BE Civil Engineering (IOE, TU) Civil Engineering Materials (IOE, CE 501) Question Paper 2080 Nepal

Hydration of Portland cement

When water is added to cement, the anhydrous compounds react chemically (an exothermic reaction) to form hydrated products that bind the aggregate together. The principal reactions are:

• Silicates ($C_3S$, $C_2S$) react with water to give C–S–H gel (calcium silicate hydrate, the main strength-giving phase) plus calcium hydroxide $Ca(OH)_2$ (portlandite).

$$2C_3S + 6H \rightarrow C_3S_2H_3 + 3CH$$ $$2C_2S + 4H \rightarrow C_3S_2H_3 + CH$$

• $C_3A$ reacts very rapidly; gypsum is added to retard the flash set, forming ettringite.
• $C_4AF$ hydrates to give calcium aluminoferrite hydrates; contributes little to strength.

The four Bogue compounds

Bogue's equations

$$C_3S = 4.071\,CaO - 7.600\,SiO_2 - 6.718\,Al_2O_3 - 1.430\,Fe_2O_3$$ $$C_2S = 2.867\,SiO_2 - 0.7544\,C_3S$$ $$C_3A = 2.650\,Al_2O_3 - 1.692\,Fe_2O_3$$ $$C_4AF = 3.043\,Fe_2O_3$$

Step 1 — $C_3S$

$$C_3S = 4.071(64.0) - 7.600(21.0) - 6.718(5.5) - 1.430(3.5)$$ $$= 260.544 - 159.600 - 36.949 - 5.005 = 58.99\%$$

Step 2 — $C_2S$

$$C_2S = 2.867(21.0) - 0.7544(58.99) = 60.207 - 44.502 = 15.71\%$$

Step 3 — $C_3A$

$$C_3A = 2.650(5.5) - 1.692(3.5) = 14.575 - 5.922 = 8.65\%$$

Step 4 — $C_4AF$

$$C_4AF = 3.043(3.5) = 10.65\%$$

Results:

Workability

Workability is the ease with which concrete can be mixed, transported, placed, compacted and finished without segregation or bleeding.

Factors affecting workability:

1. Water content — most significant; more water increases workability but lowers strength.
2. Water-cement ratio — higher w/c gives more fluidity.
3. Aggregate properties — size, shape (rounded > angular), texture, grading.
4. Aggregate-cement ratio — leaner mixes are less workable.
5. Admixtures — plasticizers/superplasticizers increase workability.
6. Fineness of cement — finer cement needs more water.
7. Time and temperature — higher temperature reduces workability (faster setting).

Abrams' water-cement ratio law

For a fully compacted concrete, the strength is inversely proportional to the water-cement ratio:

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

where $A$ and $B$ are empirical constants. Strength decreases as w/c increases (for workable, fully compacted mixes).

Cement content calculation

Let mass of cement $= C$ (kg). With ratio $1:1.8:3.2$ by mass:

• Sand $= 1.8C$, Coarse aggregate $= 3.2C$, Water $= 0.48C$.

Absolute volumes (volume = mass / (S.G. × 1000) in $m^3$):

$$V_{cement} = \frac{C}{3.15 \times 1000}$$ $$V_{sand} = \frac{1.8C}{2.65 \times 1000}$$ $$V_{CA} = \frac{3.2C}{2.70 \times 1000}$$ $$V_{water} = \frac{0.48C}{1.00 \times 1000}$$

Sum of absolute volumes $= 1\,m^3$ (no air):

$$\frac{C}{1000}\left(\frac{1}{3.15} + \frac{1.8}{2.65} + \frac{3.2}{2.70} + 0.48\right) = 1$$

Compute each term:

• $1/3.15 = 0.31746$
• $1.8/2.65 = 0.67925$
• $3.2/2.70 = 1.18519$
• water $= 0.48000$

Sum $= 0.31746 + 0.67925 + 1.18519 + 0.48000 = 2.66190$

Therefore:

$$\frac{C}{1000}(2.66190) = 1 \implies C = \frac{1000}{2.66190} = 375.67\,kg$$

Mass of cement required = ≈ 376 kg per $m^3$.

(For reference: sand $= 676.2\,kg$, coarse aggregate $= 1202.1\,kg$, water $= 180.3\,kg$ per $m^3$.)

Structure of timber (exogenous tree cross-section)

From outside to centre:

  Bark (outer + inner / bast)
  Cambium layer  -> living cells, growth
  Sapwood (alburnum) -> light, carries sap, contains moisture
  Heartwood (duramen) -> dark, dead cells, strongest, durable
  Pith (medulla) -> innermost soft core
  Medullary rays -> radial lines transferring sap
  Annual rings -> one ring per year (age & growth rate)

• Heartwood is preferred for construction (strong, durable, decay-resistant).
• Annual rings indicate age; closely spaced rings = strong, slow-grown timber.

