By the end of this chapter, you will be able to:
Mastering these skills will help you work confidently with technical drawings and ensure precise measurements in your trade projects.
Application of work up dimensions techniques is fundamental in civil engineering for accurate measurement and costing of construction projects. Precise quantification ensures proper budgeting, resource allocation, and project management. This chapter focuses on the core techniques such as timesing, abstracting, and working up quantities, which are essential skills for quantity surveyors and civil engineers working on projects in Kenya.
Timesing is the process of multiplying the dimensions of a building element to obtain a total quantity for costing or ordering materials. It involves combining length, width, and depth measurements to calculate volume, area, or length as required.
The general formula for timesing is:
$$ Q = L \times W \times D $$
where \(Q\) is the quantity, \(L\) is length, \(W\) is width, and \(D\) is depth or thickness.
Example 1: Calculate the volume of concrete required for a footing measuring 2 m length, 0.5 m width, and 0.3 m depth.
Given:
\(L = 2\,m\),
\(W = 0.5\,m\),
\(D = 0.3\,m\)
$$ Q = L \times W \times D $$
$$ Q = 2 \times 0.5 \times 0.3 $$
$$ Q = 0.3\,m^3 $$
Answer: 0.3 cubic metres of concrete
Example 2: Find the area of a wall measuring 6 m long and 3 m high.
Given:
\(L = 6\,m\),
\(H = 3\,m\)
$$ Q = L \times H $$
$$ Q = 6 \times 3 $$
$$ Q = 18\,m^2 $$
Answer: 18 square metres of wall area
Example 3: Determine the volume of soil to be excavated for a trench 10 m long, 0.6 m wide, and 1.2 m deep.
Given:
\(L = 10\,m\),
\(W = 0.6\,m\),
\(D = 1.2\,m\)
$$ Q = L \times W \times D $$
$$ Q = 10 \times 0.6 \times 1.2 $$
$$ Q = 7.2\,m^3 $$
Answer: 7.2 cubic metres of soil
Example 4: Calculate the volume of concrete for a slab 8 m long, 5 m wide, and 0.15 m thick.
Given:
\(L = 8\,m\),
\(W = 5\,m\),
\(D = 0.15\,m\)
$$ Q = L \times W \times D $$
$$ Q = 8 \times 5 \times 0.15 $$
$$ Q = 6\,m^3 $$
Answer: 6 cubic metres of concrete
Example 5: A column has a square cross-section of 0.4 m by 0.4 m and height 3 m. Calculate the volume of concrete required.
Given:
\(L = 3\,m\),
\(W = 0.4\,m\),
\(D = 0.4\,m\)
$$ Q = L \times W \times D $$
$$ Q = 3 \times 0.4 \times 0.4 $$
$$ Q = 0.48\,m^3 $$
Answer: 0.48 cubic metres of concrete
Abstracting involves extracting quantities of materials or work from drawings and specifications for preparation of a bill of quantities. It requires careful analysis of drawings to identify components and their dimensions.
The abstracted quantity \(Q_a\) is the sum of all relevant measurements for a particular item.
Example 1: A beam has dimensions 5 m length, 0.3 m width, and 0.5 m depth. Abstract the volume of concrete required.
Given:
\(L = 5\,m\),
\(W = 0.3\,m\),
\(D = 0.5\,m\)
$$ Q_a = L \times W \times D $$
$$ Q_a = 5 \times 0.3 \times 0.5 $$
$$ Q_a = 0.75\,m^3 $$
Answer: 0.75 cubic metres of concrete
Example 2: From the drawing, a floor slab area is 12 m by 9 m with thickness 0.2 m. Abstract the concrete volume.
Given:
\(L = 12\,m\),
\(W = 9\,m\),
\(D = 0.2\,m\)
$$ Q_a = L \times W \times D $$
$$ Q_a = 12 \times 9 \times 0.2 $$
$$ Q_a = 21.6\,m^3 $$
Answer: 21.6 cubic metres of concrete
Example 3: Abstract the total length of reinforcement bars if 10 beams each have 6 bars of 12 m length.
