams' cone
Compaction Factor (CF) Test	IS 1199 Pt 3	0.70–0.95	Low to medium workability; more sensitive than slump	Ratio of weight of partially compacted to fully compacted concrete
Vee-Bee Consistometer Test	IS 1199 Pt 4	3–25 seconds	Very low / stiff mixes (pavement, precast)	Time for concrete to re-mould under vibration
Flow Table Test	IS 9103	Spread diameter	Highly workable / SCC / flowing concrete	Spread of concrete under 15 jolts on flow table
Kelly Ball Test	ASTM	0–150 mm penetration	Field test; quick; fresh concrete in forms	Penetration of 30 lb ball under own weight

Slump Test — Full Details (IS 1199 Pt 2)

Apparatus: Abrams' cone: height 300 mm, top dia 100 mm, base dia 200 mm; tamping rod 16 mm dia, 600 mm long
Procedure: Fill in 3 layers, 25 tamps each; lift cone vertically; measure slump
Types of slump: True slump (uniform subsidence — desirable), Shear slump (one side shears off — repeat test), Collapse slump (complete collapse — very high w/c)

Slump Value	Degree of Workability	Suitable Structures
0–25 mm	Very low	Roads, pavements, mass concrete
25–50 mm	Low	Lightly reinforced foundations, kerbs
50–75 mm	Medium	Normal RCC — slabs, beams (manually placed)
75–100 mm	Medium-high	Columns, walls, heavily reinforced members
100–150 mm	High	Pumped concrete, pile foundations
150–175 mm	Very high	Grouting, tremie concrete, SCC precursor

Compaction Factor Test — Full Details

💡 CF = 0.75–0.80 → Very low workability · CF = 0.85 → Low · CF = 0.90 → Medium · CF = 0.95 → High. The CF test is more sensitive than the slump test, especially for stiff mixes where slump difference is very small — preferred for mixes with slump < 25 mm.

Segregation

Segregation is the separation of constituents of concrete such that the mix is no longer homogeneous — coarse aggregate settles to the bottom while mortar rises to the top.

Causes: Excessive w/c, dropping from height, over-vibration, poor grading, too large MSA
Types: (a) Coarse aggregate separates from mortar; (b) Cement paste separates from aggregate (bleeding)
Prevention: Correct w/c ratio, proper grading, limit drop height ≤ 1.5 m, controlled vibration, use of admixtures

Bleeding

Bleeding is a form of segregation where water rises to the surface of freshly placed concrete. It is caused by the inability of the solid particles to hold all the mixing water as they settle.

Effects: (a) Water channel formation → increased permeability; (b) Laitance layer on surface → weak surface; (c) Water pockets under aggregate and rebar → reduced bond; (d) Reduces compressive strength
Factors increasing bleeding: High w/c, high sand content, coarse cement, low cement content, lack of fines, high temperature
Prevention: Reduce w/c, increase cement content, use finer cement, air entrainment, pozzolans

⚠ Laitance must be removed before placing the next lift of concrete, otherwise a weak plane (cold joint) forms. Use wire brushing, sandblasting or water jetting.

Stiffening, Setting and Early Strength

Stage	Approx. Time	Description
Fresh / plastic stage	0–1 hr	Concrete fully workable; can be compacted
Initial set (IST)	~1.5–3 hrs	Concrete begins to stiffen; workability nearly lost; should be placed and compacted by now
Final set (FST)	~5–10 hrs	Concrete becomes rigid; demoulding possible (carefully)
Early strength stage	24 hrs–7 days	Rapid strength gain; curing critical
Long-term strength	7–90 days+	Continued hydration; strength increases for months

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Ch 2 · Formulas

Compaction Factor

$$ CF = \frac{W_{partial}}{W_{full}} $$

Ratio of weight of partially to fully compacted concrete; range 0.70–0.95

—

Bleeding Capacity

$$ Bleeding(\%) = \frac{V_{bleed\ water}}{V_{total\ mixing\ water}}\times100 $$

IS 9103 bleeding test

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Ch 2 · Solved Examples

GATE CE / ESE level

In a compaction factor test, the partially compacted concrete weighs 14.0 kg and the fully compacted concrete (same mould) weighs 15.5 kg. Find the CF and classify the workability.

Approach hint

$CF = W_{partial}/W_{full}$; compare against the standard CF bands.

$CF = 14.0/15.5 = 0.90$
CF = 0.90 falls in the "Medium workability" band

✓ CF = 0.90 — medium workability, suitable for normal RCC placed with vibration

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Ch 2 · Diagrams

Click any diagram to zoom

Fig 2 – Abrams' Cone (h=300 mm, base ⌀200 mm, top ⌀100 mm) and the three types of slump: True (accept), Shear (repeat), Collapse (reject).

Fig 8 – Compaction Factor Test: concrete falls freely through two hoppers into a cylinder. CF = W₂(partial) / W₁(full). Range: 0.70 (very low) to 0.95 (high workability).

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Ch 2 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

A slump test where one half of the concrete shears off and slides down is called:

Shear slump indicates a non-cohesive or poorly proportioned mix — the test should be repeated with a fresh sample ✓

Question 2

The Compaction Factor test is preferred over the slump test when:

CF is far more sensitive than slump for stiff, low-workability mixes where the slump difference between mixes is too small to distinguish ✓

Question 3

Bleeding in fresh concrete primarily results in:

Water rising to the surface leaves behind a weak, porous laitance layer and water channels that increase permeability and reduce strength/bond ✓

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Ch 3 · Water-Cement Ratio & Strength of Concrete

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Abrams' Water-Cement Ratio Law (1919)

For a given set of materials and conditions of testing, the strength of properly cured and compacted concrete is inversely proportional to the water-cement ratio.

⚠ Abrams' law is valid only for fully compacted, properly cured concrete. It breaks down at very low w/c ratios (insufficient workability) and very high w/c ratios (excessive voids).

Effective W/C Ratio

Aggregates in Saturated Surface Dry (SSD) condition → no adjustment to mix water needed
Aggregates drier than SSD → absorb water from mix → increase effective water; add extra water
Aggregates wetter than SSD → contribute free water to mix → reduce mix water

Relationship: W/C Ratio and Compressive Strength

w/c Ratio	Approx. 28-day Compressive Strength (OPC 43)
0.30	~65 MPa
0.35	~55 MPa
0.40	~45 MPa
0.45	~38 MPa
0.50	~32 MPa
0.55	~26 MPa
0.60	~21 MPa
0.65	~17 MPa

Minimum w/c Ratio for Complete Hydration

Theoretical minimum: w/c = 0.23 (water chemically combined during hydration)
Practical minimum: w/c = 0.36 (includes gel water required for C–S–H structure)
At w/c < 0.36: unhydrated cement grains remain; self-desiccation occurs
For workability: w/c ≥ 0.40 generally required without superplasticizer

Effect of W/C Ratio on Concrete Properties

Property	Low w/c (<0.40)	High w/c (>0.60)
Compressive strength	High	Low
Tensile/flexural strength	High	Low
Workability	Low (needs SP)	High
Permeability	Very low	High
Durability	Very high	Low
Shrinkage	Lower	Higher
Bleeding	Lower	Higher
Capillary porosity	Low	High

Maximum W/C Ratio Limits (IS 456:2000 Table 5)

Exposure Condition	Max w/c	Min Cement (kg/m³)	Min Grade
Mild	0.55	300	M20
Moderate	0.50	300	M25
Severe	0.45	320	M30
Very Severe	0.45	340	M35
Extreme	0.40	360	M40

Strength at Different Ages (% of 28-day strength) — OPC

Age	OPC 33	OPC 43	OPC 53 / RHPC	PPC / PBFSC
1 day	16%	20%	27%	10%
3 days	46%	55%	65%	40%
7 days	70%	75%	82%	65%
28 days	100%	100%	100%	100%
3 months	115%	115%	110%	120%
1 year	135%	130%	120%	150%

💡 IS 456 Clause 6.2.1: the increase in strength beyond 28 days can be accounted for in design if properly established, but 28-day strength remains the standard design reference.

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Ch 3 · Formulas

Abrams' Water-Cement Law

$$ f_c = \frac{A}{B^{\,w/c}} $$

A ≈ 100–125 MPa, B ≈ 3.5–4.0 for OPC at 28 days (empirical constants)

MPa

Effective Water-Cement Ratio

$$ (w/c)_{eff} = \frac{W_{total} - W_{absorbed\ by\ agg.}}{W_{cement}} $$

Adjust for aggregate moisture state relative to SSD

—

Free Water

$$ W_{free} = W_{total} - Absorption\times\frac{W_{aggregate}}{100} $$

Subtracts water absorbed into aggregate pores

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Ch 3 · Solved Examples

GATE CE / ESE level

A structure is in "Severe" exposure condition per IS 456 Table 5. State the maximum permissible w/c, minimum cement content and minimum grade.

