BE Civil Engineering (IOE, TU) Estimating and Costing (IOE, CE 703) Question Paper 2078 Nepal

Cross-sectional area at each station (level section, two-sided slope):

For a level section, $A = d\,(b + s\,d)$ where $b=10\text{ m}$ (formation width), $s=2$ (side slope), and $d$ is the depth of cutting.

(a) Trapezoidal (average end area) rule

$$V=L\left[\frac{A_0+A_4}{2}+A_1+A_2+A_3\right]$$ $$V=30\left[\frac{14.88+10.62}{2}+24.48+35.52+21.12\right]$$ $$V=30\,[\,12.75+81.12\,]=30\times 93.87$$ $$\boxed{V_{trap}=2816.10\ \text{m}^3}$$

(b) Prismoidal (Simpson's 1/3) rule — there are 5 ordinates (4 intervals, even number), so the rule applies directly:

$$V=\frac{L}{3}\left[A_0+A_4+4(A_1+A_3)+2A_2\right]$$ $$V=\frac{30}{3}\left[14.88+10.62+4(24.48+21.12)+2(35.52)\right]$$ $$V=10\,[\,25.50+4(45.60)+71.04\,]=10\,[\,25.50+182.40+71.04\,]$$ $$\boxed{V_{prism}=2789.40\ \text{m}^3}$$

Comment: The prismoidal rule treats the solid between sections as a true prismoid and is therefore more accurate. The trapezoidal value is higher by $2816.10-2789.40=26.70\text{ m}^3$ (about 1%). For final payment in earthwork the prismoidal volume is generally adopted; the difference (trapezoidal − prismoidal) is the prismoidal correction and is deducted from the trapezoidal estimate when greater precision is required.

Step 1 — Dry quantities of materials per 1 m³ of wet concrete

Sum of proportions $=1+2+4=7$. Dry volume $=1.54\text{ m}^3$.

• Cement $=\dfrac{1}{7}\times1.54=0.22\text{ m}^3$
• Sand $=\dfrac{2}{7}\times1.54=0.44\text{ m}^3$
• Coarse aggregate $=\dfrac{4}{7}\times1.54=0.88\text{ m}^3$

Cement in bags $=\dfrac{0.22}{0.035}=6.286\text{ bags}$

Step 2 — Material cost

Step 3 — Labour cost

Step 4 — Build-up of rate

• Material + Labour $=7756.57+4800.00=12{,}556.57$
• Overhead & profit @15% $=0.15\times12556.57=1{,}883.49$
• Total rate $=12556.57+1883.49=14{,}440.06$

$$\boxed{\text{Rate per m}^3\ \text{of }1{:}2{:}4\ \text{concrete}\approx \text{NRs. }14{,}440}$$

(a) Centre-line method

Wall thickness $t=0.30\text{ m}$, so the centre line lies $t/2=0.15\text{ m}$ outside each internal face.

Centre-line length of a single closed rectangular wall:

$$L_{cl}=2\big[(L_i+t)+(B_i+t)\big]=2\big[(4.0+0.30)+(3.0+0.30)\big]$$ $$L_{cl}=2\,[4.30+3.30]=2\times7.60=15.20\text{ m}$$

(For a single rectangular building no junction correction is needed because the perimeter is one continuous wall.)

Volume of brick masonry:

$$V=L_{cl}\times t\times h=15.20\times0.30\times3.0$$ $$\boxed{V=13.68\ \text{m}^3}$$

(b) Number of bricks and mortar

• Bricks $=13.68\times500=\mathbf{6{,}840\ bricks}$
• Cement mortar $=0.30\times13.68=\mathbf{4.10\ m^3}$

(c) When correction is needed: In the centre-line method, wherever walls of the same thickness meet at a junction (T-junction or cross-junction), the masonry at the meeting length is counted twice. The correction is to deduct half the wall thickness for each junction from the centre-line length, i.e. subtract $\tfrac{t}{2}$ per side of every junction. For a simple single rectangular room there is no such junction, so no deduction applies here.