Given:
Number of beams = 10,
Bars per beam = 6,
Length per bar = 12 m
$$ Q_a = \text{Number of beams} \times \text{Bars per beam} \times \text{Length per bar} $$
$$ Q_a = 10 \times 6 \times 12 $$
$$ Q_a = 720\,m $$
Answer: 720 metres of reinforcement bars
Example 4: A retaining wall has 4 panels each 3 m long and 2.5 m high. Abstract the total wall area.
Given:
Panels = 4,
Length per panel = 3 m,
Height per panel = 2.5 m
$$ Q_a = \text{Panels} \times L \times H $$
$$ Q_a = 4 \times 3 \times 2.5 $$
$$ Q_a = 30\,m^2 $$
Answer: 30 square metres of wall
Example 5: Abstract the volume of concrete in 6 columns each 0.4 m by 0.4 m cross-section and 3 m height.
Given:
Number of columns = 6,
Cross-section \(= 0.4\,m \times 0.4\,m\),
Height = 3 m
$$ Q_a = \text{Number} \times L \times W \times H $$
$$ Q_a = 6 \times 0.4 \times 0.4 \times 3 $$
$$ Q_a = 2.88\,m^3 $$
Answer: 2.88 cubic metres of concrete
A Bill of Quantities (BoQ) is a document listing all materials, parts, and labour needed for a construction project with their quantities and descriptions. It forms the basis for tendering and cost control.
The total cost \(C_t\) is calculated by summing the product of quantities and rates:
$$ C_t = \sum (Q_i \times R_i) $$
where \(Q_i\) is quantity and \(R_i\) is the unit rate for item \(i\).
Example 1: Calculate the cost of 50 m³ of concrete at Ksh 7,000 per m³.
Given:
\(Q = 50\,m^3\),
\(R = 7000\,Ksh/m^3\)
$$ C_t = Q \times R $$
$$ C_t = 50 \times 7000 $$
$$ C_t = 350,000\,Ksh $$
Answer: Ksh 350,000
Example 2: A wall requires 100 m² of plastering. Labour rate is Ksh 250 per m². Calculate labour cost.
Given:
\(Q = 100\,m^2\),
\(R = 250\,Ksh/m^2\)
$$ C_t = Q \times R $$
$$ C_t = 100 \times 250 $$
$$ C_t = 25,000\,Ksh $$
Answer: Ksh 25,000
Example 3: Find total cost for 200 bags of cement at Ksh 600 per bag.
Given:
\(Q = 200\) bags,
\(R = 600\,Ksh/bag\)
$$ C_t = Q \times R $$
$$ C_t = 200 \times 600 $$
$$ C_t = 120,000\,Ksh $$
Answer: Ksh 120,000
Example 4: Calculate cost of 500 bricks at Ksh 80 each.
Given:
\(Q = 500\),
\(R = 80\,Ksh\)
$$ C_t = Q \times R $$
$$ C_t = 500 \times 80 $$
$$ C_t = 40,000\,Ksh $$
Answer: Ksh 40,000
Example 5: Labour for tiling is Ksh 300 per m². If 45 m² requires tiling, find total labour cost.
Given:
\(Q = 45\,m^2\),
\(R = 300\,Ksh/m^2\)
$$ C_t = Q \times R $$
$$ C_t = 45 \times 300 $$
$$ C_t = 13,500\,Ksh $$
Answer: Ksh 13,500
Working up involves detailed measurement and calculation of quantities from drawings and specifications for inclusion in the BoQ. It ensures all necessary components are accounted for.
The total quantity \(Q_t\) is the sum of individual measured quantities:
$$ Q_t = \sum Q_i $$
Example 1: Calculate total volume of concrete in a footing (1 m³) and a column (0.8 m³).