Approach hint

Read directly off the IS 456 Table 5 durability requirements for "Severe" exposure.

Severe exposure row: max w/c = 0.45, min cement = 320 kg/m³, min grade = M30

✓ Max w/c = 0.45, min cement content = 320 kg/m³, minimum grade = M30

1000 kg of coarse aggregate at 1% moisture content above SSD is used, along with 180 kg of added water. If the aggregate's absorption capacity is 1.5%, find the free (effective) water available to hydrate the cement.

Approach hint

Since the aggregate is already wetter than SSD (1% above SSD, while absorption capacity is 1.5%), it is contributing free water to the mix, not absorbing from it — add this surface moisture to the batched water.

Surface moisture on aggregate = $1\% \times 1000 = 10$ kg (free water it contributes since it's wetter than SSD)
Total free water available = $180 + 10 = 190$ kg

✓ Free water ≈ 190 kg — the batched water figure must be reduced by 10 kg at the plant to hit the target w/c, since the aggregate itself is adding water

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Ch 3 · Diagrams

Click any diagram to zoom

Fig 3 – Abrams' Law: compressive strength decreases as w/c increases. Dashed lines show IS 456 max w/c limits for different exposure conditions.

Fig 4 – Strength gain with age: OPC 53 gains strength faster early; PPC has slower early gain but achieves higher long-term strength due to pozzolanic reaction.

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Ch 3 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

As per Abrams' law, compressive strength is:

Abrams' law states strength is inversely related to w/c, for fully compacted and properly cured concrete ✓

Question 2

For "Extreme" exposure per IS 456 Table 5, the maximum permissible w/c is:

Extreme exposure: max w/c = 0.40, min cement 360 kg/m³, min grade M40 — the strictest row in the table ✓

Question 3

Which cement type shows the highest 1-year strength as a % of its own 28-day strength?

PPC/PBFSC's pozzolanic reaction continues for a long time, giving the largest relative long-term strength gain (150% at 1 year) ✓

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Ch 4 · Concrete Mix Design — IS 10262:2019

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Types of Mixes

Feature	Nominal Mix	Standard Mix	Design Mix
Basis	Fixed volumetric proportions	IS prescriptive proportions	Statistical target mean strength
Applicable grades	M5 to M25 (IS 456)	M10 to M25	M25 and above (mandatory)
IS code	IS 456 Table 9	IS 456	IS 10262:2019
Economy	Conservative (over-designed)	Moderate	Most economical and reliable
Quality control required	Low	Moderate	High (batching, testing)

Nominal Mix Proportions (IS 456:2000 Table 9)

Grade	$f_{ck}$ (MPa)	Proportion (C : FA : CA) by volume	Max w/c
M5	5	1 : 5 : 10	–
M7.5	7.5	1 : 4 : 8	–
M10	10	1 : 3 : 6	–
M15	15	1 : 2 : 4	–
M20	20	1 : 1.5 : 3	0.55
M25	25	1 : 1 : 2	0.50

⚠ M20 is the minimum grade for RCC in mild exposure as per IS 456:2000. Nominal mix must NOT be used for M30 and above — only design mix.

IS 10262:2019 — Design Mix Procedure (Step by Step)

Determine target mean strength ($f'_{ck}$): $f'_{ck} = f_{ck} + 1.65\sigma$. σ = standard deviation from IS 10262 Table 1: M10–M15 → 3.5 MPa; M20–M25 → 4.0 MPa; M30–M50 → 5.0 MPa; M55+ → 6.0 MPa
Select w/c ratio: From Table 5 of IS 456 (exposure conditions) and from strength relationship
Determine water content: From IS 10262 Table 2 based on MSA and required slump; then adjust for admixtures
Calculate cement content: $Cement\ content = Water\ content / (w/c)$; check against minimum cement content from IS 456 Table 5
Determine aggregate proportions: Volume method using absolute volumes; fine aggregate fraction from IS 10262 Table 3 (based on zone and MSA)
Calculate mix quantities per m³ of concrete: Volume of concrete = Volume of cement + water + FA + CA + air; $V_{agg} = 1 - V_{cement} - V_{water} - V_{air}$; Volume of FA = $V_{agg} \times$ (% FA); Mass of FA = $V_{FA} \times S_{FA} \times 1000$
Trial mixes: Minimum 3 trial mixes at w/c ± 0.05; test workability and 28-day strength; finalise proportions

Water Content from IS 10262:2019 Table 2

Max Agg. Size (mm)	Slump 25–50 mm (kg/m³)	Slump 50–100 mm (kg/m³)	Slump 100–150 mm (kg/m³)
10	208	228	–
20	186	200	215
40	165	178	192

💡 For each 25 mm increase in slump beyond 50 mm, add ~3% water. For Zone III sand, add 12 kg/m³; Zone IV sand, add 18 kg/m³. For rounded aggregate, reduce water by 10 kg/m³.

Fine Aggregate Volume Fraction (IS 10262 Table 3)

w/c ratio	FA Zone II, MSA 20 mm	FA Zone II, MSA 40 mm
0.35	0.30	0.27
0.40	0.33	0.29
0.45	0.36	0.32
0.50	0.38	0.34
0.55	0.40	0.36
0.60	0.42	0.38

ACI Method of Mix Design (for reference, ESE)

Recommended water content from ACI 211.1 Table based on slump and MSA
w/c selected from strength and durability requirements
$Cement = Water / (w/c)$
Dry-rodded unit weight of coarse aggregate determines CA volume
FA fills remaining volume
ACI uses by weight proportioning; IS 10262 uses absolute volume method

⚖️

Ch 4 · Formulas

Target Mean Strength

$$ f'_{ck} = f_{ck} + 1.65\sigma $$

σ from IS 10262 Table 1 by grade band

MPa

Cement Content

$$ C = \frac{Water\ content}{w/c} $$

Check against IS 456 Table 5 minimum

kg/m³

Volume of Cement

$$ V_{cement} = \frac{C}{S_c \times 1000}\ m^3 $$

$S_c$ = specific gravity of cement (≈3.15)

m³

Aggregate Volume (Absolute Volume Method)

$$ V_{agg} = 1 - V_{cement} - V_{water} - V_{air} $$

Split into FA/CA by the IS 10262 Table 3 zone/MSA fraction

m³

⚖️

Ch 4 · Solved Examples

GATE CE / ESE level

Design M25 concrete (σ = 4.0 MPa) with water content 186 kg/m³ (20 mm MSA, 50–100 mm slump) and w/c = 0.45. Find (a) target mean strength and (b) cement content.

Approach hint

Apply $f'_{ck}=f_{ck}+1.65\sigma$ first, then $C = Water/(w/c)$.

$f'_{ck} = 25 + 1.65(4.0) = 25 + 6.6 = 31.6$ MPa
$C = 186 / 0.45 = 413.3$ kg/m³
Check: IS 456 minimum cement for M25 (moderate exposure) = 300 kg/m³ → 413.3 kg/m³ satisfies this comfortably

✓ Target mean strength = 31.6 MPa; cement content ≈ 413 kg/m³

⚖️

Ch 4 · Diagrams

Click any diagram to zoom

Fig 5 – IS 10262:2019 Mix Design Procedure: 7-step flow from target mean strength to trial mixes. Feedback loop adjusts proportions if trial results fail.

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Ch 4 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

As per IS 456, design mix is mandatory for:

Nominal mix is permitted only up to M25; M25 and above must use IS 10262 design mix ✓

Question 2

For M35 concrete, the standard deviation σ used in target mean strength is:

M30–M50 uses σ = 5.0 MPa as per IS 10262 Table 1 ✓

Question 3

IS 10262 mix design uses which proportioning method, as opposed to ACI's method?

