Working Loads Vs Limit State Loads 2

[axle]

Hi, I am doing some research on membrane structures (architectural sails) and have come across some information that says that these type of structures (large displacement structures) should be analysed at working loads, not limit state loads. It says that low factors of safety may result if an ultimate limit states design methodology is used. Firstly what is the definition of working loads compared to limit state loads, and secondly why is this so?

 

[JWB46]

If you have a read of 'Cable Structures' by Max Irvine Section 2.7 (a classic book) it will answer your question. Sorry for the very quick answer - I'm pushed for time. Come back if you want further thoughts.

Good luck

 

[Bbird]

It takes an oddy to answer this one! Here is my version to attract further discussions.

Working load design was the standard in the past but limit state design took over some 30 years agao.

With working load the actual load on the structure is used and the method of analysis is based on the elastic hehaviour of the material. The design is control by using a specified limit of the stress. The margin between the maximum stress at failure to the specified limit is the safety factor, approximately about 2 in many structural designs. It is simple and served us well.


Limit state design is an attempt to bring the engineer's attention to the limit state of the materialand to convince us that it is safe to use the inelastic part of the material if we are sufficiently far away from the maximum limit at the failure point. To do this we have a safety factor for the material and also a safety factor for the load. The safety factors are statistically determined. In limit state design one uses the actual stress-strain curve of the material and the member design becomes complicated, although simplied procedures are provided by the design code. In a limit state design, say at collpase, the structure should theoretically fail if the factored design load is reached and the predetermined statistically possible limit of bad quality of the materials is present. The safety in the design depends on the margins on both load and material not being exceeded.

In a way engineers are closer to reality and have to accept that a small sample of the material population will fail in any selection. The benefit of the limit state design is that we are now using more of the material's capability and less of its quantity in general, although in particular cases we could actually do the opposite because of the improved knowledge of it.

The downside of the limit state design is that we have to load our younger generation of engineers with more knowledge and more complicated design methods, resulting some of them having no need to know the simple working load design.

Working load design can have its place in many applications because it can be interpreted as using the elastic section of the stress-strain curve. A structure designed with working load is supposed to be able to fully recover every time the load is removed. It is therefore particularly suitable for a structure subjected to mainly dynamic instead of static load. For example the working design method was retained by ACI 307, for a number of years when limit state design was introduced in other ACI standards simply because engineers believe it is essential to have a chimney resilient to the daily wind. ACI 307 has now adopted the limit state design. The other important area for working load design is the reinforced concrete structures for retaining water where it is still preferable to limit the stress of the material to a predetermined level.

 

[rowe]

Most LRFD (limit state) bridge designs also require "serviceability" (service or working)checks.

These structures are designed to sustain certain factored load cases without failing, although the factored loads may cause some permanent deformation (for extreme cases such as seismic load cases).

The serviceability checks include fatigue, cracking, and deflections due to nominal loads which are meant to be comparable to the loads that we expect the structure to experience often during the serviceable life of the structure (i.e. a service live load is often in psf, but most live loads are actually discreet loads - closer to point loads).

With "limit state" design, we're not usually concerned with the amount of deflection, but with the overall capacity of the system with respect to failure or collapse.

With "working stress" design, we're concentrating on wholly "elastic" behavior and the utility of the structure during it's useful life.

Although I'm not very familiar with design of membrane structures (my shells course was long ago - and so far never used), I suspect that if deflection is a primary concern, then working stresses would give higher safety factors.

Perhaps I too will get a copy of the book that was referenced by JWB46 above.

Good luck.

 

[JAE]

Both of the above posts have stated that limit state design uses materials beyond their elastic range. This is true sometimes, but not always. AISC LRFD is a limit state design for steel and many, many designs of beams will end up defining the limit state as the yield point.

In other words, the factored loads are used to find a beam that will just yield....not go beyond yield into the plastic zone. So the limit state CAN be defined and IS defined many times as the elastic limit.

Working stress design and Limit State Design (or LRFD) really do the same thing, its just that the working stress method uses a set, somewhat arbitrary (based on experience and judgement) safety factor. LRFD uses safety factors based on statistical probability of failures so are less arbitrary except for the unpleasant fact that current specs like AISC LRFD have set load factors and phi factors to create a probability of failure similar to the traditional working stress methods.

