Construction Techniques: Foundations, Masonry, Openings, Frames, Roofs, Fire Safety, Floors, Modular Coordination and Prefabrication
2. Masonry and bonds
Brick masonry is laid in courses (horizontal layers) bedded in mortar. A brick shows its long face as a stretcher and its short end face as a header. The standard modular brick is 190 × 90 × 90 mm actual size, which with a 10 mm mortar joint occupies a 200 × 100 × 100 mm nominal space. A bond is the pattern that makes the wall act as one mass: the vertical joints (perpends) of a course must never lie directly over those of the course below, so each brick laps the ones below, usually by a quarter or half brick.
| Bond | Arrangement | Use and comment |
|---|---|---|
| Stretcher bond | Only stretchers in each course; each course shifted half a brick | Half-brick (90 mm) walls, partitions, outer leaf of a cavity wall; no headers, so no cross-tie in thicker work |
| Header bond | Only headers in each course | One-brick walls and curved work of small radius, since headers follow the curve |
| English bond | Alternate courses of headers and stretchers; a queen closer beside the quoin header sets the lap | The strongest bond and the usual choice for load-bearing walls |
| Flemish bond | Headers and stretchers alternate within every course | Better appearance, slightly weaker than English; single Flemish has Flemish facing with English backing in thick walls |
| Rat-trap bond | Bricks on edge, headers and stretchers leaving a cavity inside the wall | Saves bricks and mortar and improves thermal performance; low-rise work |
- Quoin: the external corner of a wall. Bat: a cut piece of brick (half bat, three-quarter bat) used to complete a course.
- Queen closer: a brick cut lengthwise into two halves of half width, placed beside the quoin header to break the vertical joint. King closer: a brick with one corner cut away so one end is half width.
- Rubble masonry uses undressed or roughly dressed stones, random or coursed; ashlar uses finely dressed stones with thin joints and is the costlier, finer work. Through-stones (bonders) tie a stone wall across its thickness.
Quantities. With the modular brick, 1 m³ of masonry holds 1/(0.2 × 0.1 × 0.1) = 500 bricks. Those bricks occupy 500 × (0.19 × 0.09 × 0.09) = 0.7695 m³, so wet mortar is 1 − 0.7695 = 0.2305 m³ per m³ of masonry. For a 6 m × 3 m wall, one brick (200 mm) thick, with a 1 m × 2.1 m door, the net face is 18 − 2.1 = 15.9 m², the volume 15.9 × 0.2 = 3.18 m³ and the bricks 3.18 × 500 = 1590.
3. Fenestration (doors and windows) and arches
Fenestration is the design and arrangement of openings in the envelope: doors for access and escape, windows for light, ventilation and view. Size, position and orientation decide daylight, cross-ventilation, heat gain, privacy, security, noise and fire spread, so the opening is a climatic and structural decision as well as a joinery detail. Frame parts: head, sill and jambs; a lintel carries the wall above the opening, and a sill is sloped with a drip groove (throating) to shed water.
| Type | Character |
|---|---|
| Ledged and braced door | Vertical boards held by horizontal ledges and diagonal braces that rise from the hinge side so they act in compression; cheap, for stores and sheds |
| Framed and panelled door | Stiles, top, middle and bottom rails and muntins frame panels that sit loose in grooves, so the timber can move without splitting |
| Flush door | Skeleton frame faced both sides with plywood or board; hollow or solid core; plain and light |
| Revolving, sliding, folding, rolling shutter | Revolving doors limit air exchange at busy lobbies; sliding and folding save swing space; rolling shutters give security to shops |
| Casement and sash windows | Casement sashes are side-hung and open fully; double-hung sashes slide vertically and open only half |
| Clerestory, dormer, bay, bow, oriel | Clerestory: high-level window above eye level. Dormer: vertical window projecting from a sloping roof. Bay: projects from the ground upward; bow: curved bay. Oriel: projects from an upper floor on corbels and does not reach the ground |
An arch spans an opening by turning vertical load into inclined compression along its curve, delivering a thrust to the abutments. Parts: intrados (soffit, the inner curve), extrados (outer curve), voussoirs (wedge-shaped units), keystone (crown unit), springing line (where the curve starts), haunch, skewback, spandrel, span and rise. For a masonry arch to carry load without tension in its joints, the line of thrust must stay within the middle third of the arch ring; the abutment, a buttress or a tie must resist the horizontal thrust.