IS 10262 uses the absolute volume method (all constituent volumes sum to 1 m³); ACI 211.1 proportions by weight ✓

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Ch 5 · Properties of Hardened Concrete

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Compressive Strength

Characteristic compressive strength ($f_{ck}$): 28-day cube strength below which not more than 5% of results are expected to fall
Standard cube: 150 mm × 150 mm × 150 mm (IS 516)
Standard cylinder: 150 mm dia × 300 mm height (ASTM)
Cube strength / Cylinder strength ≈ 1.25 (cube strength is ~25% higher)
Loading rate: 140 kg/cm²/min (IS 516) = 14 N/mm²/min

Acceptance Criteria for Concrete Strength (IS 456 Clause 16.1)

Criterion	Requirement
Mean of any group of 4 consecutive results	≥ $f_{ck}$ + 0.825 × s (s = established SD) or ≥ $f_{ck}$ + 3 MPa, whichever is greater
Any individual test result	≥ $f_{ck}$ − 3 MPa

Tensile Strength

Concrete is weak in tension; tensile strength ≈ 8–12% of compressive strength
Split cylinder tensile strength (Brazilian test, IS 5816): $f_t = \dfrac{2P}{\pi LD}$ [P = max load; L = length; D = diameter of cylinder]
Flexural strength (Modulus of Rupture, IS 516): Tests 150×150×700 mm beam. If failure within middle third: $f_r = PL/(bd^2)$; IS 456 formula: $f_r = 0.7\sqrt{f_{ck}}$ MPa (characteristic)

Modulus of Elasticity (IS 456 Clause 6.2.3)

Grade	$f_{ck}$ (MPa)	$E_c = 5000\sqrt{f_{ck}}$ (GPa)
M20	20	22.4
M25	25	25.0
M30	30	27.4
M35	35	29.6
M40	40	31.6

Poisson's Ratio

Concrete: μ = 0.1–0.2 (IS 456 uses 0.2 for elastic analysis)
Steel: μ = 0.3

Creep of Concrete

Creep is the time-dependent increase in strain under a constant sustained stress. It occurs due to viscous flow of cement gel and redistribution of stress to aggregates.

IS 456 values of creep coefficient θ: age at loading 7 days → θ = 2.2; 28 days → θ = 1.6; 1 year → θ = 1.1
Creep is higher with: high w/c, high cement content, early loading, low humidity, high temperature, thin members
Creep is lower with: high-strength concrete, humid curing, late loading, thick members, large aggregates
Ultimate creep strain ≈ 2–3 × elastic strain for normal concrete
Effects of creep: Increased deflection, loss of prestress, redistribution of stresses, differential settlement

Shrinkage of Concrete

Type	Cause	When Occurs	Magnitude
Plastic shrinkage	Rapid evaporation from fresh surface before set	0–6 hrs after placing	Large; leads to surface cracks
Autogenous shrinkage	Chemical shrinkage during hydration (self-desiccation)	During hardening	Significant at low w/c (<0.40)
Drying shrinkage	Loss of adsorbed water from C–S–H gel on drying	After hardening, on exposure	300–600 × $10^{-6}$
Carbonation shrinkage	$CO_2$ reacts with $Ca(OH)_2$ → $CaCO_3$	Long-term; surface first	Smaller; may be partially reversible
Thermal shrinkage	Cooling after peak hydration heat	During curing of mass concrete	Significant in large pours

Unit Weight and Density

Type of Concrete	Density (kg/m³)	Unit Weight (kN/m³)
Plain Cement Concrete (PCC)	2300–2400	24
Reinforced Cement Concrete (RCC)	2400–2500	25
Lightweight concrete	< 1900	< 19
Heavyweight (radiation shielding)	> 3200	> 32
High Strength Concrete (HSC)	2400–2500	25

Thermal Properties

Coefficient of thermal expansion: α ≈ 10–12 × $10^{-6}$/°C (same as steel → compatible)
Thermal conductivity: k ≈ 1.7 W/m·K (normal weight concrete)
Specific heat: $c_p$ ≈ 840–1170 J/kg·K
Concrete retains strength up to 300°C; serious loss above 300°C; spalling above 400°C

🧱

Ch 5 · Formulas

Split Tensile Strength

$$ f_t = \frac{2P}{\pi LD} $$

Brazilian test, IS 5816

MPa

Modulus of Rupture

$$ f_r = 0.7\sqrt{f_{ck}} $$

IS 456 characteristic flexural strength

MPa

Modulus of Elasticity

$$ E_c = 5000\sqrt{f_{ck}} $$

IS 456; ACI 318 uses $5700\sqrt{f_{ck}}$; CEB-FIP uses $9100\,f_{ck}^{1/3}$

MPa

Creep Coefficient

$$ \theta = \frac{Creep\ strain}{Elastic\ strain} $$

IS 456: 2.2 (7-day load), 1.6 (28-day), 1.1 (1-year)

—

Effective Modulus (with creep)

$$ E_{eff} = \frac{E_c}{1+\theta} $$

Used for long-term deflection calculations

MPa

Design Shrinkage Strain

$$ \varepsilon_{cs} = 0.0003 $$

IS 456 Clause 6.2.4, for design purposes

—

🧱

Ch 5 · Solved Examples

GATE CE / ESE level

Find the modulus of elasticity and modulus of rupture of M30 concrete as per IS 456.

Approach hint

Apply $E_c=5000\sqrt{f_{ck}}$ and $f_r=0.7\sqrt{f_{ck}}$ with $f_{ck}=30$.

$E_c = 5000\sqrt{30} = 5000\times5.477 \approx 27{,}386$ MPa ≈ 27.4 GPa
$f_r = 0.7\sqrt{30} = 0.7\times5.477 \approx 3.83$ MPa

✓ $E_c \approx 27.4$ GPa, $f_r \approx 3.83$ MPa

A column is loaded at age 28 days. Given $E_c = 25{,}000$ MPa for the concrete used, find the effective modulus for long-term deflection calculations.

Approach hint

Use θ = 1.6 for 28-day loading (IS 456), then $E_{eff}=E_c/(1+\theta)$.

θ (28-day load) = 1.6
$E_{eff} = 25000/(1+1.6) = 25000/2.6 \approx 9615$ MPa

✓ $E_{eff} \approx 9615$ MPa — less than half the short-term modulus, reflecting the large long-term deflection increase due to creep

🧱

Ch 5 · Diagrams

Click any diagram to zoom

Fig 16 – Concrete microstructure: C–S–H gel provides strength; Ca(OH)₂ maintains high pH; ITZ (Interfacial Transition Zone) is the weakest link at 20–50 µm around aggregates; capillary pores control durability and permeability.

Fig 6 – Creep of Concrete: on loading, instantaneous elastic strain occurs; creep strain accumulates over time. On unloading: elastic recovery + partial creep recovery; residual strain remains permanently.

Fig 10 – Shrinkage types mapped against time. Plastic shrinkage is the earliest and fastest; drying shrinkage is the most significant and longest-lasting; IS 456 design value ε_cs = 0.0003.

🧱

Ch 5 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

The Interfacial Transition Zone (ITZ) in concrete microstructure is significant because it is:

The ITZ (20–50 µm around each aggregate particle) has higher porosity and more Ca(OH)₂/ettringite than the bulk paste, making it the weakest link and common crack path ✓

Question 2

Which type of shrinkage is most significant in magnitude and occurs latest/longest?

Drying shrinkage (300–600×10⁻⁶) is the largest and longest-duration shrinkage mechanism, dominating long-term dimensional change ✓

Question 3

A concrete member is loaded at 7 days rather than 28 days. Its creep coefficient will be:

Earlier loading (7 days, less-matured concrete) gives a higher creep coefficient (θ=2.2) than loading at 28 days (θ=1.6) or 1 year (θ=1.1) ✓

🛡

Ch 6 · Durability of Concrete — Mechanisms & Prevention

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Definition (IS 456 Clause 8.1)

A durable concrete is one that performs satisfactorily in the working environment during its anticipated exposure conditions during the service life for which it was designed. The concrete must resist weathering action, chemical attack, abrasion and other degradation processes.

Permeability — The Master Parameter

Permeability governs transport of water, oxygen, $CO_2$, chlorides and sulphates → controls all durability mechanisms
Capillary pores (0.01–10 µm) are the main transport pathways
Reduces with: lower w/c, prolonged curing, mineral admixtures (fly ash, silica fume, GGBS)
Water permeability coefficient k ≈ $10^{-10}$–$10^{-12}$ m/s for dense concrete
Darcy's Law: $v = k \times i$ (flow velocity = permeability × hydraulic gradient)

Chemical Attack Mechanisms

(a) Sulphate Attack

Parameter	Details
Source of sulphates	Soil (pyrite oxidation), groundwater, seawater, industrial effluent
Reaction with $C_3A$ hydrate	$Ca(OH)_2 + CaSO_4 + 2H_2O \rightarrow CaSO_4\cdot2H_2O$ (gypsum, expansive)
Reaction with C–S–H	$CaSO_4$ + C–S–H + $H_2O \rightarrow CaCO_3$ + silica gel (decalcification)
Secondary ettringite	Gypsum + $C_3A$ hydrate → Ettringite (3CaO·$Al_2O_3$·3$CaSO_4$·32$H_2O$) — very expansive
Most aggressive form	$MgSO_4$ — attacks both $C_3A$ and C–S–H gel
Visual symptoms	White deposits, cracking, spalling, softening, loss of section
Prevention	SRC ($C_3A < 5\%$); low w/c; PPC / GGBS; dense cover; membranes

