AISC LRFD 1.pdf

Comm. A5.] DESIGN BASIS 175( )bsln( / )» b V + V £ 1n R / Q2 2R Q R Q m m(C-A5-2)In this equation, the standard deviation has been replaced by the approximation2 2VR+ VQ, whereVR =σ R / RmandVQ =σ Q / Qm( R and Q are the standard deviations,R m and Q m are the mean values, V R and V Q are the coefficients of variation,respectively, of the resistance R and the load effect Q). For structural elements andthe usual loading, R m , Q m , and the coefficients of variation, V R and V Q , can be estimated,so a calculation ofb( R Q )1nm/=V + Vm2 2R Q(C-A5-3)will give a comparative value of the measure of reliability of a structure or component.The description of the determination of as given above is a simple way of definingthe probabilistic method used in the development of LRFD. A more refinedmethod, which can accommodate more complex design situations (such as thebeam-column interaction equation) and include probabilistic distributions otherthan the lognormal distribution used to derive Equation C-A5-3, has been developedsince the publication of Ravindra and Galambos (1978), and is fully describedin Galambos, Ellingwood, MacGregor, and Cornell (1982). This latter method hasbeen used in the development of the recommended load combinations in ASCE 7.The two methods give essentially the same values for most steel structural membersand connections.Statistical properties (mean values and coefficients of variations) are presented forthe basic material properties and for steel beams, columns, composite beams, plategirders, beam-columns, and connection elements in a series of eight articles in theSeptember 1978 issue of the Journal of the Structural Division of ASCE (Vol. 104,ST9). The corresponding load statistics are given in Galambos, et al. (1982). Basedon these statistics, the values of inherent in the 1978 edition of the AISC ASDSpecification were evaluated under different load combinations (live/dead,wind/dead, etc.), and for various tributary areas for typical members (beams, columns,beam-columns, structural components, etc.). As might be expected, therewas a considerable variation in the range of values. Examination of the many values associated with ASD revealed certain trends. For example, compact rolledbeams (flexure) and tension members (yielding) had values that decreased fromabout 3.1 at L/D = 0.50 to 2.4 at L/D = 4. This decrease is a result of ASD applyingthe same factor to dead load, which is relatively predictable, and live load, which ismore variable. For bolted or welded connections, was on the order of 4 to 5. Reliabilityindices for load combinations involving wind and earthquake loads tendedto be lower. Based on a thorough assessment of implied reliabilities in existingacceptable design practice, common load factors for various structural materials(steel, reinforced concrete, etc.) were developed in Ellingwood et al. (1982).One of the features of the probability-based method used in the development ofLRFD is that the variations of values can be reduced by specifying several“target” values and selecting multiple load and resistance factors to meet thesetargets. The Committee on Specifications set the point at which LRFD is calibratedLRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION