ABSTRACT

Millimetre mm 1 in = 25.4 mm 1 mm = 0.0394 in Centimetre cm 1 in = 2.54 cm 1 cm = 0.3937 in Metre m 1 ft = 0.3048 m 1 m = 3.2808 ft

1 yd = 0.9144 m = 1.0936 yd Kilometre km 1 mile = 1.6093 km 1km = 0.6214 mile

Note: 1 cm = 10 mm 1 ft = 12 in 1 m = 1 000 mm 1 yd = 3 ft 1 km = 1 000 m 1 mile = 1 760 yd

Area Unit Conversion factors

Square Millimetre mm2 1 in2 = 645.2 mm2 1 mm2 = 0.0016 in2

Square Centimetre cm2 1 in2 = 6.4516 cm2 1 cm2 = 1.1550 in2

Square Metre m2 1 ft2 = 0.0929 m2 1 m2 = 10.764 ft2

1 yd2 = 0.8361 m2 1 m2 = 1.1960 yd2

Square Kilometre km2 1 mile2 = 2.590 km2 1 km2 = 0.3861 mile2

Note: 1 cm2 = 100 mm2 1 ft2 = 144 in2

1 m2 = 10 000 cm2 1 yd2 = 9 ft2

1 km2 = 100 hectares 1 acre = 4 840 yd2

1 mile2 = 640 acres

Volume Unit Conversion factors

Cubic Centimetre cm3 1 cm3 = 0.0610 in3 1 in3 = 16.387 cm3

Cubic Decimetre dm3 1 dm3 = 0.0353 ft3 1 ft3 = 28.329 dm3

Cubic Metre m3 1 m3 = 35.3147 ft3 1 ft3 = 0.0283 m3

1 m3 = 1.3080 yd3 1 yd3 = 0.7646 m3

Litre l 1 l = 1.76 pint 1 pint = 0.5683 l = 2.113 US pt = 0.4733 US l

Note: 1 dm3 = 1 000 cm3 1 ft3 = 1 728 in3 1 pint = 20 fl oz 1 m3 = 1 000 dm3 1 yd3 = 27 ft3 1 gal = 8 pints 1 l = 1 dm3

Mass Unit Conversion factors

Milligram mg 1 mg = 0.0154 grain 1 grain = 64.935 mg Gram g 1 g = 0.0353 oz 1 oz = 28.35 g Kilogram kg 1 kg = 2.2046 lb 1 lb = 0.4536 kg Tonne t 1 t = 0.9842 ton 1 ton = 1.016 t

Note: 1 g = 1000 mg 1 oz = 437.5 grains 1 cwt = 112 lb 1 kg = 1000 g 1 lb = 16 oz 1 ton = 20 cwt 1 t = 1000 kg 1 stone = 14 lb

Force Unit Conversion factors

Newton N 1 lbf = 4.448 N 1 kgf = 9.807 N Kilonewton kN 1 lbf = 0.004448 kN 1 ton f = 9.964 kN Meganewton MN 100 tonf = 0.9964 MN

Pressure and stress Unit Conversion factors

Kilonewton per square metre kN/m2 1 lbf/in2 = 6.895 kN/m2

1 bar = 100 kN/m2

Meganewton per square metre MN/m2 1 tonf/ft2 = 107.3 kN/m2 = 0.1073 MN/m2

1 kgf/cm2 = 98.07 kN/m2

1 lbf/ft2 = 0.04788 kN/m2

Coefficient of consolidation (Cv) or swelling

Unit Conversion factors

Square metre per year m2/year 1 cm2/s = 3 154 m2/year 1 ft2/year = 0.0929 m2/year

Coefficient of permeability Unit Conversion factors

Metre per second m/s 1 cm/s = 0.01 m/s Metre per year m/year 1 ft/year = 0.3048 m/year

= 0.9651 × (10)8m/s

Temperature Unit Conversion factors

Degree Celsius °C °C = 5/9 × (°F − 32) °F = (9 × °C)/ 5 + 32

Power Unit Conversion factors

Kilowatt kW 1kW = 1.341HP Horsepower HP 1HP = 0.746 kW

km/h m/min mph fpm

1 16.7 0.6 54.7 2 33.3 1.2 109.4 3 50.0 1.9 164.0 4 66.7 2.5 218.7 5 83.3 3.1 273.4