(b) Carbonation

$CO_2 + Ca(OH)_2 \rightarrow CaCO_3 + H_2O$
Reduces pH from 12.5 to below 9 → depassivates steel → corrosion initiates
Rate: fastest at 50–70% RH; slow in very dry and very wet conditions
Carbonation depth $\propto \sqrt{t}$ (diffusion process): $d = K_c\sqrt{t}$
Higher w/c, lower cement content, poor curing → faster carbonation
Prevention: Low w/c, dense concrete, adequate cover, polymer coatings

(c) Alkali-Silica Reaction (ASR) / Alkali-Aggregate Reaction (AAR)

Mechanism: Amorphous/reactive silica in aggregate + alkalis ($Na^+, K^+$ from cement) + moisture → expansive silica gel
Three prerequisites (Stanton's Trinity): Reactive aggregate + sufficient alkali ($Na_2O_{eq} > 0.6\%$) + moisture
Visual signs: Map cracking (crazing), gel exudation, surface popouts
Reactive aggregates: Opal, chert, flint, volcanic glass, greywacke, certain quartzites
Pessimum proportion: Maximum expansion at ~5–15% reactive content; reduces at higher amounts
Prevention: Low-alkali cement ($Na_2O_{eq} \leq 0.60\%$); fly ash ≥ 30% or GGBS ≥ 50%; silica fume; non-reactive aggregates

(d) Chloride-Induced Corrosion of Steel

$Cl^-$ ions migrate through concrete → reach steel → destroy passive $Fe_2O_3$ layer → pitting corrosion begins
Corrosion threshold: free $Cl^-$ > 0.4% by mass of cement (IS 456)
Corrosion products (rust) volume 2–6× original steel → expansive cracking and delamination
Chloride transport mechanisms: diffusion (main), absorption, permeation
Prevention: Adequate cover, low w/c (< 0.45), silica fume, epoxy-coated bars, stainless steel, cathodic protection (impressed current / sacrificial anode)

(e) Acid Attack

Any acid at pH < 6.5 attacks concrete; most aggressive at pH < 4.5
Acids dissolve $Ca(OH)_2$ and C–S–H gel → surface erosion, loss of section
Biogenic sulphuric acid attack (BSAA) in sewers: $H_2S \rightarrow H_2SO_4$
Prevention: Use HAC or SSC; GGBS; dense concrete; acid-resistant linings/tiles; epoxy coatings

(f) Freeze-Thaw Attack

Water expands ~9% on freezing → hydraulic pressure → internal cracking and surface scaling
Osmotic pressure from dissolved salts also contributes
Damage quantified by Durability Factor (DF) from ASTM C666
Prevention: Air entrainment (3–7% air with 25–250 µm bubble spacing ≤ 200 µm); low w/c; proper curing; de-icing salt resistance

Cover to Reinforcement (IS 456:2000 Clause 26.4)

Exposure Condition	Nominal Cover (mm)
Mild	20 mm
Moderate	30 mm
Severe	45 mm
Very Severe	50 mm
Extreme	75 mm
Fire resistance (2 hrs)	40 mm (beams); 35 mm (slabs)

Curing of Concrete

Method	Description	When Used
Water curing (moist curing)	Wet hessian, burlap; ponding; continuous sprinkling	Most common; all RCC
Membrane curing	Impermeable membrane (polyethylene, liquid compound) seals surface	Pavements, slabs, arid conditions
Steam curing (atmospheric)	100°C steam; 6–18 hrs; 70–80% 28-day strength in 24 hrs	Precast elements
High-pressure steam (Autoclaving)	180°C, 1 MPa; extremely fast strength gain; C–S–H → tobermorite	AAC blocks, railway sleepers
Electrical curing	Low-voltage current heats concrete	Cold weather; mass concrete
Infra-red / microwave	Radiant heating	Thin precast panels

💡 Minimum Curing Periods (IS 456 Clause 13.5): OPC — 7 days; Blended cements (PPC/PBFSC/SRC) in moderate/severe environments — 10 days; hot & dry conditions (T>40°C, RH<20%) — 14 days minimum. Curing temperature must be ≥ 10°C; concrete should not be allowed to freeze during curing.

🛡

Ch 6 · Formulas

Darcy's Law (Permeability)

$$ v = k\,i $$

$v$ = flow velocity, $k$ = permeability coefficient, $i$ = hydraulic gradient

m/s

Carbonation Depth

$$ d = K_c\sqrt{t} $$

$K_c$ = carbonation coefficient, $t$ = time in years

Chloride Corrosion Threshold

$$ Cl^- > 0.4\%\ \text{by mass of cement} $$

IS 456 free-chloride limit that initiates active corrosion

🛡

Ch 6 · Solved Examples

GATE CE / ESE level

Carbonation reaches 6 mm depth in 9 years for a slab. If the reinforcement cover is 30 mm ("Moderate" exposure), estimate the time for carbonation to reach the steel.

Approach hint

Find $K_c$ from the given data point using $d=K_c\sqrt t$, then solve for $t$ at $d=30$ mm.

$K_c = d/\sqrt t = 6/\sqrt9 = 6/3 = 2$ mm/$\sqrt{\text{year}}$
At $d=30$: $30 = 2\sqrt t \Rightarrow \sqrt t = 15 \Rightarrow t = 225$ years

✓ ≈ 225 years — illustrates why the correct exposure-based cover (here, 30 mm for Moderate) provides a long service-life margin against carbonation-induced corrosion

🛡

Ch 6 · Diagrams

Click any diagram to zoom

Fig 7a – Carbonation front moves inward with time (depth proportional to the square root of time). Phenolphthalein shows colourless zone (carbonated) and pink zone (alkaline).

Fig 7b – Chloride ions diffuse through cover → destroy passive film on steel → pitting corrosion → rust expansion → cracking and spalling of cover.

Fig 12 – ASR Mechanism: reactive silica + alkalis + moisture → expansive silica gel → swelling → internal pressure → map cracking. Prevention: Na₂O_eq ≤ 0.60%, fly ash ≥ 30%.

Fig 15a – Freeze-thaw: water in capillary pores freezes, expands 9%, generates hydraulic pressure → micro-cracking → progressive scaling.

Fig 15b – Air entrainment: small voids (25–250 µm, spacing ≤ 200 µm) act as pressure relief chambers. Ice expands into void → no cracking. Trade-off: 1% air ≈ −5% strength.

Fig 11 – IS 456:2000 Exposure Conditions Staircase: each step up the severity ladder adds 5 MPa to the minimum grade, reduces max w/c, increases min cement content and min cover.

🛡

Ch 6 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

The threshold free chloride content that initiates active corrosion of reinforcement (IS 456) is:

Free $Cl^-$ exceeding 0.4% by mass of cement is the IS 456 threshold beyond which active corrosion typically initiates ✓

Question 2

Air entrainment protects against freeze-thaw damage primarily by:

The 25–250 µm air voids act as pressure-relief chambers — ice can expand into them instead of cracking the surrounding paste ✓

Question 3

For "Very Severe" exposure per IS 456, the nominal cover to reinforcement is:

Very Severe = 50 mm cover; Severe = 45 mm; Moderate = 30 mm; Extreme = 75 mm ✓

🔬

Ch 7 · Testing of Concrete — Destructive & Non-Destructive

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Destructive Tests (DT)

1. Compressive Strength Test (IS 516:1959)

Cube: 150 × 150 × 150 mm; cylinder: 150 mm dia × 300 mm (ASTM)
3 specimens per batch; tested at 7, 28 days (and optionally 3, 56, 91 days)
Loading rate: 140 kg/cm²/min = 14 N/mm²/min
Accept average of 3 results if no individual result < $f_{ck}$ − 3 MPa
Cube vs Cylinder: $f_{cube}$ = 1.25 × $f_{cylinder}$ approximately

2. Split Cylinder / Brazilian Test (IS 5816)

Tensile strength $f_t = 2P/(\pi LD)$; typically $f_t$ ≈ 8–12% of $f_{ck}$.