Defects in timber

1. Due to natural forces / growth: knots, shakes (heart, cup, ring, star shakes), twisted fibres, rind galls, burr.
2. Due to fungi: dry rot, wet rot, blue stain, heart rot.
3. Due to insects: beetles, marine borers, termites (white ants).
4. Due to seasoning: bow, cup, twist, warp, split, check, honeycombing.
5. Due to conversion: chip marks, wane, diagonal grain.

Seasoning of timber

Seasoning = controlled reduction of moisture content of green timber to a level in equilibrium with the surrounding atmosphere (≈ 10–15 %).

Why necessary:

• Reduces weight; increases strength, stiffness and durability.
• Reduces shrinkage, warping and splitting after use.
• Makes timber resistant to fungal/insect attack.
• Allows it to take paint, polish and preservatives well.

Natural (air) seasoning vs Kiln seasoning

Stress-strain behaviour of mild steel (tension)

Stress
  ^                         U (ultimate)
  |                 ____----"""""----___
  |          B,C _/                   \ F (fracture)
  |          __/  (yield plateau)      *
  |       A /
  |      / (P limit of proportionality)
  |    /
  |  /  (linear elastic, Hooke's law)
  | /
  +--------------------------------------> Strain

• O–P (Limit of proportionality): stress ∝ strain (Hooke's law); slope = Young's modulus $E$.
• P–A (Elastic limit): still elastic but no longer linear.
• A → upper/lower yield (B, C): material yields; sudden increase in strain at nearly constant stress — yield point.
• C–U (strain hardening): stress rises again to the ultimate tensile strength at U.
• U–F: necking; cross-section reduces, load falls, then fracture at F (breaking/cup-and-cone).

Calculations

Cross-sectional area:

$$A = \frac{\pi}{4}d^2 = \frac{\pi}{4}(16)^2 = \frac{\pi}{4}(256) = 201.06\,mm^2$$

Yield stress:

$$\sigma_y = \frac{P_y}{A} = \frac{52.3 \times 10^3\,N}{201.06\,mm^2} = 260.1\,N/mm^2$$

Ultimate tensile strength:

$$\sigma_u = \frac{P_u}{A} = \frac{78.0 \times 10^3}{201.06} = 387.9\,N/mm^2$$

Percentage elongation:

$$\%\,elong = \frac{L_f - L_0}{L_0}\times 100 = \frac{98.4 - 80}{80}\times 100 = \frac{18.4}{80}\times 100 = 23.0\%$$

Results:

• Yield stress $\sigma_y = \mathbf{260.1\,N/mm^2 \;(MPa)}$
• Ultimate tensile strength $\sigma_u = \mathbf{387.9\,N/mm^2 \;(MPa)}$
• Percentage elongation $= \mathbf{23.0\%}$

Bricks vs Building stones

Tests for bricks

Field tests:

1. Shape & size — uniform, sharp edges, rectangular.
2. Colour — uniform deep red/copper colour.
3. Hardness — no impression by finger-nail scratch.
4. Soundness — two bricks struck together give clear ringing sound, no breakage.
5. Structure — broken brick shows compact, homogeneous, no flaws/lumps.

Laboratory tests:

1. Compressive strength test — crushing in compression testing machine.
2. Water absorption test — 24 h immersion; first-class ≤ 20% by weight.
3. Efflorescence test — checks soluble salts (rated nil/slight/moderate/heavy).
4. Dimension tolerance test — measure stack of 20 bricks.
5. Warpage test — flatness using steel rule and wedge.

Compressive strength calculation

Loaded (bed) face area = length × width:

$$A = 240 \times 115 = 27600\,mm^2$$ $$\sigma_c = \frac{P}{A} = \frac{310 \times 10^3\,N}{27600\,mm^2} = 11.23\,N/mm^2$$

Compressive strength = ≈ 11.23 N/mm² (MPa).

Since $11.23 > 10.5\,N/mm^2$, the brick satisfies the minimum strength requirement for a first-class brick.

Fineness modulus

Fineness modulus (FM) is an index of the fineness/coarseness of an aggregate, obtained by summing the cumulative percentages retained on the standard sieves (150 µm and coarser) and dividing by 100. A higher FM means coarser aggregate.

Significance: indicates particle-size distribution and helps in proportioning aggregates for concrete mixes; sand is normally classified by zones using FM (fine sand ~2.2–2.6, coarse sand ~2.9–3.2).

Computation

Total mass = 1000 g, so % retained = mass retained / 10.

Sum of cumulative % retained (150 µm and above):

$$\Sigma = 2.0 + 10.0 + 25.0 + 53.0 + 82.0 + 97.0 = 269.0$$ $$FM = \frac{\Sigma}{100} = \frac{269.0}{100} = \mathbf{2.69}$$

The sand has $FM = 2.69$, indicating a medium sand suitable for concrete.

