To find the weight of steel per metre. Since the formula to be derived is D^2/162, the assumed cross-section is circular and the material is the cylinder.

Weight density of steel = 7850 kg/m^3

Formula:
Weight density = weight/volume
Weight = weight density x volume

Weight density= 7850 kg/m^3

Volume of cylinder= Area * length of bar(L) = π/4  D^2 * length of bar(L)
L is the length of cylinder bar = 1m
D is diameter in mm

Volume = 3.14/4 x D^2 x 10^-6 (converted mm to m two times for D)
Volume of cylindrical bar = (7.85 x 10^-7) D^2 cum
Weight of cylindrical bar

Weight = weight density x volume

= 7850 x 7.85 x 10^-7 x D^2
= 0.00616 x D^2
= D^2 /(0.00616^-1)
= D^2/162.3
~ D^2/162

Note:

• This formula is only applicable circular shape Bar, Who density is 7850kg/m3.

Weight = D²/162 * (length of bar)

Here

Dia = mm

Length = m

Weight = kg

• D²/533 is applied when the length of the steel bar is provided in feet.

For example

Find the weight of the bar if dia of the bar is 12mm and the length of the bar is 10 meter?

Solution:-

Length of bar = 10 m

Dia of bar       = 12 mm

Weight of bar =?

Now put the values in the formula

Weight = D²/162 * length

Weight = (12)2/162 * 10

Weight = 0.88 * 10

Weight = 8.88 kg

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