3. Flexural Strength Test (IS 516) — Modulus of Rupture

Beam specimen: 150 × 150 × 700 mm; simply supported; third-point loading
Span = 450 mm (3 × depth); loads at 150 mm from each support
If failure in middle third: $f_r = PL/(bd^2)$; if failure outside middle third (a = distance from support to fracture): $f_r = 3Pa/(bd^2)$

Non-Destructive Tests (NDT) of Concrete

Test	IS Code / Standard	Principle	Output	Accuracy
Rebound Hammer Test	IS 13311 Pt 2; ASTM C805	Spring-loaded plunger impacts concrete surface; rebound number R measured	Surface hardness → estimated compressive strength	±25% variation; only surface layer
Ultrasonic Pulse Velocity (UPV)	IS 13311 Pt 1; ASTM C597	Ultrasonic pulse (50–250 kHz) travels through concrete; time measured	Pulse velocity → quality assessment; detect cracks, voids, delamination	Good for uniformity; limited for strength
Combined Method (Hammer + UPV)	RILEM NDT 4	Uses both R and V to estimate strength from empirical charts	Better strength estimate than either test alone	±15–20%
Core Test	IS 516; IS 1199	Cylindrical cores drilled from structure; tested in compression	In-situ concrete strength	Most accurate in-situ method; invasive but not fully destructive
Pull-out Test (Lok Test)	ASTM C803	Embedded disc pulled out; force measured	In-situ compressive strength	Good for early-age strength monitoring
Penetration Resistance (Windsor Probe)	ASTM C803	Steel probe driven by powder charge; penetration depth measured	Surface hardness / estimated strength	±10–15%; only near-surface
Radiography / X-ray	ACI 228	X-ray or gamma-ray penetration; film or digital detector	Location of bars, voids, cracks inside concrete	High accuracy; expensive; radiation hazard
Infrared Thermography	ASTM D4788	Thermal camera detects temperature differentials	Delamination, voids, water ingress behind surfaces	Good for large areas; depends on sun and wind conditions
Ground Penetrating Radar (GPR)	ASTM D6087	EM pulses reflect off boundaries (steel, voids, cracks)	Rebar location, cover depth, void detection	Excellent; non-contact; very fast
Half-Cell Potential (HCP)	IS 14977; ASTM C876	Measures electrochemical potential of steel against reference electrode	Probability of corrosion activity of reinforcement	Indicates active/passive; not quantitative
Carbonation Depth Test	BRE Digest 405	Phenolphthalein indicator sprayed on freshly broken concrete surface	Carbonation depth (colourless = carbonated; pink/red = alkaline)	Simple; inexpensive; accurate
Chloride Content Test	IS 14959; ASTM C1152	Core extracted; powdered; chemical or potentiometric titration	Total and free chloride content at various depths	Good; semi-destructive (core required)

Rebound Hammer — Detailed Notes

Rebound Number (R): 10–20 → very poor; 20–30 → fair; 30–40 → good; 40–50 → very good; >50 → excellent surface hardness
Factors affecting R: carbonation (↑ R), moisture (↓ R), surface texture, age, type of aggregate, direction of impact (calibration chart changes)
At least 12 readings per test location; reject outliers > 6 R from mean
Calibrate on standard anvil; R = 80 ± 2 on IS reference anvil
Not reliable for: Lightweight concrete, highly wet surfaces, surfaces with surface carbonation only

UPV Test — Detailed Notes

Velocity (km/s)	Quality of Concrete
> 4.5	Excellent
3.5–4.5	Good
3.0–3.5	Medium
2.0–3.0	Doubtful
< 2.0	Very poor / completely deteriorated

Transmission modes: Direct (most accurate), Semi-direct, Indirect/surface (least accurate)
Pulse velocity affected by: moisture content, steel reinforcement (increases velocity), aggregate type and content, temperature

Core Test — Correction Factors

Estimated cube strength = Core strength × Correction factor. L/D correction: for L/D = 2.0 → factor = 1.0; L/D = 1.0 → multiply by 1.25. IS 516: if core strength × 1.25 ≥ 0.85 × $f_{ck}$ → concrete is acceptable.

Half-Cell Potential — Corrosion Probability

Potential (mV vs Cu/$CuSO_4$ electrode)	Probability of Corrosion (ASTM C876)
More positive than −200 mV	< 10% probability of active corrosion
−200 to −350 mV	Uncertain zone; further investigation needed
More negative than −350 mV	> 90% probability of active corrosion

🔬

Ch 7 · Formulas

Flexural Strength (failure outside middle third)

$$ f_r = \frac{3Pa}{bd^2} $$

$a$ = distance from nearest support to fracture line

MPa

Core Test Acceptance

$$ Core\ strength \times 1.25 \geq 0.85\,f_{ck} $$

1.25 = L/D=1.0 correction factor; IS 516

—

Cube vs Cylinder Strength

$$ f_{cube} \approx 1.25\,f_{cylinder} $$

Cube strength reads ~25% higher than cylinder for the same concrete

—

🔬

Ch 7 · Solved Examples

GATE CE / ESE level

A core with L/D = 1.0 gives a compressive strength of 22 MPa. The design grade is M25 ($f_{ck}$=25 MPa). Is the in-situ concrete acceptable per IS 516?

Approach hint

Apply the L/D=1.0 correction factor (×1.25) to the core strength, then check against $0.85 f_{ck}$.

Corrected core strength = $22 \times 1.25 = 27.5$ MPa
Acceptance threshold = $0.85 \times 25 = 21.25$ MPa
$27.5 \geq 21.25$

✓ Acceptable — corrected core strength (27.5 MPa) exceeds the 21.25 MPa threshold

A cylinder test gives 28 MPa compressive strength. Estimate the equivalent cube strength.

Approach hint

Apply $f_{cube} \approx 1.25\,f_{cylinder}$.

$f_{cube} = 1.25 \times 28 = 35$ MPa

✓ Equivalent cube strength ≈ 35 MPa

🔬

Ch 7 · Diagrams

Click any diagram to zoom

Fig 9a – UPV transmission modes: Direct (opposite faces), Semi-direct (adjacent faces), Indirect/Surface (same face). Direct gives highest accuracy.

Fig 9b – Rebound Hammer: spring-loaded plunger impacts surface; rebound number R correlates with surface hardness and estimated strength. Accuracy ±25%.

🔬

Ch 7 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

Which NDT method gives the most accurate strength estimate among "estimation" (non-invasive) methods?

The combined method (±15–20%) improves on either single method (rebound ±25%) by cross-checking surface hardness against internal pulse velocity ✓

Question 2

A UPV reading of 4.8 km/s indicates concrete quality that is:

> 4.5 km/s is classified "Excellent" in the standard UPV quality table ✓

Question 3

A half-cell potential reading more negative than −350 mV (vs Cu/CuSO₄) indicates:

More negative than −350 mV per ASTM C876 indicates a high (>90%) probability of active corrosion ✓

🏗

Ch 8 · Production, Batching, Mixing, Placing & Compaction

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Batching of Concrete Materials

Method	Description	Accuracy	Preferred For
Weigh batching	All materials weighed individually	±1–3% cement; ±3% aggregate; ±1% water	All concrete above M20; IS 456 requirement
Volume batching	Measured by volume using gauge boxes	Lower; affected by bulking, void ratios	Nominal mix only; M15 and below

⚠ IS 456:2000 recommends weigh batching for all concrete of M20 and above. Volume batching is permitted only for grades below M20 using nominal mix. Always correct for bulking of sand and surface moisture of aggregates.

Mixing of Concrete

Method	Equipment	Minimum Mixing Time	Notes
Machine mixing (drum mixer)	Tilting drum, non-tilting drum, pan mixer	2 minutes (IS 456)	Preferred; most construction sites
Ready-mixed concrete (RMC)	Central plant + transit mixer (agitating drum)	70–100 revolutions at mixing speed; then 4–6 km/h agitation	IS 4926:2003; IS 456 permits use
Hand mixing	Manually on watertight platform	Not recommended for structural concrete	Only M10 and below; add 10% extra cement

Transportation of Concrete

Maximum time from mixing to placing: 2 hours at ≤ 25°C; 1.5 hours at > 25°C (IS 456)
No re-tempering (adding extra water) permitted — reduces strength and durability
Transit mixer: can travel up to 10–15 km if agitating; no segregation/slump loss
Chute: max slope 1 vertical : 3 horizontal; prevent segregation with baffles
Concrete pump: slump ≥ 75 mm; maximum pipe bend radius ≥ 1 m; pressure up to 100 bar
Belt conveyor: can cause segregation; use concrete of low slump; cover to prevent drying
Truck (agitator): maximum 300 revolutions before discharge; maximum 1.5 hours

Placing of Concrete

Maximum free-fall height: 1.5 m (IS 456); beyond this → use tremie or pump
Do not disturb placed concrete after 30 minutes or once initial set begins
Avoid placing against flowing water; pump out water first
Concrete placed in layers: 300–450 mm for vibrated concrete; thinner if hand-compacted
Avoid cold joints: next layer must be placed before initial set of previous layer

Hot & Cold Weather Concreting (IS 456 Clause 14)

Hot weather: concrete temperature at placing ≤ 40°C (Cl. 14.1); precautions: cool water/ice, chill aggregates, use retarder, shade, night pouring, use white cement. Every 5°C rise → ~1% more water demand → ~2 MPa strength loss
Cold weather: concrete temperature at placing ≥ 10°C (Cl. 14.2). If ambient T < 5°C: warm water, insulated formwork, accelerators, heated enclosures. Frozen aggregates must NOT be used. Protect from freezing until strength ≥ 3.5 MPa

Compaction of Concrete

Method	Type	Suitable For	Notes
Internal vibration (poker/needle vibrator)	Most common; 25–100 mm dia needle; 50–200 Hz	Most RCC, beams, columns	Best compaction; insertion at 0.5 m intervals; withdraw slowly at 80–100 mm/min
External vibration (form vibrator)	Attached to formwork	Thin members, precast panels	Limited penetration depth; supplement with internal
Vibrating table	Table vibrates at controlled frequency	Precast, small elements	Very uniform compaction
Surface vibration (screed vibrator)	Vibrating screed or plate	Slabs, pavements	Limited to ~150 mm depth
Tamping / rodding	Manual; 25 tamps per 100 cm²	Small elements; test specimens	Very limited effectiveness
Centrifugal compaction	Spinning mould	Pipes, poles, piles	Low w/c possible; very dense concrete

⚠ Over-vibration causes segregation (aggregate sinks, paste rises → laitance). Under-vibration leaves voids → honeycombing → reduced strength and durability. Optimum: insert poker at 0.5–0.75 m centres; vibrate until air bubbles cease to appear at surface.

