Limit state design

Limit state design

Limit state design (LSD) refers to a design methodology used in structural 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.


Limit state design requires the structure to satisfy two principal criteria: the ultimate limit state (ULS) and the serviceability 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 loads 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 factored bending, 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 a column 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 the building codes, the floors fall within predetermined vibration criteria, in addition to other possible requirements as required by the applicable building code. Examples of further serviceability limit requirements may include crack widths in concrete, 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 the floor, vibration caused by walking, sickened by excessive swaying of the building during high winds, or by a bridge 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 > 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

The State of the Art

Limit state design has replaced the older concept of permissible stress design in most forms of civil engineering. Notable exceptions are geotechnical engineering and 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 the UK, Steel structures are designed in accordance with BS 5950, and reinforced concrete structures to BS 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 discuss safety factors 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), and LRFD - 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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