Any advice on making a cattle grid?

Umm. If you support at mid span you create a potential path unless the support is very narrow or hidden below the tubes.

What on earth has the moment of inertia got to do with it? That's a rotating/dynamic property, a tube of (rather heavy) pastry could have the same moment of inertia as a steel pipe of the same size.

... and for a 7.5 tonne lorry?

Also need to think about draining the pit and escape routes for wildlife such as hedgehogs. Moveable grids are available which avoid the need to dig and concrete out a pit.

Oops, I wasn't clear. I was thinking that the "mid-span" supports would coincide with typical wheel track ... so there would be 2 supports, probably 2m apart. The supports would be narrow because they'd only be making contact with the bottom of the tubes.

As per initial post: I'll probably cast a concrete trough to put it in, with one side open to an adjacent dingle so water and hedgehogs can escape, and so it can be hosed-out.

Thanks for having a go, but I don't see why MoI would be relevant ... ?

I didn't describe the proposal well, what I'm thinking of is more like this:

Because of the proposed supports I was more concerned with the tube being crushed than bending, but maybe that's being naive.

(40 years ago I could have done these calculations :-( )

No, scaffold wont crush even with a 30 tonner driving over it. It will bend though

Its all a bit like renewable energy: Start with a crap idea (there is a reason why they aren't called doggie grids) add complexity to address the shortcomings, and end up with a complex expensive mess that doesn't actually solve the original problem. Bravo!

Here is the first "tube calculator" thrown up by google

MoI in physics and engineering ain't the same species. For a beam it's a measure of the cross-section that goes to the stiffness. Sums to hard for me but...

So what sized lorry? If no more than a 7.5 tonner then your axle load is presumably no more than 4 tonnes. In the worst case that might just about be applied to a single tube.

I see others have done some sums. The issue isn't so much deflection (as in flooring calcs) as whether it will bend pipes permanently. That's a bit trickier if the pipes are welded to I beams, but you'd get a good enough (and conservative) answer by assuming a simply supported beam and applying 4 tonnes in the middle. I know the lorry wheels are separated, but you could also have some dynamic loading.

You will need to know the tensile yield strength of scaffold tubes as well as the dimensions. This from a forum so not checked against source. This is 235 MPa.

"BS 12811 cites at 4.2.1.2 for steel tubes a minimum nominal yield strength of 235N/mm^2 for a nominal OD of 48.3mm and minimum minimum wall thickness of 3.2mm"

Suggest you try the calculator that I linked earlier.

How deep does the pit need to be? Could you not just cast a flat base, put RSJs on top and, if you want to discourage the dog, perhaps weld tubing or angle iron, V point up to the top. that way, every bit is supported directly by the base.

I've bent a scaffold pipe permanently by hand. wedge one end of a 10 ft section and walk with the other end,

It really is the worst grade s*it imaginable

over 200mm (unless you want to assume the tyres from each axle will spread over two scaffold tubes?)

It determines the rigidity of the beam from its cross-section

The tensile strength is low. On the other hand, the strain to failure is large, which is what you want really.

With that deflection, it will be spreading over at least three.

A quick Google gives you some idea of the standard designs for residential cattle grids . i.e.

It is nothing to do with "inertia" in a moving (or resisting moving) sense, it's how the shape of the material affects its rigidity in a particular direction e.g. a square hollow section v.s. an I beam v.s. a round tube ...