Construction Materials: Cement, Concrete, Steel, Timber, Bitumen, Bricks and Mortar
Concrete: the one ratio, and how a mix is proportioned
w/c limit that delivers a strength grade also delivers an exposure class, and IS 456 sets a maximum w/c for each exposure condition independently of strength for exactly this reason — a mix can be strong enough and still be too permeable. The practical corollary is the one every site argues about: adding water on site to a mix that has stiffened restores workability and permanently costs strength and durability. The right answer is a superplasticiser, which disperses the cement grains electrostatically and delivers workability without water — the only intervention that gives the placeability without the porosity. Note the direction of Abrams’ law: strength depends on w/c, not on cement content, so adding cement and water together in the same proportion does not make concrete stronger; it makes more concrete of the same strength.The constituents of concrete are four and their proportions are the design: cement, water, fine aggregate and coarse aggregate, with admixtures as a fifth where they are used. A mix is proportioned by the absolute volume method, which rests on a single accounting identity: the volumes of cement, water, fine aggregate, coarse aggregate and air must add to the volume of concrete produced. For w/c = 0.5, a mix of 1 : 1.5 : 3 by mass, and specific gravities of 3.15, 2.65 and 2.70, each kilogram of cement brings 1/3150 + 0.5/1000 + 1.5/2650 + 3/2700 = 0.0024946 m³ into the mix, so 1 m³ of fully compacted concrete needs 400.86 kg of cement, 200.43 kg of water, 601.30 kg of fine and 1202.59 kg of coarse aggregate. Everything about mix design is a variation on that sum, and the two properties that make it useful in an exam are that it is exact and that it makes air visible: allow 2% entrapped air and the same materials yield only 0.98 m³, so the cement required rises to 409.05 kg/m³ for concrete that is no stronger.
1/1.25 = 0.80 m³ of sand, a 20% shortfall, and the mix is short of fine aggregate by that much without anything looking wrong. The mix becomes harsh, the coarse aggregate is under-filled, segregation and honeycombing follow. Two things to hold. The correction is not linear in moisture — bulking rises to a maximum around 4–5% and then falls back to nearly zero when the sand is saturated, because water then fills the voids rather than separating the grains, which is why very wet sand and dry sand both batch correctly and only damp sand misleads. And the honest answer to the whole problem is to batch by mass, which is immune to bulking; volume batching survives only on small sites, and there the field bulking test — measuring the settled volume of a sample under water — is what supplies the correction factor. This is also why site-mixed concrete is more variable than ready-mixed: the same nominal 1:1.5:3 gives a different mix on a damp morning than on a dry afternoon.The long-term properties are where concrete stops behaving like a simple elastic material. Shrinkage is volume loss on drying, is largely irreversible, and is greater the more water the mix carried — the same w/c again. Creep is continued deformation under sustained load, roughly two to three times the elastic strain over years, and it matters because it redistributes stress: it relieves a locked-in restraint stress, which is helpful, and it increases long-term deflection and prestress loss, which is not. Carbonation is CO₂ neutralising the alkalinity that protects the reinforcement, advancing as roughly √time from the surface — so cover is the defence and its depth buys life quadratically. And sulphate and chloride attack both proceed through the pore network, which returns the chapter to where it began: the water–cement ratio decides how easily anything gets in.
Steel, timber, bitumen, bricks and mortar
- Structural steel is bought for ductility as much as strength. Raising the carbon content raises strength and destroys weldability and ductility together, which is why structural grades sit near 0.2% carbon rather than higher. Design strength is
0.87 f_y— 217.5, 361.05 and 435.0 MPa for Fe250, Fe415 and Fe500 — and the design yield strain for Fe415 is0.002 + 0.87 × 415/200,000 = 0.003805, where the added 0.002 is the code’s allowance for the gradual yield of cold-worked bars, which have no sharp yield point at all. - Timber is anisotropic and that is not a detail. Strength along the grain is many times strength across it, so a timber member is designed for the direction of its fibres, and the defects that matter — knots, shakes, cross grain — are the ones that interrupt that direction. Moisture content changes both strength and dimensions, and seasoning exists to bring timber to equilibrium with its service environment before it is fixed, not after.
- Bitumen is viscoelastic, so a single strength figure is meaningless — it is graded by penetration (consistency at 25 °C) or viscosity, and checked by softening point (which guards against summer rutting), ductility (against cracking as it ages and stiffens) and flash point (which protects the people heating it). No one grade suits every climate, which is the entire reason grading exists.
- Bricks and mortar are bought as a pair, and the rule is counter-intuitive: the mortar should be weaker than the brick. A wall moves — thermally, with settlement, with moisture — and that movement has to go somewhere. Weak mortar cracks along the joints, where the cracks are fine, distributed and repointable; strong mortar forces the movement through the bricks, where cracks are wide, structural and unrepairable. Strength here is not the property being maximised.
