Limit state design
Encyclopedia
Limit state design 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 refers 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.
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. 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 structure and ensuring the functionality of the structure.
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. Whereas Magnification Factor is used for the loads, and Reduction Factor for the resistance of members. 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 "Magnified" loads are less than their factored "Reduced" resistance.
s, 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.)
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
:
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
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 Europe, structures are designed to conform with the Eurocode
s: 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.
(AISC) is now issuing a combined manual of steel construction (the 2005 manual) that contains two methods of design side by side (newly named ASD - Allowable Strength Design
, (not to be confused with 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 former 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.
Structural engineering
Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....
. 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
Structural load
Structural loads or actions are forces, deformations or accelerations applied to a structure or its components.Loads cause stresses, deformations and displacements in structures. Assessment of their effects is carried out by the methods of structural analysis...
or other actions on the structure, while the criteria refers 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
Reliability engineering
Reliability engineering is an engineering field, that deals with the study, evaluation, and life-cycle management of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time. It is often measured as a probability of...
for each limit state. Building codes based on LSD implicitly define the appropriate levels of reliability by their prescriptions.
Criteria
Limit state designDesign
Design as a noun informally refers to a plan or convention for the construction of an object or a system while “to design” refers to making this plan...
requires the structure
Structure
Structure is a fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities. This notion may itself be an object, such as a built structure, or an attribute, such as the structure of society...
to satisfy two principal criteria: the ultimate limit state (ULS) and the serviceability limit state (SLS).
Any design process involves a number of assumptions. The load
Structural load
Structural loads or actions are forces, deformations or accelerations applied to a structure or its components.Loads cause stresses, deformations and displacements in structures. Assessment of their effects is carried out by the methods of structural analysis...
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 structure and ensuring the functionality of the structure.
Ultimate Limit State
To satisfy the ultimate limit state, the structure must not collapse when subjected to the peak design loadDesign load
In a general sense, the design load is the maximum amount of something a system is designed to handle or the maximum amount of something that the system can produce, which are very different meanings. For example, a crane with a design load of 20 tons is designed to be able to lift loads that weigh...
for which it was designed. A structure is deemed to satisfy the ultimate limit state criteria if all factored bending
Bending
In engineering mechanics, bending characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically...
, shear
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
and tensile or compressive stresses are below the factored resistance calculated for the section under consideration. Whereas Magnification Factor is used for the loads, and Reduction Factor for the resistance of members. 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
Beam (structure)
A beam is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment.- Overview...
or a column
Column
A column or pillar in architecture and structural engineering is a vertical structural element that transmits, through compression, the weight of the structure above to other structural elements below. For the purpose of wind or earthquake engineering, columns may be designed to resist lateral forces...
or other load bearing element, such as walls) is shown to be safe when the factored "Magnified" loads are less than their factored "Reduced" resistance.
Serviceability 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 codeBuilding code
A building code, or building control, is a set of rules that specify the minimum acceptable level of safety for constructed objects such as buildings and nonbuilding structures. The main purpose of building codes are to protect public health, safety and general welfare as they relate to the...
s, 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
Concrete
Concrete is a composite construction material, composed of cement and other cementitious materials such as fly ash and slag cement, aggregate , water and chemical admixtures.The word concrete comes from the Latin word...
, 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
Structural failure
Structural failure refers to loss of the load-carrying capacity of a component or member within a structure or of the structure itself. Structural failure is initiated when the material is stressed to its strength limit, thus causing fracture or excessive deformations...
. The purpose of SLS requirements is to ensure that people in the structure are not unnerved by large deflections of the floor
Floor
A floor is the walking surface of a room or vehicle. Floors vary from simple dirt in a cave to many-layered surfaces using modern technology...
, vibration caused by walking, sickened by excessive swaying of the building during high winds, or by a bridge
Bridge
A bridge is a structure built to span physical obstacles such as a body of water, valley, or road, for the purpose of providing passage over the obstacle...
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 CanadaNational Building Code of Canada
The National Building Code of Canada is the model building code of Canada. It is issued by the Institute for Research In Construction ], a part of the National Research Council 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 designPermissible stress design
Permissible stress design is a design philosophy used by civil engineers. The designer ensures that the stresses developed in a structure due to service loads do not exceed the elastic limit...
in most forms of civil engineering
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...
. Notable exceptions are geotechnical engineering
Geotechnical engineering
Geotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but is also used by military, mining, petroleum, or any other engineering concerned with construction on or in the ground...
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 Europe, structures are designed to conform with the Eurocode
Eurocode
Eurocodes are a set of harmonized technical rules developed by the European Committee for Standardisation for the structural design of construction works in the European Union.The purposes of the Eurocodes are:...
s: Steel
Steel
Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...
structures are designed in accordance with EN 1993
EN 1993
EN 1993 - Eurocode 3: Design of steel structures, is the part of the European building code that deals with the design of steel structures, using the limit state design philosophy...
, and reinforced concrete
Reinforced concrete
Reinforced concrete is concrete in which reinforcement bars , reinforcement grids, plates or fibers have been incorporated to strengthen the concrete in tension. It was invented by French gardener Joseph Monier in 1849 and patented in 1867. The term Ferro Concrete refers only to concrete that is...
structures to EN 1992
EN 1992
EN 1992, also known as Eurocode 2: Design of concrete structures, is the European Standard for the design of concrete structures, using the limit state design philosophy...
. 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.
Limit State Design in the United States
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 ConstructionAmerican Institute of Steel Construction
The American Institute of Steel Construction, often abbreviated AISC, is a not-for-profit technical institute and trade association for the use of structural steel in the construction industry of the United States. It is headquartered in Chicago, IL. Their mission is to make structural steel the...
(AISC) is now issuing a combined manual of steel construction (the 2005 manual) that contains two methods of design side by side (newly named ASD - Allowable Strength Design
Allowable strength design
Allowable Strength Design is a term used by the American Institute of Steel Construction in the 13th Edition of the Manual of Steel Construction...
, (not to be confused with 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 former 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.
See also
- Structural engineeringStructural engineeringStructural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....
- Allowable stress design
- Probabilistic designProbabilistic designProbabilistic design is a discipline within engineering design. It deals primarily with the consideration of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects are related to quality and reliability...
- Seismic performance