| Arch | Geometry |
|---|---|
| Semicircular | Rise = half the span; centre on the springing line |
| Segmental | Rise less than half the span; radius R = (c²/4 + h²)/(2h) for chord c and rise h |
| Equilateral pointed | Two arcs of radius equal to the span, centres at the opposite springings; rise = (√3/2) × span |
| Lancet and drop | Pointed arches whose radius is more than (lancet) or less than (drop) the span |
| Flat (jack) arch | Soffit horizontal, joints radiating; weak, needs firm abutments, for small openings |
4. Scaffolding and formwork
Scaffolding is a temporary platform that lets workers and materials reach height. Its parts are standards (verticals), ledgers (horizontals along the wall), putlogs (transverse members with one end in the wall) or transoms (transverse members resting on ledgers), braces, boards, guard rails and toe boards. A single (bricklayer's) scaffold has one row of standards parallel to the wall with putlogs resting in the wall; a double (mason's) scaffold has two rows of standards and is independent of the wall, which is why it is used for stone masonry where putlog holes cannot be left. A cantilever scaffold projects from the wall where the ground cannot take standards; a suspended scaffold hangs from ropes for painting and façade work; steel tubular and system scaffolds have largely replaced timber, and bamboo remains common in India.
Formwork is the temporary mould that shapes and supports wet concrete until it can carry itself. It must be strong enough for wet-concrete weight and pressure, rigid enough to hold its shape with little deflection, tight enough not to lose grout, accurate in dimension, easy to erect and strip without shock, and reusable. Materials: timber (cheap, few reuses), plywood (better finish, more reuses), steel (rigid, many reuses, heavy), aluminium (light, quick, fits repeated housing), plastic or FRP (moulds for waffle and ornamental work). Wet concrete behaves like a fluid at first, so its lateral pressure on a vertical form is at most γh: for γ = 25 kN/m³ and a 2 m pour it is 50 kN/m² at the base.
| System | How it works |
|---|---|
| Conventional (props, joists, sheeting) | Built and stripped piece by piece for each pour; flexible, labour-heavy |
| Table or flying form | Large slab form on legs, moved whole by crane to the next floor |
| Climbing (jump) form | Wall or core form lifted by crane or jacks after each pour |
| Slip form | Moves up continuously at a controlled rate as concrete is placed, without stopping; silos, chimneys, lift cores |
| Tunnel form | Room-sized forms casting walls and slab together; repetitive cellular housing |
| Permanent (stay-in-place) form | Precast thin slabs or profiled steel deck left in the structure |
| Member | Time |
|---|---|
| Vertical sides of beams, walls and columns | 16 to 24 hours |
| Slab soffit with props refixed at once | 3 days |
| Props to slabs, span up to 4.5 m; over 4.5 m | 7 days; 14 days |
| Props to beams, span up to 6 m; over 6 m | 14 days; 21 days |
5. Frame construction: timber, RCC and steel
In load-bearing construction the walls carry the floors and roof. In frame construction a skeleton of columns and beams carries the load and the walls are only infill or cladding, so planning is freer, walls are thinner, openings are larger and buildings can rise higher. The frame material changes the speed, spans, fire behaviour and detailing.
Timber frame. Heavy post-and-beam frames use widely spaced timbers joined by mortise-and-tenon and pegged joints; light stud framing uses closely spaced studs sheathed with boards that act as bracing and diaphragm. In platform framing each floor is built as a platform on which the next storey's walls are erected, so fire and shrinkage are confined to one storey; in balloon framing studs run continuous from sill to roof, which gives the fire a vertical path and unequal shrinkage, and it is now rare. Traditional Indian timber systems, such as Himachal's kath-khuni and Kashmir's dhajji dewari, laced timber through masonry to give ductility in earthquakes.