Formwork (Shuttering)

Must be watertight, strong, stiff, smooth surface; apply release agent before placing concrete

Structural Element	Min. Stripping Time (OPC, T > 15°C)
Vertical formwork (columns, walls)	16–24 hours
Soffit of slabs (props left in)	3 days
Soffit of beams (props left in)	7 days
Props to slabs (slabs spanning ≤ 4.5 m)	14 days
Props to beams and arches (span > 6 m)	28 days

Ready Mix Concrete (RMC) — IS 4926:2003

Designed and batched at central plant; delivered by transit mixer to site
Transit drum: 40–100 RPM (mixing); 2–6 RPM (agitating); max 70 revolutions at full mixing speed, thereafter agitate; total revolutions must not exceed 300
Maximum transport time: 2 hours from mixing to discharge
Advantages: Quality control, continuous supply, less labour, reduced site clutter, accurate batching
Disadvantages: Traffic delays cause slump loss, distance limitations, high cost for small quantities

Pumped Concrete

Concrete pumped through steel pipes (100–150 mm dia) at pressure up to 100 bar
Required slump: ≥ 75 mm; use plasticizer / superplasticizer
No segregation in pipe; pump pressure forces bleeding water to surface on exit
Cannot pump concrete with crushed flaky aggregate efficiently

Underwater Concreting Methods

Tremie method: 150–300 mm dia pipe; bottom always submerged in concrete; prevents water entry; most common method
Bottom dump bucket: Concrete placed in bucket and lowered; less control
Prepacked aggregate (grouted concrete): Pre-placed CA; grout injected; excellent bond
Pump method: Flexible hose pumps concrete into water; concrete must be self-compacting or of high consistency
Antiwashout admixtures (AWA) used to prevent cement paste from washing out in turbulent water

🏗

Ch 8 · Key Numbers

Max time mix-to-place

2 hr (≤25°C); 1.5 hr (>25°C)

IS 456; no re-tempering allowed

hours

Max free-fall height when placing

1.5 m

Beyond this, use tremie/pump to avoid segregation

Poker vibrator spacing

0.5 – 0.75 m centres

Penetrate 50 mm into previous layer; withdraw at 80–100 mm/min

Transit mixer revolution limit

300 total (70–100 at mixing speed)

IS 4926 RMC limit

revolutions

🏗

Ch 8 · Solved Examples

GATE CE / ESE level

Concrete is mixed at a plant at 8:00 AM on a 30°C day and must be placed by IS 456's transport-time limit. What is the latest permissible placing time?

Approach hint

30°C exceeds 25°C, so the shorter 1.5-hour limit applies.

Ambient temperature = 30°C > 25°C → apply the 1.5-hour limit
Latest placing time = 8:00 AM + 1.5 hr = 9:30 AM

✓ 9:30 AM — beyond this, the concrete must be rejected (no re-tempering with extra water is permitted to "fix" stiffened concrete)

🏗

Ch 8 · Diagrams

Click any diagram to zoom

Fig 13 – Poker vibrator insertion pattern: spaced 0.5–0.75 m centres; penetrates 50 mm into previous layer; withdrawn slowly at 80–100 mm/min. Vibration radius shown as blue circles. Over-vibration → segregation; under-vibration → honeycombing.

🏗

Ch 8 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

Weigh batching is mandatory (per IS 456) for concrete of grade:

Volume batching is permitted only below M20 (nominal mix); M20 and above requires weigh batching ✓

Question 2

Over-vibration of fresh concrete primarily causes:

Over-vibration causes heavy aggregate to sink and cement paste/laitance to rise — the opposite problem to under-vibration (which causes honeycombing/voids) ✓

Question 3

Beyond what free-fall height must concrete be placed via tremie or pump instead of direct pour (IS 456)?

Beyond 1.5 m free-fall, segregation risk becomes significant — tremie pipes or pumps must be used ✓

✨

Ch 9 · Special Concretes — Types, Properties & Applications

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High Strength Concrete (HSC)

Definition: $f_{ck} > 40$ MPa (IS); > 55 MPa (ACI)
Materials: Low w/c (0.25–0.35), silica fume (8–12%), superplasticizer, high-quality aggregates
Strength up to 100–120 MPa achievable in practice; 150+ MPa in laboratory
More brittle than normal concrete; $E_c$ is higher; less creep
Uses: High-rise buildings, bridges, offshore structures, parking garages

High Performance Concrete (HPC)

Concrete designed to achieve high strength AND high durability simultaneously
w/c ≤ 0.35; silica fume; GGBS; fly ash; superplasticizer; well-graded aggregates
Permeability: $k < 10^{-12}$ m/s (100–1000× less permeable than normal concrete)
100-year service life design
Uses: Marine structures, bridges, tunnels, nuclear facilities

Self Compacting Concrete (SCC)

Flows and consolidates under its own weight without vibration; highly flowable, non-segregating.

Test	Principle	Target Value
Slump Flow Test	Cone removed; measure spread diameter	550–850 mm
$T_{500}$ (Flow time)	Time to reach 500 mm spread	2–5 seconds
J-Ring Test	Flow through closely-spaced rebar ring	Δ height ≤ 10 mm (good passing ability)
V-Funnel Test	Time for concrete to drain from V-shaped funnel	6–12 seconds
L-Box Test	Ratio of heights after flow through rebar gate	$H_2/H_1$ ≥ 0.80
U-Box Test	Height difference between two compartments	≤ 30 mm difference
Sieve Segregation Resistance	% passing 5 mm sieve after flow	≤ 15%

Key ingredients: High powder content (> 500 kg/m³), superplasticizer (PCE type), viscosity modifying agent (VMA), low coarse aggregate content
Uses: Congested reinforcement, inaccessible locations, complex formwork, noise-sensitive sites

Fibre Reinforced Concrete (FRC)

Fibre Type	Diameter / Length	Aspect Ratio (l/d)	Properties Enhanced	Uses
Steel fibres (hooked end)	0.25–0.75 mm / 25–60 mm	40–80	Toughness, flexural strength, impact resistance, crack control	Pavements, tunnels, industrial floors, crash barriers
Polypropylene (PP) fibres	Monofilament; 6–50 mm	High	Plastic shrinkage crack control; fire resistance (melt at 165°C → vent pressure)	Slabs, walls, fire-resistant structures
Glass fibres (AR-glass)	10–15 µm dia / variable	High	Tensile strength; lightweight panels	Precast cladding panels (GRC)
Carbon fibres	7–8 µm dia	High	Very high tensile strength; low weight; expensive	Aerospace, structural retrofitting
Natural fibres (jute, sisal)	Variable	–	Low cost; limited strength gain	Low-cost housing, rural construction

Lightweight Concrete (LWC)

Category	Density (kg/m³)	Method	Uses
Lightweight aggregate concrete	1400–1900	Expanded clay (Leca), expanded shale, pumice, perlite, sintered fly ash (Lytag)	Structural elements; reduces dead load
Foamed (aerated) concrete	300–1600	Stable foam mixed into cement slurry; or aluminium powder generates $H_2$ (AAC)	Insulation, void filling, AAC blocks
No-fines concrete	1600–2000	Only CA + cement; no sand; high void content	Drainage walls, drainage base courses

Heavyweight Concrete

Density: 3200–5000+ kg/m³
Aggregates: baryte ($BaSO_4$), magnetite ($Fe_3O_4$), limonite, iron shot
Uses: Nuclear reactor shielding, medical X-ray rooms, counterweights, offshore ballast

Ready Mix Concrete (RMC) vs Site-Mixed Concrete

Aspect	RMC	Site Mixed
Quality control	Excellent (automated plant)	Moderate (human error)
Cost	Higher per m³	Lower for large projects
Suitability	Urban projects; small-medium quantities	Large projects; remote sites
Water addition at site	Not permitted (IS 4926)	Possible but not recommended

