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AASHTO 3.24.4

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>Can anyone explain to me why shear and bond need not be checked per AASHTO
>3.24.4, if bending moment demand is based on 3.24.3?

The sections you are referring to are for bridge deck design per the Standard Specifications for Highway Bridges. My mentors have informed me over the years that, in bridge decks, tests have shown that moment typically (always?) controls, even though classical design approaches may indicate the deck designed in accordance for moment will not satisfy shear requirements.
Furthermore, I have seen literature that cites an "approximate overall safety factor" based on laboratory tests for bridge decks designed under the Standard Specification in excess of 10. Hence the reason for a substantial change in the newer LRFD Bridge Design Specification which introduces the "empirical deck design method" for decks which uses significantly less reinforcing (and effort on the designer's part). The same literature shows an overall safety factor of 8 for decks designed under the empirical method. The only drawback to the method is that only it may be used if certain guidelines are met which coincide with the scope of available test data.
Thus, my experience with traditional deck design is that the serviceability of the deck is harder to ensure than strength (i.e. using proper concrete cover and limiting cracking), though both are equally important and need to be satisfied.
Hope this helps,
Chad Edward Grinsteiner
White Engineering Associates, Inc.
Oklahoma City, Oklahoma
P.S. - My apologies to the LRFD purists who object to the reference of overall safety factors. I do not intend more ASD-LRFD discussions. :-)