BE Civil Engineering (IOE, TU) Concrete Technology and Masonry Structures (IOE, CE 605) Question Paper 2079 Nepal

Step 1 — Target mean strength $f_{ck}'$

$$f_{ck}' = f_{ck} + 1.65\,s = 30 + 1.65 \times 5.0 = 30 + 8.25 = \mathbf{38.25\ \text{N/mm}^2}$$

Step 2 — Free water–cement ratio (w/c)

For M30 and moderate exposure, from the strength–(w/c) relationship for 43 grade OPC, a free w/c of about 0.45 gives the required target mean strength of 38.25 N/mm². The maximum permissible w/c for moderate exposure (IS 456) is 0.50, so adopt w/c = 0.45 (0.45 < 0.50, OK).

Step 3 — Free water content

Base water for 20 mm aggregate at 50 mm slump = 186 kg/m³.

Slump correction: required slump = 75 mm, i.e. (75 − 50)/25 = 1 step of 25 mm $\Rightarrow +3\%$.

$$W = 186 \times (1 + 0.03) = 186 \times 1.03 = \mathbf{191.6\ \text{kg/m}^3}$$

Step 4 — Cement content

$$C = \frac{W}{w/c} = \frac{191.6}{0.45} = \mathbf{425.7\ \text{kg/m}^3}$$

Minimum cement for moderate exposure = 300 kg/m³ < 425.7 kg/m³ → OK.

Step 5 — Proportion of volume of coarse and fine aggregate

Volume of coarse aggregate per unit volume of total aggregate (Zone II, 20 mm) = 0.62.

For a pumpable/RCC column the table value may be retained as 0.62 (no adjustment for w/c here since w/c ≈ 0.45 is close to the reference 0.50; a small +0.01 correction is within tolerance and is neglected).

$$V_{CA} = 0.62, \qquad V_{FA} = 1 - 0.62 = 0.38$$

Step 6 — Mix calculation by absolute volume (per 1 m³)

Total volume = 1 m³; assume entrapped air = 2% = 0.02 m³ for 20 mm aggregate.

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:

$$V_w = \frac{191.6}{1000} = 0.1916\ \text{m}^3$$

Volume of all aggregate (solid):

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

Step 7 — Mass of coarse and fine aggregate

Coarse aggregate:

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

Fine aggregate:

$$FA = V_{agg} \times V_{FA} \times G_{FA} \times 1000 = 0.6533 \times 0.38 \times 2.65 \times 1000 = \mathbf{657.8\ \text{kg/m}^3}$$

Step 8 — Final mix proportions (per m³, by mass)

Final mix proportion (C : FA : CA) = 1 : 1.55 : 2.57, w/c = 0.45.

Trial batches must follow to confirm workability and 28-day strength.

Given: thickness $t = 230$ mm, height $H = 3.0$ m, axial load $P = 90$ kN/m, $f_b = 0.96$ N/mm².

Step 1 — Effective height and effective thickness

The wall is laterally supported top and bottom by floor/roof: effective height $h_{eff} = 0.75H$ for full restraint (slab continuous), but for a slab simply resting, IS 1905 gives $h_{eff} = 1.0H$. Taking the common design value of full restraint:

$$h_{eff} = 0.75 \times 3.0 = 2.25\ \text{m} = 2250\ \text{mm}$$ $$t_{eff} = t = 230\ \text{mm (solid wall)}$$

Step 2 — Slenderness ratio (SR)

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

This is well below the maximum of 27 for load-bearing walls → OK.

Step 3 — Stress reduction factor $k_s$

From IS 1905 Table (SR vs $k_s$, eccentricity e/t = 0):

• SR = 8 → $k_s = 1.00$
• SR = 10 → $k_s = 0.97$

Interpolating at SR = 9.78:

$$k_s = 1.00 - \frac{(9.78-8)}{(10-8)}(1.00-0.97) = 1.00 - \frac{1.78}{2}(0.03) = 1.00 - 0.0267 = \mathbf{0.973}$$

Step 4 — Permissible compressive stress

$$f_{perm} = f_b \times k_s \times k_a \times k_p = 0.96 \times 0.973 \times 1.0 \times 1.0 = \mathbf{0.934\ \text{N/mm}^2}$$

Step 5 — Actual stress in the wall

Per metre run, area of cross-section $A = 1000 \times 230 = 230000\ \text{mm}^2$.

$$f_{actual} = \frac{P}{A} = \frac{90 \times 10^3\ \text{N}}{230000\ \text{mm}^2} = \mathbf{0.391\ \text{N/mm}^2}$$

Step 6 — Safety check

$$f_{actual} = 0.391\ \text{N/mm}^2 < f_{perm} = 0.934\ \text{N/mm}^2$$

The wall is SAFE in axial compression. Utilisation = 0.391/0.934 ≈ 42 %, so the section has a large reserve; thickness could be optimised but is governed by minimum-thickness/practical requirements.