Given:
\(Q_1 = 1\,m^3\),
\(Q_2 = 0.8\,m^3\)
$$ Q_t = Q_1 + Q_2 $$
$$ Q_t = 1 + 0.8 $$
$$ Q_t = 1.8\,m^3 $$
Answer: 1.8 cubic metres
Example 2: A wall requires 15 m² plaster and 10 m² painting. Find total finishing area.
Given:
Plaster \(= 15\,m^2\),
Paint \(= 10\,m^2\)
$$ Q_t = 15 + 10 $$
$$ Q_t = 25\,m^2 $$
Answer: 25 square metres
Example 3: Sum lengths of pipes: 20 m + 15 m + 10 m.
Given:
Lengths \(= 20\,m, 15\,m, 10\,m\)
$$ Q_t = 20 + 15 + 10 $$
$$ Q_t = 45\,m $$
Answer: 45 metres
Example 4: Calculate total bricks for 3 walls each needing 500 bricks.
Given:
Walls \(= 3\),
Bricks per wall \(= 500\)
$$ Q_t = 3 \times 500 $$
$$ Q_t = 1500 $$
Answer: 1500 bricks
Example 5: Calculate total excavation volume for two trenches: 3 m³ and 4.5 m³.
Given:
Volumes \(= 3\,m^3, 4.5\,m^3\)
$$ Q_t = 3 + 4.5 $$
$$ Q_t = 7.5\,m^3 $$
Answer: 7.5 cubic metres
Taking off is the process of measuring quantities directly from drawings or site measurements to prepare a BoQ. It requires precision and consistency.
The total quantity \(Q_{to}\) is the sum of all measured components.
Example 1: Measure length of wall from drawing: 15 m.
Given:
Length \(= 15\,m\)
$$ Q_{to} = 15\,m $$
Answer: 15 metres
Example 2: Measure area of floor slab: 8 m × 6 m.
Given:
Length \(= 8\,m\),
Width \(= 6\,m\)
$$ Q_{to} = 8 \times 6 $$
$$ Q_{to} = 48\,m^2 $$
Answer: 48 square metres
Example 3: Measure volume of concrete footing: 2 m × 0.5 m × 0.3 m.
Given:
\(L = 2\,m\),
\(W = 0.5\,m\),
\(D = 0.3\,m\)
$$ Q_{to} = 2 \times 0.5 \times 0.3 $$
$$ Q_{to} = 0.3\,m^3 $$
Answer: 0.3 cubic metres
Example 4: Measure length of reinforcement bar: 12 m.
Given:
Length \(= 12\,m\)
$$ Q_{to} = 12\,m $$
Answer: 12 metres
Example 5: Measure number of bricks: 600.
Given:
Number \(= 600\)
$$ Q_{to} = 600 $$
Answer: 600 bricks
Booking is the recording of quantities after measurement or taking off for inclusion in BoQ or project records. It ensures traceability and accuracy.
Total booked quantity \(Q_b\) is the recorded figure for each item.
Example 1: Book 20 m³ of concrete.
Given:
Quantity \(= 20\,m^3\)
$$ Q_b = 20\,m^3 $$
Answer: 20 cubic metres
Example 2: Book 150 m² of plastering.
Given:
Quantity \(= 150\,m^2\)
$$ Q_b = 150\,m^2 $$
Answer: 150 square metres
Example 3: Book 1000 bricks.
Given:
Quantity \(= 1000\)
$$ Q_b = 1000 $$
Answer: 1000 bricks
Example 4: Book 500 m length of pipe.
Given:
Quantity \(= 500\,m\)
$$ Q_b = 500\,m $$
Answer: 500 metres
Example 5: Book 10 m³ of excavation.
Given:
Quantity \(= 10\,m^3\)
$$ Q_b = 10\,m^3 $$
Answer: 10 cubic metres
Specifications define the quality and standards for materials and workmanship in a construction project. They guide measurement and costing by defining what is included.
Cost estimation depends on clear specifications for each item.
Example 1: Calculate cost of cement specified at 50 kg bags, 100 bags, rate Ksh 700.
