07-Str-B2 · May 2018

Question 2 of 6: Estimating — quantities, durations and bare costs from R.S. Means data

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Exams, May 2018 — 07-Str-B2 Management of Construction. Three hours, closed book, one approved Casio or Sharp calculator permitted. Six questions of equal value (20 marks each); any five constitute a complete paper and only the first five that appear in the answer book are marked. All six are worked below so the paper serves as a complete revision set whichever five a candidate elects.

Reference texts: Hegazy, T., Computer-Based Construction Project Management (Prentice Hall) — precedence (activity-on-node) networks with start-to-start lags, forward and backward passes, total and free float, the late bar chart, and contractor cash-flow and overdraft analysis; these chapters carry Questions 1 and 5. Hendrickson, C. & Au, T., Project Management for Construction (2nd ed., Carnegie Mellon) — Chapter 5 (cost estimation and unit-cost data), Chapter 8 (bidding and contract award), Chapter 10 (fundamental scheduling procedures), Chapter 11 (advanced scheduling with lags) and Chapter 12 (cost control and financing of constructed facilities). Halpin, D.W. & Senior, B.A., Construction Management (4th ed., Wiley) — quantity take-off, crew productivity, bidding strategy, bonding and construction safety management. Peurifoy, R.L. & Schexnayder, C.J., Construction Planning, Equipment and Methods (9th ed., McGraw-Hill) — excavation production and the physical determinants of backhoe daily output, behind Question 2. R.S. Means, Building Construction Cost Data (annual) — the anatomy of a unit-price line: crew, daily output, unit, and bare material / labour / equipment / total columns. Sullivan, W.G., Wicks, E.M. & Koelling, C.P., Engineering Economy (17th ed., Pearson) — Chapters 5 and 6, present-worth analysis and the repeatability (least common multiple of lives) assumption for alternatives with unequal lives, used in Question 4. Canadian Construction Documents Committee, CCDC 2 — Stipulated Price Contract (2020), CCDC 220 Bid Bond, CCDC 221 Performance Bond and CCDC 222 Labour and Material Payment Bond, with the BC Builders Lien Act holdback provisions and the Master Municipal Construction Documents (MMCD) — the Canadian tendering and payment machinery behind Questions 3 and 5. WorkSafeBC Occupational Health and Safety Regulation (Parts 8, 11, 12, 13, 18 and 33), CSA Z259 fall-protection and CSA Z94.4 respirator series, and the Transportation Association of Canada Manual of Uniform Traffic Control Devices for Canada — the Canadian rule set behind Question 6.

Check — how the two printed figures on page 2 were read. Network (Question 1): nine activity boxes with seven links — A → D carrying the printed SS = 3 lag (the line leaves A's top-left corner, runs across the top of the sheet and drops into D's top-left corner), then D → H, B → E, B → F, C → G, F → I and G → I, all finish-to-start with zero lag. No further arrows are drawn; A, B and C are the only start activities and E, H and I the only finish activities. Foundation plan (Question 2): an 80 m × 70 m rectangle with a rectangular notch 25 m deep cut into the top edge, one internal trench running the full width 20 m up from the bottom (the 50 m and 20 m dimensions meet on it), and one internal trench dropping from the bottom of the notch to that line. The notch width is not dimensioned on the paper, and Step 1 below shows the total trench length does not depend on it, so nothing is assumed. All plan dimensions are taken as trench centrelines; reading them instead to the outside face of the trench would shorten the total by about 1.6 per cent and change no conclusion.

Question 2: Estimating — quantities, durations and bare costs from R.S. Means data (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The foundation plan, the footing cross-section and the production data reproduced above; work proceeds eight hours per day.

Given data
Item	Value
Overall plan dimensions	80 m wide × 70 m deep (50 m + 20 m)
Notch in the top edge	25 m deep, width not dimensioned
Internal trenches	one full-width run 20 m up from the bottom; one run from the notch bottom down to it
Footing width	750 mm
Trench width	300 + 750 + 300 = 1350 mm (300 mm working space each side of the footing)
Footing thickness	450 mm
Top of footing below ground level	600 mm
Wall thickness	200 mm (excluded from this estimate)
Excavation output, 0.29 m³ backhoe	115 m³/day at $4.76/m³ bare
Formwork output, two uses	40.88 m²/day at $25.37/m² bare
Concrete placing rate	5 m³/h, 8 h/day
Concreting cost (material included)	$20,000

Find. For each of excavation, formwork and concrete: the take-off quantity in its own unit, the duration in working days at the stated production rate, and the bare cost.

