Maharashtra HSC General Civil Engineering (Bifocal) cheat sheet

Standard sheet sizes (ISO A series): A0 = 841 × 1189 mm; each lower number is the previous size halved on the longer side (A1 = 594 × 841, A2 = 420 × 594, A3 = 297 × 420, A4 = 210 × 297 mm).

First-angle projection: the object lies between observer and plane, so the view from the front is placed above the top view and the left-side view goes on the right. Third-angle reverses this.

Line precedence when lines coincide: visible outline > hidden (dashed) line > centre line > cutting-plane line > dimension/extension line.

Dimensioning rules: dimension lines are drawn parallel to the measured edge and never coincide with an outline; extension lines start about 1 mm clear of the object; arrowheads touch the extension line.

Scale = drawing length ÷ actual length. Representative fraction (RF) is written as 1:50, 1:100, etc.; a diagonal scale is used when three units (e.g., m, dm, cm) must be read from one scale.

An ellipse is drawn by the concentric-circle or rectangle method using the major axis AB and minor axis CD; the foci lie on the major axis at distance sqrt(a² − b²) from the centre.

A cycloid is the locus of a point on a circle rolling along a straight line; one full arch has length 2πr and height 2r.

Conic sections: eccentricity e = distance from focus ÷ distance from directrix; e < 1 ellipse, e = 1 parabola, e > 1 hyperbola.

Section views use uniformly spaced 45° hatching lines (thin, equally spaced); adjacent parts in an assembly are hatched in opposite directions.

Standard brick (Indian modular): 190 × 90 × 90 mm; with 10 mm mortar joints the nominal size is 200 × 100 × 100 mm.

Classification of bricks by compressive strength (N/mm²): class 3.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 25, 30; a first-class brick is well burnt, uniform colour, gives a clear metallic ring, and absorbs not more than about 20% water.

Brick earth for good bricks should contain roughly 20–30% alumina, 50–60% silica, and less than 5% lime; excess lime causes bricks to crack and melt.

Cement mortar proportion 1:3 to 1:6 by volume for masonry; lime mortar is weaker and used mainly for non-structural work; the mortar should be used within about 30 minutes of mixing.

Concrete block masonry uses blocks with a minimum compressive strength of 3.5–5 N/mm² and hollow blocks of 400 × 200 × 200 mm nominal size; hollow blocks reduce dead load and improve thermal insulation.

English bond alternates header and stretcher courses and is the strongest brick bond; Flemish bond alternates header and stretcher in each course and gives better appearance.

Lintels span openings; a lintel carries the load of masonry above it, while an arch transfers load by compression to its supports.

Damp-proof course (DPC) is laid at plinth level, usually 40–50 mm thick, using materials such as bitumen, polythene sheet, or cement concrete with a waterproofing compound.

Pile foundation is used where soil bearing capacity is low or the water table is high; end-bearing piles rest on a hard stratum, friction piles transfer load by skin friction.

Principle of surveying: work from the whole to the part - establish a control framework of higher accuracy first, then fill in details.

Chain survey: 1 chain = 66 ft = 20.1168 m; 1 link = 0.66 ft = 0.201 m; 1 Gunter's chain has 100 links. Metric chain lengths are 20 m and 30 m.

Ranging: direct ranging is used when both ends are intervisible; indirect (reciprocal) ranging is used when the ends are not visible, using two intermediate points aligned by trial.

Obstacles to chaining: river (use similar triangles or a parallel line), building (use perpendicular offset and Pythagoras), and hill (step chaining).

Levelling: reduced level (RL) of a point = height of instrument (HI) − staff reading. HI = RL of benchmark + backsight reading.

Rise and fall method: rise = previous staff reading − next staff reading; fall is the reverse. Arithmetic check: ΣBS − ΣFS = ΣRise − ΣFall = last RL − first RL.

Height of instrument (collimation) method check: ΣBS − ΣFS = last RL − first RL, and each RL = HI − intermediate staff reading.

The level tube axis must be parallel to the line of collimation; the two-peg test detects the collimation error, and the correction is applied at a distance d as e × (d/D).

Theodolite: the horizontal circle reads horizontal angles, the vertical circle reads vertical angles; face-left and face-right readings average out the collimation error.

Contour interval depends on scale and terrain: for a scale of 1:1000 on flat ground use about 0.25–0.5 m; on steep ground use 1–2 m.

Stress σ = P/A; strain ε = ΔL/L; Young's modulus E = σ/ε (Hooke's law valid within the proportional limit).

Poisson's ratio μ = lateral strain ÷ longitudinal strain; for steel μ ≈ 0.3, for concrete ≈ 0.2.

Thermal stress in a fully restrained bar: σ = α E ΔT. Free expansion = α L ΔT.

Bending equation: M/I = σ/y = E/R; section modulus Z = I/ymax, so σ = M/Z.

For a rectangular section b × d: I = bd³/12, Z = bd²/6. For a circular section of diameter d: I = πd⁴/64, Z = πd³/32.

Shear stress τ = VQ/(Ib); for a rectangular section the maximum shear stress is 1.5 × average (3V/2bd), occurring at the neutral axis.

Torsion of a circular shaft: τ/r = T/J = Gθ/L; polar moment J = πd⁴/32 for a solid shaft.

Euler buckling load for a pin-ended column: Pcr = π²EI/L²; effective lengths: both ends pinned L, fixed–fixed 0.5L, fixed–pinned 0.7L, fixed–free 2L.

Simply supported beam with a central point load W and span L: maximum BM = WL/4 at midspan, maximum deflection = WL³/48EI.

Cantilever with a point load W at the free end: maximum BM = WL at the fixed end, maximum deflection = WL³/3EI.

A truss is analysed by the method of joints (two unknowns per joint) or the method of sections (cut through three members, take moments about the intersection point).

Concrete grades: M20 means characteristic cube strength of 20 N/mm² at 28 days; the mix is denoted by nominal proportions such as 1:1.5:3 for M20 (cement : fine aggregate : coarse aggregate).

Water–cement ratio governs strength and durability; the workability requirement is expressed by slump (mm) or compacting factor. Typical slump for RCC work is 50–100 mm.

Cement types: OPC 33, 43 and 53 grade refer to 28-day compressive strength in N/mm²; PPC contains fly ash or slag and gives better durability and lower heat of hydration.

Initial setting time of OPC must be not less than 30 minutes; final setting time not more than 600 minutes.

Curing: concrete should be kept moist for at least 7 days for OPC and 10–14 days for blended cements; curing improves strength gain and reduces shrinkage cracking.

Nominal cover to reinforcement (IS 456): 20 mm for mild exposure, 30 mm for moderate, 45 mm for severe, 50 mm for very severe, 75 mm for extreme exposure.

Limit state of collapse in flexure: Mu = 0.87 fy Ast d (1 − fy Ast / (fck b d)); the limiting value of xu/d is 0.53 for Fe415 and 0.48 for Fe500.

Minimum tension reinforcement in a beam: Ast/bd = 0.85/fy; maximum tension reinforcement = 4% of bD.

Shear design: nominal shear stress τv = Vu/(bd); the shear strength of concrete τc depends on the percentage of tension steel; the maximum shear stress τc,max is 3.1 N/mm² for M20 and 3.5 N/mm² for M25.

Development length Ld = φ σs/(4 τbd); for deformed bars in tension, τbd is taken as 1.6 times the plain-bar value, and the value is increased by 25% for compression.

Resultant of two forces P and Q at angle θ: R = sqrt(P² + Q² + 2PQ cos θ); the direction is given by tan α = Q sin θ / (P + Q cos θ).

Lami's theorem applies to three coplanar concurrent forces in equilibrium: P/sin α = Q/sin β = R/sin γ, where each angle is opposite the corresponding force.

Equilibrium of a coplanar force system: ΣFx = 0, ΣFy = 0, ΣM = 0. A body is in static equilibrium when these three conditions hold.

Moment of a force about a point = F × perpendicular distance; the principle of moments states that for equilibrium the sum of clockwise moments equals the sum of anticlockwise moments.

Friction: limiting friction F = μN, where μ is the coefficient of friction and N the normal reaction. The angle of friction φ satisfies tan φ = μ.

Centroid of a triangle lies at one-third of the height from the base; the centroid of a semicircle of radius r is at 4r/3π from the diameter.

Parallel-axis theorem: I = IG + A d², where IG is the moment of inertia about the centroidal axis and d is the distance between axes.

Work done = force × distance moved in the direction of the force; power = work ÷ time; kinetic energy = ½mv²; potential energy = mgh.

Strain energy stored in an axially loaded bar = ½ P ΔL = P²L/(2AE); the resilience modulus is σ²/(2E).

A body is in equilibrium under the action of a general coplanar force system when ΣFx = 0, ΣFy = 0, and ΣM about any point = 0.

Approximate estimate methods: plinth area rate method (cost = plinth area × rate per m²), cubical content method (volume × rate per m³), and unit rate method (per bed, per km, etc.).

Centre-line method: total length of the centre line of walls is computed once and multiplied by the width and depth of each item; it is efficient for walls of the same thickness.

Long wall–short wall method: long walls are measured out-to-out (centre length + one breadth) and short walls in-to-in (centre length − one breadth) for each cross wall.

Earthwork by the trapezoidal rule: V = h[(A1 + An)/2 + A2 + A3 + … + An−1]; prismoidal rule: V = h/3[(A1 + An) + 4(sum of even areas) + 2(sum of odd areas)].

Deduction for openings in masonry: deduct the full volume of the opening including the frame; for plaster, deduct openings exceeding 0.5 m² in area.

Contingency allowance in a detailed estimate is typically 3–5% of the estimated cost; work-charged establishment and centage charges are added separately.

Rate analysis: the rate per unit includes materials, labour, plant, contractor's profit (usually 10%), and overheads; the lead and lift of materials affect the rate.

Bar bending schedule: cutting length of a straight bar = clear span + 2 × end cover + 2 × hook length; for a 90° bend the deduction is 2d per bend, and for a 135° hook it is 3d per hook (d = bar diameter).

Standard hooks: a semicircular hook adds 9d to the length; a 45° bend adds 1d, a 90° bend adds 2d, and a 135° bend adds 3d.

Valuation: depreciation by the straight-line method = (cost − salvage value) ÷ useful life; the sinking fund method uses annual instalments that accumulate at compound interest.

Per capita water demand in Indian towns: about 135 litres per head per day (lpcd) for domestic use; total demand including industrial and public use is usually taken as 150–200 lpcd.

Design period: 30 years for water supply schemes, 15–20 years for treatment units; peak factor for demand is usually 1.5–2.0 times the average.

Water treatment sequence: screening → aeration → coagulation–flocculation (alum) → sedimentation → filtration (rapid sand filter) → disinfection (chlorination).

Rapid sand filter: rate of filtration 100–150 litres/m²/min; slow sand filter: 100–200 litres/m²/day. Slow sand filters remove bacteria better but need more land.

Chlorine demand = chlorine dose − residual chlorine. A free residual chlorine of 0.2 mg/L after 30 minutes contact is the usual requirement.

Sewage flow: about 80% of water supplied appears as sewage; the peak factor for sewage is 2–3. BOD is measured at 20°C over 5 days (BOD5).

Standard BOD5 of domestic sewage is about 200–300 mg/L and suspended solids about 200–300 mg/L; the COD/BOD ratio indicates biodegradability.

Septic tank: detention period 12–36 hours; sludge is removed every 1–3 years; effluent is disposed of through a soak pit or drain field.

Self-cleansing velocity in a sewer is about 0.6–0.75 m/s; the maximum velocity to avoid erosion is about 3 m/s.

A water seal of 25–50 mm in a trap prevents foul gases from entering a building; the minimum diameter of a house drain is 100 mm.

Road classification (Indian): National Highways, State Highways, Major District Roads, Other District Roads, and Village Roads.

Design speed and camber: for a bituminous surface in heavy rainfall, camber is 1 in 50; in light rainfall, 1 in 60. For earth roads the camber is 1 in 25.

Superelevation e = V²/(127R) (V in km/h, R in m); the maximum superelevation is 7% for plain terrain and 10% for hilly terrain without snow.

Stopping sight distance SSD = 0.278 V t + V²/(254 f), where t is the reaction time (about 2.5 s) and f the coefficient of longitudinal friction (about 0.35–0.4).

CBR method of flexible pavement design: the total thickness depends on the soaked CBR of the subgrade; the required thickness decreases as CBR increases.

Flexible pavement layers from bottom to top: subgrade, sub-base, base course, and wearing course. Rigid pavement is a cement concrete slab that distributes load by beam action.

Bitumen grades: VG-10, VG-20, VG-30 and VG-40; the penetration test, ductility test, and softening point test characterise bitumen.

Bridges: the span is the distance between supports; the waterway is the area of the opening; the afflux is the rise in water level upstream caused by the bridge.

Traffic volume is expressed as PCU (passenger car units); a car = 1 PCU, a truck or bus = 3 PCU, a motorcycle = 0.5 PCU, a cycle = 0.5 PCU.

Culvert: a cross-drainage structure with a span up to about 6 m; a minor bridge has a span of 6–60 m, and a major bridge has a total length above 60 m.

PERT uses three time estimates: optimistic (to), most likely (tm), and pessimistic (tp). Expected time te = (to + 4tm + tp)/6; variance = ((tp − to)/6)².

CPM is activity-oriented and deterministic; the critical path is the longest path through the network and has zero total float.

Total float = LS − ES = LF − EF; free float = ES of successor − EF of current activity; the critical path has zero total float.

Earliest start (ES) is the maximum EF of predecessors; latest finish (LF) is the minimum LS of successors.

A network diagram must have a single start node and a single end node; dummy activities are used to maintain logic without consuming time or resources.

S-curve shows cumulative progress or cost against time; the cost slope = (crash cost − normal cost) ÷ (normal time − crash time) and is used for time–cost trade-off.

Labour output: a mason can lay about 1 m³ of brickwork per day with one helper; a carpenter can fix about 8–10 m² of shuttering per day.

Safety: a hard hat, safety shoes, and a safety belt are mandatory for work at height above 1.8 m; scaffolding must be inspected before use.

Work measurement: the unit of measurement for brickwork is m³, for plastering m², for painting m², and for reinforcement kg or tonne.

Personal protective equipment (PPE): helmet, safety shoes, high-visibility vest, gloves, and ear and eye protection are required on site.

Excavation safety: provide shoring or benching for trenches deeper than 1.5 m; keep the excavated soil at least 1 m away from the edge.

Scaffolding: the working platform should be at least 600 mm wide and fitted with a toe board and guard rail; the maximum height of a working platform is 2 m below the next lift.

Ladder safety: the ladder should be set at about 75° to the horizontal (1 in 4 rule) and extend at least 1 m above the landing.

Electrical safety on site: use 110 V or 230 V with an earth-leakage circuit breaker; temporary wiring must be protected and isolated after work.

First aid: for electric shock, switch off the supply first, then give artificial respiration if breathing stops; report all accidents in the accident register.

Professional ethics: an engineer must not accept a commission from a supplier, must sign only work actually inspected, and must disclose conflicts of interest.

The contract documents (drawings, specifications, bill of quantities, conditions of contract) govern the work; the bill of quantities is measured and valued at the contract rates.

Occupational health: silica dust from cutting concrete causes silicosis; wet cutting and dust masks reduce exposure.

CAD coordinate entry: absolute (x,y), relative (@x,y), and polar (@distance<angle). Ortho mode constrains drawing to horizontal and vertical directions.

Common AutoCAD commands: LINE, CIRCLE, ARC, RECTANGLE, POLYGON, OFFSET, TRIM, EXTEND, FILLET, CHAMFER, ARRAY, MIRROR, SCALE, ROTATE.

Layers control line type, colour, and line weight; the current layer is the one on which new objects are created. Objects cannot be edited on a locked layer.

Object snapping (OSNAP) snaps to endpoints, midpoints, centres, intersections, and perpendicular points; it improves accuracy compared with free-hand picking.

A block is a named group of objects inserted as a single entity; an attribute can attach text data (e.g., a door number) to a block.

Paper space and model space: draw full-size in model space and set the plot scale in the layout (paper space) viewport, e.g., 1:100.

Dimension styles control arrow size, text height, and precision; the dimension scale factor (DIMSCALE) must match the plot scale.

A DXF or DWG file is the standard exchange format for CAD drawings; a PDF is used for sharing and printing but is not editable as vector geometry in CAD.

Spreadsheet software: a formula begins with '=', SUM(range) adds values, and absolute references ($A$1) remain fixed when copied.