Given:
Bags \(= 100\),
Rate \(= 700\,Ksh\)
$$ C = 100 \times 700 $$
$$ C = 70,000\,Ksh $$
Answer: Ksh 70,000
Example 2: Cost for timber specified as 2" by 4" by 3 m lengths, 50 pieces at Ksh 1,200 each.
Given:
Pieces \(= 50\),
Rate \(= 1,200\,Ksh\)
$$ C = 50 \times 1,200 $$
$$ C = 60,000\,Ksh $$
Answer: Ksh 60,000
Example 3: Cost of bricks specified as class A, 500 pieces at Ksh 90 each.
Given:
Bricks \(= 500\),
Rate \(= 90\,Ksh\)
$$ C = 500 \times 90 $$
$$ C = 45,000\,Ksh $$
Answer: Ksh 45,000
Example 4: Cost of steel bars specified as T10, 100 m at Ksh 150 per metre.
Given:
Length \(= 100\,m\),
Rate \(= 150\,Ksh/m\)
$$ C = 100 \times 150 $$
$$ C = 15,000\,Ksh $$
Answer: Ksh 15,000
Example 5: Cost of painting specified as two coats, 200 m² at Ksh 80 per m².
Given:
Area \(= 200\,m^2\),
Rate \(= 80\,Ksh/m^2\)
$$ C = 200 \times 80 $$
$$ C = 16,000\,Ksh $$
Answer: Ksh 16,000
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Create a free accountThis chapter introduces essential terms and concepts related to measurement and costing in construction, including timesing, abstracting, bill of quantities, working up, taking off, booking, and specifications. It emphasizes the importance of accurately interpreting working drawings, covering various types such as architectural, structural, electrical, mechanical, and building drawings, alongside understanding drawing standards and reading technical specifications. The chapter also explains the process of scaling dimensions, detailing different scale types, methods for converting between scales, and important scaling rules. Further, it discusses the technique of timesing dimensions in accordance with the Standard Method of Measurement (SMM) and Civil Engineering Standard Method of Measurement (CESMM), focusing on multiplying and squaring dimensions. Guidance is provided on CESMM guidelines and SMM conventions to ensure consistency and accuracy in measurement work. Overall, the chapter equips students with the skills to work up dimensions effectively from drawings and specifications for reliable quantity estimation and cost assessment.
A rectangular slab has length 6.5 m and width 4.2 m. Calculate the area in square meters. (2 marks)
A beam has a cross-sectional dimension of 0.3 m by 0.5 m and a length of 8 m. Find the volume of concrete required in cubic meters. (3 marks)
Type: Individual
| Tools & Equipment | Materials |
|---|---|
| Architectural scale ruler | Architectural working drawing |
| Measuring tape 5m | |
| Pencil HB | |
| Eraser | |
| Calculator | |
| Notebook |
| S/N | Item | Quantity |
|---|---|---|
| 1 | Architectural working drawing of single-storey residential building | 1 per Candidate |
| 2 | Scale ruler (Architectural scale) | 1 per Candidate |
| 3 | Measuring tape 5m | 1 per Candidate |
| 4 | Pencil HB | 2 Pcs per Candidate |
| 5 | Eraser | 1 Pc per Candidate |
| 6 | Notebook for notes | 1 per Candidate |
| 7 | Calculator | 1 per Candidate |
| 8 | PPEs (Safety boots, Overall, Helmet, Gloves) | 1 set per Candidate |
| Items to be Evaluated | Marks Available | Marks Obtained | Comments |
|---|---|---|---|
| TASK 1: Interpretation and Dimensioning | |||
| Wore PPEs (Safety boots, Overall, Helmet, Gloves) (Award 3 marks for wearing all PPEs or zero) | 3 | ||
| Selected and used architectural scale ruler correctly (Award 3 marks for correct use or zero) | 3 | ||
| Identified and recorded overall building dimensions (Length and Width) (Award 4 marks for correct identification and recording or zero) | 4 | ||
