Methods of Quantity Estimate

Past Exam Questions on this Topic

1. List various methods of quantity estimate. Describe bill of quantities (BOQ) and preparation of detailed estimate of any project. [1+2+2] (2082 Bhadra, Q.2)
   The second and third parts of this question also belong to Chapter 3.
   Solution

   a) Methods of quantity estimate

   1. Long wall — short wall method
   2. Centre line method
   3. Crossing method
   4. Bay method

   b) Bill of quantities (BOQ)

   A bill of quantities is a tabulated schedule of every item of work in a project, giving a brief description of the item, the estimated quantity, the unit, the rate and the amount. It is issued with the tender documents so that all contractors price the same quantities and their offers can be compared item by item; it is afterwards used to measure and pay for the work actually done and to value variations.

   S.N.	Description of item	Quantity	Unit	Rate (Rs)	Amount (Rs)
   1	Earthwork in excavation in ordinary soil	120.00	m³	350.00	42,000.00
   2	PCC 1:3:6 in foundation	18.50	m³	9,000.00	1,66,500.00
   Total					2,08,500.00

   c) Preparation of a detailed estimate of a project

   1. Collect the data — complete drawings, specifications, the district rate and the departmental norms.
   2. List the items of work under sub-heads, in the order of construction.
   3. Find the wall length by the centre line or long wall–short wall method.
   4. Take out the quantities item by item on the measurement sheet (number × length × breadth × height), applying the deduction rules of IS 1200.
   5. Analyse the rate of each item from the norms and the district rate.
   6. Prepare the abstract of cost — quantity × rate = amount for every item, and total it.
   7. Add contingencies (3–5%) and work-charged establishment (1.5–2%), and the provisions for sanitary, water supply and electrical work (8–10% each).
   8. Write the report and attach the drawings, specifications, rate analysis and the abstract, and submit for technical sanction.

   ENCE 351 Chapter 2, §3.2 and §3.7.

2. Write down the general method of taking out quantities in load bearing brick masonry building with their suitability. [5] (2081 Bhadra, Q.3)
   Solution

   General methods of taking out quantities in a load-bearing brick masonry building, and their suitability

   Four methods are used to take out the quantities of a load-bearing masonry building. All of them must give the same total length of wall — that identity is the check on the work.

   1. Long wall — short wall method (also called the out-to-out and in-to-in method)

   • Walls running in one direction are taken as long walls and measured from centre to centre plus one breadth of the wall (out to out).
   • Walls at right angles to them are taken as short walls and measured from centre to centre minus one breadth (in to in).
   • The length changes for every footing, because the breadth changes.

   long wall L = centre-to-centre length + breadth of the item short wall S = centre-to-centre length − breadth of the item quantity = (2L + 2S) × breadth × height

   Suitability: best when the walls of a building are of different thicknesses, or when the rooms are of different sizes, because each wall is dealt with on its own.

   2. Centre line method

   • The total centre-line length of all the walls is found once.
   • It is multiplied by the breadth and the depth of each item in turn.
   • For every junction where a wall meets another, half the breadth of the item is deducted, because that corner would otherwise be counted twice.

   deduction = (number of junctions) × ½ × breadth of the item quantity = (total centre-line length − deduction) × breadth × height

   Suitability: the quickest method, and the one normally used when all the walls are of the same thickness and meet in simple T or L junctions. It becomes error-prone where junctions are many or irregular.

   3. Crossing method

   • The out-to-out length of the walls is taken in both directions.
   • The corners, which have then been counted twice, are deducted — one breadth for each crossing.

   quantity = [2(L_out + B_out) − 4 × breadth] × breadth × height

   Suitability: simple rectangular plans without internal cross walls; it becomes clumsy as soon as partitions are introduced.

   4. Bay method

   • A long building of repeating panels is divided into identical bays.
   • One typical bay is worked out in full and multiplied by the number of bays.
   • The two end bays are taken separately, since they carry the gable or end wall.

   Suitability: long repetitive structures — barracks, sheds, godowns, factory buildings, and framed buildings with equal spans.

