Question:
I have a stress question, somewhat related to all of the great threads now
running in 4130 steel, but to a specific application in my nickle-bronze
brazed mild steel 1965 British spaceframe race car!
The left hand lap belt of the 6-point harness is attached to roughly the
middle of a 24" long, 1"square 16ga mild steel tube. The attachment is a
3/8" bolt through the tube, vertical, inside of a 16ga 3/8" id round tube
welded into the square tube. We did (my tame engineering grad friend did,
not me at all) some calculations that indicated that under a 3500# load (the
design load that the seatbelt manufacturer says to engineer the belt mounts
to) the 24" long tube forms a beam that will deflect a little less than half
an inch. These calc's are based on a beam 1" square, 16ga supported at 24".
Now, what occurs to me is that the beam is actually firmly attached at each
end to the rest of the car. The places that the tube attach to are fairly
well triangulated, so that if the tube was to bend, the welds at each end
would have to fracture or the mounting points would also have to bend.
What will the fact that the ends of the tube are firmly attached to another
structure have on the calc. that the tube will bend half an inch under the
3500# load?
Will the fact that there is a vertical tube let into the square tube cause a
weak point that will promote either bending or outright failure of the tube.
If I add a 10" long double gusset .100" thick and say 1.25" tall on top of
the square tube and attach the seatbelt between the two gussets in double
shear, how much less bending might I have under the 3500# load?
Answer:
It depends upon the conditions your friend chose to do the original
calculation. Standard beam-deflection formulas are readily available
in engineering textbooks. He should have chosen formulas associated
with "fixed end supports, intermediate point load". If this is what
he did, then, the effects of the whole rest of the car as it is welded
to the ends of this 24" seatbelt-support-beam are already present.
This is a bit more interesting. A fairly trivial task for a modern
FEA program but tougher to tackle with a paper & calculator approach
due to the odd discontinuity of the small round tube passing thru the
big square tube. (Without computers, most problems get simplifed down
to constant-cross-section to make the calculations manageable).
Your point is worth making, but keep in mind as well that in the even of
a crash when you need that 3500# restraint the body is under all kinds of
other stresses as well. If there is a lot of compression on that member at
the time that the seatbelt pulls at it from the side, then it could get
ugly. I think that for the minor effort involved I'd add a vertical piece
near the seatbelt connections. Just in case. That's just a personal
opinion.
The figure comes from Willans - the manufacturers of the belts. Willans are
considered amoung the very best suppliers of belts, and are commonly used in
the top racing series - CART, F!, etc.
They specify each major load point (shoulder and lap) at 3500#, crotch
straps at less (2400#, I think). If a mount is used to attach two straps,
it has to be able to carry the combined load. Who am I to argue? To your
point about 20G's - that common in racing accidents. More to the point, the
load would be shared across the four major points, so you'd be safe up to 80
G's. Add in the two crotch straps, and you'd be safe up to 100G's. Take
into account a safety factor, and you're really designing for 40 - 50 G's,
which is totaly survivable. If the load is correctly managed over a short
period of time.
Which gets to your second point. The belts are designed to stretch in an
impact, slowing down the application of the load. Tightly cinched belts can
stretch 10" or more - and recover completely, btw, you can't tell by looking
at them that they've been stretched - and to do this they depend on totally
rigid mounts. My goal is to have the mount deflect no more than .050".under
the 3500# load. The "flex" is already designed into the belts, there's no
need to design a weak mount to boot.
