Design guide

How to pick the lightest steel section for a required moment of inertia

When deflection decides the size of a beam, you need the least steel that is stiff enough. Here is how to get the target number and how to rank sections against it.

By Trishunya InfotechPublished 8 min read
Short answer

Work out the moment of inertia the member needs about its major axis, list every IS section whose Izz meets it, and pick the one with the lowest mass per metre. Example: for Izz of at least 2500 cm⁴, LB 225 at 23.47 kg/m is the lightest, ahead of LC 225 at 24 kg/m and MC 225 and MPC 225 at 26.1 kg/m.

Why stiffness, and why lightest

Many beams are not governed by strength. They are governed by deflection, because floors, ceilings and finishes have to stay within a limit. In that case the beam only needs enough stiffness, and stiffness is the moment of inertia I about the axis of bending.

Steel is sold by weight. So once the moment of inertia is fixed, the cheapest section that meets it is the one with the lowest mass per metre. That is the lightest section that works.

Get the target Izz from a deflection limit

For a simply supported beam under a uniform service load w over span L, deflection is δ = 5wL⁴ / (384EI). Turn it around to find the I you need for an allowable deflection:

I required = 5 × w × L⁴ / (384 × E × δ allowable)

Take a 4 m span carrying 20 kN/m of service load, with an allowable deflection of span / 300, which is 13.3 mm. With w = 20 N/mm, L = 4000 mm and E = 200,000 N/mm²:

I required = 5 × 20 × 4000⁴ / (384 × 200,000 × 13.33) = 2.5 × 10⁷ mm⁴ = 2500 cm⁴

That is the target of 2500 cm⁴ used in the rest of this guide. Span / 300 is an example limit. Use the limit that applies to your member from IS 800.

Rank the sections

Now list every section with Izz at or above 2500 cm⁴ and sort by mass. This is the result Steel Table India's Section Optimizer returns for that target, across all categories.

Top four for Izz of at least 2500 cm⁴, lightest first
RankSectionIzz (cm⁴)Mass (kg/m)Izz per kg/m
1LB 225250023.47106.5
2LC 225255024.0106.3
3MC 225270026.1103.4
4MPC 225271026.1103.8

The last column is the efficiency: moment of inertia divided by mass. A higher number means more stiffness for each kilogram. LB 225 meets the target almost exactly, at 0 percent over, and carries the least steel.

Steel Table India Section Optimizer with a target moment of inertia of 2500 cm4 on the major axis, listing LB 225, LC 225, MC 225 and MPC 225 with their mass and efficiency
The Section Optimizer with a target of 2500 cm⁴ on the major axis. The ranking is lightest first.

What the lighter section saves

Mass turns into money through your rate. At an example rate of ₹80 per kg, LB 225 costs ₹1,878 per metre. MC 225 costs ₹2,088 per metre. The difference is ₹210 per metre, about 11 percent, and over 100 m of beam it is ₹21,000. Set your own rate in the app and the figures follow it. The guide to steel weight and cost shows how those per-metre numbers are built.

What lightest does not tell you

Use the Section Optimizer

In Steel Mode, open the Section Optimizer and enter the target moment of inertia in cm⁴. Choose the axis, either major (Izz) or minor (Iyy). Pick a category or leave it on all categories, and set a maximum mass in kg/m if you want one. Then rank by Lightest, by Closest MOI, or by Best I per mass. The app lists the top ten, each with its mass, cost per metre and efficiency, and an Inspect button to open the full section. Tag the options you like to compare them side by side.

Questions people ask

How do I choose the lightest steel beam for a deflection limit?

Calculate the moment of inertia you need from the deflection formula, list all sections whose Izz is at least that value, and pick the one with the lowest mass per metre.

What moment of inertia do I need for a 4 m span at 20 kN/m?

With a span / 300 limit and E = 200,000 N/mm², you need Izz of about 2500 cm⁴. Use the limit that applies to your member in IS 800.

What does Izz per kg mean?

It is the moment of inertia divided by the mass per metre. It shows how much stiffness you get for each kilogram of steel. Higher is more efficient.

Is the lightest section always the best choice?

No. You also need to check strength, lateral stability, depth limits, connections and whether the section is available. The lightest section is the cheapest one that meets the stiffness target, not a finished design.

Which axis do I use for a column?

Use the minor axis (Iyy and ry) for a column unless it is braced in that direction, because that is the direction it buckles first.

Keep reading

Find the lightest section in seconds

Steel Table India ranks IS 808:2021 sections by mass, cost and efficiency. Free on Google Play.

Get Steel Table India on Google Play

For reference, not for sign-off. Section and bolt values quoted here are as shown in Steel Table India, transcribed from the published IS 808:2021 tables and worked to IS 800:2007 methods. Transcription can contain errors, and these worked examples make simplifying assumptions stated in the text. Check critical values against the official Bureau of Indian Standards publications and have designs checked by a qualified engineer. IS 808 and IS 800 are published by the Bureau of Indian Standards.