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# Conversion of Dynamic Load to a Quasi-Static Load5

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## Conversion of Dynamic Load to a Quasi-Static Load

(OP)
Hello,
I want to convert a load of 2000 N over a time period of 0.064sec to a quasi-static load so that I can apply it to my fea model in ANSYS. Can anyone suggest any methods or references. Any help would be appreciated.

Thanks,
David Landis

### RE: Conversion of Dynamic Load to a Quasi-Static Load

Are you trying to simulate a shock load?

Tobalcane
"If you avoid failure, you also avoid success."

### RE: Conversion of Dynamic Load to a Quasi-Static Load

If you are simulating a shock load and 2000N is whatyou get with Gs*(weight of part), you will get the full 2000N and if the part has the same Fn (the .064 sec)it will 2000N plus!  However, the way I would do it (in ProM it is what I use) I would go with simulating the gravity feild to match the G load instead of Force load.

Tobalcane
"If you avoid failure, you also avoid success."

### RE: Conversion of Dynamic Load to a Quasi-Static Load

Your time period seem to be a bit too large for a shock environment. Theoretically, to do things right, you need to know the time historty of your load and conduct a dynamic analysis - which is not that difficult to do (time consuming may be). You may even assume a triangular or sinusoidal variation.

If you still want to do a quasi-static analys, then you need to know the transmissibility of your system and multiply your load (which I presume is due to impact) by the transmissibility value. Calculating transmissibility can be a royal pain.

Hope this helps some what.

Ali

### RE: Conversion of Dynamic Load to a Quasi-Static Load

(OP)
Hi,
Thanks everyone for your input. The load is a shock load for an aircraft landing gear. The loading is a triangular pulse with G levels specified at,
t = 0.000 sec, Acceleration = 0G
t = 0.032 sec, Acceleration = 42G
t = 0.064 sec, Acceleration = 0G
The load is for a crash impulse and is a design specification from a handbook so I know it is right.
I cant seem to understand what the difference is between a static load and a quasi-static load and how can I convert it into a quasi-static load?

Thanks,
David Landis

### RE: Conversion of Dynamic Load to a Quasi-Static Load

Im not a landing gear person, but it may be more complicated.  Would the landing gear have shock absobers? If so, this is a shock/damping problem. If not, it would be 42g x weight of part that will impact the landing gear.  So if weight of the part is 100lbs, then the load would be 42x100=4200lbs at full response.  For a plane with three landing gears, you would have to figure out how much weight each landing gear would have to hold staticly and then multiply that number by the 42g and that would be the load on the landing hear (with no damping).

Tobalcane
"If you avoid failure, you also avoid success."

### RE: Conversion of Dynamic Load to a Quasi-Static Load

Sounds like you are going to have to do a dynamic simulation anyway in order to work out a quasi-static equivalent.

M

--
Dr Michael F Platten

### RE: Conversion of Dynamic Load to a Quasi-Static Load

2000N/9.81 = 203.87kg@1g accell
203.87kg/42g = 4kg.

Seems a bit light??

### RE: Conversion of Dynamic Load to a Quasi-Static Load

The way I'd use that data is use a 1DOF model of the wheel/spring/shock  to derive a maximum force at the contact patch, and then apply that force to a static FEA model to get some idea of maximum stresses.

It is conservative.

Cheers

Greg Locock

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

### RE: Conversion of Dynamic Load to a Quasi-Static Load

(OP)
I will probably be solving the system as a spring mass damper equivalent and finding the max spring force. Now will this force I get from the dynamic simulation be a static or a quasi-static force? I would guess this would be a quasi-static load since I had to use a dynamic sim to get the load. What do you guys think?

Thanks,
David Landis

### RE: Conversion of Dynamic Load to a Quasi-Static Load

It's a single step calculation 2000N/42g=4.86 kg.  But, that's irrelevant, because this calculation gets you nowhere.

However, the missing information is the effective spring constant of the gear.  The 42 g acts on the shock absorber, so the amount of compression divided by the spring constant gives the actual force imparted to the gear.

As a exercise, consider the F18 at 16850kg, assume that its two main gear take all the weight and under static conditions, they compress 2 inches.  This results in a spring constant of 1.6 MN/m.  Assume that the gear compress 10 times the static value during landing; that results in 826 kN of peak force applied applied to the gear. That's assuming the spring constant is constant, natch...

So, you need to know what the static and dynamic deflections are to get to even a first-order model.  You need to know the mass of the plane and how that's distributed across the landing gear.

One possibly useful bit of information is the 42g divided by the time to peak acceleration, 32 ms, which results in a sink rate of 2600 fpm, definitely a crash condition.