Classification of lime

Based on impurities (mainly clay/silica + alumina) lime is classified as:

1. Fat lime (pure / high-calcium / quick lime): ≥ 95% CaO; from pure limestone; slakes vigorously; sets only by carbonation in air (non-hydraulic).
2. Hydraulic lime: contains clay (silica, alumina); sets under water. Sub-divided:
   • Feebly hydraulic (5–10% clay)
   • Moderately hydraulic (11–20% clay)
   • Eminently hydraulic (21–30% clay)
3. Poor (lean) lime: > 30% impurities; weak, slow setting.

Fat lime vs Hydraulic lime

Slaking of lime

Slaking is the chemical reaction of quicklime (CaO) with water to form slaked lime (calcium hydroxide), an exothermic reaction:

$$CaO + H_2O \rightarrow Ca(OH)_2 + heat$$

The lump quicklime swells, crumbles into a fine powder/putty, and a large amount of heat is liberated.

Mortar

Mortar is a workable paste of a binder (cement/lime), fine aggregate (sand) and water, used to bind masonry units, fill joints, and plaster surfaces.

Desirable properties of good mortar:

• Good adhesion/bond to masonry units.
• Adequate strength when set.
• Workability and ease of placing.
• Water retentivity (does not dry too fast).
• Durability and resistance to weathering.
• Low shrinkage and good water-tightness.
• Economical and quick setting (as required).

Bitumen vs Tar vs Asphalt

Four laboratory tests on bitumen

1. Penetration test: measures the depth (in tenths of mm) to which a standard needle penetrates the sample in 5 s at 25 °C under 100 g load. → Measures consistency/hardness (grading, e.g. 60/70).
2. Softening point test (Ring & Ball): temperature at which bitumen softens enough for a steel ball to fall through a ring. → Measures temperature susceptibility / resistance to flow at high temperature.
3. Ductility test: the distance (cm) a standard briquette stretches before breaking at 27 °C, 5 cm/min. → Measures ductility / ability to deform without cracking.
4. Flash and fire point test: lowest temperatures at which vapours flash momentarily / sustain burning. → Measures safe heating temperature / volatility.

(Other valid tests: viscosity test, specific gravity test, loss on heating, solubility test.)

Constituents of paint and their functions

1. Base (white lead, zinc oxide, titanium dioxide, etc.): the principal solid pigment; gives body, opacity (hiding power) and durability.
2. Vehicle / binder (drying oils such as linseed oil, resins): holds pigment particles together, forms the film, gives adhesion and durability.
3. Pigment / colouring matter: provides desired colour and opacity.
4. Solvent / thinner (turpentine, mineral spirit): reduces viscosity for easy application; evaporates after application.
5. Drier: accelerates drying/hardening of the film by oxidation.
6. Extender / filler (chalk, barytes): cheapens paint and modifies properties (reduces cracking, adds bulk).

Paint vs Varnish

Characteristics of a good paint

• Spreads easily and freely; good workability.
• Forms a thin, uniform, durable film with good adhesion.
• Dries in reasonable time to a hard, glossy surface.
• Good covering/hiding power (economical coverage).
• Resistant to weather, moisture and not easily affected by atmosphere.
• Does not crack, peel, fade or show brush marks.

(a) Types of glass used in buildings

• Soda-lime (sheet/float) glass: common window/glazing glass; cheap, transparent.
• Toughened (tempered) glass: heat-treated, 4–5× stronger; shatters into small blunt pieces; doors, façades.
• Laminated glass: two glass sheets bonded with PVB interlayer; safety/security glazing, holds together when broken.
• Wired glass: mesh embedded; fire-resistant glazing.
• Insulating (double-glazed) glass: two panes with air/gas gap; thermal & sound insulation.
• Float glass: flat, distortion-free; base for most processed glass.
• Tinted / reflective glass: controls solar heat and glare.

(b) Thermoplastics vs Thermosetting plastics

(a) Smart materials

Smart (intelligent) materials sense changes in their environment (stress, temperature, moisture, electric/magnetic field) and respond in a controlled, useful and often reversible way.

Three examples in civil engineering:

1. Piezoelectric materials: generate electric charge under mechanical stress (and deform under voltage); used in structural health monitoring sensors and energy harvesting.
2. Shape memory alloys (SMA, e.g. Nitinol): recover their original shape on heating; used in seismic dampers, self-centring braces.
3. Self-healing concrete: contains bacteria/encapsulated agents that precipitate calcite to seal cracks, improving durability. (Other valid: electrochromic glass, thermochromic materials.)

(b) Bonding types and properties

Thus bonding directly controls hardness, ductility, conductivity and melting point — e.g. the metallic bond makes steel ductile and weldable, while covalent silica makes glass hard but brittle.

(c) Characteristic compressive strength

Cube face area:

$$A = 150 \times 150 = 22500\,mm^2$$

Compressive strength:

$$f_c = \frac{P}{A} = \frac{787.5 \times 10^3\,N}{22500\,mm^2} = 35.0\,N/mm^2$$

Compressive strength = 35.0 N/mm² (MPa).

Since the 28-day characteristic cube strength is $35\,N/mm^2$, the concrete corresponds to grade M35.