BE Civil Engineering (IOE, TU) Concrete Technology and Masonry Structures (IOE, CE 605) Question Paper 2076 Nepal

Step 1 — Target mean strength

$$f_{target} = f_{ck} + 1.65\,s = 30 + 1.65(5.0) = 30 + 8.25 = 38.25\ \text{N/mm}^2$$

Step 2 — Selection of w/c ratio

The w/c from strength considerations is taken as 0.45 (given). This is lower than the durability limit of 0.50 for moderate exposure, so adopt w/c = 0.45 (governs).

Step 3 — Water content

Base water for 50 mm slump (20 mm aggregate) = 186 kg/m³. Required slump = 75 mm, i.e. 25 mm extra ⇒ +3% water.

$$W = 186 \times 1.03 = 191.58 \approx \mathbf{191.6\ kg/m^3}$$

Step 4 — Cement content

$$C = \frac{W}{(w/c)} = \frac{191.58}{0.45} = 425.7\ \text{kg/m}^3$$

Check minimum cement for moderate exposure = 300 kg/m³. Since $425.7 > 300$, OK. Adopt C = 425.7 kg/m³.

Step 5 — Proportion of coarse and fine aggregate volumes

Volume of coarse aggregate per unit total aggregate volume = 0.62 ⇒ fine aggregate fraction = $1 - 0.62 = 0.38$.

Step 6 — Absolute volume calculation (per 1 m³)

Total volume = 1 m³; entrapped air = 2% = 0.02 m³.

Volume of cement:

$$V_c = \frac{C}{G_c \times 1000} = \frac{425.7}{3.15 \times 1000} = 0.1351\ \text{m}^3$$

Volume of water:

$$V_w = \frac{191.58}{1 \times 1000} = 0.1916\ \text{m}^3$$

Volume of all aggregate (saturated surface dry):

$$V_{agg} = 1 - (V_c + V_w + V_{air}) = 1 - (0.1351 + 0.1916 + 0.02) = 1 - 0.3467 = 0.6533\ \text{m}^3$$

Step 7 — Mass of coarse aggregate

$$M_{CA} = V_{agg} \times 0.62 \times G_{CA} \times 1000 = 0.6533 \times 0.62 \times 2.70 \times 1000$$ $$= 0.6533 \times 0.62 \times 2700 = 1093.6\ \text{kg/m}^3$$

Step 8 — Mass of fine aggregate

$$M_{FA} = V_{agg} \times 0.38 \times G_{FA} \times 1000 = 0.6533 \times 0.38 \times 2.65 \times 1000$$ $$= 0.6533 \times 0.38 \times 2650 = 657.9\ \text{kg/m}^3$$

Step 9 — Final mix proportions (per m³, SSD basis)

By mass the ratio C : FA : CA = $1 : 1.55 : 2.57$ at w/c = 0.45.

Final answer: Cement 425.7 kg/m³, Water 191.6 kg/m³, Fine aggregate 657.9 kg/m³, Coarse aggregate 1093.6 kg/m³.

Step 1 — Effective height and slenderness ratio

With the wall laterally restrained (held in position) at top and bottom, effective height:

$$h_{eff} = 0.75 H = 0.75 \times 3000 = 2250\ \text{mm}$$

Slenderness ratio (SR) for a wall is based on effective height (height governs here, length large):

$$SR = \frac{h_{eff}}{t} = \frac{2250}{230} = 9.78$$

(a) Slenderness ratio = 9.78 (well below the limit of 27 for load-bearing walls — OK).

Step 2 — Stress reduction factor $k_s$ (interpolation)

Given SR = 8 → 0.95 and SR = 10 → 0.89.

$$k_s = 0.95 + (0.89 - 0.95)\times\frac{9.78 - 8}{10 - 8} = 0.95 + (-0.06)\times\frac{1.78}{2}$$ $$k_s = 0.95 - 0.06 \times 0.89 = 0.95 - 0.0534 = 0.8966 \approx \mathbf{0.897}$$

(b) Stress reduction factor $k_s = 0.897$.

Step 3 — Area eccentricity factor

Since eccentricity = 0, the eccentricity factor $k_p = 1.0$. (No reduction for eccentric loading.)

