Moment Magnification Question

[mchen96]

Hi,

I have a question regarding an inconsistency between the AASHTO LRFD and the ACI moment magnification equations.

When calculating the critical buckling load P_c (ACI 318-14 Eq. 6.6.4.4.2 / AASHTO LRFD-2017 4.5.3.2.2b-5), one has to calculate an effective EI. To account for creep effects when calculating the effective EI, both the AASHTO and the ACI equations incorporate the factor β_d, which relates the ratio of the sustained loads to the maximum loads.

That being said, there is an inconsistency in the definition of β_d between both codes.

ACI 318-14 6.6.4.4.4. defines β_dns as the ratio between the sustained axial load and the maximum axial load.
AASHTO LRFD-2017 5.6.4.3 defines β_d as the ratio between the sustained moment and the maximum moment.

Anyone knows how the equation was derived and/or which formulation is more accurate?

I have a hunch that the AASHTO equation is probably more accurate, since I would tend to think that the lateral deflections due to the sustained moments are a lot more significant when trying to identify second order effects. However, I haven't found the original derivation of that equation and I'm curious about what others may say.

 

[BridgeSmith]

The AASHTO spec provisions are for columns which have low axial load and high moment, thus the reason use the relationship between moments. Don't know about ACI, but I suspect it's written for columns where the axial load is high.

 

[rapt]

The design axial load and moment for biaxial calculations should come from the same load combination, so the ratio would be the same for both.

But as mentioned above,if axial was very small or even 0, it may be better to use the moment ratio.