Step 1 — Number of bars

Main bars are distributed across the 5.0 m width:

$$n_{main}=\frac{5.0-2(0.025)}{0.15}+1=\frac{4.95}{0.15}+1=33+1=34\ \text{bars}$$

Distribution bars are distributed across the 4.0 m span:

$$n_{dist}=\frac{4.0-2(0.025)}{0.20}+1=\frac{3.95}{0.20}+1=19.75+1\approx 20\ \text{bars}$$

Step 2 — Cutting length of each bar (length $=$ clear span between covers $+$ two end bends of $9d$)

Main (12 mm), runs along 4.0 m span:

$$L_{main}=(4.0-2\times0.025)+2\times9\times0.012=3.95+0.216=4.166\text{ m}$$

Distribution (10 mm), runs along 5.0 m width:

$$L_{dist}=(5.0-2\times0.025)+2\times9\times0.010=4.95+0.180=5.130\text{ m}$$

Step 3 — Total length and weight

$$\text{Total steel}=125.78+63.30$$ $$\boxed{\approx 189.08\ \text{kg}\ (\text{say }189\ \text{kg})}$$

Adding a customary 3% wastage/laps allowance gives $\approx194.8\text{ kg}$ for ordering.

(a) Straight-line depreciation

Depreciable amount $=C-S=25{,}00{,}000-2{,}50{,}000=22{,}50{,}000$.

Annual depreciation:

$$D=\frac{C-S}{n}=\frac{22{,}50{,}000}{50}=\mathbf{NRs.\ 45{,}000\ per\ year}$$

Book value after 20 years:

$$BV_{20}=C-20D=25{,}00{,}000-20\times45{,}000=25{,}00{,}000-9{,}00{,}000$$ $$\boxed{BV_{20}=\text{NRs. }16{,}00{,}000}$$

(b) Sinking-fund instalment (annual deposit to accumulate $C-S$ in $n$ years at rate $i$):

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

With $i=0.08,\ n=50$:

$$(1.08)^{50}=46.9016\ \Rightarrow\ (1.08)^{50}-1=45.9016$$ $$\frac{0.08}{45.9016}=0.0017429$$ $$I=22{,}50{,}000\times0.0017429$$ $$\boxed{I\approx \text{NRs. }3{,}921\ \text{per year}}$$

(c) Scrap vs. salvage value:

• Scrap value is the value of the dismantled material (e.g. broken concrete, old steel) when the structure is demolished at the end of its life, after deducting the cost of demolition — usually about 10% of the cost.
• Salvage value is the value a utility/asset still fetches when sold without being dismantled, i.e. it can still be useful to another buyer at the end of its useful life to the present owner.

Estimate: An estimate is the anticipated/approximate computation of the quantities of various items of work and the probable cost of a project, prepared before execution from drawings, specifications and prevailing rates. It also gives a forecast of materials, labour, plant and time required.

Four types of estimates:

1. Preliminary (approximate / rough cost) estimate — made from the plinth-area or per-unit (per-bed, per-km) rate to decide the financial feasibility of a scheme and to obtain administrative approval.
2. Detailed estimate — the complete item-wise estimate prepared from finalized drawings and detailed measurements; it forms the basis of tendering and execution.
3. Revised estimate — a fresh detailed estimate prepared when the original estimate is exceeded by more than 5% (or when the scope changes), giving reasons for the increase.
4. Supplementary estimate — prepared for additional works that become necessary while the original work is in progress; submitted along with the original for sanction.

(Other valid types: quantity estimate, annual repair/maintenance estimate, complete estimate.)

