Formula (d^2/162) for calculation of per meter weight of rebar derived

To find : weight of steel per metre.

Since the formula to be derived is d^2/162, assumed cross section is circular and the material is cylinder.

Weight density of steel = 7850 kg/m^3.


Rod Number Rod Size
(in)
Rod Weight
(lb per linear foot)
2 0.250 = 1/4″ 0.17
3 0.375 = 3/8″ 0.38
4 0.500 = 1/2″ 0.67
5 0.625 = 5/8″ 1.04
6 0.750 = 3/4″ 1.50
7 0.875 = 7/8″ 2.04
8 1.000 = 1″ 2.67
9 1.128 = 1 1/8″ 3.40
10 1.270 = 1 1/4″ 4.30
11 1.410 = 1 3/8″ 5.31
14 1.693 = 1 3/4″ 7.65
18 2.257 = 2 1/4″ 13.60

Formula:
Weight density = weight/volume.
Weight = weight density x volume.
Volume of cylinder= πh d^2 /4
h is the height 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
= 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
Since d’s unit is converted into the formula from mm to m, you can directly use the dia number to find out the weight per metre. For example:
25 mm dia bar:
625/162 = 3.85 kg

 

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