Limit state design
Limit state design refers to a design methodology used in
structural engineering. 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. Canada, Australia and New Zealand also utilise limit state theory.
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. Limit state
design requires the
structure to satisfy two principal criteria: the ultimate limit state (ULS) and the
serviceability limit state (SLS).
To satisfy the ultimate limit state criteria, all
bending,
shear and
tensile or
compressive stresses which would be obtained under factored loading, must be below the limit stress (maximum allowable stress dependent on the loading condition - i.e. tensile yielding or fracture, bending, buckling stress, etc., or combinations thereof dictated by the structural system - i.e. edge beams with bending and torsion at the same time) in the structural element being analysed (e.g. a
beam or a
column or other load bearing element, such as walls). Material and load
safety factors are used to ensure that these loads can be carried safely. These factors are customarily 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 (One or lower) applied to the resistances of the material, as such, Wood and masonry typically has smaller factors than concrete, which 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 typically greater than one and are normally not dependent on the type of material. 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). While this technique is 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. Permissible stress design simply limits the stress by a value, usually determined by the function of the piece in question (beam, tie rod, column, hanger, etc.) where the probability of failure is not assured to be consistent.
To satisfy the serviceability limit state criteria, the structural element must not deflect by more than certain limits laid down in the
building codes. In addition to deflection, there may be other serviceability criteria that apply; for example, crack widths in
concrete 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.)
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.
It is also true that Limit State(s) design is more thouroughly 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). Concrete design is most commonly performed using Ultimate stress design / Limit state(s) design.
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Structural engineering