   For a load-bearing building the answer really turns on one number — the total length of wall. Every item from the excavation to the superstructure masonry is that length multiplied by a different breadth and depth, so choosing the method that gets the length right with the fewest chances of error is the whole art of the thing.

   ENCE 351 §2.1–§2.4.

3. What are the various methods of taking out quantities? What are the sub-heads of items of work for building project? [4+4] (2080 Baishakh, Q.2)
   The second part of this question also belongs to Chapter 3.
   Solution

   a) Various methods of taking out quantities

   Four methods are used to take out the quantities of a load-bearing masonry building. All of them must give the same total length of wall — that identity is the check on the work.

   1. Long wall — short wall method (also called the out-to-out and in-to-in method)

   • Walls running in one direction are taken as long walls and measured from centre to centre plus one breadth of the wall (out to out).
   • Walls at right angles to them are taken as short walls and measured from centre to centre minus one breadth (in to in).
   • The length changes for every footing, because the breadth changes.

   long wall L = centre-to-centre length + breadth of the item short wall S = centre-to-centre length − breadth of the item quantity = (2L + 2S) × breadth × height

   Suitability: best when the walls of a building are of different thicknesses, or when the rooms are of different sizes, because each wall is dealt with on its own.

   2. Centre line method

   • The total centre-line length of all the walls is found once.
   • It is multiplied by the breadth and the depth of each item in turn.
   • For every junction where a wall meets another, half the breadth of the item is deducted, because that corner would otherwise be counted twice.

   deduction = (number of junctions) × ½ × breadth of the item quantity = (total centre-line length − deduction) × breadth × height

   Suitability: the quickest method, and the one normally used when all the walls are of the same thickness and meet in simple T or L junctions. It becomes error-prone where junctions are many or irregular.

   3. Crossing method

   • The out-to-out length of the walls is taken in both directions.
   • The corners, which have then been counted twice, are deducted — one breadth for each crossing.

   quantity = [2(L_out + B_out) − 4 × breadth] × breadth × height

   Suitability: simple rectangular plans without internal cross walls; it becomes clumsy as soon as partitions are introduced.

   4. Bay method

   • A long building of repeating panels is divided into identical bays.
   • One typical bay is worked out in full and multiplied by the number of bays.
   • The two end bays are taken separately, since they carry the gable or end wall.

   Suitability: long repetitive structures — barracks, sheds, godowns, factory buildings, and framed buildings with equal spans.

   b) Sub-heads of items of work for a building project

   Sub-heads of items of work for a building project

   The items of a building estimate are grouped under sub-heads, taken in the order in which the work is actually built:

   1. Earthwork — site clearance, excavation in foundation, refilling, plinth filling, disposal of surplus earth.
   2. Concrete work — PCC in foundation and floors, RCC in footings, columns, beams, slabs, lintels and stairs, with formwork and reinforcement.
   3. Masonry / brickwork — brick or stone masonry in foundation, plinth and superstructure, partition walls.
   4. Damp proofing — DPC at plinth level, waterproofing of roof and wet areas.
   5. Wood work / joinery — door and window frames and shutters, cupboards, railings, with fittings and fastenings.
   6. Steel work — grills, gates, rolling shutters, structural steel.
   7. Roofing — roof slab or truss and covering, gutters, rain-water pipes.
   8. Flooring — base concrete, floor finish, skirting and dado.
   9. Finishing — internal and external plastering, pointing, white washing, distempering and painting.
   10. Sanitary and water supply installation — fittings, pipes, septic tank and soak pit — usually 8–10% of the building cost.
   11. Electrical installation — internal wiring, fittings and fixtures — usually 8–10%.
   12. Miscellaneous and external works — compound wall, gate, approach road, paving, landscaping.

   Grouping under sub-heads is not decoration. It makes the estimate easy to check, lets the work be split into separate contracts, and allows the departmental percentages for sanitary and electrical work to be applied to the right base.

   ENCE 351 Chapter 2 and §3.6.

4. You are working for a design project of a building. Your Team Leader instruct you to perform a work break down structure for the quantity calculation work. How are you planning to do so for the frame structure building project? [4] (2079 Bhadra, Q.1)
   Solution

   Work breakdown structure for the quantity calculation of a framed structure building

   A work breakdown structure (WBS) splits the whole project into progressively smaller deliverables until each is small enough to be measured, priced and assigned to one person. For the quantity take-off of a framed building I would break it down as follows.