6 100.0 3.7 328.1 7 116.7 4.3 382.8 8 133.3 5.0 437.4 9 150.0 5.6 492.1

10 166.7 6.2 546.8

11 183.3 6.8 601.5 12 200.0 7.5 656.2 13 216.7 8.1 710.8 14 233.3 8.7 765.5 15 250.0 9.3 820.2

16 266.7 9.9 874.9 17 283.3 10.6 929.6 18 300.0 11.2 984.3 19 316.7 11.8 1038.9 20 333.3 12.4 1093.6

21 350.0 13.0 1148.3 22 366.7 13.7 1203.0 23 383.3 14.3 1257.7 24 400.0 14.9 1312.3 25 416.7 15.5 1367.0

26 433.3 16.2 1421.7 27 450.0 16.8 1476.4 28 466.7 17.4 1531.1 29 483.3 18.0 1585.7 30 500.0 18.6 1640.4

31 516.7 19.3 1695.1 32 533.3 19.9 1749.8 33 550.0 20.5 1804.5 34 566.7 21.1 1859.1 35 583.3 21.7 1913.8

36 600.0 22.4 1968.5 37 616.7 23.0 2023.2 38 633.3 23.6 2077.9 39 650.0 24.2 2132.5 40 666.7 24.9 2187.2

41 683.3 25.5 2241.9 42 700.0 26.1 2296.6 43 716.7 26.7 2351.3 44 733.3 27.3 2405.9 45 750.0 28.0 2460.6

km/h m/min mph fpm

46 766.7 28.6 2515.3 47 783.3 29.2 2570.0 48 800.0 29.8 2624.7 49 816.7 30.4 2679.4 50 833.3 31.1 2734.0

Figure Diagram of figure Surface area Perimeter

Square a2 4a

Rectangle ab 2ðaþ bÞ

Triangle 12 ch aþ bþ c

where 2r ¼ d

2r d

Parallelogram ah 2ðaþ bÞ

Trapezium 12 hðaþ bÞ aþ bþ cþ d

Ellipse Approximately ab

ðaþ bÞ

Hexagon 2:6 a2

Figure Diagram of figure Surface area Perimeter

Octagon 4:83 a2 6a

Sector of a circle

note b ¼ angle q360 2r

Segment of a circle

S T where S = area of sector,

T = area of triangle

Figure Diagram of figure Surface area Volume

Cube 6a2 a3

Cuboid/ rectangular block

2ðabþ acþ bcÞ abc

Prism/ triangular block

bdþ hcþ dcþ ad 12 hcd

Cylinder 2r2 þ 2h r2h 1 4d

Segment of sphere

2ð3R HÞ

Pyramid ðaþ bÞIþ ab 13 abh

Figure Diagram of figure Surface area Volume

Frustum of a pyramid

Iðaþ bþ cþ dÞ þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðabþ cdÞp [rectangular figure only]

ffiffiffiffiffiffiffiffiffiffiffi abcd

p Þ

Cone rl (excluding base)

rlþ r2 (including base)

Frustum of a cone

r2 þ R2 þ lðRþ rÞ 13ðR2 þ Rr þ r2Þ

Formula Description

Pythagoras theorem A2 = B2 + C2

where A is the hypotenuse of a right-angled triangle and B and C are the two adjacent sides

Simpsons Rule The Area is divided into an even number of strips of equal width, and therefore has an odd number of ordinates at the division points

area = SðAþ 2Bþ 4CÞ

where S = common interval (strip width) A = sum of first and last ordinates B = sum of remaining odd ordinates C = sum of the even ordinates

The Volume can be calculated by the same formula, but by substituting the area of each coordinate rather than its length

Trapezoidal Rule A given trench is divided into two equal sections, giving three ordinates, the first, the middle and the last

volume = S ðAþ Bþ 2CÞ

where S = width of the strips A = area of the first section B = area of the last section C = area of the rest of the sections