Key takeaways
- The water–cement ratio sets strength, durability, shrinkage and workability at once — surplus water leaves capillary pores.
- C₃S gives early strength, C₂S ultimate strength, C₃A flash set and heat (gypsum retards it), C₄AF the colour.
- Absolute volume: at
w/c = 0.5and 1:1.5:3, one m³ needs 400.86 kg of cement — and 2% air raises it to 409.05. - Damp sand bulks 20–30%, so volume batching under-sands the mix; bulking peaks near 4–5% moisture and vanishes when saturated.
- Design strength of steel is
0.87 f_y; the design yield strain adds 0.002 because cold-worked bars have no sharp yield point. - Mortar should be weaker than the brick, so movement cracks the repointable joints rather than the bricks.
Practice questions (8)
Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.
Concrete is proportioned 1 : 1.5 : 3 by mass with a water–cement ratio of 0.5. Specific gravities are 3.15 for cement, 2.65 for fine aggregate and 2.70 for coarse aggregate. By the absolute volume method, the cement content for 1 m³ of fully compacted concrete, in kg, is ______ (round to two decimal places)
Numerical answer — type the value.
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Answer: 400.86
400.86 kg. The absolute volume method rests on one identity: the volumes of the ingredients add to the volume of concrete produced. Per kilogram of cement the mix occupies1/3150 + 0.5/1000 + 1.5/2650 + 3/2700 = 0.00031746 + 0.00050000 + 0.00056604 + 0.00111111 = 0.00249461 m³. For 1 m³,C = 1/0.00249461 = 400.86 kg, and the rest follow: water200.43 kg, fine aggregate601.30 kg, coarse aggregate1202.59 kg. Check the volumes and they return exactly 1.000000 m³. Two things this method makes visible that a mass ratio alone hides. First, water occupies volume — 200 litres is a fifth of the concrete, more space than the cement itself, and this is why increasingw/cdoes not just weaken the paste but dilutes the whole mix. Second, air is a material. The calculation above assumes full compaction; allow 2% entrapped air and the same ingredients yield only 0.98 m³, so producing a full cubic metre needs400.86/0.98 = 409.05 kgof cement — 2.04% more cement for concrete that is no stronger. That is the arithmetic behind insisting on vibration: poor compaction is not a finish issue, it is paid for in materials and again in strength, since a few per cent of voids costs several times that in compressive strength. Note finally what the method does not do: it proportions a mix to a specified ratio, but it does not tell you the ratio. That comes from the target strength viaw/c, and then from workability and aggregate grading — the design proper, of which this arithmetic is the last step.Water is added on site to a concrete mix that has stiffened, to restore workability. The most accurate description of the consequence is that
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Answer: A — strength and durability are both permanently reduced, because the surplus water leaves capillary pores behind
Both are permanently reduced, and by the same mechanism. Cement hydrates completely with only about 0.23–0.25 of its own mass of water. Every mix carries more, and the surplus is there purely for workability — but it occupies volume in the fresh concrete, and when it eventually dries it leaves that volume behind as capillary porosity. Those pores do two things at once. They reduce strength, because there is less solid per unit volume and every void concentrates stress. And they reduce durability, because a connected pore network is the route by which chloride, sulphate, moisture and carbon dioxide reach the reinforcement — which is why IS 456 specifies a maximumw/cfor each exposure condition independently of the strength grade: a mix can be strong enough and still be too permeable. Option (d) is the most tempting wrong answer and inverts the physics: the water leaving is precisely what creates the damage; nothing is recovered by drying, because the pore is what remains. Option (b) is wrong because cover and permeability are complementary, not alternative — cover only helps if the concrete it is made of resists ingress. Option (c) is the subtle one, and it fails on Abrams’ law: strength depends on thew/cratio, not on the cement content, so adding cement and water in the same proportion keepsw/cunchanged and simply produces more concrete of the same strength — useless if the aim was to restore what was lost, and in any case unmixable into a batch already in the truck. The correct remedy is a superplasticiser, which disperses the cement grains electrostatically and delivers workability without adding water at all.Sand at its field moisture content bulks by 25%. A gauge box of volume 1 m³ is filled with this damp sand. The volume of sand actually delivered, expressed as a fraction of 1 m³ in its unbulked state, is ______ (round to four decimal places)
Numerical answer — type the value.