Step 4 — Permissible compressive stress

$$f_{perm} = f_b \times k_s \times k_p = 0.50 \times 0.897 \times 1.0 = 0.4485\ \text{N/mm}^2$$

Step 5 — Permissible load per metre run

Cross-sectional area per metre run:

$$A = t \times L = 230\ \text{mm} \times 1000\ \text{mm} = 230{,}000\ \text{mm}^2$$

Permissible axial load:

$$P = f_{perm} \times A = 0.4485 \times 230{,}000 = 103{,}155\ \text{N} = 103.2\ \text{kN}$$

(c) Permissible axial load per metre run = 103.2 kN/m.

Summary: SR = 9.78, $k_s = 0.897$, permissible load $\approx \mathbf{103.2\ kN/m}$.

(a) Hydration of Portland cement

When water is added to cement the anhydrous compounds react exothermically to form hydration products, chiefly calcium silicate hydrate (C-S-H gel) and calcium hydroxide (CH). The C-S-H gel is the main binding phase responsible for strength.

The four principal Bogue compounds:

1. Tricalcium silicate (C₃S, alite) — hydrates rapidly; responsible for early strength (first 7–28 days) and liberates a large amount of heat.
2. Dicalcium silicate (C₂S, belite) — hydrates slowly; contributes to later-age strength (beyond 28 days) and gives off comparatively little heat.
3. Tricalcium aluminate (C₃A) — hydrates almost instantly; gives very high early heat and rapid setting (gypsum is added to retard it). Contributes little to strength and is vulnerable to sulphate attack.
4. Tetracalcium alumino-ferrite (C₄AF) — hydrates moderately fast, gives moderate heat, contributes little to strength but improves sulphate resistance and gives cement its grey colour.

Low-heat cement minimises C₃S and C₃A and raises C₂S.

(b) Total heat of hydration

$$H = \sum (\text{fraction} \times \text{specific heat})$$ $$H = 250.0 + 57.2 + 77.94 + 33.6 = 418.7\ \text{J/g}$$

Total heat of hydration ≈ 418.7 J/g (≈ 419 kJ/kg).

Comment: Ordinary Portland cement typically liberates about 400–500 J/g. The value here (≈419 J/g) is typical of OPC and is on the higher side for mass concrete. The relatively high C₃S (50%) and C₃A (9%) make this cement prone to a large early temperature rise, risking thermal cracking in a large pour. For mass concreting it would be preferable to use low-heat or Portland-pozzolana cement (lower C₃S, lower C₃A, higher C₂S), partial cement replacement by fly ash/GGBS, and pre-cooling of ingredients.

(a) Comparison of rebound hammer and UPV

The two are often combined (SonReb method) to improve strength estimation.

(b) Pulse velocity calculation

Path length $L = 350\ \text{mm} = 0.350\ \text{m}$, transit time $t = 58.5\ \mu s = 58.5 \times 10^{-6}\ \text{s}$.

$$V = \frac{L}{t} = \frac{0.350}{58.5 \times 10^{-6}} = 5982.9\ \text{m/s} = \mathbf{5.98\ km/s}$$

Since $5.98 > 4.5\ \text{km/s}$, the concrete quality is excellent.

Suspect zone — transit time for V = 3.10 km/s:

$$t = \frac{L}{V} = \frac{0.350}{3100} = 1.129 \times 10^{-4}\ \text{s} = \mathbf{112.9\ \mu s}$$

The suspect-zone velocity (3.10 km/s) falls in the medium/doubtful band, and the transit time nearly doubles (112.9 µs vs 58.5 µs), indicating likely internal voids or microcracking that warrant further investigation.

Step 1 — Slenderness ratio (column, least dimension)

$$SR = \frac{h_{eff}}{\text{least dimension}} = \frac{2800}{460} = 6.09$$

Step 2 — Stress reduction factor $k_s$

SR = 6.09 is just above 6. Interpolate between SR 6 → 1.00 and SR 8 → 0.95:

$$k_s = 1.00 + (0.95 - 1.00)\times\frac{6.09 - 6}{8 - 6} = 1.00 - 0.05 \times \frac{0.09}{2}$$ $$k_s = 1.00 - 0.05 \times 0.045 = 1.00 - 0.00225 = 0.9978 \approx \mathbf{0.998}$$

Step 3 — Area reduction factor (small section check)

Sectional area:

$$A = 0.460 \times 0.460 = 0.2116\ \text{m}^2$$

Since $A = 0.2116\ \text{m}^2 > 0.2\ \text{m}^2$, the small-area reduction does not apply. Area factor $k_a = 1.0$.