RCC frame. Columns, beams and slabs are cast monolithically, so joints are rigid and carry moment; masonry infill is non-structural. Reinforcement needs adequate cover for durability and fire resistance. Construction joints go where shear is least, usually the middle third of a beam or slab span, and at a column just below the beam soffit and at the top of the footing. Expansion joints divide very long buildings, commonly at about 45 m. The frame is slower than steel because concrete must gain strength, but it is fire-resistant, monolithic and locally buildable.
Steel frame. Rolled I-sections (beams and columns), channels, angles, tees and hollow sections are fabricated off site and erected by crane, joined by bolts (ordinary or high-strength friction-grip) or welds; riveting is obsolete. Beam-to-column joints are simple (web cleats, carrying shear only) or rigid (flange plates or extended end plates, carrying moment). Steel is light for its strength and fast to erect, and composite floors tie a concrete slab on profiled deck to the beams with shear studs. But it needs corrosion protection and, because it loses strength in fire, fire protection. Pre-engineered buildings use tapered built-up portal frames, purlins and sheeting for factories and warehouses; light-gauge steel framing uses cold-formed sections for low-rise work.
| Aspect | Timber | RCC | Steel |
|---|---|---|---|
| Speed on site | Fast, dry work | Slower; curing and formwork | Fastest erection |
| Fire behaviour | Chars; large sections keep a core | Good; cover protects bars | Poor unprotected; needs protection |
| Typical use | Low-rise houses, roofs | Most mid- and high-rise buildings | Long spans, tall towers, sheds |
6. Roofs and roof coverings
Flat roofs are nearly level, with a slight fall for drainage: an RCC slab with a screed to falls and waterproofing, or older forms such as brick-bat coba terracing (lime concrete with brickbats laid to a slope) and the jack-arch roof (shallow brick arches springing between rolled steel joists). Pitched roofs shed water by slope and suit heavy rain.
- Terms: ridge (top horizontal line where slopes meet), eaves (lower edge), hip (external angle where two slopes meet), valley (internal angle where two slopes meet), verge (edge of a gable), rafter, purlin (carries the covering, rests on the truss at panel points), tie beam, rise and span.
- Types: lean-to (single slope against a wall); gable or couple roof; couple-close roof (a tie joins the rafter feet, so no outward thrust on the walls); hip and hipped-gable; mansard (each side has a steep lower slope and a gentle upper one); butterfly; and the saw-tooth roof, whose glazed faces look away from the sun for steady light in factories.
Trusses span larger widths. A king post truss has one central vertical post; a queen post truss has two posts and a straining beam, for longer spans. Under vertical roof load the principal rafters and struts are in compression, the tie beam in tension, and the king post is a tension member that hangs the tie beam from the apex. Steel trusses (Fink, Howe, Pratt, Warren) follow the same triangulation. Pitch is rise/span: for a span of 8 m and a rise of 3 m the pitch is 3/8, the half-span run is 4 m and the rafter length is √(4² + 3²) = 5 m, at a slope angle of 36.9°.
| Covering | Character |
|---|---|
| Galvanised corrugated sheets | Light, cheap, noisy in rain, hot, corrodes at cut edges |
| Fibre-cement sheets | Low cost; asbestos-cement sheets are restricted or banned in many countries for health reasons, and non-asbestos fibre cement is replacing them |
| Clay (Mangalore) tiles, slates | Heavy, good insulation; small units need a steeper pitch and a closer framework |
| Thatch | Grass, straw or palm; very good insulation, flammable, short life, needs a steep pitch |
| Profiled coated steel, standing-seam metal | Long lengths and low pitch; used in pre-engineered buildings |
| Membranes, green and cool roofs | Bitumen or polymer membranes waterproof flat roofs; green roofs add insulation and retain rain; cool roofs reflect solar radiation |
7. Lightweight construction, fire protection and flooring
Lightweight construction cuts dead load, so foundations and frames shrink, and since earthquake force grows with mass it also lowers seismic force. Examples: AAC and cellular lightweight concrete blocks, lightweight aggregates (expanded clay, pumice, perlite), light-gauge steel framing, sandwich panels (an insulating core between steel skins), dry-wall partitions of gypsum or fibre-cement board on metal studs, tensile membranes and space frames. Its weaknesses: low mass gives poor sound insulation and little thermal storage, and fixings, moisture and fire need care.
