These attached figures are captured from Concrete Frame Design Manual using ACI-318 attached with Etabs Design examples.
It calculates the amplified moment due to second order effects using this equation:
M=deltans* (Mnonsawy+deltas*Msway)
, not by the equation proved in all stability books
M=deltans*Mnonsawy+deltas*Msway
I tried a design example in Etabs to verify this and I found that it does use the first equation.
Dear Khaled:
ACI 318 allows second-order moments for slender columns to be calculated using moment magnifiers, and specific formulas for the magnifiers are offered for non-sway and sway columns. These magnifiers, however, are approximations that tend to overestimate the second-order moments. Therefore, ACI also allows second-order moments to be computed using 'exact' analysis procedures that are based on large-displacement theory, and consider either elastic or non-linear material properties. This computation is what Etabs and other computer software use for second-order moments. However, care must be exercised when modeling columns using such software because ACI 318 requires that the analysis also "consider section properties determined taking into account the influence of axial loads, the presence of cracked regions along the length of the member, and the effects of load duration."
I hope that this information helps you.
Sincerely,
Arturo
Thank you so much Dr. Arturo E Schultz for your answer. But, if I want to implement these magnifiers in my manual design, which equation ACI 318 follows:
M=deltans* (Mnonsawy+deltas*Msway)
or
M=deltans*Mnonsawy+deltas*Msway
Dear Khaled:
For the case of a non-sway column (i.e. braced), use
M=deltans*(Mnonsway)
For the case of a sway column (i.e. unbraced) use
M=deltans*Mnonsway + deltasway*Msway
The first formula you listed is no longer used.
Arturo
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