ViaParadise
Structural
- Aug 22, 2024
- 7
Δδ
Currently reviewing a design where the intention is to use section H of the AISC for verification. The issue I have is that while i'm familiar with the equation itself (H1-1A), I can't understand exactly why the factor 8/9 is used. If there is a reference to how this number is derived somewhere and/or explained or if someone has a decent answer then I would greatly appreciate that.
My current understanding from trying to read through the commentary explanation is this:
δ: For a member subject to bending and axial force the member will deform a small delta, δ, along its length due to bending. As a result when evaluating the section where this δ occurs, the compression remains the same but due to δ caused by bending (or can it also include due to imperfections?) then additional moment is P*δ.
Δ: For the same member, as its ends deflect relative to one another (maybe because of a lateral force acting on the member) the end cross section furthest from the applied axial load is subject to a moment, P*Δ.
8/9: when calculating the utilization per H1-1A, we consider the axial and bending plastic capacity ignoring their interaction. I.e. pretend our beam-column is a beam for bending capacity and a column for axial capacity. Our demands, Pu and Mu, consider PΔ and Pδ already for both the Mu and Pu individually so we reduce the Mu demand to avoid double-counting. My question is where do we base that number 8/9 on assuming this is the reasoning?
Again, a bit confused with how exactly this equation and specifically that 8/9 factor is derived and the assumptions (and when those assumptions don't hold). Thanks to anyone who can help.
Currently reviewing a design where the intention is to use section H of the AISC for verification. The issue I have is that while i'm familiar with the equation itself (H1-1A), I can't understand exactly why the factor 8/9 is used. If there is a reference to how this number is derived somewhere and/or explained or if someone has a decent answer then I would greatly appreciate that.
My current understanding from trying to read through the commentary explanation is this:
δ: For a member subject to bending and axial force the member will deform a small delta, δ, along its length due to bending. As a result when evaluating the section where this δ occurs, the compression remains the same but due to δ caused by bending (or can it also include due to imperfections?) then additional moment is P*δ.
Δ: For the same member, as its ends deflect relative to one another (maybe because of a lateral force acting on the member) the end cross section furthest from the applied axial load is subject to a moment, P*Δ.
8/9: when calculating the utilization per H1-1A, we consider the axial and bending plastic capacity ignoring their interaction. I.e. pretend our beam-column is a beam for bending capacity and a column for axial capacity. Our demands, Pu and Mu, consider PΔ and Pδ already for both the Mu and Pu individually so we reduce the Mu demand to avoid double-counting. My question is where do we base that number 8/9 on assuming this is the reasoning?
Again, a bit confused with how exactly this equation and specifically that 8/9 factor is derived and the assumptions (and when those assumptions don't hold). Thanks to anyone who can help.
