Equivalent Static Load 1

[Eltron]

I have an application in which a vessel must be restrained against movement if gases escape suddenly. I have calculated the instantaneous force generated by the escaping gases easily enough, but the structural guys are asking me to convert that into an equivalent static load. Despite my Googling and reference book digging I am not sure of the exact number they are looking for. Can anyone suggest a reference or a series of equations that I should be using? Thanks in advance.

Dan

http://www.eltronresearch.com

Dan's Blog

 

[rb1957]

presumably the instanteous force (before the vessel has vented any pressure) is too high for the structures guys.
if the force decays quickly thee you can say that the support structure doesn't need to react the peak load, but some other "static equivalent" load.

it might be enough for you to calculate how the force decays, then tell them "make your structure withstand these loads, invent your own static equivalent".

Quando Omni Flunkus Moritati

 

[Eltron]

Yeah, the venting force decays within a few hundred milliseconds.

Dan

http://www.eltronresearch.com

Dan's Blog

 

[rb1957]

so as an "impact" load the supporting structure probably doesn't need to react to instanteous peak load, the load will disapate before it gets to the supporting structure.

justifying an "equivalent static load" is difficult ... 1/2 the peak load might be reasonable (based on load magnification for a load applied as an impact, yes?). for you (personally) it's easiest just to calc the load vs time and have the stress guys say the structure is good. But it's easier for them if they can get you (or someone else) to take that "responsibility" on !

In today's world, i think it's not unreasonable to run a time domain FEA (with something like LS-DYNA or MARC)

Quando Omni Flunkus Moritati

 

[SAIL3]

usually the vent panel is designed to blow at a certain press....NFPA is a good reference....
1. Permanent deformation , but not rupture of the enclosure..
Pes=1.5Pred/Fu
2. Permenant deformation of the enclosure not acceptable..
Pes=1.5Pred/Fy
Pes=enclosure design press
Pred=maximum pressure developed in a vented enclosure...
get a copy of the latest NFPA standard

 

[JStephen]

I took the original post to refer to the force of the vessel on the supporting structure due to the jet effect of the contents escaping- not to the pressure of the contents when released in an enclosed building.

Suggested approach:
Assume steady force applied over short duration.
Get spring constant of supporting steel.
Using that steady force and spring constant and mass of vessel & part of supporting structure, calculate acceleration, velocity, deflection over the time period that the force is acting- should be able to integrate that numerically via spreadsheet or whatever if the solution isn't easy-
Using velocity and zero jet force, calculate additional deflection until the vessel starts bouncing back.
If that deflection is a reasonable number for the structure, then you have your solution.
If the deflection is just a little high, you could consider the reduction in pressure relative to time, with velocity decreasing as a function of time.
If that deflection is an unreasonable number (say, 4 feet), then you know you need to do something else.
But what this approach would do is give you a reasonable value IF the duration is short enough.

Also, I'm awfully hazy on compressible flow, but if there is sonic choking or something like that, it may limit the flow rate to a much lower value than Bernouli's equation would indicate, which would lower the force.

 

[Eltron]

Sorry, guys. I left my question open to interpretation. When the vessel vents it will blow through an enclosed exhaust pipe to a roof vent. I just need to restrain the movement of the vessel against the force incurred during a release by attaching it to the structure so it doesn't tip over. The structural guys want to know how that dynamic load looks as an equivalent static load. I've found a couple of references, but each has a different method which results in differing numbers.

According to "Design of Welded Structures" p.2.8-3: "It is common practice to apply an impact factor to a load and design as though it were a steady load." Where the equivalent static load is equal to 2 times the weight of the body impacting the structure. So, basically multiply the force by two.

According to "UFC-3-340-02": (Section 4-47) An axial load times 1.2 equals the equivalent static load. However, this is for columns loaded axially. So I don't think it necessarily applies in this situation. Section 5-22.3 states that the equivalent static load is equal to a dynamic load factor times the pressure times the length of a beam, ending up with lbs/ft units.

Obviously, these equations will all give me different results. I'm just not sure which one (if any) to apply in this instance.

