- Limit state design
**Limit state design**(LSD) refers to a design methodology used instructural engineering . The methodology is in fact a modernization and rationalization of engineering knowledge which was well established prior to the adoption of LSD. Beyond the concept of a limit state, LSD simply entails the application of statistics to determine the level of safety required by or during the design process.**Criteria**Limit state

design requires thestructure to satisfy two principal criteria: theultimate limit state (ULS) and theserviceability limit state (SLS). A limit state is a set of performance criteria (e.g. vibration levels,deflection , strength, stability, buckling, twisting, collapse) that must be met when the structure is subject to loads.Any design process involves a number of assumptions. The

load s to which a structure will be subjected must be estimated, sizes of members to check must be chosen and design criteria must be selected. All engineering design criteria have a common goal: that of ensuring a safe and functional structure.**Ultimate Limit State**To satisfy the ultimate limit state, the structure must not collapse when subjected to the peak

design load for which it was designed. A structure is deemed to satisfy the ultimate limit state criteria if all factoredbending , shear and tensile or compressive stresses are below the factored resistance calculated for the section under consideration. The limit state criteria can also be set in terms of stress rather than load. Thus the structural element being analysed (e.g. a beam or acolumn or other load bearing element, such as walls) is shown to be safe when the factored loads are less than their factored resistance.**erviceability Limit State**To satisfy the serviceability limit state criteria, a structure must remain functional for its intended use subject to routine (read: everyday) loading, and as such the structure must not cause

occupant discomfort under routine conditions. A structure is deemed to satisfy the serviceability limit state when the constituent elements do not deflect by more than certain limits laid down in thebuilding code s, the floors fall within predeterminedvibration criteria , in addition to other possible requirements as required by the applicable building code. Examples of further serviceability limit requirements may include crack widths inconcrete , which typically must be kept below specified dimensions. A structure where the serviceability requirements are not met, e.g. the beams deflect by more than the SLS limit, will not necessarily fail structurally. The purpose of SLS requirements is to ensure that people in the structure are not unnerved by large deflections of thefloor , vibration caused by walking, sickened by excessive swaying of the building during high winds, or by abridge swaying from side to side and to keep beam deflections low enough to ensure that brittle finishes on the ceiling above do not crack, affecting the appearance and longevity of the structure. Many of these limits depend on the finish materials (sheetrock, acoustical tile) selected by the architect, as such, the limits in the building codes on deflections are generally descriptive and leave the choice to the engineer of record (this may not be as true outside the U.S.)**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. 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. These factors can differ significantly for different materials or even between differing grades of the same material. Wood and masonry typically have smaller factors than concrete, which in turn has smaller factors than steel. The factors applied to resistance also account for the degree of scientific confidence in the derivation of the values - i.e. smaller values are used when there isn't much research on the specific type of failure mode). Factors associated with loads are normally independent on the type of material involved, but can be influenced by the type of construction.

In determining the specific magnitude of the factors, more deterministic loads (like dead loads, 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. While arguably not philosophically superior to permissible or

allowable stress design , it does have 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 Codes**The following is the treatment of LSD found in the

National Building Code of Canada :NBCC 1995 Format φR > α

_{D}D + ψ γ {α_{L}L + α_{Q}Q + α_{T}T}where φ = Resistance Factor ψ = Load Combination Factor γ = Importance Factor α

_{D}= Dead Load Factor α_{L}= Live Load Factor α_{Q}= Earthquake Load Factor α_{T}= Thermal Effect (Temperature) Load Factor**The State of the Art**Limit state design has replaced the older concept of

permissible stress design in most forms ofcivil engineering . Notable exceptions aregeotechnical engineering andtransportation 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 the UK,Steel structures are designed in accordance withBS 5950 , andreinforced concrete structures toBS 8110 , both of which are codes based on limit state theory. 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 discusssafety factor s when working with LSD, as there are concerns that this may lead to confusion.**United States: Late Majority, or Laggard?**The United States has been particularly slow to adopt Limit State(s) design (known as Load and Resistance Factor Design in the US), and as a result it is more thoroughly adopted outside the United States. Inside the U.S. there has been significant resistance to this technique, so much so that the

American Institute of Steel Construction (AISC ) is now issuing a combined manual of steel construction (the 2005 manual) that contains both methods of design side by side (ASD -Allowable Stress Design , last updated in 1989), andLRFD - load and resistance factor design). In terms of the US steel code, research and progress has been reserved to LRFD code, with the exception of addenda regarding safety concerns. Even so, many American engineers continue to prefer the ASD code. The difficulty may lie in the high regionalization of US Engineering practice, coupled with the high number of governing bodies, codes and states which each regulate the engineering profession individually.**ee also***

Structural engineering

*Allowable stress design

*Probabilistic design

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