Converting dynamic load to point load for guard rail 1

[CAA1000]

I'm looking to verify that the dynamic load for a guard rail will withstand a 6000 lb point load. The rail is 10 gauge galvanized steel and the manufacturer's crash rating is 4000 lbs at 4 mph.

I know that KE = 1/2 x m x v^2 and
F = m x a
but calculating kinetic energy doesn't seem to help and I'm not sure how to find the acceleration without knowing the stopping time or distance. Any help would be appreciated.

 

[JStephen]

It would probably be simpler to get the cross-sectional properties and just work it like a static problem in the first place.

 

[dhengr]

CAA1000:
Your question hits upon the very crux of these kinds of dynamic problems. Search this subject, it has been discussed a number of times here on E-Tips, and specifically on the Structural forums; dynamic loading, impact loading, highway guard rails, falling loads, and the like. You don’t know the stopping time or distance without some elaborate testing program. So, you are kinda left with good engineering judgement and picking (iterating on) on of the variables to see what result that gives you on the other variable. Then, you can start talking about a range of loads and range of times and stopping distances that the entire system might see. You won’t likely find an exact number with much confidence. But, then, final testing will help you hone in on some improved range of answers.

 

[rb1957]

actually, can you use the data you've got ? … as I understand it ...

if the rail is good for 4000lbs at 4mph, then you can calc the impulse of this.
or if you're interested in a 6000lbs load then the equivalent speed is (4000/6000)*4mph … no?

another day in paradise, or is paradise one day closer ?

 

[JStephen]

I understood it to mean he's got a guardrail rated for 4,000 lb vehicle at 4 mph and wants to support a 6,000 lb static load off of it.

 

[CAA1000]

For clarification, the guard rail is rated for 4,000 lbs at 4 mph but the drawings for the project cannot be approved unless the rail is shown to withstand a 6,000 lb point load. The manufacturer's information doesn't provide the rail's rating as a static load, which is where my issue lies.

 

[BridgeSmith]

I second JStephen's suggestion to just use the section properties of the rail to calculate the load capacity of it. If it comes out that the 6000lbs is between the yield capacity and the ultimate (plastic) moment capacity, you have a bit of a dilemma.

Specifying only a force, without an allowable deflection to go along with it, is a strange way to go about it. Of course, the railing being rated a large load at such a low speed seems odd also. What kind impact are they anticipating, a really slow forklift?

 

[Tomfh]

Ugh, I hate using a static load to calculate these sort of things. It’s not a statics problem, it is fundamentally dynamic.

 

[BridgeSmith]

I agree, Tomfh. However, when the only limit that is given is a static load, what other option is there?

 

[rb1957]

but is the OP saying that ? (using a static load as a substitute for a dynamic one)

I'm reading CAA's second post as saying the problem is the there is no static allowable load for the railing. I sort of wonder how there could be, given the infinite number of designs that could be used. Isn't this "just" basic calculations … P/A and M/Z ?? And if you don't have material allowables, then run a small test to show the allowable moment in the railing.

another day in paradise, or is paradise one day closer ?

 

[chucklesNOLA]

CAA1000,

Is there any data on exactly what they used for the "barrier" portion of the barrier? There is some section modulus information for guard railings tested in NCHRP Report 115 Table 4 on page 15 of the PDF.

One of them looks like a 10-gauge steel W-beam (not a wide flange, but the W-shaped steel highway barrier beam). If that's comparable to your barrier section, that should at least allow you to assess the nominal flexural capacity of the steel component under a point load. Without a better idea of exactly which barrier system you're considering and how it's attached, it's hard to tell how to evaluate the various pieces of the barrier for the ASCE 7 6000# static vehicle barrier load.

 

[XR250]

Don't these things just turn into a cable member when they get hit?

 

[chucklesNOLA]

At freeway speeds where you significantly overcome Mp, I could see that. However, at low speed impacts (it looks like CAA1000 is dealing with a parking lot/structure problem here), it's mostly about deformation (energy absorption) in the railing and its attachments, and designing which bit goes inelastic to control the behavior.