Part 0 — Factors affecting compressive strength of hardened concrete

1. Water–cement ratio — the single most important factor; strength falls as w/c rises (Abrams' law).
2. Degree of compaction — voids drastically reduce strength (≈5–6 % strength loss per 1 % voids).
3. Cement type and content; quality of aggregate (shape, texture, grading, strength of parent rock).
4. Curing (moisture and temperature) and age — strength increases with continued hydration.
5. Admixtures, transition-zone (ITZ) quality, and testing variables (specimen shape/size, rate of loading, capping, moisture state).

Part (a) — Cube strengths and acceptance

Cube area $A = 150 \times 150 = 22500\ \text{mm}^2$.

$$f_1 = \frac{565\times10^3}{22500} = 25.11\ \text{N/mm}^2$$ $$f_2 = \frac{590\times10^3}{22500} = 26.22\ \text{N/mm}^2$$ $$f_3 = \frac{548\times10^3}{22500} = 24.36\ \text{N/mm}^2$$

Mean strength:

$$\bar f = \frac{25.11 + 26.22 + 24.36}{3} = \frac{75.69}{3} = \mathbf{25.23\ \text{N/mm}^2}$$

Acceptance check (M25, $f_{ck}=25$):

• Individual minimum: $f_{ck} - 4 = 25 - 4 = 21\ \text{N/mm}^2$. Lowest cube = 24.36 N/mm² > 21 → OK.
• Mean minimum: $f_{ck} + 0.825 s = 25 + 0.825\times4 = 25 + 3.30 = 28.30\ \text{N/mm}^2$.

Mean = 25.23 N/mm² < 28.30 N/mm² → the mean criterion is NOT satisfied.

Conclusion: Although every individual result exceeds the lower limit, the sample mean falls short of $f_{ck}+0.825s$. The batch does not meet the statistical acceptance criterion and the concrete in question is liable to rejection / further investigation (core tests, load test).

Part (b) — Cylinder strength estimate

Using cylinder/cube ratio ≈ 0.80:

$$f_{cyl} = 0.80 \times 30 = \mathbf{24\ \text{N/mm}^2}$$

The cylinder strength is lower because of its greater height-to-diameter ratio (less platen confinement / end-restraint effect than a cube).

(a) Classification of chemical admixtures (IS 9103 / ASTM C494 types):

1. Water-reducing (plasticizers, Type A): disperse cement flocs (electrostatic/steric repulsion), giving the same workability at lower water → higher strength and durability. Use: general structural concrete.
2. Retarders (Type B): delay setting (e.g., sugar, lignosulphonates) by slowing C₃A/C₃S hydration. Use: hot-weather concreting, large pours, ready-mix transport.
3. Accelerators (Type C): speed up setting/early strength (e.g., CaCl₂ for plain concrete, non-chloride for RCC). Use: cold-weather, repair, early formwork removal.
4. Air-entraining agents: create stable micro air bubbles for freeze–thaw resistance and workability.
5. Superplasticizers (Type F/G): high-range water reducers (15–30 % water reduction).

(Any three classes described earns full marks for this part.)

(b) Superplasticizer (high-range water reducer)

A superplasticizer is an admixture that produces a large reduction in mixing water (15–30 %) without loss of workability, by strong dispersion of cement particles.

• Constant w/c → more workability: keep water and cement fixed, add SP → flowing/self-levelling concrete (high slump) for congested reinforcement or pumping.
• Constant workability → more strength: keep slump fixed but cut water (and keep cement) → lower w/c → denser paste → higher strength and durability.

Two main chemical families: (i) Sulphonated naphthalene formaldehyde (SNF) and sulphonated melamine formaldehyde (SMF) condensates (older, electrostatic action); (ii) Polycarboxylic ether (PCE) polymers (modern, steric + electrostatic, longer slump retention).

(c) Durability

Durability is the ability of concrete to resist weathering action, chemical attack and abrasion while retaining its desired engineering properties (serviceability) over its design life with minimum maintenance.

(Any four mechanisms with measures suffice.)

Given: $P = 320$ kN, $f_b = 1.10$ N/mm², $h_{eff} = 2.4$ m.

Step 1 — First trial size (ignore $k_a$, $k_s$)

Required area ≈ $P/f_b = \dfrac{320\times10^3}{1.10} = 290909\ \text{mm}^2 = 0.291\ \text{m}^2$.