   Level 1 — the project. Quantity estimate of the framed building.

   Level 2 — by physical division, because a framed building is built floor by floor:

   • Substructure (up to plinth level)
   • Superstructure, floor by floor
   • Roof
   • Finishing
   • Services
   • External works

   Level 3 — by trade / sub-head within each division:

   Division	Packages
   Substructure	Excavation for isolated footings · PCC bed · footing pads · column pedestals · plinth beams · backfilling and plinth filling · DPC
   Superstructure (repeat per floor)	Columns · beams · slab · staircase · infill brickwork · lintels and sunshades
   Roof	Roof slab · parapet · waterproofing · rain-water pipes
   Finishing	Internal plaster · external plaster · flooring and skirting · painting · doors and windows
   Services	Sanitary and water supply · electrical
   External works	Compound wall · gate · paving · septic tank and soak pit

   Level 4 — the measurable item (work package). Each package is broken into the items that actually appear in the bill of quantities, with its unit:

   • Concrete of each grade, per element — m³
   • Formwork to each element — m²
   • Reinforcement, by bar diameter, from the bar bending schedule — kg
   • Brickwork of each thickness — m³
   • Plaster of each mix and thickness — m²

   How I would carry it out

   1. Number every element on the drawing with a unique mark (C1, C2, B1, S1…) so that no member is measured twice or missed.
   2. Prepare a column, beam and slab schedule giving the size, number and floor of every member — for a framed building this is the backbone of the take-off, just as the centre-line length is for a load-bearing building.
   3. Measure floor by floor, since floors repeat: measure a typical floor once and multiply, then take the ground and top floors separately.
   4. Prepare the bar bending schedule element by element and convert to weight at w = d²/162 kg/m.
   5. Assign each level-3 package to a team member, with a common measurement sheet format and a single agreed set of drawings and revisions.
   6. Roll the quantities up the WBS — item → package → division → project — and cross-check the totals against an approximate plinth-area estimate to catch gross errors.

   Two rules make a WBS work: the 100% rule — the children of any node must add up to exactly the parent, nothing left out and nothing counted twice — and mutual exclusivity, so that no item of work appears under two packages.

   ENCE 351 Chapter 2 and §3.2.

5. What are the various methods of taking out quantities of civil engineering? Explain briefly. State the different factors considered during detailed estimation. [4+2] (2078 Bhadra, Q.2)
   The second part of this question also belongs to Chapter 3.
   Solution

   a) Methods of taking out quantities of civil engineering works

   Four methods are used to take out the quantities of a load-bearing masonry building. All of them must give the same total length of wall — that identity is the check on the work.

   1. Long wall — short wall method (also called the out-to-out and in-to-in method)

   • Walls running in one direction are taken as long walls and measured from centre to centre plus one breadth of the wall (out to out).
   • Walls at right angles to them are taken as short walls and measured from centre to centre minus one breadth (in to in).
   • The length changes for every footing, because the breadth changes.

   long wall L = centre-to-centre length + breadth of the item short wall S = centre-to-centre length − breadth of the item quantity = (2L + 2S) × breadth × height

   Suitability: best when the walls of a building are of different thicknesses, or when the rooms are of different sizes, because each wall is dealt with on its own.

   2. Centre line method

   • The total centre-line length of all the walls is found once.
   • It is multiplied by the breadth and the depth of each item in turn.
   • For every junction where a wall meets another, half the breadth of the item is deducted, because that corner would otherwise be counted twice.

   deduction = (number of junctions) × ½ × breadth of the item quantity = (total centre-line length − deduction) × breadth × height

   Suitability: the quickest method, and the one normally used when all the walls are of the same thickness and meet in simple T or L junctions. It becomes error-prone where junctions are many or irregular.

   3. Crossing method

   • The out-to-out length of the walls is taken in both directions.
   • The corners, which have then been counted twice, are deducted — one breadth for each crossing.

   quantity = [2(L_out + B_out) − 4 × breadth] × breadth × height

   Suitability: simple rectangular plans without internal cross walls; it becomes clumsy as soon as partitions are introduced.

