BE Civil Engineering (IOE, TU) Civil Engineering Materials (IOE, CE 501) Question Paper 2077 Nepal

(a) Role of water-cement ratio and Abrams' law

The water-cement (w/c) ratio is the ratio of the mass of free water to the mass of cement in a mix. It is the single most important factor controlling the strength of fully compacted concrete:

• Cement needs only about 23-25% of its weight in water for complete chemical hydration. Any excess water is added purely for workability.
• Excess water, after the concrete hardens, evaporates and leaves capillary pores and voids, which reduce density and strength and increase permeability.
• A lower w/c ratio gives higher strength and durability but reduces workability; a higher w/c ratio improves workability but lowers strength.

Abrams' law (1918): For a given set of materials and conditions, the strength of fully compacted concrete is inversely related to the water-cement ratio:

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

where $f_c$ is the compressive strength, $w/c$ is the water-cement ratio, and $A$, $B$ are empirical constants. Strength decreases as $w/c$ increases.

(b) Quantities for 1 m³ of concrete

Let the mass of cement be $C$ kg. By the weight ratio:

• Fine aggregate (FA) $= 1.8\,C$
• Coarse aggregate (CA) $= 3.2\,C$
• Water $W = 0.48\,C$

Absolute volumes (volume = mass / (specific gravity × 1000), with water density 1000 kg/m³):

$$V_{cement} = \frac{C}{3.15 \times 1000} = 3.1746\times10^{-4}\,C$$ $$V_{FA} = \frac{1.8C}{2.65 \times 1000} = 6.7925\times10^{-4}\,C$$ $$V_{CA} = \frac{3.2C}{2.70 \times 1000} = 1.18519\times10^{-3}\,C$$ $$V_{water} = \frac{0.48C}{1000} = 4.8000\times10^{-4}\,C$$

Total solid + water volume:

$$V_{s} = (3.1746 + 6.7925 + 11.8519 + 4.8000)\times10^{-4}\,C = 26.6190\times10^{-4}\,C$$

With 2% entrapped air, the solids+water occupy 98% of the 1 m³:

$$26.6190\times10^{-4}\,C = 0.98$$ $$C = \frac{0.98}{26.6190\times10^{-4}} = 368.16\ \text{kg}$$

Therefore:

(c) Number of cement bags

$$\text{Bags} = \frac{368.16}{50} = 7.36 \approx \mathbf{7.4\ bags\ per\ m^3}$$

(In practice, 7.5 bags would be ordered per m³.)

(a) Wet process of Portland cement manufacture

In the wet process the raw materials are ground and blended in the presence of water to form a slurry (35-50% water), which is then burnt in a rotary kiln.

Flow sequence:

Limestone (CaCO3) + Clay/Shale (SiO2, Al2O3, Fe2O3)
          |
   Crushing & proportioning
          |
   Wet grinding in ball/tube mill (+ water)
          |
   SLURRY (corrected in slurry tanks)
          |
   Rotary kiln (~150 m long, inclined, rotating)
     - Drying zone (up to ~100 C): water driven off
     - Calcination zone (~700-900 C): CaCO3 -> CaO + CO2
     - Burning/clinkering zone (~1400-1500 C): clinker forms
          |
   CLINKER (cooled rapidly in coolers)
          |
   + Gypsum (~3-5%)  ->  Final grinding
          |
   PORTLAND CEMENT  ->  packing/storage

Chemical changes in the burning (clinkering) zone (~1400-1500 °C):

• $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2\uparrow$ (completed)
• Lime combines with silica, alumina and iron oxide to form the cement compounds:
  • $2\text{CaO}\cdot\text{SiO}_2$ (C₂S)
  • $3\text{CaO}\cdot\text{SiO}_2$ (C₃S)
  • $3\text{CaO}\cdot\text{Al}_2\text{O}_3$ (C₃A)
  • $4\text{CaO}\cdot\text{Al}_2\text{O}_3\cdot\text{Fe}_2\text{O}_3$ (C₄AF)

Partial fusion takes place and the material balls up into hard, greenish-grey clinker. Gypsum is added afterwards to retard the flash-set caused by C₃A.

(b) The four major Bogue compounds

Contribution of each:

• C₃S (Alite): Hydrates rapidly; responsible for early strength (up to ~7 days) and contributes substantially to setting. Liberates a high heat of hydration (~500 J/g).
• C₂S (Belite): Hydrates slowly; contributes little to early strength but is responsible for ultimate/long-term strength (beyond ~28 days). Low heat of hydration (~250 J/g) and good for durability.
• C₃A: Hydrates almost instantly, causing flash set; controlled by gypsum. Contributes to early setting but little strength; very high heat of hydration (~865 J/g) and is vulnerable to sulphate attack.
• C₄AF: Hydrates rapidly but gives little strength; gives cement its grey colour and acts as a flux during clinkering. Moderate heat of hydration (~420 J/g).

(a) Sieve analysis computation

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

Fineness modulus (FM) = (Σ cumulative % retained on standard sieves) / 100.