For a big sail type structure, the designation you refer to about using working stress design is puzzling. Both methods design for similar probabilities of failure and both methods will required checks of deflections (servicability) at non-factored load conditions.

Why they would figure that limit state methods would create a lower safety factor does not sound logical. In fact, using LRFD for a structure primarily loaded with wind may actually provide a higher safety factor as the load factors are adjusted to account for the variability of the load and wind is highly variable.

The ASCE 7 load factors provide the following safety factor: 1.6 load factor and assume 0.9 strength reduction factor:

1.6 / 0.9 = 1.777 safety factor for LRFD

For working stress: roughly 1/ 0.6 = 1.666 safety factor for working stress (1/3 stress increase no longer valid)

 

[Bbird]

I am concious of the fact we are engineers from different background and different countries but in reinforced concrete design the ultimate limit state is when concrete reaches a compressive strain of 0.0035 (in European countries, the USA practice uses 0.003 I think) and the reinforcement can be stressed well beyond the yield point.

One thing is certain - at ultimate limit state the structure is not considered serviceable.

rowe covered the serviceability limit state very well. I have written a few words on it but refrained from putting them forward in my first response, for afraid of confusion. From stress analyses of reinforced concrete I find the serviceability state generally differs very little from the solution by working load approach based on elastic analysis. This is because at service condition we often use unity for the load factor and seldom load the structure significantly to pass its elastic range. I feel a need to defend the working load approach because of its association with the elastic or linear stress-strain concept. Like rowe said it concentrates on the utility of the structure during it's useful life and therefore directly relevant. In my understnading, an engineer attempting to analyse a member loaded beyond its inelastic limit must be first able to solve the same problem when the stress is in the elastic range.

Both working load and limit state load methods of design are just means to size up the members. With the former we can do it quicker while the latter keeps us in check more with reality (like knowing statistics, limits of the material etc). In term of analysing the structure we are still using the liner and elastic theory all the time (i.e. we can put 100 times more load and the computer returns 100 times more deflections and member forces. Unless the engineer uses his brain he would not know the structure has failed or not.

It would appears that the sail structure mentioned by axle will require large deflection theory which is simply to calculate the equilibrium condition after the the structure has been loaded. This can be achieved by performing the analysis iterativelly by additing deflection to the no-load geometry until the deflection converges. For expedency engineers analyse a structure primarily with the equilibrium calculated at the "no load" configuration. This simplification generally works satisfactorily as serviceable structures rarely can deflect by more than 5%, unless it is something like the wall of a rubber tyre. Thus I would describe the sail structure problem as nonlinear-elastic (geometry nonlineear while material elastic). If limit state design is applied then the full analysis should be nonlinear-inelastic. A further complication of the sail structure is that some materials could have strength in tension only (like cable and fabric) and repetitive analyses are needed to ignore members in compression.

I would rate the nonliner aspect of the deflection and the nonhomogeneous of the material behaviour more important than the limit state loading for the design of the sail structure.

 

[mhnds]

I don't know more about shell structures, but i want to mention about Limit State Desing and RC structures.I think LSD method is the best for Rc structures. Because you don't have to calculate some stress values in the material which is not very homegenous compared with many other structural materials.Working Load method is better for steel structures since in this case the calculated stress values are much more close to the real stresses occured in the material.Besides the non-homegenty of the material,also its inelasticity (probably this is the most important ) make us be suspicious about our desing in which we assume concrete elastic(Workind Load case).
regards

 

[axle]

Thank you all for your comments. As a young engineer (only a year out of my studies) I am finding that most of the standards or textbooks I come across seem to be written in a way that makes it very hard to understand unless you have some prior knowledge of the subject or an expert on hand to assist you. I would have thought that they would be written in a way so that anyone could decipher the author’s intentions.

