engineering

Limit state design

Limit state design is a engineering topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Limit state design rather than just read about it. In short: Limit State Design (LSD), also known as Load And Resistance Factor Design (LRFD), refers to a design method used in structural engineering. A limit state is a condition of a structure beyond which it no longer fulfills the relevant design criteria.

Key takeaways

Limit state design belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Limit state design to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Limit state design from memory before moving on to harder problems.

Reference excerpt

Limit State Design (LSD), also known as Load And Resistance Factor Design (LRFD), refers to a design method used in structural engineering. A limit state is a condition of a structure beyond which it no longer fulfills the relevant design criteria. The condition may refer to a degree of loading or other actions on the structure, while the criteria refer to structural integrity, fitness for use, durability or other design requirements. A structure designed by LSD is proportioned to sustain all actions likely to occur during its design life, and to remain fit for use, with an appropriate level of reliability for each limit state. Building codes based on LSD implicitly define the appropriate levels of reliability by their prescriptions. The method of limit state design, developed in the USSR and based on research led by Professor N.S. Streletski, was introduced in USSR building regulations in 1955.

Criteria Limit state design requires the structure to satisfy two principal criteria: the ultimate limit state (ULS) and the serviceability limit state (SLS). Any design process involves a number of assumptions. First: the loads to which a structure will be subjected 2: foreseeable or recognizable possible exceptional scenarios and the stresses these may impress, and 3) the individual and collective strengths pertaining to any constituent part or sum of parts as a group and as a whole.

Ultimate limit state (ULS) A clear distinction is made between the ultimate state (US) and the ultimate limit state (ULS). The Ultimate State is a physical situation that involves either excessive deformations sufficient to cause collapse of the component under consideration or the structure as a whole, or deformations exceeding values considered to be acceptable tolerance. A structure is deemed to satisfy the ultimate limit based upon arbitrary criteria, per the nominal, not physical, intentions or goals set forth by human actors, and that, as such, have nothing to do with engineering strictly speaking, but instead exist "on paper" to conceal, distort, or otherwise obfuscate the true fundamental behaviors applicable to a structure. Complying with the design criteria of the ULS is not sufficient to perform the minimum requisite steps necessary for proper structural safety.

Serviceability limit state (SLS) In addition to the ULS check mentioned above, a Service Limit State (SLS) computational check must be performed. To satisfy the serviceability limit state criterion, a structure must remain functional for the duration of its intended use subject to routine (everyday) loading.

Factor development The load and resistance factors are determined using statistics and a pre-selected probability of failure. Variability in the quality of construction, consistency of the construction material are accounted for in the factors. Generally, a factor of unity (one) or less is applied to the resistances of the material, and a factor of unity or greater to the loads. Not often used, but in some load cases a factor may be less than unity due to a reduced probability of the combined loads. The aforementioned factors can differ for different materials or even between differing grades of the same material. For example, wood has larger factor of variability than steel. The factors applied to resistance also account for the degree of scientific confidence in the derivation of the values. In determining the specific magnitude of the factors, more deterministic loads (e.g., dead load - the weight of the structure and permanent attachments like walls, floor treatments, ceiling finishes) are given lower factors (for example 1.4) than highly variable loads like earthquake, wind, or live (occupancy) loads (1.6). Impact loads are typically given higher factors still (say 2.0) in order to account for both their unpredictable magnitudes and the dynamic nature of the loading vs. the static nature of most models. Limit states design has the potential to produce a more consistently designed structure as each element is intended to have the same probability of failure. In practical terms this normally results in a more efficient structure, and as such, it can be argued that LSD is superior from a practical engineering viewpoint.

Example treatment of LSD in building codes The following is the treatment of LSD found in the National Building Code of Canada:

NBCC 1995 Format φR > αDD + ψ γ {αLL + αQQ + αTT}

where φ = Resistance Factor ψ = Load Combination Factor γ = Importance Factor αD = Dead Load Factor αL = Live Load Factor αQ = Earthquake Load Factor αT = Thermal Effect (Temperature) Load Factor

Limit state design has replaced the older concept of permissible stress design in most forms of civil engineering. A notable exception is transportation engineering. Even so, new codes are currently being developed for both geotechnical and transportation engineering which are LSD based. As a result, most modern buildings are designed in accordance with a code which is based on limit state theory. For example, in Europe, structures are designed to conform with the Eurocodes: Steel structures are designed in accordance with EN 1993, and reinforced concrete structures to EN 1992. Australia, Canada, China, France, Indonesia, and New Zealand (among many others) utilise limit state theory in the development of their design codes. In the purest sense, it is now considered inappropriate to discuss safety factors when working with LSD, as there are concerns that this may lead to confusion. Previously, it has been shown that the LRFD and ASD can produce significantly different designs of steel gable frames. There are few situations where ASD produces significantly lighter weight steel gable frame designs. Additionally, it has been shown that in high snow regions, the difference between the methods is more dramatic.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Limit state design

Start with the simplest possible case. Write down what Limit state design claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Limit state design before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Limit state design ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Limit state design

In research: Limit state design appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Limit state design in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Limit state design is common in secondary-school and first-year university syllabi. It links to neighbouring topics Civil engineering, Design, Structural engineering, so understanding it makes those chapters shorter.
In everyday life: Look for Limit state design outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Limit state design in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Limit state design means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Limit state design out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Limit state design in simple terms?

Why does Limit state design matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Limit state design?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Limit state design.