   4. Bay method

   • A long building of repeating panels is divided into identical bays.
   • One typical bay is worked out in full and multiplied by the number of bays.
   • The two end bays are taken separately, since they carry the gable or end wall.

   Suitability: long repetitive structures — barracks, sheds, godowns, factory buildings, and framed buildings with equal spans.

   b) Factors considered during detailed estimation

   1. Completeness and correctness of the drawings — every dimension needed must be available and consistent; the estimate can be no better than the drawing.
   2. The specification of each item — the class of material and the mix decide both the quantity and the rate.
   3. The standard method of measurement (IS 1200) — particularly the deduction rules, which decide whether an opening is deducted at all.
   4. Prevailing rates of materials, labour and carriage at the site, and the district rate in force.
   5. Site conditions — nature of soil, water table, ground slope, access, and the lead and lift involved.
   6. Availability of materials, skilled labour, water and power locally, and the distance from which they must be brought.
   7. Season and duration of the work, and the likely escalation over that period.
   8. Method of construction and the plant proposed — manual or mechanised.
   9. Provisions for contingencies (3–5%), work-charged establishment (1.5–2%), and the percentage allowances for sanitary, water supply and electrical work.
   10. Overheads, profit and taxes applicable.

   ENCE 351 Chapter 2 and §3.2.

6. What are various methods of taking quantities of works? [4] (2075 Ashwin, Q.2)
   Solution

   Four methods are used to take out the quantities of a load-bearing masonry building. All of them must give the same total length of wall — that identity is the check on the work.

   1. Long wall — short wall method (also called the out-to-out and in-to-in method)

   • Walls running in one direction are taken as long walls and measured from centre to centre plus one breadth of the wall (out to out).
   • Walls at right angles to them are taken as short walls and measured from centre to centre minus one breadth (in to in).
   • The length changes for every footing, because the breadth changes.

   long wall L = centre-to-centre length + breadth of the item short wall S = centre-to-centre length − breadth of the item quantity = (2L + 2S) × breadth × height

   Suitability: best when the walls of a building are of different thicknesses, or when the rooms are of different sizes, because each wall is dealt with on its own.

   2. Centre line method

   • The total centre-line length of all the walls is found once.
   • It is multiplied by the breadth and the depth of each item in turn.
   • For every junction where a wall meets another, half the breadth of the item is deducted, because that corner would otherwise be counted twice.

   deduction = (number of junctions) × ½ × breadth of the item quantity = (total centre-line length − deduction) × breadth × height

   Suitability: the quickest method, and the one normally used when all the walls are of the same thickness and meet in simple T or L junctions. It becomes error-prone where junctions are many or irregular.

   3. Crossing method

   • The out-to-out length of the walls is taken in both directions.
   • The corners, which have then been counted twice, are deducted — one breadth for each crossing.

   quantity = [2(L_out + B_out) − 4 × breadth] × breadth × height

   Suitability: simple rectangular plans without internal cross walls; it becomes clumsy as soon as partitions are introduced.

   4. Bay method

   • A long building of repeating panels is divided into identical bays.
   • One typical bay is worked out in full and multiplied by the number of bays.
   • The two end bays are taken separately, since they carry the gable or end wall.

   Suitability: long repetitive structures — barracks, sheds, godowns, factory buildings, and framed buildings with equal spans.

   ENCE 351 §2.1–§2.4.

7. Explain various methods of building estimate with suitable sketch. Explain the term contingencies and work charge establishment. [5+5] (2074 Chaitra, Q.2)
   The second part of this question also belongs to Chapter 3.
   Solution

   a) Methods of building estimate

   Four methods are used to take out the quantities of a load-bearing masonry building. All of them must give the same total length of wall — that identity is the check on the work.