| Identified and recorded room dimensions from the drawing (Award 1 mark for each correctly identified room dimension x6) | 6 | ||
| Noted door and window sizes and types as per the drawing (Award 2 marks for doors, 2 marks for windows or zero) | 4 | ||
| Recorded wall thickness and foundation details from the drawing (Award 3 marks for correct recording or zero) | 3 | ||
| Made neat and accurate notes and sketches in the notebook (Award 3 marks for clarity and accuracy or zero) | 3 | ||
| Sub-Total | 26 | ||
| PRODUCT CHECKLIST | |||
| Recorded building overall dimensions 10,000mm x 8,000mm within ±5mm accuracy (Award 4 marks for correct dimensions or zero) | 4 | ||
| Recorded room dimensions as per drawing within ±5mm accuracy (Award 1 mark for each correct room dimension x6) | 6 | ||
| Correctly identified door sizes (900mm x 2100mm) and window sizes (1200mm x 1500mm) as per drawing (Award 2 marks each for doors and windows or zero) | 4 | ||
| Accurately recorded wall thickness (150mm) and foundation details (Award 4 marks for correct recording or zero) | 4 | ||
| Notes and sketches are legible, organized and correspond with the drawing (Award 3 marks for neatness and relevance or zero) | 3 | ||
| Sub-Total | 21 | ||
| GRAND TOTAL | 47 | ||
Type: Individual
| Tools & Equipment | Materials |
|---|---|
| Scale ruler (metric) | Structural working drawing of reinforced concrete beam |
| Pencil HB | PPE (Safety boots, Overall, Safety helmet) |
| Eraser | |
| Calculator | |
| Notebook |
| S/N | Item | Quantity |
|---|---|---|
| 1 | Structural working drawing of reinforced concrete beam | 1 per Candidate |
| 2 | Scale ruler (metric) | 1 per Candidate |
| 3 | Pencil HB | 2 Pcs per Candidate |
| 4 | Eraser | 1 Pc per Candidate |
| 5 | Notebook | 1 per Candidate |
| 6 | Calculator | 1 per Candidate |
| 7 | Safety boots | 1 Pair per Candidate |
| 8 | Overall | 1 per Candidate |
| 9 | Safety helmet | 1 per Candidate |
| Items to be Evaluated | Marks Available | Marks Obtained | Comments |
|---|---|---|---|
| TASK 1: Interpretation of Structural Working Drawing | |||
| Wore PPE (Safety boots, Overall, Helmet) (Award 3 marks or zero) | 3 | ||
| Identified beam dimensions (length, width, depth) correctly from the drawing (Award 4 marks or zero) | 4 | ||
| Extracted main reinforcement bar size, number, and arrangement (Award 6 marks for complete and correct extraction) | 6 | ||
| Extracted shear reinforcement details including stirrup size and spacing (Award 5 marks for accurate details) | 5 | ||
| Noted cover to reinforcement as per drawing standards (Award 3 marks or zero) | 3 | ||
| Recorded all reinforcement details clearly and legibly in notebook (Award 4 marks for clarity and completeness) | 4 | ||
| Sub-Total | 25 | ||
| PRODUCT CHECKLIST | |||
| Correct identification and recording of beam dimensions (4000mm length, 300mm width, 500mm depth) (Award 4 marks or zero) | 4 | ||
| Correct main reinforcement details: 4Y20 main bars at bottom and 2Y16 top bars (Award 6 marks or zero) | 6 | ||
| Correct shear reinforcement: R10 links @ 150mm c/c spacing (Award 5 marks or zero) | 5 | ||
| Correct cover: 40mm clear cover to all reinforcement (Award 3 marks or zero) | 3 | ||
| Neat and accurate presentation of extracted data matching drawing standards (Award 7 marks for neatness and accuracy) | 7 | ||
| Sub-Total | 25 | ||
| GRAND TOTAL | 50 | ||
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