l>Units and also formulas

*The prefixes `centi\" and also `deci\" are only supplied with the metre. Centimetre is a recognised unit the length yet centigram is no a recognised unit that mass.

Tables of procedures for mass, length, area and also volume are set out below

MASS SI basic unit: kilogram (kg)

 Metric system, signs & unitsThe metric system, and especially that component of it dubbed the SI (le Systéme international d\"Unités or, in level English, the international System of Units), is by far the simplest and also most rational device of units devised.One that the main reasons for this is the an easy compatibility the the metric system with our world-wide numerals and also arithmetic based upon the 10 digits and also their place relative to a decimal point. This outcomes from the handy system of attaching to unit name (symbols) traditional prefixes that stand for few of the powers of 10 such together 0.001 (milli), 1000 (kilo). For instance, since the prefix kilo (k) stands for 1000, 1 kilometre (km) amounts to 1000 metres (m), and any adjust from metres come kilometres or angry versa simply involves a decimal suggest or zeros as shown below. The typical Prefixes and also Units Prefix & Symbol Meaning Value Factor micro (μ) one millionth 0.000 001 10-6 milli (m) one thousandth 0.001 10-3 centi (c)* one hundredth 0.01 10-2 deci (d)* one tenth 0.1 10-1 kilo (k) a thousand 1000 103 mega (M) a million 1,000,000 106 giga (G) a thousands million 1,000,000,000 109 1000 micrograms (μg) = 1 milligram (mg) 1000 milligram (mg) = 1 gram 1000 grams (g) = 1 kilogram (kg) 1000 kilograms (kg) = 1 megagram (Mg) = 1 tonne (t)
LENGTH SI basic unit: metre (m)
 1000 micrometres (μm) = 1 millimetre (mm) 10 millimetres (mm) = 1 centimetre (cm) 10 centimetres (cm) = 1 decimetre (dm) 100 centimetres (cm) = 1 metre (m) 1000 millimetres (mm) = 1 metre (m) 1000 metres (m) = 1 kilometre (km)

AREA SI unit: square metre (m²)
 100 square millimetres (mm²) = 1 square centimetre (cm²) 10 000 square centimetres (cm²) = 1 square metre (m²) 1000 000 square millimetres (mm²) = 1 square metre (m²) 10 000 square metres (m²) = 1 hectare (ha) 100 hectares (ha) = 1 square kilometre (km²)

VOLUME SI unit: cubic metre (m³)1000 millilitres (mL)
 1000 cubic centimetres (cm³) = 1 cubic decimetre (dm³) 1 cubic decimetre (dm³) = 1 litre (L) 1000 cubic decimetres (dm³) = 1 cubic metre (m³) = 1 kilolitre (kL) Or alternatively, for use with liquids and gases: 1 cubic centimetre (cm³) = 1 millilitre (mL) = 1 litre (L) 1000 litres (L) = 1 kilolitre (kL) = 1 cubic metre (m³) 1000 kilolitres (kL) = 1 megalitre (ML)

 Symbols and base units provided in Competency Units You should try to memorise the symbols and also units listed below. (Many symbols room unfortunately Greek letters) You are watching: Unit weight of concrete in kn m3 The amount of (Greek letter sigma; resources letter S) Mass m kg Mass density kg/m³ (Greek letter rho) Original length lo mm (units must be compatible) Difference in length l mm (Greek letter delta; capital letter D) Normal stress (or f) MPa (N/mm²) (Greek letter sigma small letter s) Shear stress MPa (N/mm²) (Greek letter tau) Moment of a force M newton metre (N m) Deflection mm (Greek letter delta; little letter d) Slenderness ratio Sr dimensionless Velocity v m/s (meter every second) Acceleration a m/s² (meter per 2nd per second) Gravitational acceleration g m/s² (meter per 2nd per second) Force or weight F N (newton) additionally

Students must familiarise themselves through quantities, symbols and units. Shot to learn them by heart as they will certainly be described in various units of competency.

The following will emphasize the prestige of the units:If someone borrowed 10 dollars from you and also the borrower handle his debt through 10 cents you wouldn\"t it is in happy around it, return the number is identical. If who borrows 10 dollars from you, friend would insist of the very same unit, wouldn\"t you? This simple example points out that the unit is of great important.MPa (Strength of material). The complying with relationship have to be learned by heart:1 Pa=1 N/m21 kPa=1 kN/m21 MPa=1 MN/m2= 1 N/mm2The definition of kP and also MPa is an extremely important due to the fact that you\"ll require to understand the concept of stress and strenght. Look because that prefixes choose k and also M in the table above.FormulaeHowever, the most usual formulae are listed below:
Stresses (tension and also compression)

= pressure / area ( = F / A)

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MaterialMass density (kg/m3)Weight density (kN/m3)Concrete (reinforced)2500 kg/m325 kN/m3Concrete (unreinforced)2300 kg/m323 kN/m3Brickwork1900 kg/m319 kN/m3Timber (Softwood)600 to 800 kg/m36 come 8 kN/m3Timber (Hardwood)800 come 1100 kg/m38 come 11 kN/m3Steel7850 kg/m378.5 kN/m3By carefully looking in ~ the systems we can quickly work the end the exactly answer the a propblem by substituting the units right into the formula.Consider the following example to job-related out the weight of a structural component or member: To calculation the weight of a ingredient or member we usage the formula: weight (W) = density × VolumeRemember unit for density is kg/m3 and also the unit because that volume is m3 however the unit for weight is measure up in newton. We need to convert the mass into a weight figure.Weight = massive × gravitational accelerationW =m × g(g = 9.81 m/s2 however we use 10 m/s2)Having converted the fixed unit right into a weight number we can now calculate the load of any type of structural component or member in newtons through using:

W = kN/m3 × m3Example 1:Calculate the dead pack (DL) for a concrete slab, size 4.0 m × 3.5 m that 172 mm thickness . Density of concrete is 2500 kg/m3Solution:First transform mass thickness in weight density. 2,500 kg/m3 = 25,000 N/m3 = 25 kN/m3Now we have the right to calculate the weight of the slab:W = 4.0 × 3.5 × 0.172 × 25 =60 kNExample 2:Calculate the live fill (LL) because that a room that a residential building, dimension 5.5 m × 3.8 m. The LL according to together 1170 component 1 (Dead and live load) is 1.5 kPa).Remember 1 kPa = 1 kN/m2Solution:Using the formula LL = m (length) × m (width) × kN/m2 LL = 5.5 × 3.8 × 1.5 = 31.35 kN