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.

 

[BUGGAR]

If you consider energy methods, plastic yield in a member will absorb a lot more energy than elastic deformation (per unit of deformation).

 

[BUGGAR]

Can we attach spreadsheets?

 

[BUGGAR]

Did this work?

 

[ThomasH]

Interesting discussion. Based on the information that I have seen I think it shouldn't be to difficult since the guard rail section is known (W-beam).

But I have made a few observations.

The crash ration is 4000 lbs at 4 mph, since I am more comfortable with SI units I prefer ~1800 kg at 6.4 km/h or 1.8 m/s. That is basically an suv going very slowly. Can that be accurate for a crach rated railing? The standards I have seen is usually based on the mass and the speed of the vehicle but the numbers are higher.

If I understand the data correct and the loading is assumed as accidental the rail should deform significantly during the crach.

But I find the rating low.

Thomas

 

[BridgeSmith]

You are correct, BUGGAR. The sticking point for this particular problem is that we don't know whether the 4000lbs at 4mph is calculated using elastic deformation or plastic. Assuming it's the elastic deformation limit (what it can sustain without damage) greatly overestimates the capacity of the system if it's actually the plastic deformation limit (railing is permanently deformed, but ultimately contains the vehicle).

Sorry SRE, but your statement "...to keep the guard rail from distorting, deflection is less than 0.359'..." is an assumption. We don't know what the limit state is that was used to calculate the 4000lbs at 4mph capacity, at least I haven't seen anything that indicates it. If it's elastic, then your conclusion is correct. However, if that capacity was calculated at some limit of plastic deformation, then it may or may not be adequate for the 6000lb load. If the capacity is calculated at the ultimate plastic deformation limit (rupture), then the capacity for a static load is 4000lbs, well short of the 6000lbs required.

Without the deformation of the rail under the 4000lbs at 4mph impact, it would seem to be unusable information in evaluating the railing for a static load. It seems to me we're back to an evaluation based on the section moduli (elastic and plastic), modulus of elasticity, yield stress and ultimate tensile stress of the rail.

 

[BUGGAR]

As noted, crashes are typically a combination of elastic and plastic energy absorption. Watching the extensive crash test footage available, you can estimate how much the mass springs back (elastic) vs. how much it doesn't (plastic), and proportion the total energy accordingly to get an estimated g force.

 

[BridgeSmith]

BUGGAR, you still can't get the static force capacity of a railing system, based on only an impact load and speed; you need either the displacement of the railing or the limit state corresponding to that load and speed.

 

[bob33]

This guardrail requires 3 posts, so the span is 6'. The requirement is that the guardrail and posts resist a point load of 6 kips applied anywhere along the length of the guardrail and at a certain height. It appears this guardrail/post arrangement is meant for forklifts. Many North American codes just require guards of various types to resist static loads in lieu of dynamic loads. This is no different. The designer should contact the manufacturer in China for the strength and geometric properties of the railing, calculate the required section modulus and check the railing and posts for the specified point load. If the manufacturer is unable to provide their information, a load test on a piece of the railing is another option. One could assume continuous one end where applicable.

 

[JLNJ]

Attached is a paper which uses the vehicle crush and the barrier deflection in the energy calculations.

 

[BUGGAR]

Yes, zero deflection equals infinite loading.
That was a good paper.

 

[CAA1000]

Interesting paper JLNJ, thank you. Solving Equation 1 with the 4000 lbs and 4 mph given in the guardrail's crash rating, as well as the approximation given in the paper for δc, gives an impact force of 2650 lbs with 0 in. of barrier deflection, 2402 lbs with 1 in. deflection, and so on. Is this an appropriate use of the equation? If so, it seems that calculating the deformation of the guardrail is unnecessary seeing as the force will always be below the required 6000 lbs.

 

[chucklesNOLA]

If so, it seems that calculating the deformation of the guardrail is unnecessary seeing as the force will always be below the required 6000 lbs.

The only issue with that approach is that what it's rated for might be a function of what it's required to be rated for, similar to the IBC use of 6000# static load for parking structure barriers. That is, it might be capable of withstanding a 10000 lbm vehicle impacting at 10 mph elastically, but since the rating is only required for 4000 lbm at 4 mph (did this originate as metric 1800 kg @ 6.5 kph +/-), that's all they list.

I think the advice from bob33 to reach out to the manufacturer for more information is probably the best so far, CAA1000. We can all cogitate on how we would extract an equivalent static force for the system, but, as much as I am enjoying the mental calisthenics, I'm not sure it's really moving you closer to your goal.

 

[BridgeSmith]

"the approximation given in the paper for δc, gives an impact force of 2650 lbs with 0 in. of barrier deflection, 2402 lbs with 1 in. deflection, and so on. Is this an appropriate use of the equation?"

I haven't reviewed the equation you're referring to, but as I and others have stated, zero deflection = infinite load with any impact. Something's gotta give when a vehicle hits the railing.

The railing is 'good' for 4000lbs at 4mph, but does that mean it will deflect elastically under that load, deflect 6" under that load, or deflect 36" under that load? That load on the rail will have an effect somewhere between it bouncing back without damage and being massively deformed but not breaking. Without knowing where the design is in that range of outcomes, any calculations based on that information is a WAG.

 

[bones206]

[CAA1000]the manufacturer's crash rating is 4000 lbs at 4 mph[/quote]

What defines the crash rating in this case? In other words, what is the structural limit state criteria that defines whether something is rated for x load at x speed? Assume for example the max allowed ductility ratio = 1.5:

Kinetic energy of the car: (Eq 1) KE = 0.5mV[sup]2[/sup].

Say 100% kinetic energy (KE) becomes strain energy in the guardrail: (Eq 2) KE = E[sub]s[/sub]

E[sub]s[/sub] = Area under the resistance(F)-deflection(x) curve

Define the resistance curve:

From 0 to yield, resistance function F = k*x, where k is the structural stiffness/elastic spring constant and x is the displacement.​

From yield(x[sub]y[/sub]) to target ductility 1.5x[sub]y[/sub], the resistance function = F[sub]y[/sub] = k*x[sub]y[/sub]​

If we know the maximum displacement is 1.5x[sub]y[/sub], then setting the strain energy equal to the area under the resistance curve, you get: (Eq 3) E[sub]s[/sub] = elastic work + inelastic work = 0.5F[sub]y[/sub]x[sub]y[/sub] + F[sub]y[/sub](1.5x[sub]y[/sub] - x[sub]y[/sub])

You get the terms k, F[sub]y[/sub] and x[sub]y[/sub] from standard beam bending and displacement equations along with guardrail section and material properties.

Knowing velocity V, you can back-calculate the mass/weight by setting Eq 1 equal to Eq 3. That will be the maximum weight @ velocity V, for a target ductility ratio of 1.5.

 

[ThomasH]

Just out of curiosity, is the rating of the guard rail independent of the properties for the supporting post? In reality there will be deformation in the guard rail, the post and possibly also in the foundation for the post.

The thing is that in a dynamic analysis they can all be used to help absorb the crash energy. But for a static analysis it is not obvious that a "soft" support can be a positive factor. When the guard rails rating is exceeded, what happens? How does it fail?

I find the rating to be very low, strangely low actually. The numbers don't match the standards I have seen. So I'm not sure I would trust that structure with a 6000 lbs static load .

Thomas
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