From your comments I think that I now have a clearer picture of the differentiation between working loads and limit state loads. However I would just like to verify a few points.
Firstly, are the loadings that were used in a working load design the same as that, that are prescribed in current versions of the relevant standards. For example could I use a live load as listed in AS/NZS 1170.1: 2002 – Structural Design actions, Part 1: Permanent, imposed and other actions (being from Australia I will reference Australian Standards in my questions) to carry out a working load design. Obviously no load factor would be applied to this load when carrying out the design. In the case of wind loadings, AS 1170.2 – 1989 gives a basic wind speed value Vp (the p referring to permissible stress). In relation to AS 1170.2 – 2002 this corresponds to a recurrence interval of 50 years. Am I right to assume that to obtain the working loads on a structure in relation to wind, one would just follow the procedure prescribed in AS 1170.2 using a basic wind speed equal to Vp or a recurrence interval of 50 years.

Secondly, in order to carry out the design of a member in accordance with working load theory, the current relevant standards cannot be used as the equations that are presented in them deal with the inelastic behaviour of the member. For example you could not simply just calculate the member moment capacity of a steel beam under working loads using the latest version of AS 4100 – Steel Structures, with the capacity reduction factor removed to obtain a design that complies with working load theory.

Finally, I have some more queries on the membrane structures that I mentioned in my first post. The type of membrane structure that I am concerned about are the small architectural type structures that are usually found over outdoor eating or entertainment areas at a private residence or small café, coffee shop or the like. These structures usually just consist of the membrane being stretched between and attached to a number of freestanding columns. Alternatively the membrane can also be attached to parts of existing buildings such as that of a block wall or can be a combination of both. These structures generally have a plan area of no more than 30m2 and take the shape of hyperbolic paraboloid (hypar) roofs or monoslope free roofs. At present I have a local supplier and erector of these structures who is being asked by the local building authority to have the structures certified for liability reasons. What I am looking for is some feedback in relation to the design of such structures. The actual membrane is not of major concern; the local building authority’s main concern is the supporting structure and its associated fixings.
The latest version of the Australian Wind Loading Code, AS/NZS 1170.2:2002 does give information for wind loads on hypar free roofs (Table D7) however I am having some trouble understanding the table. Also, can the coefficients for monoslope free roofs provided in the standard be applied to this type of structure, as these are not rigid structures in the sense? From watching these membrane structures respond to wind loadings, they do not seem to ‘retain’ the wind as such. They seem to ‘expel’ the wind that is caught in the membrane once it reaches a certain threshold. Can any allowance be made for this phenomenon? In relation to the design of the supporting columns, in my opinion deflection is not of major concern. Being an independent structure that is supporting a flexible medium, if the columns deflect a relatively large amount under loading it should not be a problem. Is this a fair assumption? Any comments/feedback in relation to the design of these structures would be greatly appreciated.

 

[sabrepoint]

Hello axle

Interesting topic, and fills in quite a few gaps for me. I'd be particularly interested in any response regarding your first point "Firstly, are the loadings that were used in a working load design ...".

I stand to be corrected, but I think the scheduled Ultimate LS windloads are different (greater) than those used in the old Safety Factor days, so I don't think one can simply interchange the wind speeds. I'm not sure if this is exactly what you are looking to do, but thought it worth a mention.

I'll keep an eye out for more responses!

Bill

 

[Bbird]

Hi axle,

Not sure if I can help much but this is my attempt below.

I am not a regular user of Australian codes but the loads published in a design code are "design loads" for a structure to withstand in service. They are the working loads as long as I have been involved. This applies to the wind even if its magnitude occurs once every 50 years. It is a common practice to define a basic wind speed with occurrence once in 50 years at a specified terrain generally at 10m above ground measured as either a 3-sec maximum gust or an average over a longer duration. However for the working condition a “design” wind speed must incorporate other factors (reflecting the structure's height, shape, importance etc) into the basic wind speed. I expect this to be fully documented in the code.

On the section capacity calculation you should find earlier codes based on elastic design helpful. They also provide the permissible limits for the stresses.

Lastly on the selection of design parameter I can't help you as I need the document and time, both of which I do not have. However when dealing with such a problem one can always carry out a sensitivity study to see the effect of the selecting available choices and then make some sense out of the exercise. It may be the case the difference is not great enough and designing for the worst case can protect you. The behaviour of your sail structure may lie outside the bounds of the design code and you must approach it with an open mind.