General vs. Detailed specification

Detailed specification — First-class brickwork in cement mortar (1:6), superstructure:

• Bricks: First-class, well-burnt, of uniform deep-red colour, regular size, sharp edges, free from cracks and flaws; minimum crushing strength as specified; water absorption not more than 20% of dry weight.
• Mortar: Cement and sand in the ratio 1:6 by volume; sand to be clean, sharp and well graded; cement of standard make; mortar to be mixed in a mechanical mixer (or on a clean platform) and used within 30 minutes of adding water.
• Soaking: Bricks shall be fully soaked in clean water for at least 6–12 hours (until air bubbling stops) before use.
• Laying: Bricks laid in English bond in horizontal courses with frogs upward; every course truly level and plumb; vertical joints broken (staggered); joint thickness not exceeding 10 mm and completely filled with mortar; courses checked with plumb-bob and spirit level.
• Curing: The completed brickwork shall be kept wet by curing for at least 7 days. Height of brickwork raised in a day shall not exceed 1.0–1.5 m. Joints raked to 10–12 mm depth where plastering/pointing is to follow.
• Measurement: Measured in m³ of finished work, deducting openings as per the code of measurement.

Essential tender / contract documents:

1. Title page and index
2. Notice inviting tender (NIT) / invitation for bids
3. Instructions to bidders and general & special conditions of contract
4. Drawings (architectural, structural, services)
5. General and detailed technical specifications
6. Bill of Quantities (BoQ) / schedule of rates
7. Form of agreement, form of bid, and bid security/EMD details
8. Schedule of issue of materials and tools, time of completion and penalty (liquidated damages) clauses

Item-rate vs. Lump-sum contract

Wall (vertical) plaster area — internal faces

Inner perimeter $=2(4.0+3.0)=14.0\text{ m}$.

Gross wall area $=$ perimeter $\times$ height $=14.0\times3.0=42.0\text{ m}^2$.

Deductions for openings (for 12 mm plaster, full opening area is deducted):

• Door $=1.0\times2.1=2.10\text{ m}^2$
• Windows $=2\times(1.2\times1.5)=2\times1.80=3.60\text{ m}^2$
• Total deduction $=2.10+3.60=5.70\text{ m}^2$

Net wall plaster $=42.0-5.70=36.30\text{ m}^2$.

Ceiling plaster $=4.0\times3.0=12.0\text{ m}^2$.

Total net plaster area

$$=36.30+12.0$$ $$\boxed{=48.30\ \text{m}^2}$$

Long-wall and short-wall (separate / individual wall) method

• Walls running in one direction are taken as long walls and those in the perpendicular direction as short walls.
• Long-wall length is measured out-to-out (centre-line length $+$ one wall thickness, i.e. $+\tfrac{t}{2}$ at each end).
• Short-wall length is measured in-to-in (centre-line length $-$ one wall thickness, i.e. $-\tfrac{t}{2}$ at each end).
• Quantity $=\sum(\text{length}\times \text{breadth}\times \text{height})$ for long and short walls separately.

Centre-line method

• A single centre-line length is taken for the whole building: $L_{cl}=2(L_i+B_i+2t)$ type expression, and quantity $=L_{cl}\times t\times h$.
• Junction corrections ($-\tfrac{t}{2}$ per junction side) are applied where same-thickness walls meet.

Relationship (single rectangular building):

$$\text{Total long-wall length} + \text{Total short-wall length} = 2\,L_{cl}$$

because each long wall is $+\tfrac{t}{2}$ longer and each short wall is $-\tfrac{t}{2}$ shorter than the centre line, so the additions and subtractions cancel and the combined length equals twice the centre-line length.

Advantages:

• Long-wall/short-wall: gives wall-wise quantities directly, convenient when walls differ in thickness or height.
• Centre-line: much quicker for buildings with walls of uniform thickness, as one length serves all items (excavation, footing, masonry).

Valuation: Valuation is the technique of estimating the fair, present worth (market value) of a property — land, building or other engineering asset — for purposes such as buying/selling, taxation, rent fixation, mortgage, insurance or acquisition.

Three methods of valuation:

1. Rental (capitalized-value) method — the net annual rental income is capitalized using a suitable year's purchase to give the capital value; suited to rented/income-yielding property.
2. Cost (land-and-building / replacement) method — value $=$ cost of land $+$ present cost of constructing the building $-$ depreciation; used when reliable rental data are unavailable.
3. Comparative (market / sales-comparison) method — value is derived by comparing recent sale prices of similar properties in the same locality, with adjustments for differences.

(Other valid methods: development method, profit-based method, depreciation method.)