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Re: Stopping That Truck !!

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Stan Caldwell wrote:

<<Question:  What is the design force on the bollard?  on the wire rope?>>

Interesting problem. It seems very similar to the "fall arrest force"
problem where you have to design a fall restraint system for a guy working
with a safety line.

Here's my basic take on it which may be similar to the thought process you
have already gone through.

Your 7500 lb truck travelling at 20 mph has a kinetic energy (1/2 mv^2) of
about 100 kip-ft.

So you basically need a system that will absorb 100 kip-ft of energy.

Some of the energy will be absorbed in totalling the truck.

Then again it could be one of the Ford trucks built up here at the Oshawa
truck plant in which case it will remain elastic and all the energy will go
into your cables and bollards.

I guess you could figure out some kind of spring constant "k" for the
system. In that case the deflection of the system, d, would be Fmax/k. Fmax
is the maximum force applied to the truck. If the "spring" is elastic, the
work done in stopping the truck will be Fmaxd/2 because the force will ramp
up linearly from 0 to Fmax. Since d = Fmax/k then the work done = Fmax^2/2k.

So Fmax = sqrt(100kip-ft/2k) = 7 x sqrt(1/k) kip or

Fmax = 100kip-ft/2d = 50 kip-ft/d

So if you can stop the truck in 1 ft, Fmax = 50 kip; 2ft, Fmax = 25 kip; 6",
Fmax = 100 kip; etc.

If the deflection is 12" midway between the bollards (spaced at 12')  then
Fmax = 50kip. The tension in the cable would be 50 kip x sqrt(12^2+72^2)/12
= 304 kip. If the deflection includes movement of the bollards then the
force would be even greater since the cable angle would be smaller.

The hard thing is to figure out what k or d is. There's going to be some
non-linearity in the system. Primarily, I would think, in your clay
foundations. I've also got a feeling that the cable system will be
non-linear due just to geometry.

I would be inclined to do a rough design of a system based on a 50 kip load
then work out a spring constant for the system and cycle back through the
design til I was happy. I would assume very little if any energy was
absorbed by crunching sheet metal. I would tend to assume the system was
stiff rather than flexible. I would tend not to design the bollards to yield
if possible. There is a certain deterrence in the simple appearance of
strength (as Stalin used to say "quantity has a certain quality all it's
own").

I'm not totally clear on how the bollards work. Is the cable continuous
across several bollards and anchored intermittently or is it anchored to
each bollard. If the cable is anchored to the bollards then the bollards
would have to be designed for the cable force. If the cable slides through
an eye at the bollard then it would have to be designed for the impact of
the truck hitting the bollard itself which is a whole nother problem (but
similar).

There's my take for what it's worth.

Cheers,
John MacLean
Vancouver, BC



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