### RE: Conversion of Dynamic Load to a Quasi-Static Load

I don't know where the 2000N comes from, it is very low for any full size A/C

Oh I made a mistake, it is not conservative. IF there is an undamped resonance in that frequency range then you won't excite it properly with a static load.

Cheers

Greg Locock

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

### RE: Conversion of Dynamic Load to a Quasi-Static Load

3
Okay, here we go:

It all comes down to finding the magnification factor for your model.

A quasi-static analysis simply ignores modal effects in the response of your model.  I use it all the time.

What is the definition of "static"?

A static load is one where the rate of application (period of application) is long compared to the fundamental period of the structure.   In terms of transmissibility, the ratio f_load/f_structure is going to be zero (or very near zero).  This is equivalent to a transmissibility of 1.   That is the structure will "see" all of the applied load.   as f_load/f_structure approaches 1, the transmissibility will be greater than 1.   This means the forces the structure sees will be equivalent to the applied load multiplied by the magnification (or sometimes called transmissibility) factor.

Now for any f_load/f_structure > 0 there will be some magnification of the load seen by the structure.  However, for small values (typically less than 0.33) you won't introduce much error on your calculations by assuming your problem is static (transmissibility~1)
The advantage here is that you don't need to do a full transient analysis since modal effects are negligible.  This saves computing time.  Also if you can model your system as a 1DOF spirng-mass-damper you can easily calculate the magnification factor.

For a system to be modeled as 1DOF, the 2nd lowest mode must be AT LEAST one octave above the fundmental.  Otherwise dynamic coupling can occur between modes and you will get very large responses.

For example, in the case of a half-sine pulse, if your system can be modeled as a 1DOF spring-mass-damper then all you need to know is the frequency ratio.   The response spectrum for a half-sine pulse can be found in any dynamics book or from an internet search.  if you know the frequency ratio R you can pick the Magnification ratio right off of the graph.  Then you take the load and multipy it by the magnification ratio  and apply it as a body force to your model.  For a half-sine pulse, when the frequency of the structure is five times or more the frequency of the pulse, the magnification factor varies between 1 and 1.2.   As a rule of thumb, when I do a shock analysis and the fundamental frequency of the structure is at least 5X that of the shock pulse, I simply apply the peak acceleration as a body load to my model.

My advice on how to solve the problem:

Run a modal analysis of your structure.  The frequency of the shock pulse is 15.625 Hz. If the fundamental frequency is at least 78.125Hz then you can simply apply the 42G load to your model as a body force and run a static analysis.

If the natural frequency of your model is closer to the frequency of your shock pulse, you will need to come up with the magnification factor.   The brute force method would be to do a full transient FEA.   If your model isn't too large this is probably a good option.   If the model is too large/complex to run then your only real choice is to try and convert it to an equivalent spring-mass-damper system.   Then run a transient FEA on the simple model.   Compare the peak response acceleration to the input acceleration.  This will give you the magnification factor.  Apply the factor to the 42 G's and run the static analysis on your full model.

As an aside, if the frequency of the structure is half or less than that of the shock pulse, your transmissibility will be less than 1.  This is the isolation region.

### RE: Conversion of Dynamic Load to a Quasi-Static Load

spongebob00

I too have to perform FEA dealing with shock pulses upto 25g 11ms half sine I have a couple of questions if you are still monitoring this post:

1)When you talk about response spectrum for a half sine pulse, I presume you are referring to dynamic load factor graphs?

2) The 2nd lowest mode being at least an octave above fundamental, can you tell me how this is calculated?

It would be incredibly useful to be able perform a static analysis on a structure rather than perform a full blown dynamic analysis, so if i read this properly the steps would be for a 25g 11ms half sine input (f=90.91hz):

a) Run a modal analysis and ensure the 2nd mode is at least an octave above fundamental

b) If a) above is correct, then as long as the natural frequency of the structure is 5 times higher than the input frequency, use this ratio to read the magnification factor direct from a dynamic load factor graph for half sine

Regards

J

### RE: Conversion of Dynamic Load to a Quasi-Static Load

spongebob007

I too have to perform FEA dealing with shock pulses upto 25g 11ms half sine I have a couple of questions if you are still monitoring this post:

When you talk about response spectrum for a half sine pulse, I presume you are referring to dynamic load factor graphs?

It would be incredibly useful to be able perform a static analysis on a structure rather than perform a full blown dynamic analysis, so if i read this properly the steps would be for a 25g 11ms half sine input (f=90.91hz):

1) Run a modal analysis and ensure the 2nd mode is at least an octave above fundamental

2) If 1) above is correct, then as long as the natural frequency of the structure is 5 times higher than the input frequency, use this ratio to read the magnification factor direct from a dynamic load factor graph for half sine

Regards

J

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