Step 4 — Eccentricity factor

Load is axial ⇒ $k_p = 1.0$.

Step 5 — Permissible compressive stress

$$f_{perm} = f_b \times k_s \times k_a \times k_p = 0.70 \times 0.998 \times 1.0 \times 1.0 = 0.6985\ \text{N/mm}^2$$

Step 6 — Safe axial load

Area in mm² = $460 \times 460 = 211{,}600\ \text{mm}^2$.

$$P = f_{perm} \times A = 0.6985 \times 211{,}600 = 147{,}803\ \text{N} = 147.8\ \text{kN}$$

Safe axial load ≈ 147.8 kN.

Workability is the property of fresh concrete that determines the ease with which it can be mixed, transported, placed, compacted and finished without segregation or bleeding, for a given amount of work. It is closely linked to the consistency and the energy required for full compaction.

Factors affecting workability:

• Water content / water–cement ratio
• Aggregate properties: size, shape, texture, grading
• Aggregate–cement ratio (mix proportions)
• Use of admixtures (plasticizers/superplasticizers)
• Fineness of cement and use of supplementary cementitious materials
• Time and ambient temperature

Slump test:

• Apparatus: Slump cone (frustum: bottom dia 200 mm, top dia 100 mm, height 300 mm), tamping rod (16 mm dia, 600 mm long), base plate.
• Procedure: Place the cone on a level surface; fill in 4 layers, each tamped 25 times; strike off the top; lift the cone vertically; measure the vertical subsidence (slump) of the concrete.
• Types of slump: (i) True slump – mass subsides evenly (valid result); (ii) Shear slump – top portion shears off and slips sideways (test should be repeated); (iii) Collapse slump – concrete collapses completely (very wet/harsh mix).

Unsuitable situation: The slump test is unsuitable for very dry/stiff mixes (low workability, e.g. zero-slump concrete) and for very wet/collapse mixes; for such concrete the compaction factor or Vee-Bee consistometer test is preferred.

Classification of admixtures:

• Chemical admixtures: plasticizers (water reducers), superplasticizers (high-range water reducers), retarders, accelerators, air-entraining agents, water-proofing/permeability-reducing admixtures.
• Mineral (supplementary cementitious) admixtures: fly ash, GGBS, silica fume, rice husk ash, metakaolin.

(i) Superplasticizers (high-range water reducers): Mechanism: They are surface-active polymers (sulphonated naphthalene/melamine formaldehyde or polycarboxylate ethers) that adsorb onto cement particles and impart a strong negative charge or steric repulsion, deflocculating the cement grains. The released entrapped water greatly increases fluidity. Uses: (a) produce flowing/self-compacting concrete at the same w/c; (b) achieve very low w/c (high strength) at the same workability; reduce water by 15–30%.

(ii) Air-entraining agents: Mechanism: Surfactants that stabilise millions of tiny, well-distributed air bubbles (≈10–300 µm) in the paste. These bubbles act as pressure-relief voids for water expanding on freezing. Uses: Greatly improve freeze–thaw durability and resistance to de-icing salts; also improve workability and reduce bleeding/segregation.

Adverse effect of superplasticizer overdose: Severe segregation/bleeding and excessive set retardation (delayed setting), and possible loss of cohesion of the mix.

Durability is the ability of concrete to resist weathering action, chemical attack and abrasion while retaining its desired engineering properties over its service life. It is governed largely by permeability, which depends on the w/c ratio, compaction and curing.

(a) Sulphate attack Mechanism: Sulphates (from soil, groundwater, seawater) react with hydrated cement compounds. Sulphate ions react with calcium hydroxide and with hydrated calcium aluminate (C₃A) to form gypsum and ettringite (calcium sulphoaluminate), which are expansive. The expansion causes cracking, spalling and progressive disintegration of concrete. Preventive measures:

1. Use sulphate-resisting Portland cement (SRC) with low C₃A content, or PPC/PSC.
2. Use low w/c ratio and dense, well-compacted concrete (low permeability); adequate cover and curing.

(b) Corrosion of reinforcement Mechanism: The high alkalinity (pH ≈ 13) of concrete forms a passive protective film on steel. Carbonation (CO₂ lowering pH) or chloride ingress destroys this film. An electrochemical cell forms (anode/cathode); iron oxidises to rust, which occupies a larger volume, generating internal pressure that cracks and spalls the cover. Preventive measures:

1. Provide adequate cover and low-permeability concrete (low w/c, good compaction and curing).
2. Limit chloride content; use corrosion-inhibiting admixtures, coated (epoxy/galvanised) bars, or protective coatings/cathodic protection.