Other Special Concretes

Shotcrete (Gunite): Concrete pneumatically projected onto a surface (no formwork). Dry-mix: water added at nozzle, rebound 10–40%. Wet-mix: premixed, pumped, rebound 5–15%. Uses: tunnel linings, slope stabilisation, dam repair
Vacuum Dewatered Concrete: Extra water removed from surface by vacuum mat; reduces w/c by 15–25% → surface strength up by 40–60%; used in industrial floors, pavements, airfield slabs
Roller Compacted Concrete (RCC dams): Zero-slump concrete, thin lifts (150–300 mm), compacted by vibratory rollers; very low cement content; much faster/cheaper than conventional dam concrete
Pervious (Permeable) Concrete: No fines; high void content (15–25%); flow rate 200–750 L/min/m²; compressive strength 3.5–28 MPa; used for stormwater management, parking lots
Polymer Concrete types: PIC (hardened concrete impregnated with monomer, 100–200 MPa), PCC (latex partially replaces water), PC (resin entirely replaces cement — chemical plant floors)
Autoclaved Aerated Concrete (AAC): Al powder + $Ca(OH)_2$ → $H_2$ bubbles create pores; autoclaved at 180°C, 1 MPa → C–S–H converts to tobermorite; density 400–800 kg/m³, strength 2–8 MPa; non-load-bearing walling
Sulphur Concrete: Molten sulphur binder instead of cement+water; very high early strength; excellent acid/chemical resistance; used in chemical plants and (experimentally) lunar/Martian construction

✨

Ch 9 · Formulas & Key Values

Fibre Aspect Ratio

$$ AR = \frac{l}{d} $$

Length ÷ diameter of fibre; typical 40–100

—

Critical Fibre Volume Fraction

$$ V_{f,crit} \approx \frac{f_{mu}}{f_{fu}(1-V_f)} $$

$f_{mu}$ = matrix strength, $f_{fu}$ = fibre strength

—

SCC L-Box passing ratio

$$ H_2/H_1 \geq 0.80 $$

Measures passing ability through congested rebar

—

HPC Permeability

$$ k < 10^{-12}\ \text{m/s} $$

100–1000× less permeable than normal concrete

m/s

✨

Ch 9 · Applied Scenarios

"Which special concrete?" — common ESE descriptive style

A basement raft slab has extremely congested reinforcement with no room to insert a poker vibrator. Which special concrete solves this?

Approach hint

Think of a concrete that consolidates under its own weight.

The problem is inaccessibility for vibration in congested reinforcement
Self Compacting Concrete (SCC) flows and consolidates under its own weight, no vibration needed

✓ Self Compacting Concrete (SCC)

An X-ray room in a hospital needs walls that block radiation without excessive thickness. What type of concrete would you specify?

Approach hint

Radiation shielding needs very high density per unit thickness.

Radiation attenuation improves with mass per unit area
Heavyweight concrete (baryte/magnetite aggregate, 3200–5000+ kg/m³) gives high shielding mass in a compact thickness

✓ Heavyweight concrete using baryte or magnetite aggregate

✨

Ch 9 · Diagrams

Click any diagram to zoom

Fig 14 – SCC workability tests: (a) Slump Flow – spread 550–850 mm, T₅₀₀ = 2–5 s; (b) L-Box – H₂/H₁ ≥ 0.80 measures passing ability through reinforcement; (c) V-Funnel – flow time 6–12 s measures viscosity.

✨

Ch 9 · Quick Quiz

3 questions · tap an option to reveal answer

Question 1

Which special concrete is characterised by a zero-slump mix, thin lifts, and compaction with vibratory rollers?

RCC (used for gravity dams, pavements) is placed at zero slump in thin lifts and compacted with rollers, unlike conventional or self-compacting concrete ✓

Question 2

Autoclaved Aerated Concrete (AAC) develops its pores through:

Aluminium powder reacts with Ca(OH)₂ to release H₂ bubbles, which create the porous structure before autoclaving converts C–S–H to tobermorite ✓

Question 3

For SCC, the target slump-flow spread diameter is:

SCC's slump flow test targets a 550–850 mm spread, with T₅₀₀ (time to reach 500 mm) of 2–5 seconds ✓

📚

Ch 10 · Revision & Practice

IS codes, all formulae, quick-recall tables, mnemonics, PYQ pattern, mini quiz and practice questions

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Complete IS Code Reference for Concrete

IS Code	Year	Subject
IS 456	2000	Plain and Reinforced Concrete – Code of Practice (primary design code)
IS 10262	2019	Concrete Mix Proportioning – Guidelines
IS 516	1959	Methods of Tests for Strength of Concrete
IS 1199	Various Pts	Sampling and Analysis of Concrete (fresh concrete tests)
IS 383	2016	Coarse and Fine Aggregates from Natural Sources
IS 2386	Pts I–VIII	Methods of Test for Aggregates for Concrete
IS 4926	2003	Ready-Mixed Concrete – Code of Practice
IS 7320	1974	Specifications for Concrete Slump Test Apparatus
IS 5816	1999	Split Cylinder Tensile Strength of Concrete
IS 9013	1978	Method of Making, Curing and Determining Compressive Strength of Accelerated Cured Concrete Cubes
IS 9103	1999	Admixtures for Concrete
IS 13311 Pt 1	1992	Non-Destructive Testing – Ultrasonic Pulse Velocity Method
IS 13311 Pt 2	1992	Non-Destructive Testing – Rebound Hammer Method
IS 14977	2001	Assessment of Corrosion in Steel Reinforcement by Half-Cell Potential Method
IS 4991	1968	Criteria for Blast Resistant Design of Structures for Explosions Above Ground
IS 2974	Various Pts	Design and Construction of Machine Foundations
IS 1343	2012	Prestressed Concrete – Code of Practice
IS 3812	2013	Pulverised Fuel Ash (Fly Ash)
IS 12089	2013	Granulated Slag for Portland Slag Cement
IS 15388	2003	Silica Fume

All Key Formulae — Concrete Technology

Target Mean Strength

$$ f'_{ck} = f_{ck} + 1.65\sigma $$

σ by grade band, IS 10262 Table 1

MPa

Cube vs Cylinder

$$ f_{ck,cube} \approx 1.25\,f_{ck,cylinder} $$

—

Modulus of Elasticity

$$ E_c = 5000\sqrt{f_{ck}} $$

IS 456

MPa

Modulus of Rupture

$$ f_r = 0.7\sqrt{f_{ck}} $$

IS 456

MPa

Split Tensile Strength

$$ f_t = \frac{2P}{\pi LD} $$

Brazilian test

MPa

Effective Modulus (creep)

$$ E_{eff} = \frac{E_c}{1+\theta} $$

θ: 2.2 (7d), 1.6 (28d), 1.1 (1yr)

MPa

Design Shrinkage Strain

$$ \varepsilon_{cs} = 0.0003 $$

IS 456

—

Thermal Expansion

$$ \alpha = 10\text{–}11\times10^{-6}/°C $$

Same order as steel

—

Cement Content (mix design)

$$ C = \frac{Water}{w/c} $$

Check against IS 456 minimum

kg/m³

Compaction Factor

$$ CF = \frac{W_{partial}}{W_{full}} $$

Range 0.70–0.95

—

Bulking of Sand

$$ Bulking(\%)=\frac{V_{bulked}-V_{dry}}{V_{dry}}\times100 $$

Zero at 0% and full saturation

Carbonation Depth

$$ d = K_c\sqrt{t} $$

Core acceptance: core×1.25 ≥ 0.85 f_ck

Critical Numerical Values — Master List

Parameter	Value
Min. grade for RCC (mild exposure)	M20 (IS 456)
Max. water fall height (placing)	1.5 m
Max. time from mix to placing (T ≤ 25°C)	2 hours
Max. time from mix to placing (T > 25°C)	1.5 hours
Min. concrete temp. at placing	10°C
Max. concrete temp. at placing	40°C
Min. curing period (OPC)	7 days
Min. curing period (PPC / blended)	10 days
Standard cube size (IS 516)	150 × 150 × 150 mm
Cube loading rate (IS 516)	14 N/mm²/min
Cube strength / Cylinder strength	≈ 1.25
Slump test cone height	300 mm
Slump test base dia / top dia	200 mm / 100 mm
Slump test tamping rod	16 mm dia, 600 mm long; 25 blows/layer, 3 layers
MSA ≤ (minimum member dimension)	1/4 of min. dimension
MSA ≤ (bar spacing)	3/4 × clear spacing between bars
Mixing time (machine mixer)	Min. 2 minutes (IS 456)
Transit mixer max. revolutions	300 total; 70–100 at mixing speed
Min. w/c for complete hydration (theory)	0.23
Min. w/c for complete hydration (practical)	0.36
Unit weight – PCC	24 kN/m³
Unit weight – RCC	25 kN/m³
Poisson's ratio (concrete)	0.1–0.2 (IS 456 uses 0.2)
Thermal coefficient (concrete = steel)	10–12×10⁻⁶/°C
Creep coefficient θ (age 28 days)	1.6
Design shrinkage strain (IS 456)	0.0003
UPV — Excellent concrete	> 4.5 km/s
Corrosion threshold (half-cell)	< −350 mV (90% probability)
Carbonation indicator	Phenolphthalein (pink = alkaline; colourless = carbonated)
SCC slump flow target	550–850 mm
SCC L-box ratio	$H_2/H_1$ ≥ 0.80
Chloride limit (free, IS 456) for steel corrosion	> 0.4% by mass of cement
Phenolphthalein — turning pH	~pH 9.5 (pink above; colourless below)
Hand mixing — extra cement	Add 10% over design
Core acceptance criteria (IS 456)	Core × 1.25 ≥ 0.85 × $f_{ck}$
Standard deviation σ (M20–M25)	4.0 MPa
Standard deviation σ (M30–M50)	5.0 MPa