Fire protection works on several principles at once. Fire load is the heat potential of the combustibles per unit floor area. Fire resistance is the time, in hours, that an element keeps its stability, integrity and insulation in a standard fire test; note that a material can be non-combustible (steel) and still have poor fire resistance. The principles: (1) limit ignition and fire load; (2) detect early and alarm; (3) compartmentation: divide the building with fire-resisting walls, floors and self-closing doors, enclose stairs, lifts and service shafts, fire-stop every service penetration, and limit spread over façades; (4) protect the structure for the required period; (5) provide escape; (6) suppress and give fire-fighters access (details in the services section).
- Structural protection: RCC cover protects the bars; steel is boxed in concrete, brick or gypsum board, coated with intumescent paint that swells when hot, or sprayed with vermiculite or mineral fibre, because unprotected steel falls to about half its yield strength at roughly 550 to 600 °C. Large timber sections char on the outside and keep a sound core.
- Escape: at least two independent routes from every floor; exits within permitted travel distance; stair enclosures that are fire-resisting and smoke-protected; doors opening in the direction of travel; signage and emergency lighting; refuge areas and a fire lift in tall buildings (the National Building Code treats buildings 15 m and above as high-rise for fire provisions). Smoke, not flame, is the commonest killer.
Flooring. A ground floor is built up from compacted subgrade, sand or brickbat filling, a plain cement concrete base, and a finish, with a polythene sheet or DPC against rising damp. Choose the finish by wear, slip resistance, cleaning, comfort, noise and cost. IPS (cement concrete topping laid in panels with dividing strips), granolithic concrete and metallic-hardener floors stand up to industrial wheeled traffic; terrazzo (marble chips in cement, ground and polished) and kota stone, marble and granite suit public areas; ceramic or vitrified tiles suit wet and kitchen areas, with an anti-skid texture where wet; timber and resilient floors (vinyl, linoleum, rubber) are warm and quiet; epoxy coatings serve laboratories and plants; raised access floors let services run below an office floor. Upper floors are RCC slabs, composite deck, precast hollow-core planks or timber joists.
8. Modular coordination and prefabricated construction
Modular coordination (MC) is dimensional coordination of buildings and components in a common unit, so that parts made by different makers fit with little cutting and waste. The basic module M is 100 mm. Multi-modules are whole multiples (3M = 300 mm, the commonly preferred planning module in plan, 6M, 12M and so on); sub-modules are fractions of M (such as 50 mm and 25 mm), used for thin items and joints. The modular brick follows from this: a nominal 200 × 100 × 100 mm size, with a 10 mm joint, means a work size of 190 × 90 × 90 mm, so that work size = modular size − joint.
- Modular grid: a rectangular network of lines spaced at the module or a multi-module. Components are placed on or between controlling lines. In a single-line grid an element sits on the line; in a double-line (zone) grid two sets of lines enclose a neutral zone in which a column or wall may have a non-modular thickness.
- Gains: fewer sizes, so mass production; interchangeable parts; less waste and cutting; simpler drawing and estimating; faster erection. Limits: a rigid grid is awkward for curved or free forms, and it needs an industrial base to pay off. A bay of 3.6 m × 4.8 m on a 3M grid is 12 × 16 grid squares, and 13 grid lines run across the 12 modules.
