# Limit State Design

# Limit States Design

All structures have two basic requirements in common: safety from collapse and satisfactory performance of the structure for its intended use. The limit states define the various ways in which a structure fails to satisfy these basic requirements. Ultimate limit states relate to safety and correspond to strength, stability and very large deformation. Serviceability limit states relate to satisfactory performance and correspond to excessive deflection, vibration and local deformation.

Limit states design refers to the calculations made by the designer to ensure that these failures do not occur

In the figure the loads are defined as the dead weight, wind, snow, temperature change, etc., which are expected to act on a structure during its projected life. They are generally specified in codes. Loads generally tend to cause failure, but sometimes they resist failure as in the case of dead weight holding a structure in place during a windstorm. For the ultimate limit states, the loads are multiplied by load factors which take into account the probability of deviations of the load from the value specified in the code. For example, dead weight is more predictable than wind or snow load so its load factor is closer to 1.0. When a load is combined with other loads, its load factor is decreased by means of a load combination factor to take into account the reduced probability of different loads acting simultaneously. Finally, the load factor may be adjusted by an importance factor to increase the safety of the structure when the consequences of failure are very severe and to decrease it when they are not. Nuclear containment structures, for example, are designed for much greater safety than storage sheds. All load factors for the serviceability limits states are made equal to 1.0 since these limit states relate to performance under normal use. Once the loads are factored, the designer then calculates forces or deformations within the structure. These calculations are based on a theory of structural behaviour which appropriately reflects the behaviour of the structure as the limit state is approached. For example, simple elastic theory, which takes into account shrinkage and creep, is appropriate for most structures for the serviceability limit states, whereas simple strength or stability theories are appropriate for most structures for the ultimate limit states. In the case of the ultimate limit states, the component forces obtained are then compared (Figure 2) with calculated component resistances. These resistances are determined by analyzing the strength of the component as a function of the material properties and dimensions specified in the design. A component may be a member, a connection or a material component in a composite structure, or it may be a mode of failure such as shear or compression. Resistance factors are applied to the component resistances and take into account the variability of material properties and dimensions, workmanship, type of failure, and uncertainty in the strength analysis. For example, the yielding of steel is more gradual and more predictable than the crushing of concrete; therefore, its resistance factor is closer to 1.0. The resistance factor may be further adjusted for certain members to take into account the importance of these members or the greater uncertainties involved in their application. Foundation piles, for example, are associated with greater uncertainties in application than columns in buildings. In the case of the serviceability limit states, a deflection, stress or acceleration due to the loads is compared (Figure 2) with an allowable deflection, stress or acceleration. The latter are based on user acceptability and specific requirements such as for the operation of equipment. In order to unify future structural codes and standards and to minimize their number and size, it is planned to adopt the following principle. The loads, load factors and main serviceability requirements depend only on the use of the structure and will therefore be given in the use codes (National Building Code, CSA Standards for bridges, towers, etc.). The resistances, resistance factors and structural theory depend only on the material and type of structure and will therefore be contained in the material design standards (CSA Standards for concrete, steel, etc.).

## Reliability

The load and resistance factors in the codes and standards are chosen to ensure a level of reliability (safety) consistent with the consequences of failure for a broad range of loads and materials. Methods for doing this are given in Reference (1). Instead of adopting the load and resistance factors stipulated in the codes, the designer may in some cases calculate the safety factor for an appropriate level of risk. This approach has recently been introduced in the evaluation of existing bridges, where a more precise estimate of strength and reliability is required as a result of the substantial increase in truck loads. The reliability of structures in service, however, depends not only on design safety factors but also on quality assurance procedures to counteract human error in the design, construction and use of the structure (2). Human error in structural design is most effectively counteracted by an adequate consideration of the way in which a structure behaves and the loads and influences it may be required to withstand (3).

## Advantages of Limit States Design

.1 The limit states provide a checklist of the basic structural requirements for which design calculations may be required.

2. Limit states design, by providing consistent safety and serviceability, ensures an economical use of materials and a wide range of applications.

3. Limit states design provides both a basic calculation tool for designing and evaluating civil engineering structures and a means for unifying structural codes and standards.