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Answer: 0.8
0.8000 m³ — a 20% shortfall. Bulking means the sand has swollen: what occupies 1.25 m³ when damp occupied 1.00 m³ when dry. So a box of 1 m³ filled with damp sand contains1/1.25 = 0.80 m³of sand measured on the unbulked basis, and the mix is short of fine aggregate by 20% while everything on site looks perfectly normal. Note the asymmetry that catches candidates: a bulking of 25% produces a shortfall of 20%, not 25%, because the two are reciprocals —1 − 1/1.25 = 0.20. The physical cause is thin films of surface moisture holding the grains apart, and its most useful feature is that it is not monotonic in moisture. Bulking rises to a maximum near 4–5% moisture and then falls back to almost nothing as the sand approaches saturation, because water then fills the voids rather than separating the grains. So dry sand and very wet sand both batch correctly, and only damp sand — the most common state on any site after rain or overnight dew — misleads. The consequence is a harsh, under-sanded mix: the coarse aggregate is not properly filled, and segregation and honeycombing follow. Two remedies exist and only one is real. On a small site the field bulking test — measuring the settled volume of a sample under water — supplies a correction factor to be applied to the gauge box. On any site that can manage it, batch by mass, which is completely immune to bulking. That is a large part of why site-mixed concrete is more variable than ready-mixed: the same nominal 1:1.5:3 gives a materially different mix on a damp morning than on a dry afternoon.A mass concrete gravity dam is to be built. The most appropriate cement is one in which
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Answer: A — C₂S is raised and C₃A reduced, so that less heat is evolved during hydration
Raise C₂S and cut C₃A — low-heat cement. The governing problem in mass concrete is not strength but heat. Hydration is exothermic, and in a thick pour the heat is generated far faster than it can escape through the surface, so the interior warms while the exterior stays near ambient. The interior then expands against a cool, restraining shell, and when it finally cools it contracts against concrete that has already hardened — producing thermal cracking from the inside out, in a structure whose entire purpose is to be watertight. Reading the Bogue table as a set of levers gives the answer directly: C₃A evolves the most heat per unit mass and contributes almost nothing to strength, so it is cut; C₃S hydrates fast and evolves high early heat, so it is reduced; C₂S hydrates slowly with low heat and supplies the ultimate strength, so it is raised. The cost is real and accepted: low-heat cement gains strength slowly, which suits a dam built over years and would be intolerable in a building on a fast programme. Supplementary measures follow the same logic — replacing part of the cement with fly ash or slag, pre-cooling the aggregate and mixing water, embedding cooling pipes, and casting in lifts with pauses so each layer sheds its heat before the next is placed. Option (b) is the recipe for rapid-hardening cement, which is the worst possible choice here: finer grinding and moreC₃Smaximise exactly the heat that must be minimised. Option (c) is wrong twice —C₃Agives heat and flash set rather than useful strength, and a dam has no need of a fast set at all. Option (d) is dangerous: without gypsum to retardC₃Athe cement would flash set and be unusable in any structure.For Fe415 steel with E = 2 × 10⁵ MPa, the design yield strain used in IS 456 limit state design is ______ (round to six decimal places)
Numerical answer — type the value.
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Answer: 0.003805
0.003805. The design yield stress is0.87 f_y = 0.87 × 415 = 361.05 MPa, so the purely elastic strain at that stress is361.05/200,000 = 0.0018053. IS 456 then adds 0.002, giving0.002 + 0.0018053 = 0.0038053, universally quoted as 0.0038. The added constant is not a safety factor and not arbitrary — it is a description of how cold-worked bars actually behave. Mild steel (Fe250) has a sharp, well-defined yield point: the stress–strain curve has a plateau, and yield is an event. Cold-worked deformed bars (Fe415, Fe500) have none: the curve bends over gradually, so there is no single strain at which yield occurs and a proof stress must be defined instead — conventionally the stress at 0.2% permanent set. The 0.002 in the formula is that 0.2%: the code’s idealised curve is elastic to about 0.8f_yd, then curved, and reaches full design yield at the elastic strain plus the 0.2% offset. Two consequences are examined regularly. Because the design yield strain rises with grade — 0.003087 for Fe250, 0.003805 for Fe415, 0.004175 for Fe500 — and the concrete strain at failure is fixed at 0.0035, the limiting neutral axis depthx_u,max/dfalls as the steel gets stronger: 0.53, 0.48 and 0.46 for the three grades. Higher-grade steel therefore does not simply give proportionally more moment capacity; it reaches its balanced condition sooner. And a candidate who usesf_y/E = 0.002075instead of the design value has ignored both the partial safety factor and the 0.2% offset, which is a large error in the wrong direction on any strain-compatibility calculation.Which of the following statements about construction materials are correct?
