## Mechanical engineering of a tinyhouse

Would using steel studs be better?

What happens to a tinyhouse in a crash?

Will vibration on the road be a problem, loosening screws?

I don’t know much about mechanical engineering, but you can still do some estimating and eyeballing if you know some of the basics. You can jump right in by reading about tensile strength and the modulus of elasticity.

Then you need to think about the geometry to see it the design is enough to with stand the loads, say snow loads, or wind loads while on the highway (which you can compute from the aerodynamic drag).

Suppose you look at the drawing below, the thick black lines are the 2 by 4s of the wall framing, before sheathing is added:

Suppose there is a force trying to skew the frame. This force gets translated, by the leverage involved, into a much greater force down near the base of the 2 by 4. How much greater is a function of the relative lengths of the lever’s effort and load sections. Obviously the ratio is very large, so you can imagine you could cause the structure to become skewed without working too hard.

Just suppose you had a situation here where the surface of the end of the 2×4 is bonded to the lower, horizontal 2×4. So the strength of that bond interface (assuming it is the weakest link) is what determines the force to break the joint, but obviously areas closer to the fulcrum are subject to a higher leverage than parts farther away. You take the integral of the function of the (tensile strength x width) required to break the bond over the length of the bond (from fulcrum to end), but I forget what it is now (the integral of a/x over x from 0 to the length).

Also, of course the forces at the base of each 2 x 4 sort of add up, right, so you would get more strength if you had 5 rather than 4 vertical 2 x 4s.

They do not add up perfectly, of course, one of the connection areas at the base of one 2×4 may end up taking an unfairly high share of the load (the stress) for some reason. Obviously if the joints are all the same strength that joint would break first when the force got high enough. Then, with that one no longer taking the stress up, if the load was not well enough balanced between the 3 remaining joints, another would break too, and the others, one after the other. So obviously the structure would break well before the theoretical maximum strength you could get if they were all perfectly sharing the stress at all times.

So, anyway, you could add some plywood sheathing to up the amount of resistance this structure had to breaking when a force was applied in this particular way.

How much force could it resist? Well I guess you could start by thinking about the geometries involved. If it is only screwed on (not the glue and screw method that Jay Shaffer uses) then if you assume the screws would break before the plywood sheet, I would think the screws would break by being sheared apart, basically. So the the shear strength of the material they are made of, multiplied by their cross sectional area, is a handy way to estimate the amount of force each screw could resist.

Obviously you need to take that number and think about the geometry and the numbers of screws and how evenly the stress is distributed and stuff to actually see how much force it would all resist before breaking. Then you have your quick and dirty strength estimate….

So then from there you could look at the geometry and estimate if your design, made from several such walls, would be capable of withstanding the wind forces on the house at highway speeds. Add some suitable safety margin, like 3 or 4 and voila. Actually you probably wouldn’t want to use the ultimate strength for this method of estimating, maybe more like the http://en.wikipedia.org/wiki/Yield_strength.

For what happens to a tinyhouse in a crash, the acceleration multiplied by the mass produce the relevant forces in accordance with Newton’s law/s (second?), so once you have the strength estimate you can try to estimate stuff like that.

Any people in the crowd that know more about this?

I don’t know how to figure this out but I think its a concern. Here’s a tiny house that seem very tall: http://naturallytiny.blogspot.com/.

Shear, sway and then the momentum of 50 miles/hour – I will do my homework before i build!

ETNovember 16, 2010 at 14:03

Just returning a favor to Gregor…help for help…

got your trig…

get your parallelogram of forces….learn how to flop it around..

your a structural engineer…congratulations!!!

rulgertDecember 12, 2010 at 17:06

and always finish your numbers at 200% (tight figure, -0) 400% for overhead (same)…

rulgertDecember 12, 2010 at 17:17

and don’t forget about compression in resolving load vectors…

tension, compression, flexural, and shear

rulgertDecember 12, 2010 at 17:28

Hey Rulgert, thanks for the info, I’ll have to google these terms, but still finding the right terms is half the battle… see you at the next con maybe, then.

gregortheinventorDecember 18, 2010 at 19:53

the *parallelogram of forces* is the key term then, under which all else falls into place….

sorry i missed the last con…will be at this next that is upcoming.

rulgertDecember 19, 2010 at 16:42