Is there a reason you don't want to calculate it based on the steel section alone?

This thing has to stop a 5,000 pound vehicle travelling at 30 mph.  I need all the strength I can get.  Hence the concrete fill.

Well yes, I know bollards are always filled with concrete. That gives the steel pipe resistance to local buckling, so that full bending capacity based on the section modulus mutiplied by .66Fy can be used. Also, the concrete gives a bit of inertia during impact. Other than that, I am not aware of any further rocket science on this issue. Can anyone else give more insight? If not, I would leave it at that. A car may weigh 5000 lbs, but as it "crumples", the force of impact should be lessened to a significant degree.
This looks like a question for a highway design engineer.

I think the concrete would add negligible strength to the assembly, and with that wall thickness, you should be able to develop full strength of the pipe without the concrete.

If you wanted, you could convert the compressive area of the concrete to an equivalent (small) steel area, but it should have minimal effect on the answer.  You might also consider how you know the concrete is actually bonded to the wall of the pipe, which is what this assumes.

JS, I think he means that the impact from a sharp of edge of car bumper could buckle the the pipe locally, leading to a premature failure. If this is like a security barrier thing, I would use a larger pipe and not worry about splitting hairs calculation-wise

In most cases....coming down to earth here....bollards are not really designed to physically stop something like a vehicle.  In fact, impact forces from vehicles are difficult to calculate and the forces are really quite large.

Most bollards are psychological barriers...not physical barriers.  A 5000 lb object hitting a pipe at 30 mph - bollard loses.

I think the bollard would be only one consideration in a vehicle collision sceanario. You could design the stiffest bollard imaginable and it might not bend during a collision but what about the moment at the anchor bolts pulling it out(so now it is laying flat on the ground but still straight and the car is driving over it) or the foundation failing in overturning or bearing(simialar sceanrio). Checki FEMA and Military info. They might have something on this.

They're not entirely psychological barriers.  You're most likely to hit one if you're backing up, or for other reasons can't see it, and then you'll bump the bollard instead of whatever it's protecting.  I agree that most are not intended to stop a vehicle at speed.  And if they did, they'd be road hazards in themselves- they'd just cut a car in half.

I guess I need to expound upon what it is I'm doing.  We have a requirement to install a security barrier.  This barrier is composed of posts set in concrete at 10 feet on center with two strands of wire rope run continuously - a post and cable barrier.  The end posts are the most critical part of this assembly.  Not only are they needed to hold the tension of the cables, but they must also be capable of resisting a direct hit from a vehicle.

It will be very tough to design anything to take the load for a vehicle travelling at 30 mph.  The problem is that the stiffer you make the member, the higher the load.  However, the system you're describing is commonly used at Nuclear Power Plants for perimeter protection.  The cables are used to absorb the energy of the vehicle and stop it.  There must be some literature available describing the analysis required.  It might be a little tough to get to, since it is security related.
Don't forget that the system doesn't need to be designed for repetitive occurances.  If the cables yield, but stop the intruder, they can be replaced.

I appreciate the responses, but I'd like to get back to the original question, more for pure engineering knowledge.  If you have a steel pipe filled with concrete, what is the bending strength?  I'm not sure you can rely on the concrete to bond to the steel pipe, so transformation may not be appropriate.  But, the concrete will give the composite structure some additional strength.  How do you account for the benefits of the concrete?

The concrete would help to disallow local wall buckling inward to the pipe, but not outward from the pipe diameter...but how you quantify that I don't know.  But I think that the bendning capacity (agreeing with you here) isn't really helped all that much.

Also, the barrier you are talking about seems to be very similar to what highway designers use - AASHTO in the US, and these are usually set up as standards because they aren't usually designed with algorithums but trial and error field testing with real vehicles hitting the side barriers at set speeds.  You might try AASHTO or associated sites for this.

Thanks JAE.  The application is for military use, so they have unique requirements.  I also agree that the benefit of the concrete is probably minimal.  I suppose I could analyze the pipe using ultimate strength capacity and ignore any reduction due to potential local buckling.  We are not concerned about reuse of the post after it's hit.

Watch the whole load path - the bollard, if its sunk in a concrete mini-pier, may just lean over, pulling up the dirt...or as jjeng2 states, if you use anchor bolts, they would be the first to go.

