Advanced Civil Engineering Handbook › Chapter 13

Chapter 13 of 14 · 37 formulas · 75 one-liners

Estimating, Costing and Valuation — formulas & one-liners

Types of estimates, IS 1200 units of measurement, rate analysis, material quantities for concrete, brickwork, plaster and reinforcement (BBS), earthwork volumes, valuation and contract types.

13.1 Types of estimates and approximate methods

Plinth area estimate

Cost = Plinth area \times Plinth area rate

Plinth area in m²; rate in ₹/m² from similar recent buildings

Used for preliminary (approximate) estimates

Cubical content estimate

Cost = (Plinth area \times Height) \times Cube rate

Height of the building in m; cube rate in ₹/m³

More accurate than plinth area method for buildings of different heights

Service unit (unit base) estimate

Cost = N \times Cost per unit

N = number of units, e.g. beds in a hospital, students in a school, seats in a hall

Total estimated cost of a work

Estimate = \sum (Quantity \times Rate) + Contingencies + W.C.E.

W.C.E. = work-charged establishment

Contingencies usually 3–5%; W.C.E. usually 1.5–2%

A preliminary or approximate estimate is used to obtain administrative approval, while a detailed estimate is the basis for technical sanction.
A detailed estimate is prepared by taking out quantities of every item from the drawings and specifications and multiplying them by current rates.
Approximate estimating methods include the plinth area method, cubical content method, service unit method, bay method and approximate quantity method.
A revised estimate is prepared when the sanctioned estimate is likely to be exceeded by more than 5% (rule given in standard Indian estimating texts) or when the work is materially changed.
A supplementary estimate is prepared for additional work found necessary while the original work is in progress.
An annual repair (maintenance) estimate keeps a structure in proper condition and is commonly about 1–1.5% of its capital cost.
Contingencies of about 3–5% are added to an estimate to cover petty items and unforeseen expenses not provided for in the item list.
Work-charged establishment, about 1.5–2% of the estimate, covers staff such as chowkidars and work supervisors employed for that particular work.
Plinth area and carpet area of buildings are measured as per IS 3861.
Quantities are recorded in the measurement (details of measurement) sheet and then priced in the abstract of estimate.

13.2 Units and modes of measurement (IS 1200)

Length of long walls (long wall–short wall method)

L_{long} = L_{c / c} + b

L_c/c = centre-to-centre length; b = width of wall or trench at that level

Measured out-to-out

Length of short walls (long wall–short wall method)

L_{short} = L_{c / c} - b

Symbols as above

Measured in-to-in

Effective length in centre-line method

L_{eff} = L_{CL} - n \cdot \frac{b}{2}

L_CL = total centre-line length of walls; n = number of T-junctions; b = width at that level

No deduction at corners (L-junctions)

As per IS 1200, dimensions are measured to the nearest 0.01 m, areas worked out to the nearest 0.01 m² and volumes to the nearest 0.01 m³.
Earthwork, plain and reinforced concrete, and brickwork of one brick and above are measured in m³.
Half-brick walls and partitions, plastering, pointing, painting, white washing, flooring and damp-proof course are measured in m².
Reinforcement steel is measured by mass (kg, quintal or tonne), computed from bar lengths and standard unit masses.
Formwork (centering and shuttering) is measured in m² of the surface in contact with concrete (IS 1200 Part 5).
Woodwork for door and window frames is measured in m³, while shutters are measured in m².
Pipes, handrails and similar linear items are measured in running metres.
In plastering (IS 1200 Part 12), no deduction is made for openings up to 0.5 m²; for openings of 0.5–3 m² one face is deducted and jambs are not added; for openings above 3 m² both faces are deducted and jambs, soffits and sills are added.
In brickwork, no deduction is made for openings up to 0.1 m² in area (IS 1200 Part 3).
Lead is the horizontal distance and lift the vertical height through which excavated earth is carried; CPWD earthwork rates include a lead up to 50 m and lift up to 1.5 m.