Try a square of side 460 mm (4 half-bricks): $A = 460\times460 = 211600\ \text{mm}^2 = 0.2116\ \text{m}^2$. Side 345 mm gives 0.119 m² (too small once factors applied). Start the check with 460 mm × 460 mm.

Step 2 — Slenderness ratio and $k_s$

$$SR = \frac{h_{eff}}{t} = \frac{2400}{460} = 5.22 \;(<6)$$

For SR ≤ 6, $k_s = 1.0$ (no slenderness reduction).

Step 3 — Area reduction factor $k_a$

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

Step 4 — Permissible stress and capacity

$$f_{perm} = f_b \, k_s \, k_a = 1.10 \times 1.0 \times 1.0 = 1.10\ \text{N/mm}^2$$ $$P_{cap} = f_{perm}\times A = 1.10 \times 211600 = 232760\ \text{N} = 232.8\ \text{kN}$$

$P_{cap} = 232.8$ kN < 320 kN → unsafe. Increase the section.

Step 5 — Next trial: 575 mm × 575 mm (5 half-bricks)

$$A = 575\times575 = 330625\ \text{mm}^2 = 0.3306\ \text{m}^2 \;(>0.2\ \text{m}^2 \Rightarrow k_a=1.0)$$ $$SR = \frac{2400}{575} = 4.17 < 6 \Rightarrow k_s = 1.0$$ $$P_{cap} = 1.10 \times 330625 = 363688\ \text{N} = \mathbf{363.7\ \text{kN}}$$

$P_{cap} = 363.7$ kN > 320 kN → SAFE.

Step 6 — Result

Adopt a 575 mm × 575 mm square masonry column. Utilisation = 320/363.7 ≈ 88 %, an efficient design.

(Note: the $k_a = 0.7 + 1.5A$ rule is shown for completeness; here every adequate trial has $A>0.2\ \text{m}^2$, so $k_a$ stays 1.0. A 460 mm column would only reach $k_a$-territory if $A<0.2\ \text{m}^2$, which it is not.)

(a) Bogue compounds (with abbreviations):

• Early strength → C₃S.
• Ultimate (long-term) strength → C₂S.

(b) Fineness of cement

Fineness is the measure of the particle size / specific surface area of cement (expressed as surface area in m²/kg by the Blaine air-permeability test, or as residue on a 90-micron sieve).

Effect of increased fineness:

• Faster hydration — more surface area exposed to water → quicker reaction.
• Higher early strength and better workability/cohesion of paste.
• Greater (and faster) heat of hydration, increasing risk of thermal/shrinkage cracking in mass concrete.
• Increased water demand and somewhat greater drying shrinkage; also more prone to deterioration if stored (rapid aeration).

(a) Workability

Workability is the property of freshly mixed concrete that determines the ease and homogeneity with which it can be mixed, placed, compacted and finished without segregation or bleeding.

(Any three with ranges earn full marks.)

(b) Compacting factor calculation

$$\text{Compacting factor} = \frac{\text{weight of partially compacted concrete}}{\text{weight of fully compacted concrete}} = \frac{9.8}{11.2} = \mathbf{0.875}$$

Comment: A compacting factor of about 0.85–0.92 corresponds to medium workability. The value 0.875 indicates a mix of medium workability suitable for normally reinforced sections compacted by vibration. (Low workability ≈ 0.78; high ≈ 0.95.)

Rebound (Schmidt) hammer test

A spring-loaded mass is released against a plunger held on the concrete surface; the rebound number (R) depends on the surface hardness, which correlates with compressive strength. It is quick and cheap but assesses only the surface layer and needs calibration; results are affected by surface finish, moisture, carbonation and aggregate type. Used for uniformity assessment and comparative strength estimation.

Ultrasonic pulse velocity (UPV) test

An ultrasonic pulse (≈ 50–60 kHz) is sent through the concrete between a transmitter and receiver; the transit time is measured and velocity = path length / time. Higher velocity → denser, sounder, more homogeneous concrete; it detects voids, cracks and assesses uniformity through the full depth of the member.

Calculation

$$V = \frac{L}{t} = \frac{0.300\ \text{m}}{75 \times 10^{-6}\ \text{s}} = 4000\ \text{m/s} = \mathbf{4.0\ \text{km/s}}$$

Quality grading (IS 13311 Part 1):

Since $V = 4.0$ km/s falls in the 3.5–4.5 range, the concrete quality is GOOD.

(a) Bulking of sand

Bulking of sand is the increase in the apparent (loose) volume of sand caused by surface moisture. Films of water around the sand particles keep them apart by surface tension, pushing the grains apart and increasing voids; the volume can increase by 20–40 % at about 4–6 % moisture. Beyond saturation (sand fully wet/inundated), the films merge and the volume returns to nearly the dry value.