Prismoidal Rule A given trench is divided into two equal sections, giving three ordinates, the first, the middle and the last

volume = L ðAþ 4Bþ CÞ

where L = total length of trench A = area of the first section B = area of the middle section C = area of the last section

Material kg/m³ lb/cu yd

Adobe 1914 3230 Ashes 610 1030 Asphalt, rock 2400 4050 Basalt 2933 4950 Bauxite: alum ore 2619 4420

Borax 1730 2920 Caliche 1440 2430 Carnotite 2459 4150 Cement 1600 2700 Chalk (hard) 2406 4060

Cinders 759 1280 Clay: dry 1908 3220 Clay: wet 1985 3350 Coal: bituminous 1351 2280 Coke 510 860

Conglomerate 2204 3720 Dolomite 2886 4870 Earth: dry 1796 3030 Earth: moist 1997 3370 Earth: wet 1742 2940

Feldspar 2613 4410 Felsite 2495 4210 Fluorite 3093 5220 Gabbro 3093 5220 Gneiss 2696 4550

Granite 2690 4540 Gravel, dry 1790 3020 Gypsum 2418 4080 Hardcore (consolidated) 1928 120 Lignite broken 1244 2100

Limestone 2596 4380 Magnesite, magnesium ore 2993 5050 Marble 2679 4520 Marl 2216 3740 Peat 700 1180

Potash 2193 3700 Pumice 640 1080 Quarry waste 1438 90 Quartz 2584 4360 Rhyolite 2400 4050

Material kg/m³ lb/cu yd

Sand: dry 1707 2880 Sand: wet 1831 3090 Sand and gravel – dry 1790 3020

– wet 2092 3530 Sandstone 2412 4070

Schist 2684 4530 Shale 2637 4450 Slag (blast) 2868 4840 Slate 2667 4500 Snow – dry 130 220

– wet 510 860

Taconite 3182 5370 Topsoil 1440 2430 Trachyte 2400 4050 Traprock 2791 4710 Water 1000 62

Type of vehicle Capacity of vehicle

Payload Heaped capacity

Wheelbarrow 150 0.10 1 tonne dumper 1250 1.00 2.5 tonne dumper 4000 2.50 Articulated dump truck (Volvo A20 6 × 4) 18500 11.00 Articulated dump truck (Volvo A35 6 × 6) 32000 19.00 Large capacity rear dumper (Euclid R35) 35000 22.00 Large capacity rear dumper (Euclid R85) 85000 50.00

Machine type Cycles per minute Volume per minute (m3)

1.5 tonne excavator 1 0.04 2 0.08 3 0.12

3 tonne excavator 1 0.13 2 0.26 3 0.39

5 tonne excavator 1 0.28 2 0.56 3 0.84

7 tonne excavator 1 0.28 2 0.56 3 0.84

21 tonne excavator 1 1.21 2 2.42 3 3.63

Backhoe loader JCB3CX excavator 1 0.28 Rear bucket capacity 0.28m3 2 0.56

3 0.84

Backhoe loader JCB3CX loading 1 1.00 Front bucket capacity 1.00m3 2 2.00

Machine type Loads per hour Volume per hour (m3)

1 tonne high tip skip loader 5 2.43 Volume 0.485m3 7 3.40

10 4.85

3 tonne dumper 4 7.60 Max volume 2.40m3 5 9.50 Available volume 1.9m3 7 13.30

10 19.00

6 tonne dumper 4 15.08 Max volume 3.40m3 5 18.85 Available volume 3.77m3 7 26.39

10 37.70

Type of soil Approximate bulking of 1m3 after excavation

Vegetable soil and loam 25-30% Soft clay 30-40% Stiff clay 10-20% Gravel 20-25% Sand 40-50% Chalk 40-50% Rock, weathered 30-40% Rock, unweathered 50-60%

Type of soil Approximate bulking of 1m3 after excavation

Clay 10% Gravel 8% Gravel and sand 9% Loam and light sandy soils 12% Loose vegetable soils 15%

Material m3 of voids/m3

Alluvium 0.37 River grit 0.29 Quarry sand 0.24 Shingle 0.37 Gravel 0.39 Broken stone 0.45 Broken bricks 0.42