[Figure not reproduced: Foundation plan re-drawn from the paper. The trench runs on every wall line: the full outline including the two 25 m sides of the notch, one internal run across the full width 20 m up from the bottom, and one internal run from the notch bottom down to it. The notch width is not dimensioned on the pa. See the official exam paper.]

Trench cross-section. The trench is excavated 1350 mm wide — the 750 mm footing plus the printed 300 mm working space on each side — and down 1050 mm to the underside of the footing; formwork is the two 450 mm vertical faces of the footing, and the 200 mm wall is excluded from this estimate.

Approach. Every quantity on this job is the trench centreline length multiplied by a cross-sectional property, so measure the length once from the plan, take the depth, width and form height off the section, then divide each quantity by its daily output for duration and multiply by its bare unit rate for cost.

Measure the trench centreline length, and show the undimensioned notch does not matter. Walk the outline once. The two lengths of top edge either side of the notch, plus the notch bottom, always add to the overall width whatever the notch width $w$ is, because the notch removes $w$ from the top edge and returns $w$ at its base; only the two 25 m notch sides are extra. With $W=80$ m, $H=50+20=70$ m and a notch depth of 25 m, $$L_{\text{perim}}=2W+2H+2(25)=160+140+50=350\ \text{m}$$ The internal run at the 20 m line spans the full width, $L_{\text{int,h}}=80$ m, and the run from the notch bottom down to it spans the difference between the 50 m dimension and the 25 m notch depth, $L_{\text{int,v}}=50-25=25$ m. Adding the three, $$L=350+80+25=\boxed{455\ \text{m of trench}}$$
Read the excavation cross-section off the section drawing. The dimension ticks under the printed section fall on the two trench walls and on the two edges of the footing, so the 750 mm is the footing and each 300 mm is working space between the footing and the trench wall. The trench is dug to the full width and down to the underside of the footing, so $$b=300+750+300=1350\ \text{mm}=1.35\ \text{m},\qquad b_f=750\ \text{mm}=0.75\ \text{m},\qquad h=600+450=1050\ \text{mm}=1.05\ \text{m}$$ The 1.05 m depth sits inside the “0.3 m to 1.2 m deep” band of the R.S. Means line, which confirms the correct row has been selected.
Compute the excavation quantity. Volume is length times the neat trench section, $$V_{\text{exc}}=L\,b\,h=455\times1.35\times1.05=\boxed{645\ \text{m}^3}$$ (645.0 m³ to one decimal, 644.96 m³ unrounded).
Convert the excavation quantity to a duration and a bare cost. The question specifies the 0.29 m³ machine, so the 115 m³/day line governs and the 0.38 m³ line is a distractor: $$t_{\text{exc}}=\frac{644.96}{115}=5.61\ \text{days}\ \rightarrow\ \textbf{6 working days},\qquad C_{\text{exc}}=644.96\times4.76=\boxed{\$3{,}070}$$ of which $1,948 is labour and $1,122 equipment; there is no material content in an excavation line.
Take off the formwork contact area. Only the footing is formed — the wall is expressly excluded — and a continuous strip footing is formed on both vertical faces to its full thickness, so the contact area is twice the footing depth times the length: $$A_{\text{form}}=2\,t_f\,L=2\times0.45\times455=\boxed{409.5\ \text{m}^2}$$
Price the formwork on the correct re-use line. The question states the material serves two uses, so the “2 use” row applies: the material rate drops from $12.80 to $7.00/m² because the panel cost is spread over two pours, and the crew is faster the second time, 40.88 m²/day rather than 34.84. Hence $$t_{\text{form}}=\frac{409.5}{40.88}=10.02\ \text{days}\ \rightarrow\ \textbf{10 working days}$$ $$C_{\text{form}}=409.5\times25.37=\boxed{\$10{,}389}$$ made up of $2,867 material, $7,248 labour and $274 equipment.
Compute the concrete quantity and its placing duration. The footing is a constant 750 mm × 450 mm section along the whole trench — the working space either side is backfilled, not concreted — so $$V_{\text{conc}}=L\,b_f\,t_f=455\times0.75\times0.45=\boxed{153.6\ \text{m}^3}$$ At 5 m³/h over an eight-hour day the placing rate is 40 m³/day, so $$t_{\text{conc}}=\frac{153.56}{5\times8}=3.84\ \text{days}\ \rightarrow\ \textbf{4 working days}$$
Assemble the bare estimate. Concreting is priced by the question itself at a lump $20,000 including material, so no unit rate is needed for it. Summing the three trades, $$C_{\text{total}}=3{,}070+10{,}389+20{,}000=\boxed{\$33{,}459\ \text{bare}}$$ and the three activity durations total 19.5 working days if the trades follow one another end to end, which is the sequence a strip footing normally demands.