Prefabrication is manufacture of components in a factory or a casting yard, then transport and erection. Levels: components (columns, beams, slabs, lintels, blocks), panels (large wall and floor panels), volumetric units (finished rooms or boxes) and kit buildings. Systems: precast frame (columns, beams and slabs joined on site), large-panel systems (load-bearing walls and floors), box systems, steel and timber panels. Gains: speed, factory quality control, less site labour and formwork, weather-independent work, safety, economy through repetition. Limits: transport and crane capacity, low design flexibility, high initial investment, and joints that decide watertightness and, in earthquakes, whether the structure acts monolithically.
- Joints: dry connections (bolted or welded steel plates and inserts) are quick; wet connections (cast-in-situ concrete or grout in stitches and sleeves) give continuity. Open systems use components from many suppliers that fit by modular coordination; closed systems use one maker's components only. Prefabrication therefore depends on MC.
- Handling stresses often govern a precast member's design. A uniform beam of length L lifted at two symmetric points a from each end has hogging moment wa²/2 and sagging moment wL²/8 − wLa/2; equating them gives a = 0.207 L, the position that makes the two equal.
Key takeaways
- A foundation spreads load so the soil neither fails nor settles unevenly; Rankine's minimum depth is D = (q/γ)[(1 − sin φ)/(1 + sin φ)]², with the square.
- A bond keeps vertical joints from lining up: English bond alternates courses of headers and stretchers (strongest), Flemish alternates within each course; count bricks with the 200 × 100 × 100 mm nominal size, 500 per m³.
- An arch carries load in compression and pushes on its abutments; the line of thrust must stay in the middle third. Segmental radius R = (c²/4 + h²)/(2h); an equilateral arch rises (√3/2) × span.
- Formwork must be rigid, tight and strippable: sides first (16 to 24 hours), then slab and beam props over days; slip forms rise continuously, climbing forms in stages.
- In a king post truss the king post is in tension; steel frames are quick but need fire protection because they lose about half their yield strength near 550 to 600 °C; non-combustible does not mean fire-resisting.
- Basic module M = 100 mm, planning grid 3M = 300 mm, work size = modular size − joint; prefabrication needs modular coordination, depends on repetition, and is governed by its joints and handling stresses (lifting points at 0.207 L).
Practice questions (20)
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.
Which description fits English bond in brickwork?
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Answer: C — Alternate courses of headers and stretchers, with a queen closer beside the quoin header
English bond alternates whole courses of headers and stretchers, and a queen closer beside the quoin header sets the lap so that vertical joints do not line up. Flemish bond is the tempting alternative, but it alternates headers and stretchers within each course. Stretcher-only courses are stretcher bond, and edge-laid bricks enclosing a cavity are rat-trap bond.An edge column cannot project beyond the property line. Its footing is joined by a beam to the footing of an interior column, and the beam balances the eccentric load. This arrangement is called a
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Answer: D — strap (cantilever) footing
In a strap footing two separate bases are tied by a strap beam that carries the moment from the eccentric edge load to the interior footing. A combined footing is the tempting alternative, but it is one common slab under both columns rather than two bases linked by a beam. A pad centred under the edge column would need to cross the boundary.A one-brick-thick (200 mm nominal) wall of modular bricks is 6 m long and 3 m high and has one door opening of 1 m × 2.1 m. Taking 500 bricks per m³ of masonry (nominal size), the number of bricks required is
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Answer: B — 1,590
Net face = 6 × 3 − 1 × 2.1 = 15.9 m²; volume = 15.9 × 0.2 = 3.18 m³; bricks = 3.18 × 500 = 1,590. The figure 1,800 is the tempting one because it ignores the door. The figure 2,066 comes from dividing by the actual brick volume (about 650 per m³), which counts mortar space as brick.Which formwork system rises continuously at a controlled rate while concrete is being placed, and so suits silos, chimneys and lift cores?