To be perfectly smart-a**, we (in the USA) should be able to make the friggin' bollards 12" diameter.

Agreed.  In fact, the lateral deformation of the post foundation in the soil will help to absorb some of the energy of the vehicle.  The foundation hole and the pipe are filled with concrete at the same time just like a fence post, there are no anchor bolts.  However, I need to insure that the foundation fails before the post.  Thus the reason for my original post.

vmirat,

Keep in mind that from a security standpoint, barriers are designed to either absorb or deflect a potential threat. That said, a barrier should be designed be deformed on impact. The owner or other governing authority should dictate what is acceptable.

I have worked on a number of  security projects where barriers also created legal issues. For example, if you were to design a barrier to stop a vehicle dead in its tracks at 30 mph, there would be SEVERE injuries to the occupants (even with airbags). There have been similar lawsuits (some frivolous lawsuits) against various DOTs for highway barriers that resulted in injury, death, etc.

On the other hand, if the bollard is just for a store parking lot, any time spent designing a bollard would be a waste of time and money. Use your best judgement.

Good luck.

Whoops, I got ahead of FalsePrecision on my response back to JAE.

FalsePrecsion, I agree with your sense of logic.  However, we are also bound by aesthetics (this is for a location in the US, not overseas).  The 8-inch pipe dimension is the agreed-upon standard that I must work with.  There is this constant battle between the security guys who don't want anyone inside and the architects who want everything to look pretty.  Us poor engineers get stuck in the middle.

Here is another idea:
Locate a #11 or so rebar so that it goes down the whole length   of bollard and into the concrete pier foundation. Use super-high strength, non-shrink grout at least in the bollard.

NASCAR tracks have a barrier that keeps the race cars from crashing into the stands. I think that I saw somewhere that their cable system is anchored by mass concrete buried in the ground (similiar to cable bridge anchorage).

I saw something in a post that got me thinking on another concept. If the purpose of the bollards is to stop a threat and then be replaced if they are too damaged, you might need to think more in terms of energy absorption instead of static strength. If you can sacrifice the bollard as long as it stops a threat, then you should be maximizing energy absorption, which many times means maximum deformation.

I had to check concrete light pole bases for impact from a truck at 5mph.  From the equations of kinematics and allowing the concrete base to only deflect a small amount, the impact force was friggin HUGE.  I'd love to hear what your final design was to stop 5kips going 30mph with a 8" bollard.

LPPE,
Read the info posted by vmirat, about half way up. Bollards at 10' on center. 2 wire ropes. End posts to take direct impact or tension in ropes. (I assume the end posts are something other than these 8" dia. pipes) Theory - would the vehicle deflect the ropes, to produce a catenary effect, thus absorbing a large amount of energy (the bollards would be "rotated" out of plumb by a large amount). The tension in the ropes would be very large, to produce a more gradual full deceleration of the vehicle. See the other posts above mentioning cables and energy absorption.

What if the vehicle hits the bollard directly instead of cables?  Accidents rarely happen where you want them to.  (not that you want accidents to happen...).  Overall, would it be safe to say, then, that the bollards are only used once per impact?  They'd slow the car in a safe manner, but be completely destroyed in the process?

If each bollard was part of the cable "network", then if a car hit a bollard head-on, then the bollard would be deflected, plus the cables would be tensioned -the net effect is to provide maximum stopping power without using a larger bollard. That was the architect's request - to keep bollard size to 8" maximum. Since this is for security, I am assuming that the damage to the car and occupants is not an issue.

I would design these like harbor bumpers and use an energy technique.  The energy of the vehicle is easy... (.5mv^2).  The energy capacity of the bollard is the area under the load-deflection curve.  Where to take the area up to is a matter of judgment.  Not letting the pipe yield is nuts (a triangular area, while above yield is ~rectangular... where the real energy capacity comes from is plastic deformation).  Letting it deflect until extreme fibers approach ultimate is the failure point.  I'd take it 50-70% of the way towards ultimate from yield.  Also depends on the max. bumper height you have to consider (duh).

Wow! A fused liveware in a truck determined at high speed to break in and blow it apart and you guys want to stop him with a bollard!

Make it with solid steel then.

Ciao.