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13.3 Rate analysis and concrete quantities

Rate per unit of an item (analysis of rates)

Rate = \frac{( M + L + T ) ( 1 + w ) ( 1 + p )}{Q}

M = materials; L = labour; T = tools, plant and sundries; w = water charges; p = contractor's profit and overheads; Q = quantity analysed

CPWD: w = 1%, p = 15%

Dry volume of concrete materials

V_{dry} = 1.54 V_{wet}

V_wet = volume of finished concrete

Allows for voids and bulking; some texts use 1.52 or 1.57

Volume of cement in a nominal mix 1 : s : a

V_{c} = \frac{1}{1 + s + a} \times 1.54 V_{wet}

s, a = parts of sand and coarse aggregate by volume

Sand = s·V_c, aggregate = a·V_c

Number of cement bags

N_{bags} = \frac{V _{c}}{0.0347}

V_c in m³; one 50 kg bag = 0.0347 m³

Bulk density of cement 1440 kg/m³

Mass of cement

W_{c} = 1440 V_{c}

W_c in kg; V_c in m³

Water required

W_{w} = (w / c) \times W_{c}

w/c = water-cement ratio; W_w in litres (kg)

Rate analysis determines the cost per unit of an item from the cost of materials, labour, tools and plant, water charges, and contractor's profit and overheads.
Rates for items are taken from the Schedule of Rates (e.g. CPWD DSR); items not in the schedule are priced by market rate analysis.
One bag of cement weighs 50 kg and has a volume of about 0.0347 m³ (about 28.8 bags per m³ of loose cement).
Cement required per m³ of concrete is about 11.1 bags for 1:1:2, 8.06 bags for 1:1.5:3 and 6.34 bags for 1:2:4 (using the 1.54 dry factor).
Cement required per m³ of concrete is about 4.44 bags for 1:3:6 and 3.41 bags for 1:4:8 (using the 1.54 dry factor).
One m³ of 1:2:4 concrete needs about 0.22 m³ of cement (about 317 kg), 0.44 m³ of sand and 0.88 m³ of coarse aggregate.
Nominal mixes M5, M7.5, M10, M15 and M20 correspond roughly to 1:5:10, 1:4:8, 1:3:6, 1:2:4 and 1:1.5:3 proportions.
IS 456 Table 9 limits total aggregate per 50 kg of cement to 800, 625, 480, 330 and 250 kg for nominal mix M5, M7.5, M10, M15 and M20.
IS 456 Table 9 sets water per 50 kg of cement for nominal mixes at 60, 45, 34, 32 and 30 litres for M5, M7.5, M10, M15 and M20.

13.4 Brickwork, mortar and plaster

Number of bricks per m³ of brickwork

N = \frac{1}{( l + t ) ( b + t ) ( h + t )}

l, b, h = actual brick size (m); t = mortar joint thickness (m)

Modular brick 190 × 90 × 90 mm with 10 mm joints → 500 bricks

Wet mortar in 1 m³ of brickwork

V_{m, wet} = 1 - N (l b h)

N = bricks per m³; l b h = volume of one brick without mortar

Add frog filling and wastage as required

Dry volume of mortar

V_{m, dry} = 1.27 V_{m, wet}

V_m,wet = wet mortar volume

Factor 1.27 is common; some texts use 1.33

Wet volume of plaster

V_{p} = A \times t

A = plastered area (m²); t = thickness (m)

Add allowance for filling joints and uneven surfaces, then convert to dry volume

A modular brick (IS 1077) measures 190 × 90 × 90 mm and its nominal size with mortar is 200 × 100 × 100 mm.
One m³ of modular brickwork needs 500 bricks, with wet mortar of about 0.23 m³ before allowing for frogs and wastage.
Cement for a mortar of ratio 1 : n is found by dividing the dry mortar volume by (1 + n).
Common plaster thicknesses are 12 mm on the smooth (internal) face of a brick wall, 15 mm on the rough face and 6 mm on ceilings.
Pointing of brick or stone masonry is measured in m² of the face area pointed.