Type of soil Degrees

Clay – dry 30 – damp, well drained 45 – wet 15-20

Earth – dry 30 – damp 45

Gravel – moist 48 Sand – dry or moist 35

– wet 25 Loam 40

Ratio of base to height Angle in degrees

5:1 11 4:1 14 3:1 18 2:1 27 1½:1 34 1:1 45 1:1½ 56 1:2 63 1:3 72 1:4 76 1:5 79

Degrees Percent Degrees Percent

1 1.8 24 44.5 2 3.5 25 46.6 3 5.2 26 48.8 4 7.0 27 51.0 5 8.8 28 53.2 6 10.5 29 55.4 7 12.3 30 57.7 8 14.0 31 60.0 9 15.8 32 62.5

10 17.6 33 64.9 11 19.4 34 67.4 12 21.3 35 70.0 13 23.1 36 72.7 14 24.9 37 75.4 15 26.8 38 78.1 16 28.7 39 81.0 17 30.6 40 83.9 18 32.5 41 86.9 19 34.4 42 90.0 20 36.4 43 93.3 21 38.4 44 96.6 22 40.4 45 100.0

Ground conditions Bearing power

kg/m2 lb/in2 Metric t/m2

Rock, broken 483 70 50 solid 2415 350 240

Clay, dry or hard 380 55 40 medium dry 190 27 20 soft or wet 100 14 10

Gravel, cemented 760 110 80

Sand, compacted 380 55 40 clean dry 190 27 20

Swamp and alluvial soils 48 7 5

Ground conditions Feet (ft) Metres (m)

Compact soil 12 3.66 Drained loam 6 1.83 Dry sand 1 0.3 Gravelly earth 2 0.61 Ordinary earth 3 0.91 Stiff clay 10 3.05

Type of material kg/m³ lb/cu ft

Ordinary concrete (dense aggregates)

Non-reinforced plain or mass concrete Nominal weight 2305 144 Aggregate – limestone 2162 to 2407 135 to 150

– gravel 2244 to 2407 140 to 150 – broken brick 2000 (av) 125 (av) – other crushed stone 2326 to 2489 145 to 155

Reinforced concrete Nominal weight 2407 150 Reinforcement – 1% 2305 to 2468 144 to 154

– 2% 2356 to 2519 147 to 157 – 4% 2448 to 2703 153 to 163

Special concretes

Heavy concrete Aggregates – barytes, magnetite 3210 (min) 200 (min)

– steel shot, punchings 5280 330

Lean mixes Dry-lean (gravel aggregate) 2244 140 Soil-cement (normal mix) 1601 100

Type of material kg/m2 lb/sq ft per mm thick per inch thick

Ordinary concrete (dense aggregates)

Solid slabs (floors, walls etc.) Thickness: 75mm or 3 in 184 37.5

100mm or 4 in 245 50 150mm or 6 in 378 75 250mm or 10 in 612 125 300mm or 12 in 734 150

Ribbed slabs Thickness: 125mm or 5 in 204 42

150mm or 6 in 219 45 225mm or 9 in 281 57 300mm or 12 in 342 70

Special concretes

Finishes etc. Rendering, screed etc. Granolithic, terrazzo 1928 to 2401 10 to 12.5

Glass-block (hollow) concrete

1734 (approx) 9 (approx)

Prestressed concrete Weights as for reinforced concrete (upper limits)

Air-entrained concrete Weights as for plain or reinforced concrete

Materials Voids % Weight kg/m3

Sand 39 1660 Gravel 10-20mm 45 1440 Gravel 35-75mm 42 1555 Crushed stone 50 1330 Crushed granite (over 15mm) 50 1345 (n.e. 15mm) 47 1440 'All-in' ballast 32 1800-2000

Material kg/m³ lb/cu yd

Vermiculite (aggregate) 64-80 108-135

All-in aggregate 1999 125

Recommended mix

Class of work suitable for Cement Sand Coarse aggregate

Nr 25 kg bags cement per

m3 of combined aggregate

(kg) (kg) (kg)

1:3:6 Roughest type of mass concrete such as footings, road haunching over 300mm thick

208 905 1509 8.30

1:2.5:5 Mass concrete of better class than 1:3:6 such as bases for machinery, walls below ground etc.