   1. Long wall — short wall method (also called the out-to-out and in-to-in method)

   • Walls running in one direction are taken as long walls and measured from centre to centre plus one breadth of the wall (out to out).
   • Walls at right angles to them are taken as short walls and measured from centre to centre minus one breadth (in to in).
   • The length changes for every footing, because the breadth changes.

   long wall L = centre-to-centre length + breadth of the item short wall S = centre-to-centre length − breadth of the item quantity = (2L + 2S) × breadth × height

   Suitability: best when the walls of a building are of different thicknesses, or when the rooms are of different sizes, because each wall is dealt with on its own.

   2. Centre line method

   • The total centre-line length of all the walls is found once.
   • It is multiplied by the breadth and the depth of each item in turn.
   • For every junction where a wall meets another, half the breadth of the item is deducted, because that corner would otherwise be counted twice.

   deduction = (number of junctions) × ½ × breadth of the item quantity = (total centre-line length − deduction) × breadth × height

   Suitability: the quickest method, and the one normally used when all the walls are of the same thickness and meet in simple T or L junctions. It becomes error-prone where junctions are many or irregular.

   3. Crossing method

   • The out-to-out length of the walls is taken in both directions.
   • The corners, which have then been counted twice, are deducted — one breadth for each crossing.

   quantity = [2(L_out + B_out) − 4 × breadth] × breadth × height

   Suitability: simple rectangular plans without internal cross walls; it becomes clumsy as soon as partitions are introduced.

   4. Bay method

   • A long building of repeating panels is divided into identical bays.
   • One typical bay is worked out in full and multiplied by the number of bays.
   • The two end bays are taken separately, since they carry the gable or end wall.

   Suitability: long repetitive structures — barracks, sheds, godowns, factory buildings, and framed buildings with equal spans.

   Worked check — the three methods give the same answer

   A room whose walls are 5.00 m × 4.00 m centre to centre, wall thickness 0.30 m, height of masonry 1.00 m.

   Long wall — short wall method

   long wall = c/c + breadth = 5.00 + 0.30 = 5.30 m × 2 = 10.60 m short wall = c/c − breadth = 4.00 − 0.30 = 3.70 m × 2 = 7.40 m --------- total effective length 18.00 m

   Centre line method

   total centre line = 2 (5.00 + 4.00) = 18.00 m no junction deduction arises here — the centre line of a single closed rectangle already closes on itself, with no wall running into it

   Crossing method

   out-to-out = (5.00 + 0.30) × (4.00 + 0.30) = 5.30 × 4.30 m length = 2 (5.30 + 4.30) − 4 × 0.30 = 19.20 − 1.20 = 18.00 m

   Quantity of masonry

   V = 18.00 × 0.30 × 1.00 = 5.40 m³ ( by all three methods )

   All three methods give an effective wall length of 18.00 m and 5.40 m³ of masonry. Agreement between any two of them is the standard arithmetical check on a quantity sheet.

   The junction deduction in the centre-line method applies only where one wall runs into another — a T-junction with an internal partition, or a cross wall. If this room had one internal cross wall, that wall would make two T-junctions, and the deduction would be 2 × ½ × 0.30 = 0.30 m. A plain closed rectangle has none.

   b) Contingencies and work-charged establishment

   Contingencies. A lump-sum provision, normally 3–5% of the estimated cost of the work, added to every estimate to meet unforeseen and petty expenses that cannot be foreseen or itemised at the time of estimating — small omissions in the quantities, minor changes at site, small variations in rates, and incidental charges. It is not intended to pay for a change in the scope of the work; that requires a supplementary or a revised estimate. The amount can be spent only with the sanction of the competent authority.

   Work-charged establishment. A provision of about 1.5–2% of the estimated cost to pay the staff engaged specifically and temporarily for that one work and charged directly to it — the site overseer, work sarkar, chowkidar, storekeeper, work assistant and similar staff whose appointment ends when the work ends. It is distinct from the regular establishment (the permanent departmental staff), whose salaries are met from the department's own budget and are not charged to the work.

   	Contingencies	Work-charged establishment
   Provision	3–5% of estimated cost	1.5–2% of estimated cost
   Meets	Unforeseen petty expenses and minor omissions	Pay of temporary staff engaged for that work only
   Nature	A reserve that may or may not be spent	A definite recurring expense during the work

   ENCE 351 Chapter 2 and §3.6.