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Answer: A — Mortar in a brick wall should be weaker than the bricks, so that movement cracks the joints rather than the bricks; B — Gypsum is interground with cement clinker to retard C₃A and prevent flash set; C — Raising the carbon content of structural steel increases strength but reduces ductility and weldability
(a), (b) and (c). (a) is the counter-intuitive one and the most useful. A masonry wall moves — thermally, with foundation settlement, with moisture — and that movement must be accommodated somewhere. If the mortar is the weaker component, cracking occurs along the joints: fine, distributed, following the bed lines, and repairable by raking out and repointing. If the mortar is stronger than the brick, the movement is forced through the units themselves, producing wide cracks straight through the bricks that cannot be repaired without rebuilding. So "stronger is better" is simply false here, and a rich cement mortar on soft handmade bricks is a classic and expensive mistake. (b) is straightforward and worth knowing as a mechanism, not a fact:C₃Ahydrates within minutes and would set the cement before it could be placed; gypsum reacts with it preferentially to form ettringite and slows it to a usable rate. Without gypsum, ordinary cement would be unusable in any structure. (c) is the trade that defines structural grades. Carbon strengthens steel and simultaneously destroys the two properties a structure most needs from it — ductility, so the member warns before it fails and can redistribute moment, and weldability, since high-carbon steel forms brittle zones on cooling. Structural grades therefore sit near 0.2% carbon and gain strength by alloying and processing rather than by carbon alone. (d) is wrong, and it is wrong in a way that matters structurally: timber is strongly anisotropic, with strength along the grain many times that across it. That is why timber members are designed for the fibre direction, why the defects that matter — knots, cross grain, shakes — are exactly those that interrupt the fibres, and why a joint loaded across the grain is the weak point of any timber structure.A concrete mix uses 350 kg of cement per m³ at a water–cement ratio of 0.45. The water content in kg per m³ is ______ (round to one decimal place)
Numerical answer — type the value.
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Answer: 157.5
157.5 kg/m³.water = w/c × cement = 0.45 × 350 = 157.5 kg, which is 157.5 litres since water has a density of 1 kg/litre — a convenient identity worth using, since site batching is in litres and design is in kilograms. The number is more interesting placed against the chemistry. Cement hydrates completely with only about 0.23–0.25 of its own mass of water, so about0.24 × 350 = 84 kgof this is doing chemical work and the remaining 73.5 kg is present purely to make the concrete placeable. Nearly half the water in a normal mix has no job except workability, and it is that half that eventually leaves and becomes capillary porosity. Raise the ratio to 0.60 and the water becomes 210 kg, adding another 52.5 kg of eventual pore space per cubic metre; drop it to 0.40 and the water is 140 kg, which is a stiffer and considerably more durable concrete that may not be placeable without a superplasticiser. That is the whole trade in three numbers. Two practical points. Water already present in the aggregate counts towards the ratio: aggregate delivered damp brings free surface moisture that must be measured and deducted from the added water, and ignoring it is one of the most common ways a site produces a mix wetter than its design. And a maximumw/cis specified by exposure class independently of strength — a mix can meet its strength grade comfortably and still fail its durability requirement, which is why the two limits are checked separately and the lower governs.Fly ash and ground granulated blast furnace slag improve the durability of concrete more than they improve its 28-day strength. The reason is that
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Answer: A — they consume the free calcium hydroxide left by hydration, converting a weak soluble by-product into more binding gel and refining the pore structure
They consume the free calcium hydroxide and refine the pore structure. Cement hydration produces the calcium silicate hydrate gel that gives concrete its strength, and as a by-product it also produces a substantial quantity of calcium hydroxide — a compound that contributes little strength, is soluble, and is the point of attack for sulphates and for leaching. Pozzolanic materials such as fly ash and silica fume, and the latent hydraulic slag, react with that calcium hydroxide in the presence of water to form more C-S-H gel. Two things follow, and they are the answer. The weak, soluble phase is converted into a binding one, and — more importantly for durability — the new gel is deposited inside the capillary pores, subdividing a connected pore network into a discontinuous one. Permeability falls by an order of magnitude or more, and since chloride, sulphate, moisture and carbon dioxide all arrive by that network, the durability improvement is much greater than the strength improvement. The timing is the other half of the picture and explains the 28-day observation directly. The pozzolanic reaction can only begin once ordinary hydration has produced calcium hydroxide to react with, so it is slow: a fly ash concrete is typically behind plain cement concrete at 28 days and ahead of it at 90 days and beyond. Judging such a mix on a 28-day cube alone therefore understates it, which is why durability-driven specifications extend the test age. Option (b) is wrong on the central point — these materials are reactive, not inert fillers, though it is true that they also lower the heat of hydration, which is a real secondary benefit in mass concrete. Option (c) is backwards: fly ash generally reduces water demand, because its spherical particles improve workability. Option (d) overstates and misdirects — supplementary materials actually consume alkalinity by consuming calcium hydroxide, and nothing prevents chloride ingress entirely.