Bases for ASD and LRFD

ASD is based on elastic theory. Design limits the maximum unit stress a member is permitted to bear under service loads to a level determined by a judgmental, but  experience-based, safety factor. Building codes establish allowable unit stresses, which are normally related to the minimum yield stress for each grade of steel.

Plastic design is based on the ultimate strength of members. A safety factor, comparable to that established for elastic design, is applied to the design load to determine the ultimate-load capacity required of a member.
LRFD is based on the concept that no applicable limit state should be exceeded when the structure, or any member or element, is subject to appropriate combinations of factored loads.
A limit state is defined as a condition in which a structure or structural component becomes unfit for further structural service. A structural member can have several limit states.
Strength limit states relate to maximum load-carrying capacity.
Serviceability limit states relate to performance under normal service conditions with respect to such factors as deflection and vibration.
Design specifications establish load factors to be applied to each type of service load, such as dead, live, and wind loads, the values of the factors depending on the specific combination of loads to be imposed on a structure (Art. 5.1.3).
The AISC Load and Resistance Factor Design Specification for Structural Steel Buildings requires that structures be designed so that, under the most critical combination of factored loads, the design strength of the structures or their individual elements is not exceeded. For each strength limit state, the design strength is the product of the nominal strength and a resistance factor , given in the specification.
Derived with the use of probability theory,  provides an extra margin of safety for the limit state being investigated. Nominal strength of a member depends  on its geometric properties, yield or ultimate strength, and type of loading to be resisted, such as tension, compression, or flexure.
The AISC LRFD specification permits structural analysis based on either elastic or plastic behavior. Elastic theory is most commonly used. Where plastic theory is used for complex structures, all possible mechanisms that may form in the structure should be investigated. The collapse mechanism is the one that requires the lightest load for collapse to occur.
Numerous computer programs for analysis and design of members or structures are available. If data input describing the structure and loading are accurate, most of these programs yield a quick and accurate design. For complex structures, care should be taken in use of computer programs to check the results to ensure that they are logical, since a critical input error may not be easily found. If a program can produce a plot of the configuration of the loaded structure based on the data input, the plot should be used as a check, inasmuch as omission of a member or other errors in connectivity data can be readily discerned from the plot.
(Plastic Design in Steel A Guide and Commentary, M & R No. 41, American Society of Civil Engineers.)

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