M.o.S vs F.o.S 7

[ItsMeLah]

May i know what is the difference between 'Margin of Safety' and 'Factor of Safety'? How to appropriately use both of them in aircraft structural design analysis?

TQ.

 

[rb1957]

FoS = Reserve Factor ... it is the factor that the applied loads can be multiplied by to create a critical loading (ie applied stress = failure stress)
a FoS < 1 means failure

MoS (usually MS) = FoS (or RF) -1
an MS < 0 means failure

 

[tbuelna]

ItsMeLah-

rb1957 gives a good explanation of FoS and MoS. An analysis that shows a negative MoS is usually unacceptable.

Most every structural analysis approach requires some amount of simplification in order to make the task manageable. FoS is a factor applied to calculations to compensate for inaccuracies that can result from simplifying things. It is also common practice to have different FoS requirements for validation by analysis only (ie. typically something like FoS=1.50) and for validation by analysis plus structural testing (ie. typically something like FoS=1.25).

Lastly, besides the general FoS applied to aircraft structural analyses, there are often other knockdown factors that are required for things like material quality, manufacturing variables, operating conditions, etc. For example, aircraft structures that are made from castings usually must apply a "casting factor" to the analysis (ie. casting factors are typically =2.0), to compensate for variations in the cast structure that tend to be much greater than in structures made from wrought materials.

Hope that helps.
Terry

 

[YoungTurk]

With respect to rb - I think MS = FS - 1 is a misconception of sorts, though I fall back into it myself.

Margin is how much additional strength you have, AFTER all of the relevant factors have been applied. A more accurate formulation is

MS = Strength / (Stress x Factor) - 1

The difference is whether the factors are reflected in the margin, which they are not. For example, typical large aircraft structure has a required base factor of safety of 1.5 (ultimate load = limit x 1.5). If MS = FS - 1, the margin would always be >=0.50. In actuality you will see reports showing margins down to "+0". This means that there is no ADDITIONAL margin after the required factor of safety is applied.

For another aircraft example, look at the 1.15 fitting factor. If you are required to apply a fitting factor, typically over and above the 1.5 ultimate factor, you will reflect the margin AFTER doing so. In this example a zero margin implies that your ultimage strength is equal to your limit stress x 1.5 ultimate load x 1.15 fitting factor.

MS = Strength / (Stress x 1.5 x 1.15) - 1

So, margin basically reflects how over-designed your structure is, after the required factors have already been accounted for. A margin of +1 does not mean that your structure can take twice as much load, it means that your structure can take twice as much load and still have the required factor of safety.

 

[rb1957]

additional factors (eg fitting factor) are (IMHO) applied before the margin (or RF) is calculated, and often noted ("FF inc") ...

thus RF = Allowable/(Applied*FF)
and MS = RF-1

 

[YoungTurk]

I think we're saying the same thing "reflect the margin after (applying the FF)" = "additional factors are applied before margin"

I've even seen some places apply the FF factor directly to the loads, which is WAY before calculating the margin, though my personal preference is to show it in or near the final calculation.

 

[ItsMeLah]

By applying FoS to MoS meaning that the design is capable to resist the design load and at the same time is justified for critical loading?

 

[blakmax]

My understanding is that the maximum load case is determined from analysis of flight loads. This is defined in terms of LOADS and BENDING MOMENTS and defines Design Limit Load (DLL). This is the maximum load case the aircraft may be expected to see once in its service life. Limit Load may be different for each component. For example, the maximum loads for a wing skin under bending loads will not be the same load case as for a rudder under maximum yaw.

A Factor of Safety is then applied to those loads, to determine Design Ultimate Loads (DUL), still in terms of loads and specific to each structure. This is the load case used to design the structure. Typically the Factor of Safety is 1.5.

Each part is then subject to analysis to determine the maximum STRESS at DUL (not DLL). This is then compared with material ultimate stress (the material allowable strength, be it shear compression or tensile strength) and then the margin of safety (MOS) is calculated from 1 - max-stress/(material allowable stress).

As already stated the MOS must always be > 0 at DUL.

Such analyses must also be used in conjunction with Damage Tolerance Analysis (DTA) IAW FAA Part 14 2x.573 to ensure that, even though the structure has sufficient static strength when first produced, the strength of the structure is not degraded below acceptable levels during the life of the structure in the presence of defects e.g. fatigue cracks, corrosion pits, impact damage etc. I believe for example that the USAF requires that at the projected end of the life of the structure, there must be a residual strength sufficient to sustain 1.2 DLL. This is known at the Reserve Factor. At no time during the service life may the strength degrade below the RF.

DTA is based on fracture mechanics, which predicts rapid fracture failure in the presence of cracks. (This is reliable in metallic strictures but application to composite structures is unreliable because of the multiplicity of failure modes). Failure occurs when the stress intensity exceeds the critical stress intensity factor (SIF) or K[sub]c for the material configuration in question. Stress Intensity is usually of the form Stress*Beta*SQRT(PI*a). Beta is an edge correction factor which is geometry defined, PI is the usual 3.14159 etc, and "a" is the characteristic defect size. For a crack in an infinite plate, a is half the crack length. For an edge crack in a half-infinite plate a IS the crack length. You need to look up the SIF expression for your particular case. The stress intensity calculated is compared with the Fracture Toughness (critical SIF).

Typically, DTA assumes a pre-existing defect size to reflect the capability of NDI to detect defects. This often relies on an assumption that a pre-existing small undetected defect (usually 0.05 inches long) exists, and then a fracture mechanics fatigue analysis is applied to demonstrate that a sufficient RF exists at the termination of the life of the structure. If not repair action will be required.

Of interest, if the same DTA analysis was applied to most current approved mechanical repairs, they would fail these requirements. In contrast, bonded repairs to cracks in metallic structure can and have been demonstrated both analytically and practically to meet or exceed the requirements for providing adequate static strength and RF for the service life of metallic structures, provided that only valid methods for surface preparation and repair application were employed. This has been demonstrated by many cases in the military aviation system. I have personally driven repair management from a situation where 43% of bonded repairs performed IAW OEM procedures failed, to a situation where the repair failure rate was about 0.07% and for each of these failures, our quality management system could identify technician errors (not process deficiencies) as the cause.

So why is it that we do not see any civil applications of adhesive bonded repairs for defects in metallic structures?

I was once told by a repair specialist from a large US manufacturer that they would never use bonded repairs because if the bond failed and caused a crash, they could be sued. My response was that if ever I was involved in a crash because of fatigue of a mechanical repair, then my partner will sue them for using an inferior repair methodology.

I would welcome further discussion.

Regards

Blakmax

 

[rb1957]

"By applying FoS to MoS ..." ... we're not doing this as i understand our terminology.

FoS is equivalent to MS (=FoS-1).

One interpretation for FoS might be the ultimate factor, re FAR25.303, but then i wouldn't tie this definition to MS.

so having written that, maybe we are, but the terms are unrelated. let's see if this helps ...

1) first we define a limit load on the structure, say a maneouvre load. the allowable for limit load is yield, ie no plasic deformation.

2) then ultimate load = 1.5*limit; 1.5 is defined in FAR25.303 as FoS. the allowable for ultimate load is ultimate strength, plastic deformation is acceptable.

3) then we calc RF = allowable/applied or MS = RF-1

4) then we apply other factors as required, fitting factor, casting factor, ... RF = (allowable/applied)/(FF*...) or MS = RF-1.

basically RF tells you the factor you can apply to the applied loads to create a critical stress, however you've defined critical stress, with whatever factors (inc ultimate factor) applied.

clear as mud ?
i'd've thought a basic text (like Michael Niu's) would have explained this in detail.

 

[YoungTurk]

6 Nov 12 1:25
By applying FoS to MoS meaning that the design is capable to resist the design load and at the same time is justified for critical loading?

Kind of, maybe, but no. It simply means that we are choosing to express our result in terms of how much margin is remaining after all required/requested factors are applied. You could argue that a perfecly optimized structure (for weight/performance) would have zero margin everywhere, but then there are fatigue, repair, DTA, tolerance, etc., issues as well. rb also alludes to some of the nuance with the regulations regarding limit loads, ultimate loads, deformation, etc.

rb -

MS = RF-1
Agree

MS (=FoS-1).
Disagree - as explained above

Yes, the basic formula is explained in texts, but it is a source of lots of misunderstanding so worth a discussion.


An illuminating (for me) example of what margin means, was related by a professor in grad school who worked on NASA projects. Apparently some of the launch vehicles and companies involved have some pretty tremendous factors they apply over and above the already high launch loads to ensure safe launch. Obviously, there are also tremendous constraints and structure size and weight (not to mention material choices, etc.). He related the experience of going to a late stage design review for space hardware structure and showing a slight negative margin due to some challenges which arose during detailing and fabrication. Apparently after the project managers stopped having heart attacks he tried to explain that negative margin implied that they were not hitting the large combined factors of safety which had been somewhat arbitrarily specified at the beginning of the program, and that relative to the actual expected loads he still had an ample amount of strength. "NO - its NOT going to fail!" I think in his case, he won out, which isn't going to happen for FAA certifiction; but then our factors are not that large and we put our products into service day and day again, not just once.


blakmax, WHOA - deep DTA discussion for another thread and another day. You've got adhesives stuck on the mind.

 

[rb1957]

yeah, i started thinking/using FoS in it's generic sense (like RF or MS). but then i thought that maybe the question is coming for a more pedantic (studious ?) background and then i remembered the ultimate factor is (pedantically) called the safety factor in the FARs.

agree with the DTA spin !

 

[tbuelna]

blakmax does a very good job of illustrating just how complex aircraft structural analyses can become, especially when the effects of fatigue life and fracture control must be considered.

For fun, I would just like to add the extreme analysis case for something like a crash, where permanent plastic deformation (bending, crumpling, etc.) of the structure is acceptable, but complete mechanical failure is not (ie. bent, but not broken).

Great discussion!

 

[ItsMeLah]

This discussion is getting really deep n more confusing to me...lol...