Mnemonics & Memory Aids

💡 Exposure → Minimum Grade (steps of 5 MPa): Mild=M20, Moderate=M25, Severe=M30, Very Severe=M35, Extreme=M40 — "Men Must Suffer Very Extreme"

Workability Tests (increasing sensitivity for stiff mixes): Slump → Compaction Factor → Vee-Bee → Flow Table — "Slippery Concrete Vibrates Fast"

Cover (mm) by exposure: Mild=20, Moderate=30, Severe=45, Very Severe=50, Extreme=75 (not uniform steps; severe jumps to 45)

Standard deviation σ for target mean strength: M10–M15: 3.5 | M20–M25: 4.0 | M30–M50: 5.0 | M55+: 6.0

Which special concrete for which problem:
No vibration access → SCC · High strength + durability → HPC + silica fume · Slope/tunnel lining → Shotcrete · Pavement/industrial floor → Vacuum dewatered / FRC · Thermal insulation → AAC / LWC · Radiation shielding → Heavyweight concrete (baryte) · Dam (fast construction) → Roller Compacted Concrete (RCC)

GATE / ESE Previous Year Question Pattern

Topic	Exam Frequency	Question Type
Target mean strength formula: $f'_{ck} = f_{ck} + 1.65\sigma$	Every year (GATE)	NAT
Modulus of elasticity: $E_c = 5000\sqrt{f_{ck}}$	Very high	NAT / MCQ
Mix design water content / cement content calculation	High (GATE)	NAT
Workability test identification and ranges	High (SSC JE / ESE)	MCQ
Slump test types (true / shear / collapse)	Moderate	MCQ
Cover requirements by exposure	High (ESE)	MCQ
Durability mechanisms (ASR, carbonation, sulphate)	High (GATE / ESE)	MCQ / Descriptive
Creep coefficient and effective modulus	Moderate (GATE)	NAT
NDT — UPV quality table and rebound hammer	High (SSC JE / ESE)	MCQ
Core test acceptance criteria	Moderate	NAT / MCQ
Special concretes — SCC, FRC, RCC identification	Moderate (ESE)	MCQ
W/C ratio vs strength relationship	High (all exams)	MCQ / NAT
Formwork stripping times	Moderate (SSC JE)	MCQ
Bulking of sand percentage and mechanism	Moderate	MCQ
Half-cell potential corrosion threshold	Moderate (GATE)	MCQ / NAT

Mini Quiz

For M40 concrete (σ=5.0 MPa), what is the target mean strength?

$f'_{ck} = 40 + 1.65(5.0) = 40 + 8.25 = 48.25$ MPa ✓

Which workability test is most sensitive for very stiff, low-slump mixes?

CF is more sensitive than slump for very stiff mixes, where the slump reading barely changes between mixes ✓

What is the nominal cover for "Mild" exposure per IS 456?

Mild exposure requires 20 mm nominal cover, the smallest in the IS 456 table ✓

The IS 456 design value for concrete's drying shrinkage strain is:

ε_cs = 0.0003 (IS 456 Cl. 6.2.4), a frequently tested direct-recall value ✓

A UPV reading of 2.5 km/s classifies concrete quality as:

2.0–3.0 km/s falls in the "Doubtful" band, warranting further investigation ✓

Practice Questions

EasyState the practical minimum w/c ratio for complete hydration of cement, and why it differs from the theoretical minimum.

Practical minimum is 0.36 (vs theoretical 0.23) because it must also supply the gel water needed for the C–S–H structure, not just the chemically-combined water.

EasyWhy is nominal mix prohibited above M25?

Nominal mix uses fixed volumetric proportions without statistical strength control, which cannot reliably guarantee the higher, more variable strength requirements of M30+ — IS 456 mandates the statistically-designed IS 10262 mix instead.

MediumAn M30 mix (σ=5.0 MPa) uses water content 200 kg/m³ with w/c=0.42. Find the target mean strength and cement content.

f'ck = 30 + 1.65(5.0) = 38.25 MPa. Cement content = 200/0.42 ≈ 476 kg/m³ (comfortably above the IS 456 minimum of 320 kg/m³ for severe exposure).

MediumA rebound hammer gives R=35 and UPV gives 3.2 km/s on the same structure. What do these two readings suggest individually, and why would you use both together?

R=35 → "Good" surface hardness; UPV=3.2 km/s → "Medium" internal quality. Using both together (combined method) cross-checks surface condition against internal homogeneity, catching cases where a good surface hides internal voids or vice versa — accuracy improves from ±25% to ±15-20%.

HardExplain why a low w/c ratio simultaneously improves strength, durability AND reduces shrinkage/bleeding, tracing the mechanism back to capillary porosity.

Lower w/c means less excess (unreacted) water beyond what hydration consumes, so fewer/smaller capillary pores remain after hydration (pore refinement). Fewer capillary pores directly increases strength (denser matrix), reduces permeability/durability risk (less pathway for CO2, Cl-, SO4), and reduces bleeding (less free water to rise) and drying shrinkage (less water to lose on drying) — all four properties trace back to the same capillary-porosity mechanism.

Criterion	Requirement
Mean of any group of 4 consecutive results	≥ \(f_{ck}\) + 0.825 × s (s = established SD) or ≥ \(f_{ck}\) + 3 MPa, whichever is greater
Any individual test result	≥ \(f_{ck}\) − 3 MPa

Parameter	Details
Source of sulphates	Soil (pyrite oxidation), groundwater, seawater, industrial effluent
Reaction with \(C_3A\) hydrate	\(Ca(OH)_2 + CaSO_4 + 2H_2O \rightarrow CaSO_4\cdot2H_2O\) (gypsum, expansive)
Reaction with C–S–H	\(CaSO_4\) + C–S–H + \(H_2O \rightarrow CaCO_3\) + silica gel (decalcification)
Secondary ettringite	Gypsum + \(C_3A\) hydrate → Ettringite (3CaO·\(Al_2O_3\)·3\(CaSO_4\)·32\(H_2O\)) — very expansive
Most aggressive form	\(MgSO_4\) — attacks both \(C_3A\) and C–S–H gel
Visual symptoms	White deposits, cracking, spalling, softening, loss of section
Prevention	SRC (\(C_3A < 5\%\)); low w/c; PPC / GGBS; dense cover; membranes

Topic	Exam Frequency	Question Type
Target mean strength formula: \(f'_{ck} = f_{ck} + 1.65\sigma\)	Every year (GATE)	NAT
Modulus of elasticity: \(E_c = 5000\sqrt{f_{ck}}\)	Very high	NAT / MCQ
Mix design water content / cement content calculation	High (GATE)	NAT
Workability test identification and ranges	High (SSC JE / ESE)	MCQ
Slump test types (true / shear / collapse)	Moderate	MCQ
Cover requirements by exposure	High (ESE)	MCQ
Durability mechanisms (ASR, carbonation, sulphate)	High (GATE / ESE)	MCQ / Descriptive
Creep coefficient and effective modulus	Moderate (GATE)	NAT
NDT — UPV quality table and rebound hammer	High (SSC JE / ESE)	MCQ
Core test acceptance criteria	Moderate	NAT / MCQ
Special concretes — SCC, FRC, RCC identification	Moderate (ESE)	MCQ
W/C ratio vs strength relationship	High (all exams)	MCQ / NAT
Formwork stripping times	Moderate (SSC JE)	MCQ
Bulking of sand percentage and mechanism	Moderate	MCQ
Half-cell potential corrosion threshold	Moderate (GATE)	MCQ / NAT