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Answer: D — Slip form
A slip form creeps upward without stopping as the concrete in it sets, giving a joint-free shaft. The climbing form is the near miss: it is raised in stages between pours, so it leaves construction joints. Table and tunnel forms serve slabs and repetitive cells.Under vertical load on a king post truss, the king post acts as
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Answer: A — a tension member hanging the tie beam from the apex
The principal rafters and the struts are in compression and push on the tie beam, which is in tension; the king post hangs the middle of the tie beam from the apex, so it is a tension member. Calling it a compression strut is the tempting error because it looks like a column.Structural steel does not burn, yet an unprotected steel frame needs fire protection. The main reason is that
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Answer: C — steel loses much of its strength at a few hundred degrees, so loaded members can fail early
At roughly 550 to 600 °C steel keeps only about half its yield strength, which a building fire can reach in minutes, so a loaded unprotected member can fail. It melts only at far higher temperatures, which is the tempting wrong answer, and it adds no fire load because it is non-combustible.A modular brick has a nominal (modular) size of 200 × 100 × 100 mm and is laid with a 10 mm mortar joint. Its work (manufacturing) size is
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Answer: B — 190 × 90 × 90 mm
Work size = modular size − joint = 200 − 10 = 190 mm, and likewise 90 and 90 mm. Adding the joint (210 mm) reverses the relation, and leaving the size unchanged ignores the joint that completes the module.A uniform precast beam 10 m long is lifted at two points placed symmetrically, each at distance a from an end. The hogging moment at the lifting points is to equal the sagging moment at midspan. The distance a is
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Answer: C — 2.07 m
With self-weight w, hogging = wa²/2 and sagging = wL²/8 − wLa/2. Equating gives 4a² + 4La − L² = 0, so a = 0.207 L = 2.07 m. A quarter-length pick, 2.50 m, is the tempting round figure, but it gives a larger hogging moment than sagging moment.A workshop floor will carry wheeled loads and heavy abrasion. The most appropriate finish is
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Answer: B — a granolithic or metallic-hardened concrete topping
Hard aggregate or metallic hardener in the topping resists abrasion and wheel loads. Marble is the tempting prestige finish, but it is soft, polishes slippery and chips under impact. Parquet and thin vinyl wear through in a workshop.In the usual sequence of stripping formwork from a floor cast with ordinary Portland cement, which is removed first?
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Answer: A — The vertical side forms of beams, after about 16 to 24 hours
Side forms carry no load and can come off as soon as the concrete resists damage, about 16 to 24 hours. Props and soffits carry the self-weight and wait for days: slab props about 7 days for spans up to 4.5 m, beam props about 14 days for spans up to 6 m. The slab props are the tempting pick because slabs look lighter than beams, but they still wait days.Stone masonry is to be raised with scaffolding. A double (mason's) scaffold is preferred to a single scaffold because
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Answer: A — its two rows of standards stand clear of the wall, so no putlog holes are needed
In a double scaffold the two rows of standards carry their own ledgers, braces and transoms, so the stone wall is not pierced for putlogs. The single scaffold relies on putlogs resting in the wall, which suits brick, where a brick can be left out and filled later, but not irregular stone. The suspended scaffold is hung from ropes and is a different type.Which of the following are requirements of good formwork?
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Answer: A — It must be rigid enough to keep its shape under the pressure of wet concrete; B — Its joints must be tight enough to prevent loss of cement grout; D — It should be removable without shock or damage to the young concrete
Rigidity, tight joints and damage-free stripping are the standard requirements, together with accuracy of size and reuse. A form that bonds to the concrete is a defect, because it tears the surface at stripping; release agents are used to prevent that. Only a permanent form is designed to stay, and it is a separate system.Which of the following are sound fire-protection measures in principle?
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Answer: B — Filling the gaps around service pipes that pass through a fire wall with fire-stopping; C — Giving every floor at least two independent escape routes; D — Enclosing stairs and lift shafts in fire-resisting construction
Fire-stopping keeps compartment walls intact where services pierce them; two independent routes keep an escape open if one is blocked; and enclosed shafts stop smoke and flame using stairs and lifts as chimneys. A fire door held open defeats compartmentation, because only a closed, self-closing door contains the fire.Which statements about roofs are correct?