Check — the estimating assumptions behind these numbers. Excavation is priced to the printed 1350 mm trench width, which already carries 300 mm of working space either side of the 750 mm footing, with vertical sides and no side slopes or bulking allowance, because the R.S. Means line quoted is a bank-measure trench line; a real bid would add bulking for haul-off, and at 1.05 m the trench is below the depth at which BC's OHSR Part 20 requires shoring or sloping, so no shoring is priced. Formwork is the two vertical faces of the footing only, with no allowance for stop-ends or waste. Plan dimensions are read as trench centrelines. Trench intersections are not deducted; the four T-junctions involved are worth under 4 m³ of double-counted excavation, well inside estimating tolerance. These are bare costs as the question asks — no overhead, profit, bond or escalation is included.

Question 2 — results (bare costs)
Task	Quantity	Production rate	Duration	Bare cost
Trench excavation (0.29 m³ backhoe)	645.0 m³	115 m³/day	5.61 days → 6 days	$3,070
Footing formwork (2 uses)	409.5 m²	40.88 m²/day	10.02 days → 10 days	$10,389
Concreting the footings	153.6 m³	40 m³/day	3.84 days → 4 days	$20,000 (given)
Trench centreline length used throughout	455 m	—	—	—
Total	—	—	19.5 days if sequential	$33,459

Topic. Quantity take-off from a foundation plan and section, and unit-price estimating from a published production database.

Key relations. Quantity = centreline length × cross-sectional property; duration = quantity ÷ crew daily output; bare cost = quantity × (material + labour + equipment) rate; labour-hours per unit = crew labour-hours per day ÷ daily output, which is the invariant when crew size changes.

Why this works. A strip foundation is a prismatic solid: every quantity the estimator needs — excavated volume, formed area, concrete volume — is the same single length multiplied by a different property of one cross-section. Measuring that length once and carrying it through is therefore both faster and less error-prone than taking off each trade separately, and it makes the sensitivity of the whole estimate to one measurement explicit. The R.S. Means daily output then does the second half of the job: it is a crew-level productivity figure, so dividing a quantity by it converts work into calendar time on the same basis that the unit rates convert work into money, which keeps duration and cost internally consistent.

Common pitfall. Candidates lose marks by adding the undimensioned notch width as an assumption instead of noticing it cancels, and by pricing the formwork on the “1 use” line when the question explicitly says the material serves two uses — that single row choice changes the formwork cost by 36 per cent. A third recurring error is forming all four faces of the footing, or including the 200 mm wall, when the question excludes it. A fourth is reading the 300 + 750 + 300 dimension string as a 1350 mm footing: the ticks fall on the trench walls and the footing edges, and concreting the full trench width overstates the concrete by 80 per cent.

Source. Hendrickson & Au, Project Management for Construction, Chapter 5 (unit-cost estimation); Halpin & Senior, Construction Management, quantity take-off and productivity chapters; R.S. Means, Building Construction Cost Data, front matter on how a unit-price line is structured; Peurifoy & Schexnayder, Construction Planning, Equipment and Methods, Chapter on excavating equipment production.

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