The standard sieves for FM of fine aggregate run from 4.75 mm down to 150 μm (the pan is not included):

$$\Sigma = 2.0 + 9.0 + 24.0 + 52.0 + 84.0 + 97.0 = 268.0$$ $$\boxed{FM = \frac{268.0}{100} = 2.68}$$

(b) Grading zone and suitability

Compare the % passing with IS 383 grading limits:

Every value falls within the Zone II limits, so the sand is classified as Grading Zone II.

Comment: A fineness modulus of 2.68 lies in the typical range for medium sand (2.6-2.9) and Zone II sand is regarded as the most suitable, well-graded medium sand for general structural concrete. It gives a good balance of workability and economy of cement/water without excessive fines.

(a) Stress-strain curve for mild steel

Stress
  ^
  |              U  (Ultimate strength)
  |            .'  '.
  |          .'      '.
  |        .'          '. B (Breaking/fracture point)
  |      Yu
  |     /  \__ Yl (lower yield)
  |    P,E   (Yu = upper yield)
  |   /
  |  /   <- Linear elastic region (Hooke's law)
  | /
  +------------------------------------> Strain

• P = Limit of proportionality (end of straight line)
• E = Elastic limit (just after P)
• Yu = Upper yield point, Yl = Lower yield point (load drops, large strain at ~constant stress)
• U = Ultimate strength (maximum stress; necking begins)
• B = Breaking/fracture point (stress on original area falls as section necks)

(b) Computations

Original cross-sectional area:

$$A_0 = \frac{\pi}{4}d^2 = \frac{\pi}{4}(16)^2 = 201.06\ \text{mm}^2$$

Yield stress:

$$f_y = \frac{62.8\times10^3}{201.06} = 312.3\ \text{N/mm}^2 \approx \mathbf{312\ MPa}$$

Ultimate tensile strength:

$$f_u = \frac{94.2\times10^3}{201.06} = 468.5\ \text{N/mm}^2 \approx \mathbf{469\ MPa}$$

Percentage elongation:

$$\% \text{elong} = \frac{L_f - L_0}{L_0}\times100 = \frac{98.4-80}{80}\times100 = \frac{18.4}{80}\times100 = \mathbf{23.0\%}$$

Percentage reduction in area:

$$A_f = \frac{\pi}{4}(11.3)^2 = 100.29\ \text{mm}^2$$ $$\% \text{RA} = \frac{A_0 - A_f}{A_0}\times100 = \frac{201.06-100.29}{201.06}\times100 = \frac{100.77}{201.06}\times100 = \mathbf{50.1\%}$$

The high elongation (~23%) and reduction in area (~50%) confirm the ductile behaviour expected of mild steel.

(a) Four field tests for bricks

1. Visual / shape test: A good brick should be uniform in size, rectangular with sharp, straight edges and parallel faces; free of cracks, flaws and stones.
2. Colour test: Good bricks have a uniform deep red / copper colour throughout, indicating thorough and even burning.
3. Hardness test (scratch test): When scratched with a fingernail, a good brick leaves no impression, showing it is sufficiently hard.
4. Soundness / ringing test: When two bricks are struck together, a good brick gives a clear metallic ringing sound and does not break.

(Other acceptable tests: structure test — break and inspect for compact, homogeneous, void-free section; water-absorption / efflorescence test.)

(b) Compressive strength and water absorption

Bedding (loaded) area:

$$A = 190 \times 90 = 17100\ \text{mm}^2$$

Compressive strength:

$$f_c = \frac{178\times10^3}{17100} = 10.41\ \text{N/mm}^2$$ $$\boxed{f_c \approx 10.4\ \text{N/mm}^2}$$

This is marginally below the 10.5 N/mm² requirement, so the brick just fails to meet the first-class compressive-strength criterion (it would be rejected, or downgraded to second class).

Water absorption:

$$\% \text{absorption} = \frac{W_{wet} - W_{dry}}{W_{dry}}\times100 = \frac{3480-3120}{3120}\times100 = \frac{360}{3120}\times100$$ $$= \mathbf{11.54\%}$$

Since 11.54% < 20%, the brick satisfies the water-absorption limit for a first-class brick.

Conclusion: The brick passes on water absorption but narrowly fails the compressive-strength criterion for first-class classification.

(a) Seasoning of timber

Seasoning is the process of reducing the moisture content of freshly felled (green) timber to a level in equilibrium with the surrounding atmosphere (usually 10-15%) in a controlled manner.

Objectives:

• Reduce moisture content and the weight of timber.
• Increase strength, stiffness, hardness and durability.
• Prevent warping, shrinkage, splitting and decay/fungal attack.
• Make timber suitable for painting, polishing and gluing.

(b) Natural seasoning vs kiln seasoning

(c) Two natural defects in timber

1. Knots: Bases of branches embedded in the trunk. They appear as dark, hard rings that interrupt the grain, reduce tensile strength and cause local weakness.
2. Shakes: Cracks or separations of fibres caused by natural forces — e.g. heart shake (radial cracks from the pith), cup/ring shake (separation along annual rings), star shake (radial cracks from bark to centre). They reduce strength and allow moisture ingress.