8. Explain in short the various methods of taking quantities in building works. [4] (2070 Chaitra, Q.1(b))
   Solution

   Four methods are used to take out the quantities of a load-bearing masonry building. All of them must give the same total length of wall — that identity is the check on the work.

   1. Long wall — short wall method (also called the out-to-out and in-to-in method)

   • Walls running in one direction are taken as long walls and measured from centre to centre plus one breadth of the wall (out to out).
   • Walls at right angles to them are taken as short walls and measured from centre to centre minus one breadth (in to in).
   • The length changes for every footing, because the breadth changes.

   long wall L = centre-to-centre length + breadth of the item short wall S = centre-to-centre length − breadth of the item quantity = (2L + 2S) × breadth × height

   Suitability: best when the walls of a building are of different thicknesses, or when the rooms are of different sizes, because each wall is dealt with on its own.

   2. Centre line method

   • The total centre-line length of all the walls is found once.
   • It is multiplied by the breadth and the depth of each item in turn.
   • For every junction where a wall meets another, half the breadth of the item is deducted, because that corner would otherwise be counted twice.

   deduction = (number of junctions) × ½ × breadth of the item quantity = (total centre-line length − deduction) × breadth × height

   Suitability: the quickest method, and the one normally used when all the walls are of the same thickness and meet in simple T or L junctions. It becomes error-prone where junctions are many or irregular.

   3. Crossing method

   • The out-to-out length of the walls is taken in both directions.
   • The corners, which have then been counted twice, are deducted — one breadth for each crossing.

   quantity = [2(L_out + B_out) − 4 × breadth] × breadth × height

   Suitability: simple rectangular plans without internal cross walls; it becomes clumsy as soon as partitions are introduced.

   4. Bay method

   • A long building of repeating panels is divided into identical bays.
   • One typical bay is worked out in full and multiplied by the number of bays.
   • The two end bays are taken separately, since they carry the gable or end wall.

   Suitability: long repetitive structures — barracks, sheds, godowns, factory buildings, and framed buildings with equal spans.

   ENCE 351 §2.1–§2.4.

9. Write short notes on (any three):
   • i) Approximate estimate
   • ii) Revised estimate
   • iii) Centre line method
   • iv) Capitalized value (Items i, ii belong to Chapter 3 and item iv belongs to Chapter 7.)
   [6] (2066 Bhadra, Q.2(b))
   Solution

   Answer any three. All four are given below.

   i) Approximate estimate. A rough estimate prepared at the proposal stage, before detailed drawings exist, from a single overall parameter — plinth area, cube content, cost per bed, per student, per km of road. It is used to judge whether the scheme is worth pursuing, to obtain administrative approval and to provide the amount in the budget. It is supported by a report, a site plan and line drawings, and is accurate only to about ±15–20%.

   ii) Revised estimate. A fresh detailed estimate prepared for a work already sanctioned, when the expenditure exceeds or is likely to exceed the sanctioned amount by more than 5%, or when the rates or the design change materially. It shows the original and the revised quantity and cost of every item side by side, with the reason for each variation, and must be sanctioned afresh by the competent authority.

   iii) Centre line method. A method of taking out quantities in which the total centre-line length of all the walls is found once and then multiplied by the breadth and the depth of each item in turn. Where walls meet, half the breadth of the item is deducted for each junction, because that corner would otherwise be counted twice.

   deduction = (number of junctions) × ½ × breadth of the item quantity = (total centre-line length − deduction) × breadth × height

   It is the quickest method and is best suited to buildings in which all the walls have the same thickness.

   iv) Capitalized value. The amount of capital whose interest, at the prevailing rate, would yield the net annual income actually received from the property. It is the value of the property on an income basis:

   capitalized value = net annual income × year's purchase year's purchase (perpetuity) = 100 / rate of interest = 1 / i net annual income = gross annual income − all outgoings

   For example, a property yielding a net income of Rs 1,20,000 a year, capitalised at 8%, has a capitalized value of 1,20,000 × (100/8) = 1,20,000 × 12.5 = Rs 15,00,000.

   ENCE 351 Chapters 2, 3 and 7.