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Answer: A — A hip roof slopes on all four sides of a rectangular building; B — A valley is the internal angle where two roof slopes meet; C — A couple roof without a tie pushes the supporting walls outward
A hip roof has four slopes, a valley is an internal meeting of slopes, and without a tie the rafter feet spread and push the walls out. The mansard statement is reversed: the lower slope is the steep one and the upper slope is gentle, which is the tempting slip.Which statements about foundations are correct?
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Answer: A — A raft foundation reduces differential settlement by tying the whole building to one slab; B — Under-reamed piles suit expansive black cotton soil because their bulbs anchor below the zone of seasonal moisture change; D — A strap footing is used when an edge column's footing cannot be centred under the column
A raft ties the whole plan together, under-reamed bulbs anchor against swelling and shrinkage, and a strap beam handles an eccentric edge footing. The Rankine statement is wrong: the ratio (1 − sin φ)/(1 + sin φ) falls as φ rises, so the minimum depth falls, which is the tempting reversal.A foundation is to be taken down to Rankine's minimum depth D = (q/γ)[(1 − sin φ)/(1 + sin φ)]². With q = 200 kN/m², γ = 18 kN/m³ and φ = 30°, the depth in metres, correct to two decimal places, is ____.
Numerical answer — type the value.
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Answer: 1.23
sin 30° = 0.5, so (1 − 0.5)/(1 + 0.5) = 1/3 and its square is 1/9. q/γ = 200/18 = 11.111 m. D = 11.111/9 = 1.2346, which is 1.23 m to two decimal places. Check: 11.111 × 0.1111 = 1.2346.A wall of modular brick is 10 m long, 3 m high and 0.2 m thick, with openings of 2.0 m² and 1.8 m². One m³ of this masonry holds 500 bricks of actual size 190 × 90 × 90 mm, and the rest is wet mortar. The wet mortar volume for the wall, in m³ correct to two decimal places, is ____.
Numerical answer — type the value.
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Answer: 1.21
Net area = 30 − (2.0 + 1.8) = 26.2 m²; volume = 26.2 × 0.2 = 5.24 m³. Bricks per m³ occupy 500 × 0.19 × 0.09 × 0.09 = 0.7695 m³, so mortar is 0.2305 m³ per m³. Mortar = 5.24 × 0.2305 = 1.2078, which is 1.21 m³. Check: 5.24 − 5.24 × 0.7695 = 5.24 − 4.0322 = 1.2078.A room measures 6.0 m × 4.5 m and is laid out on a 3M planning grid (M = 100 mm). The number of 300 mm × 300 mm grid squares in the room is ____.
Numerical answer — type the value.
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Answer: 300
3M = 300 mm. Along 6.0 m there are 6000/300 = 20 modules and along 4.5 m there are 4500/300 = 15 modules. Squares = 20 × 15 = 300. Check by area: 27 m² ÷ 0.09 m² = 300.A segmental arch has a clear span (chord) of 10 m and a rise of 2 m. Using R = (c²/4 + h²)/(2h), the radius of its intrados, in metres to two decimal places, is ____.
Numerical answer — type the value.
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Answer: 7.25
c²/4 = 100/4 = 25 and h² = 4, so the numerator is 29; 2h = 4. R = 29/4 = 7.25 m. Check from geometry: half-chord 5 and R − h = 5.25 give 5² + 5.25² = 25 + 27.5625 = 52.5625 = 7.25². The check holds.A symmetrical gable roof has a span of 12 m and a rise of 4.5 m, with no overhang. The length of each rafter, in metres, is ____.
Numerical answer — type the value.
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Answer: 7.5
Half-span = 6 m. Rafter = √(6² + 4.5²) = √(36 + 20.25) = √56.25 = 7.5 m. Check: a 3-4-5 triangle scaled by 1.5 gives 4.5-6-7.5.