# Steel Joists: Moment of Inertia?

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Steel Joists: Moment of Inertia???

I thought it might well be worth while asking here, as the Forum is awash with knowledge about most things.

I am planning to do a loft conversion and I need to know about the strength of steel beams (Universal Joists, in fact). I keep seeing the expression 'Moment of Inertia' in literature and I couldn't see what it could have to do with a static structure. Then I realised that it must be to do with the cross section and how the bits further from the middle are more effective in the strength of the beam. So it must relate to the sum of each element of the cross section times the distance from the middle - which has the dimension L^4, the same as MI. It makes some sense but it just seems inappropriate, somehow. Does this terminology go back to the year dot or is it new?

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What I was really interested in was to find the equivalent steel beam for some of the existing timber, for instance the purlins and trusses.

AlephZero
Homework Helper

"Second moment of area" would be a better name, but "Moment of Inertia" is very commonly used.

You are right, the relevance is that when the beam bends, the material furthest away from the neutral axis is compressed or stretched the most along the length of the beam, so it is more highly stressed. That's why structural metal beams usually have an I or H shaped cross section, to put the material where it is doing something useful, not just adding to the mass.

But if you don't know much about either beam bending theory or building regulations, you definitely need some professional advice about the design, even if you do the work yourself.

Gold Member

"Second moment of area" would be a better name, but "Moment of Inertia" is very commonly used.

You are right, the relevance is that when the beam bends, the material furthest away from the neutral axis is compressed or stretched the most along the length of the beam, so it is more highly stressed. That's why structural metal beams usually have an I or H shaped cross section, to put the material where it is doing something useful, not just adding to the mass.

But if you don't know much about either beam bending theory or building regulations, you definitely need some professional advice about the design, even if you do the work yourself.
No need to worry about my needing help and I have, only today, contacted an SE. But I still want to know where we're heading. The point is that it seems very easy (well, you know what I mean) to determine things like permissible live and dead loads on floor joists and there are tables of timber joist sizes for given loads, spacings and spans. There even seems to be info about the requirements for timber rafters and purlins. But, when you want to find out what's needed for steels to do the same thing, life gets harder.
For instance, There is a ancient timber purlin in my roof. It's 130X75mm timber and has a span of 5.6m. (According to a table I found, this is only marginally adequate). If I wanted a straight replacement for this in steel, you'd think it would be in a table somewhere. (Is there?) As it happens I need to split the load between two purlins to make room for Velux windows. This would involve two (lighter?) purlins of the same span but I could ignore this if all I wanted was a ball park figure so I could ring the steel supplier and get a rough price.

I know that I would probably be dubious if someone were to ask an equivalent Electrical Engineering question (installing an electrical supply to a factory, perhaps) but I could give some ball park figures along with some caveats. But?

Whilst the structural calcs are more complex than domestic electric supply calcs, it is usually fire regs compliance that causes the difficulty in UK loft conversions which is why they have become less popular these days.

Fire regs also have a bearing (ha ha) on the structural use of steel, since it needs protection from buckling in a fire.

go well

nvn
Homework Helper
sophiecentaur: Could you tell us the load capacity your 130 x 75 x 5600 mm timber purlin is supposed to have, according to the table you found? Does this purlin have a span length of 5600 mm, between supports? Are you sure you have the purlin actual cross-sectional dimensions exactly correct, as listed above? What is the lateral spacing between this purlin and the adjacent purlin?

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AlephZero
Homework Helper

There are tables that give all the necessary properties of standard steel beam sections, e.g. http://www.structural-drafting-net-expert.com/steel-sections-BS-J.html

There are calculators on the web that do the (simple) math requred, e.g. http://www.engineeringcalculator.net/beam_calculator.html

For structural steel, Youngs modulus = 200 GPa and yield stress = 250 MPa, so a maximum stress of say 100 MPa would be a reasonable number to design to (but see the disclaimer below!)

So given the loading, the design process is basically to work through the tables of standard sections plus a supplier's price list, and find the cheapest one (in terms of cost per unit length) that meets the requirements.

There may be other practical considerations like choosing a section that wll fit in the existing holes in the walls.

DISCLAIMER: I'm familiar with mech eng design, but I don't have any professional experience of this type of civil engineering, the building regulations, etc.