(Other acceptable: wane, twisted fibres, rind galls, upsets/rupture.)

(a) Classification of lime

Lime is broadly classified (per IS 712) as:

• Fat lime (Class C, high-calcium / pure lime): Obtained from pure limestone; slakes vigorously, sets only by carbonation in air. No hydraulicity.
• Hydraulic lime (Classes A & B): Contains clay (silica/alumina); sets under water and in air. Subdivided into feebly, moderately and eminently hydraulic lime.
• Poor lime (Class D): Impure, contains > 25% clay; slakes slowly and gives poor mortar.

Fat lime vs hydraulic lime:

(b) Mortar

Mortar is a workable paste made by mixing a binding material (cement or lime) with fine aggregate (sand) and water, used to bind bricks/stones in masonry.

Functions of mortar:

• Binds individual masonry units into a monolithic mass.
• Distributes load uniformly over the bed and fills the joints/voids.
• Provides a level bed and accommodates dimensional irregularities of units.
• Gives a finished, weather-tight and aesthetic surface (pointing/plaster).

Two desirable properties of good mortar:

1. Good adhesion/bond with masonry units.
2. Adequate strength and durability with low shrinkage, good workability and water retentivity.

(a) Bitumen and its distinction from tar

Bitumen is a black or dark-brown, viscous, water-insoluble but carbon-disulphide-soluble hydrocarbon obtained as a residue from the fractional distillation of crude petroleum. It is used as a binder in road construction and waterproofing.

(b) Penetration test

The penetration test measures the consistency/hardness of bitumen. A standard needle is allowed to penetrate vertically into a bitumen sample maintained at 25 °C, under a load of 100 g for 5 seconds. The depth of penetration is measured in units of one-tenth of a millimetre (0.1 mm = 1 penetration unit).

• A higher penetration value indicates softer bitumen.
• A lower penetration value indicates harder bitumen.

(c) Penetration grade of the given sample

Penetration depth = 6.5 mm = 65 × 0.1 mm.

$$\text{Penetration value} = 65\ \text{units}$$

This corresponds to a grade of about 60/70 penetration bitumen (the 65 reading falls in the 60-70 band).

Comment: A penetration of 65 is a medium-to-relatively-soft grade. Compared with hard grades such as 30/40, this 60/70 bitumen is softer and is typically used for road surfacing in moderate-temperature regions.

(a) Four requirements of a good building stone

1. Strength: High crushing strength (generally > 100 N/mm² for good stones) to carry loads.
2. Durability: Resistance to weathering, frost and chemical action.
3. Hardness and toughness: Resistance to abrasion and impact (especially for road/floor work).
4. Low water absorption (≤ ~5%) and good appearance: Dense, fine-grained, with uniform colour and ability to take polish.

(Other acceptable: ease of dressing, fire resistance, good seasoning.)

(b) Crushing strength

Loaded area:

$$A = 50 \times 50 = 2500\ \text{mm}^2$$

Crushing strength:

$$f_c = \frac{425\times10^3}{2500} = 170\ \text{N/mm}^2$$ $$\boxed{f_c = 170\ \text{N/mm}^2 = 170\ \text{MPa}}$$

This is a high value, indicating a good, strong building stone (e.g. granite-class).

(c) Dressing of stones

Dressing is the process of cutting, shaping and finishing quarried stone blocks to the required size, shape and surface texture so that they can be properly placed in masonry. It gives the stone proper bedding faces, regular joints and the desired finish (e.g. hammer-dressed, chisel-drafted, polished).

(a) Objectives / functions of painting

• To protect the surface (timber, metal, plaster) from weathering, moisture, corrosion and decay.
• To give a decorative, clean, smooth and pleasing appearance.
• To provide a hygienic, washable and damp-proof surface.
• To prevent insect/fungal attack on wood and rusting of metals.

(b) Main constituents of an oil paint

(c) Paint vs varnish

(a) Thermoplastics vs thermosetting plastics

(b) Four uses of plastics in civil construction

1. PVC pipes and fittings for water supply, drainage and electrical conduits.
2. Floor and wall coverings (vinyl tiles, laminates) and damp-proof membranes/sheets.
3. Doors, windows, panels and skylights (uPVC frames, acrylic/polycarbonate sheets).
4. Water tanks, geomembranes, insulation (expanded polystyrene) and decorative fittings.

(c) Float process and types of glass

Float (flat) glass manufacture: The batch — silica sand, soda ash, limestone and cullet — is melted in a furnace at about 1500 °C. The molten glass is then made to float continuously over a bath of molten tin. Because glass floats on the denser tin, the two surfaces become perfectly flat and parallel, producing glass of uniform thickness and a smooth, distortion-free, fire-polished finish. The ribbon is then gradually cooled (annealed) in a lehr and cut to size.

Three common types of glass:

(Other acceptable: wired glass — fire-resistant doors; insulating/double-glazed units — thermal insulation.)