Dan

http://www.eltronresearch.com

Dan's Blog

 

[rb1957]

"Where the equivalent static load is equal to 2 times the weight of the body impacting the structure. So, basically multiply the force by two." ... i understood this to mean that a dynamically applied load is roughly twice the static load, dynmaic magnification factor = 2. in your case you have the dynamic (instanteous peak) load, so a static equivalent would be 1/2, no?

you've cal'd the initial pressure (and derived a load) ... could you develop the load as a time function, and use the average pressure over a time period, 1 sec, 1 minute, ... ?


Quando Omni Flunkus Moritati

 

[Archie264]

Absent a non-linear FEA one way to get a sanity check on dynamic loads applied to structures is to calculate the kinetic energy it generates, set that equal to the work done on the structure using an initial assumed amount of deflection, and solve for the force. Then use that force to check the initial deflection assumption and refine the calculations iteratively to the degree of accuracy you want. It may not be perfect but it should get you in the ball park. I think that's how the vehicle barrier manufacturers sometimes approach it when actual testing is not possible. For what it's worth, buyer beware, take with a grain of salt...

 

[SAIL3]

the enclosure mentioned in my reply above refers to the vessel in this case....if the venting duct is vertical as it exits the bldg, then you would only have a vertical force on the restraining strucure and all horiz loads are reacted internally by vessel and duct....your info is not complete...is there a blowout panel....if so, the design of this panel should also include the release press, etc...

 

[Eltron]

There is no blowout panel. It is a rupture disc that feeds to an open vent. The rupture disc is not vertical so in the unlikely event of a release there may be some lateral force that the vessel must be restrained against.

Dan

http://www.eltronresearch.com

Dan's Blog

 

[Eltron]

OK. I think I've bent my thick skull around this one. I calculated a reactive force generated by the escaping gases. Then I used the formula on pg. 2.8-1 of "Design of Welded Structures" which stated that F=2xThrust. In this instance the thrust would be the force of the gases. Hopefully that gets the structural people what they are looking for.

Thanks for the help everyone.

Dan

http://www.eltronresearch.com

Dan's Blog

 

[TXStructural]

The use of a factor of 2 is for suddenly applied, non-dynamic (non-energetic) loads. It was part of Timoshenko's Elements of Strengths of Materials (1935). It was in reference to displacement due to the sudden application of a load. The mechanism is that the load results in a deflection according to PL/AE, and then the velocity of the load arising from the deflection itself results in a peak deflection equivalent to twice the static deflection. An energetic event will be different.

You mention a very fast decay, which makes me think it is either a very large opening, or it is not a high-volume, low specific gravity discharge.

(At NASA, we always pointed discharges in a direction that made sense, if for no other reason than to not unscrew a pressure relief device as the result of a discharge.)

 

[WARose]

As others have noted, the max. DLF (Dynamic Load Factor) is 2. But if you need to back off of that (because it produces something impractical), you might try a Structural Dynamics book. One of the ones I have ('Structural Dynamics: Theory and Computation' by: Mario Paz, 2nd edition), has a number of charts that give the DLF based on loading type (i.e. ramp, rectangular, etc.) and duration to frequency ratio.

 

[SAIL3]

since you mentioned that you have a vent duct also the pressure may be greater than the pressure required to activeate the rupture discs...get a copy of the latest NFPA68 standard..it has alot of info pertinent to your siuation.....

 

[chicopee]

Eltron, your second,revised, post makes more sense. A reference with 'muchos" examples about forces reacting on P.V.'s relief valves when venting are found in the appendices of theANSI/ASME B31.1 Power piping. The equations presented can be modified to the medium that your tank contain.

 

[StruteK]

The proper way will be to use Duhamel's integral or various other methods which will give you the structure's response to the impulse load.

Dynamics of structures J. Humar Champter 8.7

http://books.google.ca/books?hl=en&...age&q=carleton dynamics of structures&f=false

or

http://www.civil.utah.edu/~bartlett/CVEEN6330/Duhamel's_integral.pdf