In the US the Standard Operating Procedure is this:
1. In major cities, the city will adopt a model building code. This is usually some version of the International Building Code (IBC)
2. Each version of the IBC has a reference section (Chapter 35) where it lists all of the external standards, codes and specifications for the various materials and topics.
3. Each of these references includes the particular year or edition of the document that is applicable.
4. One of these external references is the AISC steel specification and it will designate the applicable version/edition of the spec that is dependent on that code.
5. So for example - the IBC 2012 code might be adopted by a city. In Chapter 35 of that code is refers to AISC 360-10 as the governing steel specification. That is what you'd use.
Now having said all that, the building code is a minimum standard and an engineer is always OK to use whatever they'd like to use - providing they still meet that minimum standard.
In AISC's specification, they still equally maintain both ASD and LRFD - both based on a nominal strength. They no longer include general provisions for ASD (allowable STRESS design)
IN ACI for concrete - there is only LRFD as ACI has walked away from continued support of Allowable Stress Design. ASD used to be in the code, then moved to the appendix, then only included in a commentary referring back to an earlier version in ACI 318-99 I believe. Now it isn't included or mentioned at all as far as I know.
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