13.5 Bar bending schedule (BBS)

Unit mass of a steel bar

w = \frac{d ^{2}}{162}

w in kg/m; d = bar diameter in mm

From density 7850 kg/m³: (π/4)d² × 10⁻⁶ × 7850 ≈ d²/162

Cutting length of a bar

L_{cut} = \sum L_{straight} + hook allowances - bend deductions

Straight lengths measured along the bar outside dimensions

Bend deductions: 1d (45°), 2d (90°), 3d (135°), 4d (180°)

Extra length due to a 45° crank (bent-up bar)

Δ L = 0.42 D

D = vertical height of the crank (centre-to-centre of bar levels)

Exact 0.414D; for 30° crank 0.27D, for 60° crank 0.58D

Number of stirrups or bars at a spacing

n = \frac{L - 2 c}{s} + 1

L = length of member; c = end cover; s = spacing

Round up to a whole number

Steel density is taken as 7850 kg/m³ for computing the mass of reinforcement.
Unit mass of bars is about 0.395, 0.617, 0.888, 1.58, 2.47 and 3.85 kg/m for 8, 10, 12, 16, 20 and 25 mm diameters.
A bar bending schedule lists bar mark, shape, diameter, number of bars, cutting length, total length and mass for each member.
IS 2502 is the code of practice for bending and fixing of bars for concrete reinforcement.
A standard 180° hook on a mild-steel bar (internal radius 2d) adds about 9d to the straight length.
IS 13920:2016 requires stirrups and ties in earthquake-resistant members to end in 135° hooks with an extension of 6d but not less than 65 mm.

13.6 Earthwork quantities

Area of a level cross-section (embankment or cutting)

A = B d + s d^{2}

B = formation width; d = depth or height at centre; s = side slope (s horizontal : 1 vertical)

Mid-sectional area method

V = L (B d_{m} + s d_{m}^{2}), d_{m} = \frac{d _{1} + d _{2}}{2}

L = distance between sections; d₁, d₂ = depths at the two ends

Mean (average) area method

V = L \cdot \frac{A _{1} + A _{2}}{2}

A₁, A₂ = end areas; L = distance between them

Same as the end-area (trapezoidal) rule for one interval

Trapezoidal (end-area) rule for a series of sections

V = D [\frac{A _{1} + A _{n}}{2} + A_{2} + A_{3} + \dots + A_{n - 1}]

D = common interval; A₁ … A_n = cross-sectional areas

Prismoidal formula (two end sections)

V = \frac{L}{6} (A_{1} + 4 A_{m} + A_{2})

A_m = area of the mid-section (not the mean of A₁ and A₂)

Prismoidal (Simpson's) rule for a series of sections

V = \frac{D}{3} [A_{1} + A_{n} + 4 (A_{2} + A_{4} + \dots) + 2 (A_{3} + A_{5} + \dots)]

D = common interval; n must be odd

Requires an even number of intervals

Prismoidal correction (level sections)

C_{p} = \frac{L s ( d _{1} - d _{2} ) ^{2}}{6}

s = side slope; d₁, d₂ = end depths

Prismoidal volume = trapezoidal volume − C_p

Volume from spot levels (borrow pit, grid of squares)

V = \frac{A}{4} (\sum h_{1} + 2 \sum h_{2} + 3 \sum h_{3} + 4 \sum h_{4})

A = area of one square; h₁, h₂, h₃, h₄ = depths common to 1, 2, 3 and 4 squares

The prismoidal formula is the most accurate of the common methods; the trapezoidal (end-area) rule generally over-estimates the volume.
Simpson's (prismoidal) rule needs an odd number of cross-sections; if the number is even, the last interval is computed separately.
On a mass-haul diagram, a rising curve indicates excavation (cutting) and a falling curve indicates embankment (filling).
On a mass-haul diagram, a maximum point marks the change from cut to fill and a minimum point the change from fill to cut.
Free haul is the distance up to which earth is carried without extra payment; carriage beyond it is paid as overhaul.
A borrow pit supplies earth for an embankment when cutting is insufficient, and a spoil bank receives surplus excavated earth.

