### Calculate the Weight of Steel

Wed, Aug 7, 2019 6-minute read

The weight of steel is one of the most important metrics available for consumers, designers, project managers and well everyone. Steel is typically priced per tonne (1000kg) from a fabricator, therefore keeping the weight of steel to an absolute minimum with a safe design is key for a cost effective project.

This post is going to cover the basics of how to calculate the weight of steel and where to find the weights of steel from reference tables such as the ‘blue book’ provided by Tata Steel. Examples will be provided to show you how to calculate various different types of steel products such as:

• Steel plates
• Steel beams
• Reinforcement steel, rebar or steel bars
• Steel hollow sections such as circular hollow sections

Instead of just showing you where to find the values for the above, which is all accessible via a table, we are going to break the formula step by step and explore the fundamental physics of what ‘weight’ actually is. This can then be applied to any material of any shape to find the desired weight. Let’s begin.

## Density of a Material

The most important material property in relation to the weight is the density. Each material has a density, although this is not unique, depending on the manufacturing process and the elements that make up the composition of the material will affect the density. Confused? Need not worry, as engineers we are used to making sensible assumptions. Below is a table that shows the average density of the most common building materials. The units are shown in both metric and imperial.

kg/m3

lb/ft3

Steel

7850

485

Concrete (Unreinforced)

2250

140

Timber (Maple)

600

40

Soil (Sandy)

1800

110

Water

1000

62.5

The table above shows a few different materials but from now on our focus will only be for the weight of steel, but once you know the technique to calculate it, you can simply substitute out the density value.

## Using the Density Formula

Now onto the juicy part, the formula that will help us calculate the density of the steel members. We have two options, both extremely useful to use in differing conditions. Calculating the weight of steel per linear metre or foot or calculating the overall weight of steel.

1. Total Weight of Steel
2. Weight of steel per linear metre or foot.

## Total Weight of Steel

Weight of Steel Member = Density x Volume

For this one we will use the imperial unit system to explain it. The density units are in lb/ft3 (pounds per feet cubed). Using unit analysis and multiplying it by the volume in ft3  the final value is in lbs, volume calculated by depth x width x breadth. Thus we have correctly managed to obtain the correct units we want.

Top tip… If I’m ever struggling with a complex formula or I’m getting unexpected answers my first check is that the units all check out.

Dimensions of a Plate

## Weight of Steel per Linear Metre

Weight of Steel Member = Density x Cross Sectional Area

Next up is calculating the weight per unit of length. Using metric, we will look at the weight of an object per metre. The values of beams and columns are shown in section tables by weight per unit metre, as it is a more accurate portrayal due to the various lengths required in a structure. We take the density (kilograms per metre cubed) and multiple it by the cross sectional area of the object.

Cross Sectional Area of an I-Beam

## Using Section Tables for Steel Weight

Since construction industries use weight for cost purposes and design, it is important that we can obtain values for steel sections quickly and accurately. To aid with this a lot of structural analysis books and online tables have the information in and many steel products are actually sized by the weight too.

Below is one of my personal go-to tables that I use when I’m working and have an internet connection available. A snippet of the table is shown and the link is in the caption. Just a note, I did not create or have any involvement with SteelConstruction.Info or the interactive blue book, it is just a great resource worth sharing!

https://www.steelforlifebluebook.co.uk/

## Using a Coefficient - Weight of Steel Bars per metre

One final neat little trick that I stumbled upon is the use of coefficients to calculate the weight of steel bars. Due to the geometry of the shape it is very easy to derive the formula. It takes the volume of a cylinder, the density of steel and simplifies the equation to obtain.

Weight of Steel Bar  = D****2 / 162

D in this equation is the diameter of the bar. The one downside to this equation is it assumes that density is 7850kg/m3, whilst this is generally the case, different types of steel will have varying densities. Use with caution, and if doubt, stick to one of the other methods.

Now we will jump into some examples of how to calculate the weights of various steel shaped products. Plates, beams and a rod, all commonly used in the construction industry. Remember, if you forgot part of any of the equations above, use the units to try and solve it. We will do it in both metric units and imperial, so both sides of the planet are happy!

## Worked Example - Weight of Steel Plate (Imperial)

Time for the first example, a rather large steel plate.

Weight of a Steel Plate - Worked Example

Weight of Steel Member = Density x Volume

= 485 x 15 x 100 x 200

= 145,500,000 lbs

## Worked Example - Weight of Steel Column

Now we will look at the weight of a steel column per unit length, this time in metric. Just be aware that in our example, I’m going to assume that there is no root radius at all present. Thus simplifying the calculation for us to go through. The cross sectional area, or area as steel as it is labelled can be found in the section properties tables.

Weight of a Steel Column - Worked Example

Weight of Steel Member = Density x Cross Sectional Area

First, we will calculate the cross sectional area.

Cross Sectional Area = 2 x Flange Area + 1 x Web Area

= 2 x (102 x 10) + (254-20) x 7

= 3678mm2

And to finish it.

= 7850 x (3678 / 106)

= 28.87 kg/m

## Worked Example - Weight of Bar

Next up, the weight of a steel bar, this will be in metric as we will be applying the coefficient to quickly calculate the weight of the bar per metre.

Weight of a Steel Bar - Worked Example

Weight of Steel Bar  = D****2 / 162

= 102 / 162   = 0.617kg/m

I hope this post was useful, as always, if you have any questions, spot a typing mistake, or would like to suggest the title of the next post, please comment below or get in touch via the contact form. Any feedback is much appreciated.