How to calculate the weight steel bar with example OR derivation of formula ( D²/162.131)-

In this article we shall discuss

1 - Derivation of D²/162.131 in details

2- How to calculate weigh of steel bar with example

We know that
Mass = volume × Density

Calculation to calculate the volume of steel bar -

Length = 1 met. = 1000 mm

Let us consider that the steel bar is of circular shape. So

Area of bar = (π/4)× D² square mm

Where 'D' is diameter of steel bar in millimetre ("Diameter is considered in mm because steel bars come with diameter specified in millimetre in market. Viz. 8mm Φ, 16 mmΦ, 20mm Φ")

Then

Volume of bar= length of bar ×area of bar

= 1000×( π /4)×D² = 1000 x (π/4)D² cubic mm

To convert the volume in cubic metre from cubic mm

We know that
1 cubic mm = 10^(-9) cubic metre

= 1 cubic metre

(1000× 1000 ×1000)
Then volume in cubic metres can be calculated as-

= 1000× π × D²
(4× 1000× 1000 ×1000)

= πD² cubic metre
( 4 × 1000 ×1000)

We know that
Density of steel bar = 7850 kg/m^3

Hence
Mass = Volume × density

              After putting the value in above formula
Mass = π × D² × 7850   m^3 (KG /m^3)
( 4 ×1000 ×1000 )

                = π × D² × 7850   KG
( 4 ×1000 ×1000 )
After calculation we'll get-

Mass  =   D²
162.131
Where 'D' is the diameter of steel bar in mm

○Example - calculate the weight of 16 mm diametre of steel bar if the length of bar is 12 met.
Solution-
                 Diameter of bar(D)= 16 mm
                 Length of bar = 12 met.
We know that
Weight of 1 met. Steel bar =   D² /162.131 KG

                                           = 16²
162.131

                                           = 16 × 16
162.131
Weight of 1 met.16 mm diameter Steel bar= 1.579 KG

Weight of 12 met. Length steel bar =
            = 12 × weight of 1 met. Steel bar
           = 12 × 1.579
           = 18.948 KG
Note- same method can be used to calculate the weight of various diameters steel bars.

Thank you
www.Gyanofcivilengineering.com
Mukesh Kumar

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