13.7 Valuation and depreciation

Annual depreciation, straight-line method

D = \frac{C - S}{n}

C = original cost; S = scrap value; n = life in years

Equal depreciation every year

Book value after m years, constant percentage (declining balance) method

V_{m} = C (1 - p)^{m}

p = fixed annual rate of depreciation (as a fraction)

Value never reaches zero

Rate for the constant percentage method

p = 1 - (\frac{S}{C})^{1/ n}

S = scrap value; C = original cost; n = life

Annual sinking fund instalment

I = \frac{S i}{( 1 + i ) ^{n} - 1}

S = amount to be accumulated; i = interest rate (fraction); n = years

i/((1+i)ⁿ − 1) is the coefficient of sinking fund

Years' purchase in perpetuity

Y P = \frac{1}{i} = \frac{100}{rate %}

i = expected rate of return (fraction)

For freehold property

Years' purchase for a limited period (dual rate)

Y P = \frac{1}{i + i _{c}}, i_{c} = \frac{i ^{'}}{( 1 + i ^{'} ) ^{n} - 1}

i = rate of return; i_c = sinking fund coefficient at rate i'

Used for leasehold property or buildings with limited life

Capitalised value

Capitalised value = Net annual income \times Y P

Net income = gross income − outgoings

Present value of an annuity (single rate)

P V = A \frac{( 1 + i ) ^{n} - 1}{i ( 1 + i ) ^{n}}

A = annual instalment; i = interest rate; n = years

The factor is the single-rate YP for n years

Methods of computing depreciation are the straight-line method, constant percentage (declining balance) method, sinking fund method and quantity survey method.
The constant percentage method charges heavy depreciation in early years and the book value never becomes zero.
Book value is the original cost less the total depreciation charged up to that date.
Scrap value is the value of the dismantled materials at the end of a structure's life, commonly taken as about 10% of the original cost for buildings.
Salvage value is the value of a property at the end of its useful life without dismantling it.
Market value is the price obtainable in the open market at a given time; distress value is the lower price realised in a forced sale.
Obsolescence is the loss in value of a property due to outdated design, new technology or changed requirements, even when it is structurally sound.
Outgoings deducted from gross rent include taxes, repairs, insurance, management charges and sinking fund.
Gross rent equals net rent (the return on the capital invested) plus outgoings.
Freehold property is owned absolutely, whereas leasehold property is held for a fixed period under a lease.
An easement is a right enjoyed over land owned by another, such as a right of way or right to light and air.

13.8 Contracts and tendering

In a lump-sum contract the contractor agrees to complete the whole work for a fixed total price, so it suits works with complete drawings and specifications.
In an item-rate (unit-rate) contract the contractor quotes a rate for each item and is paid on the quantities actually measured; it is the most common type in Indian public works.
In a percentage-rate contract the contractor quotes a percentage above, below or at par with the department's schedule of rates.
In a cost-plus-percentage contract the contractor has no incentive to economise, which a cost-plus-fixed-fee contract avoids.
In a labour contract the department supplies the materials and the contractor supplies only labour.
Piece-work agreements are used for small works paid at agreed rates, without a formal contract document.
In an EPC (turnkey) contract one contractor is responsible for engineering, procurement and construction of the whole project.
In a BOT contract the concessionaire builds and operates the facility and recovers its investment from user charges before transferring it to the government.
Under the Hybrid Annuity Model (HAM) used for highways, the government pays 40% of the project cost during construction and the rest as annuities.
Earnest money deposit (EMD) is submitted with the tender as a guarantee of the bidder's seriousness and is forfeited if the bidder withdraws after the tenders are opened.
Security deposit is retained from the contractor to ensure proper performance and is refunded after the defect liability period.
The measurement book (MB) is the basic record of all measurements and the basis for every payment to the contractor.
A running account (RA) bill is an interim payment for work done so far, and the final bill settles the contract on completion.
Under CPWD, secured advance may be paid on non-perishable materials brought to site, up to 75% of their assessed value.
Under CPWD GCC Clause 2, compensation for delay by the contractor is limited to 10% of the tendered value.
A price variation (escalation) clause compensates the contractor for rise in the cost of materials and labour during the contract.
A force majeure clause excuses delay or non-performance caused by events beyond control, such as natural calamities or war.
Construction contracts in India are governed by the Indian Contract Act, 1872, and disputes are settled under the Arbitration and Conciliation Act, 1996.

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Values follow the current Indian Standards and IRC / Indian Railways documents named in each item. Always check the latest amendment of a code before using a value in design.