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