Practical importance: In volume batching, a fixed measuring box of damp sand actually contains less solid sand than dry sand of the same volume. Ignoring bulking leads to under-batching of sand (a richer, sandy-deficient mix), poorer grading and inconsistent strength. Hence either an allowance for bulking is made (extra volume added) or, better, sand is batched by mass.

(b) Calculation

Dry-sand bulk density = 1600 kg/m³; bulking increases loose volume by 28 %.

The 0.40 m³ measured is the bulked (loose, damp) volume. The equivalent dry loose volume is:

$$V_{dry} = \frac{V_{bulked}}{1 + 0.28} = \frac{0.40}{1.28} = 0.3125\ \text{m}^3$$

Mass of dry sand actually supplied:

$$m = V_{dry} \times \rho_{dry} = 0.3125 \times 1600 = \mathbf{500\ \text{kg}}$$

If bulking were ignored, one would assume 0.40 m³ of dry sand:

$$m_{assumed} = 0.40 \times 1600 = 640\ \text{kg}$$

But only 500 kg is really present. Shortfall = 640 − 500 = 140 kg.

$$\text{Error} = \frac{640 - 500}{640}\times 100 = \frac{140}{640}\times100 = \mathbf{21.9\%}$$

Ignoring bulking would over-estimate the sand by about 22 %, i.e. the mix would actually receive ~22 % less sand than intended.

(i) Fibre-Reinforced Concrete (FRC)

• Composition: ordinary concrete with discrete short fibres (steel, polypropylene, glass, or natural) dispersed uniformly, typically 0.5–2 % by volume.
• Key property: greatly improved post-cracking ductility / toughness and resistance to cracking; fibres bridge cracks and arrest their propagation, improving tensile/flexural behaviour and impact/fatigue resistance.
• Application: industrial floors and pavements, tunnel linings (shotcrete), bridge decks, precast elements.

(ii) Self-Compacting Concrete (SCC)

• Composition: highly flowable mix with high-range water reducer (PCE superplasticizer), high fines/powder content and a viscosity-modifying agent; balanced to resist segregation.
• Key property: flows and consolidates under its own weight without vibration, completely filling formwork and encapsulating reinforcement (high filling and passing ability). Tested by slump-flow / V-funnel / L-box.
• Application: heavily congested reinforcement, complex/inaccessible formwork, architectural concrete, precast.

(iii) High-Performance Concrete (HPC)

• Composition: low w/c (often <0.4), superplasticizer and supplementary cementitious materials (silica fume, fly ash, GGBS) for a dense microstructure.
• Key property: high strength and superior durability / low permeability (and good workability) — performance criteria beyond ordinary concrete.
• Application: high-rise columns, long-span bridges, marine and aggressive-environment structures.

(Any two of the above answered fully earn the marks.)

(a) Functions of mortar and grades

Functions of mortar:

• Binds the masonry units into a monolithic whole and transmits/distributes loads uniformly between units.
• Fills the joints, making the wall weather-tight and preventing air/water penetration.
• Accommodates dimensional irregularities of units and provides a uniform bedding so stress concentrations are avoided.
• Provides bond for any reinforcement and contributes to appearance (pointing).

Common cement-mortar grades (nominal cement:sand by volume):

(Proportions vary slightly between codes; the trend richer M1→M3 is the key point.)

(b) Brick–mortar interaction in prism strength

Under vertical load the mortar joint tends to expand laterally more than the stiffer brick (Poisson effect). Because the brick restrains the mortar, the mortar is put into a triaxial (confined) compression while the brick is put into lateral tension. Failure of masonry is therefore usually by vertical splitting (tension) cracking of the brick, not crushing of the mortar.

Consequently:

• Masonry strength is always less than the brick crushing strength and increases only slowly with mortar strength.
• A mortar much stronger (and stiffer) than the brick is not desirable: it gives little extra prism strength (brick still governs), is uneconomical, and a rigid mortar causes brittle cracking and poor accommodation of movement/settlement. A slightly weaker, more workable mortar yields better bond, ductility and crack distribution. Hence "the mortar should be no stronger than necessary."

(c) Estimate of masonry strength

$$f_m \approx 0.25\sqrt{f_b \cdot f_{mo}} = 0.25\sqrt{15 \times 3} = 0.25\sqrt{45}$$ $$\sqrt{45} = 6.708$$ $$f_m \approx 0.25 \times 6.708 = \mathbf{1.68\ \text{N/mm}^2}$$

The estimated masonry (prism) compressive strength is about 1.68 N/mm², i.e. only ~11 % of the brick crushing strength — confirming that masonry strength is governed largely by the brick and the joint interaction, not the mortar alone.