Step 1 — Cube cross-sectional area

$$A = 150 \times 150 = 22{,}500\ \text{mm}^2$$

Step 2 — Individual cube strengths ($f = \dfrac{P}{A}$, with $P$ in N):

Step 3 — Mean strength

$$\bar{f} = \frac{32.00 + 30.67 + 34.00}{3} = \frac{96.67}{3} = 32.22\ \text{N/mm}^2$$

Step 4 — Acceptance checks (M25, $f_{ck}=25$, $s = 4$)

Mean criterion:

$$f_{ck} + 0.825\,s = 25 + 0.825(4) = 25 + 3.30 = 28.30\ \text{N/mm}^2$$

Mean = 32.22 N/mm² $\ge$ 28.30 N/mm² → satisfied.

Individual criterion:

$$f_{ck} - 3 = 25 - 3 = 22\ \text{N/mm}^2$$

Lowest individual = 30.67 N/mm² $\ge$ 22 N/mm² → satisfied.

Conclusion: Both criteria are met, so the concrete is acceptable as M25. (The mean of 32.22 N/mm² is also close to the target mean strength of 33 N/mm², confirming satisfactory quality control.)

(i) Self-Compacting Concrete (SCC) Definition/principle: A highly flowable, non-segregating concrete that spreads and fills formwork and encapsulates reinforcement under its own weight without any vibration. It balances high deformability (flowability) with adequate segregation resistance (viscosity). Key constituents: High powder/fines content, high-range water reducer (polycarboxylate superplasticizer), often a viscosity-modifying agent (VMA), and a limited coarse-aggregate content. Tested by slump-flow, V-funnel and L-box. Application: Heavily reinforced/congested sections, complex shapes, and pours where vibration is difficult (e.g. deep beams, columns, tunnel linings).

(ii) Fibre-Reinforced Concrete (FRC) Definition/principle: Concrete containing discrete, uniformly distributed fibres (steel, glass, polypropylene, etc.) that bridge cracks, improving tensile strength, ductility, toughness, impact and fatigue resistance, and controlling shrinkage cracking. Key constituents: Normal concrete plus fibres (volume fraction typically 0.5–2%) characterised by aspect ratio (length/diameter). Application: Industrial floors and pavements, tunnel linings (shotcrete), bridge decks, and crack-control in slabs.

(iii) High-Performance Concrete (HPC) Definition/principle: Concrete engineered to give superior performance in strength and/or durability beyond ordinary concrete — high strength, low permeability, long service life. Achieved through a very low w/c ratio with superplasticizers and supplementary cementitious materials (silica fume, fly ash). Key constituents: Low w/c (often < 0.35), high-range water reducer, silica fume/fly ash, well-graded quality aggregates. Application: High-rise columns, long-span bridges, marine and aggressive-exposure structures.

(Any two of the above earn full marks.)

(a) Desirable properties of good building bricks

• Uniform size, shape and sharp, well-defined edges
• Uniform deep red/copper colour, well burnt (not over- or under-burnt)
• Sufficient compressive strength (first-class ≥ 10.5 N/mm² for IOE/Nepali practice, min ~7 N/mm² as per IS)
• Low water absorption (≤ 20% for first-class by 24-hour immersion)
• Free from cracks, flaws, stones and lumps of lime
• Should give a clear metallic ringing sound when struck
• Should not show efflorescence; adequate hardness (no scratch by fingernail)

Water absorption = the increase in mass when a dry brick is immersed in water for 24 h, expressed as a percentage of the dry mass; it indicates porosity and durability.

Efflorescence = the deposit of white salts on the brick surface when soluble salts in the brick migrate to the surface and crystallise on drying; tested by repeated wetting/drying and rated nil/slight/moderate/heavy.

(b) Water absorption calculation

Dry mass $M_1 = 3120\ \text{g}$, saturated mass $M_2 = 3556\ \text{g}$.

$$\text{Water absorption} = \frac{M_2 - M_1}{M_1}\times 100 = \frac{3556 - 3120}{3120}\times 100$$ $$= \frac{436}{3120}\times 100 = 13.97\% \approx \mathbf{14.0\%}$$

Comment: Since 14.0% < 20%, the water absorption is within the permissible limit, so the brick satisfies the first-class brick requirement for water absorption.