Question 5 of 6: Estimating — brickwork quantity take-off and crew duration

Question 5: Estimating — brickwork quantity take-off and crew duration (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. Two brick faces of one house, dimensioned on the page-3 drawing, and a table of brick coverage rates and mason production rates for three brick sizes. The crew is four brick masons and two labourers; openings are to be ignored, and the coverage rates already include a waste factor.

Find. The wall surface area to be bricked, the number of bricks required for each of the three brick sizes, and the crew duration for each.

[Figure not reproduced: Figure 5.1 — the two faces to be bricked, redrawn flat from the page-3 elevation. The front face resolves into a rectangle, a gable triangle and the triangular strip carried below the eave-line datum; the side wall is a plain rectangle because the eave line is level. The two elevations are dra. See the official exam paper.]

Approach. Decompose each face into rectangles and triangles, take the gross area with the openings ignored as instructed, convert area to brick count with the coverage rate, and convert brick count to duration with the crew's daily output — noting that the production rate is stated per mason, so it must be multiplied by the four masons and not by the six-person crew.

1. Take off the front face. The face resolves into three simple shapes. The main rectangle runs the full width for the 10′-6″ to the eave:

   $$A_{\text{rect}}=22.333\times10.5=234.50\ \text{SF}$$

   The gable above it is a triangle on the same base, 6′-6″ high, which the 17′ overall dimension confirms since $10.5+6.5=17$:

   $$A_{\text{gable}}=\tfrac12\times22.333\times6.5=72.58\ \text{SF}$$

   Below the eave-line datum the wall is carried down to 2′ over the last 9′ of its length, a right triangle:

   $$A_{\text{strip}}=\tfrac12\times9\times2=9.00\ \text{SF}$$

   so the front face totals $234.50+72.58+9.00=316.08$ SF.

2. Take off the side face. A gable roof puts the ridge on the end wall, so the eave line along the flank is level and the side wall is a plain rectangle of the eave height:

   $$A_{\text{side}}=59\times10.5=619.50\ \text{SF}$$

3. Sum the wall surface area.

   $$A=316.08+619.50=\boxed{935.58\ \text{SF}}$$

   The instruction to ignore openings means this gross figure is the take-off quantity; the two windows and the door drawn on the elevation are deliberately not deducted. That is also why the coverage rates carry a waste allowance — the estimate is made deliberately slightly generous rather than exactly right.

4. Convert area to brick quantities. Each coverage rate is bricks per square foot of wall face, so $N=A\times n_{\text{SF}}$ and the results are rounded up, since bricks are ordered in whole units:

   $$N_{\text{Standard}}=935.58\times7.4=6{,}923.3\ \Rightarrow\ \boxed{6{,}924\ \text{bricks}}$$

   $$N_{\text{King}}=935.58\times5.7=5{,}332.8\ \Rightarrow\ \boxed{5{,}333\ \text{bricks}}$$

   $$N_{\text{Jumbo}}=935.58\times3.3=3{,}087.4\ \Rightarrow\ \boxed{3{,}088\ \text{bricks}}$$

   In practice these would be ordered by the cube or by the thousand and rounded up again to the supplier's packing unit.

5. Convert brick quantities to crew duration. The table gives production per brick mason, so the crew's daily output is four times it — the two labourers tend the masons, mixing and carrying, and do not lay brick, so they add no output but do add cost and are included in the crew-hour figure below:

   $$Q_{\text{crew}}=4\times400=1{,}600;\quad 4\times385=1{,}540;\quad 4\times360=1{,}440\ \text{bricks/day}$$

   and the duration follows as $t=N/Q_{\text{crew}}$:

   $$t_{\text{Standard}}=\frac{6{,}923.3}{1{,}600}=\boxed{4.33\ \text{days}}\quad\left(5\ \text{working days}\right)$$

   $$t_{\text{King}}=\frac{5{,}332.8}{1{,}540}=\boxed{3.46\ \text{days}}\quad\left(4\ \text{working days}\right)$$

   $$t_{\text{Jumbo}}=\frac{3{,}087.4}{1{,}440}=\boxed{2.14\ \text{days}}\quad\left(3\ \text{working days}\right)$$

6. Cross-check the durations a second way. Convert each production rate to wall area instead of bricks, $Q_{\text{SF}}=Q_{\text{crew}}/n_{\text{SF}}$, giving 216.2, 270.2 and 436.4 SF per crew-day. Dividing the 935.58 SF of wall by each returns 4.33, 3.46 and 2.14 days, matching step 5 exactly. The check is worth doing because it exercises the coverage rate and the production rate in the opposite order and would expose a mismatched pairing — using the King coverage with the Standard production rate, say — which is the easiest slip to make on a three-column problem of this kind.
7. Convert to crew-hours for pricing. The crew is six workers on an eight-hour shift, so 48 crew-hours per day, and

   $$H=t\times48=207.7,\quad166.2,\quad102.9\ \text{crew-hours}$$

   for Standard, King and Jumbo respectively. Multiplying these by the assembled crew rate — four mason hours and two labourer hours per six crew-hours, at the applicable collective-agreement or prevailing wage — gives the labour cost, to which the delivered brick and mortar cost is added.

8. Interpret the comparison. Jumbo brick needs 55 % fewer units than Standard for the same wall and finishes in less than half the time — 2.14 days against 4.33 — because a mason's output is governed far more by the number of units handled and jointed than by their size. Whether that is the right choice is a cost and appearance decision, not a duration one: a Jumbo unit costs more each and gives a coarser bond pattern, so the saving in labour has to be weighed against the material premium and the architectural intent.