 

[CAA1000]

chucklesNOLA: thanks for the link to that NCHRP report. This is the guard rail that's being used and the cross section looks comparable to the W beam in the table. It will be going into a parking garage so high speeds aren't really a design issue.

 

[BridgeSmith]

The relationship between dynamic impact and static load is one of deceleration distance. Without an allowable deflection for the static load or an actual deflection for the dynamic load, there's no way that I know of to convert from one to the other. With zero deflection, even the 4000lbs at 4 mph theoretically generates an infinitely large instantaneous load. OTOH, with a foot of deflection, the force on the rail from the same 4000lbs at 4mph is fairly small.

 

[SlideRuleEra]

I'm looking to verify that the dynamic load for a guard rail will withstand a 6000 lb point load.
The rail... manufacturer's crash rating is 4000 lbs at 4 mph

Agree with HotRod10 that deceleration distance is the key to using the information provided. Don't have to determine load magnitude... just that it is greater than 6000 lb. to make a reasonable judgement call.

F = M x A
6000 lb. = (4000 lb. / 32.2 ft/sec[sup]2[/sup]) x A
A = 48.3 ft/sec[sup]2[/sup]

V = A x T
5.87 ft/sec (4 MPH) = 48.3 ft/sec[sup]2[/sup] x T
T = 0.122 sec.

S = 0.5 x A x T[sup]2[/sup]
S = 0.5 x 48.3 ft/sec2 x (0.122 sec.)[sup]2[/sup]
S = 0.359 ft.

For any deflection < 0.359 ft., the force will be > 6000 lb.

Is a deflection of 0.359 ft. "reasonable"?
We don't know how the rail is supported, but I'll assume simple supports at each end of 12' guard rail length shown in the OP's link with impact at the center.

0.359' Deflection for a 12' Span = L/33

IMHO, deflection of 0.359' would permanently distort the guard rail. Therefore, to keep the guard rail from distorting, deflection is less than 0.359' ... making the equivalent static loading > 6000 lb.

http://www.SlideRuleEra.net

 

[BridgeSmith]

Well done SRE! Apparently, it's been too long since I took physics. I'm presuming it's been longer for you, and yet you were able to follow it through, so a star for you!

 

[miguelbbr]

CAA100
How to convert dynamic load to point load for guard rail?
In a first approach, you would consider the guard-rail in the elastic regime and the car as a rigid body.
In this approach, the Hooke's law F = kx is used.
The first thing is to calculate the spring constant for the guardrail structure. Considering the guardrail posts as rigid, and the guardrail as a beam, like in the figure below,then the deflection of the guardrail beam under a force F would be:
x = F ab/(3EIL)
where E is the Young's modulus and I is the moment of inertia of the beam.

So, the spring constant is k = 3EIL/(ab).
Then, the deformation energy of the beam is U = F[sup]2[/sup]/(2k).
Next, the car kinetic energy is K = 1/2 mv[sup]2[/sup].
When the car momentarily stops after hitting straight into the guardrail, its kinetic energy is transformed in the guardrail deformation energy.
1/2 mv[sup]2[/sup] = F[sup]2[/sup]/(2k)
So, F = √[mk]v = √[3 mEIL/(ab)]v
This is how the kinetic energy is converted to a point load.
However, for a more realistic approach, one would have to consider the plastic deformations in both the guardrail and the car.

 

[SlideRuleEra]

Thank you, HotRod. Yes, half a century.

http://www.SlideRuleEra.net

 

[BridgeSmith]

After sleeping on this, I realized there's still one more pertinent piece of information needed about the '4000lbs at 4mph' capacity - Is that before yield, or before rupture? While L/33 is very likely beyond yield of the steel, what I've seen of impacts to highway guardrails would indicate it is well below the plastic deformation limit of the system.

The limited exposure to this subject that I've had, leads me to believe the only way to evaluate this for a static force is to check the capacity of the posts with a straight (F x L) / Z < rupture stress. That's 6000lbs times the distance from the post base to centroid of the railing, divided by the plastic section modulus of the post, less than the yield strength of the post (assuming steel posts). It's the only check using a static point load that makes any sense to me.