Does anyone know why (in the green book) that in order to get the number of studs for 100% composite action you find the smaller of 0.85f'cAc/2 and FyAs/2?? Why are they both divided by 2? This makes a pretty big difference in the % of composite action you get for a given number of studs (you get a much higher % composite for a given number of studs compared to the 13th ed spec) or the the number of studs needed for a given % of composite action (you can use fewer studs to gain a specific % of composite action compared to the 13th ed spec). This obviously makes a difference in deflection calcs as well.
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Another composite question
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I initially thought it had something to do with half the studs on each side of the point of max moment, but that's not the case. The full shear has to be resisted on each side of the point of max moment. That full shear is either 0.85f'cAc or FyAs (for full composite action).
I think haynewp and miecz are correct. When I was comparing the values from the green book and the black book before I was adding in the 0.6 Rpg factor for the black book and not doing the corresponding reduction for the green book. The ratio of ultimate shear stud value (AsFu) to the allowable out of the green book (for f'c>4ksi - when the stud actually controls) is 2.15, which is greater than the factor that AsFy (or 0.85f'cAc) is divided by (2). This makes more sense.
Thanks all.
I initially thought it had something to do with half the studs on each side of the point of max moment, but that's not the case. The full shear has to be resisted on each side of the point of max moment. That full shear is either 0.85f'cAc or FyAs (for full composite action).
I think haynewp and miecz are correct. When I was comparing the values from the green book and the black book before I was adding in the 0.6 Rpg factor for the black book and not doing the corresponding reduction for the green book. The ratio of ultimate shear stud value (AsFu) to the allowable out of the green book (for f'c>4ksi - when the stud actually controls) is 2.15, which is greater than the factor that AsFy (or 0.85f'cAc) is divided by (2). This makes more sense.
Thanks all.
Yes, I think I am the one who is confused, which is not surprising. Where I became muddled was that I looked up the formulas in the 8th edition of AISC, which was allowable stress design, but forgot that composite design at that stage used USD approaches to agree with ACI.
You guys made me doubt, so I looked it up in S&J, 2nd Edition, which says:
"It may be noted that the connection and the beam must resist the same ultimate load. However, under service loads the beam resists dead and live loads, but unless shores are used the connectors resist essentially only the live load. Working stress method might design the connection only for live load; however, an increased factor of safety should be used, since ultimate capacity would otherwise be inadequate.
AISC-1.11 uses an ultimate strength concept but converts both the forces to be designed for and the connector capacities into the service load range by dividing them by a factor. The loads to be carried, either Eq. 16.8.2 or Eq. 16.8.3, are divided by a nominal factor of 2."
S&J goes on to say that the "connector ultimate capacities must also be divided by factors to give "allowable values" for working stress method." This factor is also about 2.0.
Requires a bit of reading to get your head around it.
You guys made me doubt, so I looked it up in S&J, 2nd Edition, which says:
"It may be noted that the connection and the beam must resist the same ultimate load. However, under service loads the beam resists dead and live loads, but unless shores are used the connectors resist essentially only the live load. Working stress method might design the connection only for live load; however, an increased factor of safety should be used, since ultimate capacity would otherwise be inadequate.
AISC-1.11 uses an ultimate strength concept but converts both the forces to be designed for and the connector capacities into the service load range by dividing them by a factor. The loads to be carried, either Eq. 16.8.2 or Eq. 16.8.3, are divided by a nominal factor of 2."
S&J goes on to say that the "connector ultimate capacities must also be divided by factors to give "allowable values" for working stress method." This factor is also about 2.0.
Requires a bit of reading to get your head around it.
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