I believe an accurate understanding of the structural behaviour of the sail structure is central to the design and for that you may need access to some specialised software which can analyse the structure interactively. Basically the sail equilibrium condition must be computed at the deflected configuration and you may need to remove members in compression from the structure if they are tension-only elements. Thus the expel-wind case can be simulated by reversing the wind direction.

On the large deflection of the column is OK I think nobody here can agree to that because a large deflection creates a large moment arm for the axial load and could be dangerous to the column. In your case you actually use it as a beam, even if it is place vertically, for supporting the sail structure and the column may even be in tension. Thus large deflection may be acceptable in practice in your case. Anyway I can confirm that if you calculate the equilibrium at the deflection configuration then your column will be safe even with large deflection.

I did a undergraduate project on nonlinear analysis and found the large deflections can be solved by at least three alternatives:-

(1) Using linear software that designer uses (except specialists with particular applications), which compute the equilibrium condition at no-load configuration, and feed the deflection to the original geometry to recalculate until the deflection converges to an acceptable limit. This approach work well with the least amount of work. From my previous experience between 5 to 6 iterations should be suffice. You can simply write a post-processor by adding the linear portion of the delection (ie. dx, dy and dz) to original nodal coordinates. By comparing the sum of the squares of the deflection of any two successive runs you will be able to see where the solution is likely to be.

(2) Adjust the element matrix with the stability functions. The stability functions are axial load dependent thus making the element less stiff if carrying a high axial load or become more stiff when under tension. For line elements the stability functions are well documented e.g. in Coates, Coutie and Kong's book "Structural Analysis". I do not have information on the equivalent for the plate elements for your sail structure. One need access to the analysis software for this approach. Two iterations are needed with the first one to provide the axial load data.

(3) Using large deflection theory – This is a common method by adding a second order term to the element matrix. Again I dealt with only line elements in my project and two iterations similar to (2) above are needed. Some specialised software, claiming able to cope with large deflection, will have this built into the code.

The accuracy of all three methods is comparable and I didn’t find any one stood out better than the rest when I programmed them. I used them on both compressive ( to find out collapse) and tension (to investigate stiffening effect) members.

The sail structure is an interesting object to deal with. As long as an equilibrium condition exists then I believe you should be able to crack this nut.

Good luck

 

[BryanStein]

I haven't read much that I agree with yet.

Concrete is not designed with Limit State Design (LSD). It is designed with Ultimate Strength Design (USD). There is a huge difference. Steel LRFD is not a limit state design. LSD in steel is more like full plastic design. LSD in concrete is a upper limit and results in more strength.

Basically, LSD is an upper failure limit of which steel or concrete design does not recognize. LSD is only significant in failure analysis, and depends GREATLY on boundary conditions of element in question.

If the original post was refering to Working STRESS design (WSD) vs Ultimate STRENGTH design (USD), then most of the information above is correct if you remove the limit state wording and replace it with Ultimate strength wording.

It seems a lot of people love to read their own posts.

 

[Bbird]

Bryanstein,

It is possible that we all work in different countries , different fields and use the terms differently.

For reinforced concrete two limit states are used in UK; the ultimate limite state which we use for deisgn and the serviceability limit state which we use to check the structure in service conditions. The ultimate limit state design of BS 8110 is similar to the strength design of ACI 318 although the American strength reduction factor is absence in the British code which uses a partial safety factor on the material instead. As ACI 318 is used extensively outside USA it is regarded as variant of the ultimate limit state design by the international engineers having to work routinely with major national codes.

The words designing to limit state generally refers to the ultimate limit state as we cannot always size the components with the serviceability state, which usually carries the unity load factor and so its load can be identical to the working load.

To design to the limit state and check for serviceability is universally understood. Every country has its own way to define the ultimate limit state and you can certainly insist on it being called the ultimate strength design for your own application.

Although the ultimate strength design and the ultimate limit state design can be the same thing, at least conceptually, it is difficult to explain the ultimate strength for a RC column loaded with an axial load and a bending moment. This is because there are infinite number of combinations of the axial load with the moment that could cause a failure.

However it is easy to understand by defining concrete attaining its ultimate limit state if the strain reaches 0.0035 (in Europe or 0.003 in USA & Australia). ACI 318 defines the limit as the ultimate or maximum usable strain.