Design Moment Calculations (column and wall: ACI 318)
For each combination and for each analysis model (Building Analysis, Grillage Analysis, FE Analysis) the end moments about the two local member axes, 'major' and 'minor' are established. From these and the local load profile, the moments and axial force at any position in the member can be established. These moments will be from a first-order or second-order analysis at user choice - (in making the choice, the value of the 'stability index', Q should be taken into account).
Note that M2 and M1 are the end moments with M2 being the larger numeric value.
Step 1, minimum moment
Calculate the minimum moment due to non-concentric axial force in each of the two directions from,
| Mmin |
|
Pu*(0.6+0.03*h)] in |
|
|
Pu*(15+0.03*h)] mm |
|
| h |
|
The major dimension of the column in the direction under consideration |
| Pu |
|
The max compression force at any design position in the stack under consideration. If stack is in tension set to zero |
Step 2 - member slenderness
It is determined whether the member is slender or not. Note that in the determination for braced columns M1 and M2 are always the end moments even if lateral loading is present.
Step 3 - non-slender column
Calculate the design moment at the top, bottom and mid-fifth of the column in each direction taking into account if lateral loads are “significant”, or “not significant”.
As the column is non-slender no further calculations are required to establish design moments.
Step 4 - slender member amplifier
Calculate the “amplifier” due to buckling about each of the major and minor axes excluding the uniform moment factor which is dealt with separately,
| kns |
|
1/(1 - (Pu / (0.75*Pc))) ≥ zero |
| Pc |
|
The critical buckling load | |
|
π²*(EI)/(k*lu)² | ||
where EI can be computed by Eq. (10-14) or Eq (10-15)
Step 5 - uniform moment factor
For lateral loads that are “not significant”,
| Cm |
|
0.6 + 0.4 *(M1 / M2) |
|
Else
| Cm |
|
1.0 | ||
Step 6 - moment magnifier
Calculate the moment magnifier from Equ. 10.12 as,
| dns |
|
MAX [Cm * kns, 1.0] |
Step 7 - amplified minimum moment
Calculate the amplified minimum moment as,
| Mmin_amp |
|
Mmin * kns |
Step 8 - design moments
Calculate the design moment at the top, bottom and mid-fifth of the column in each direction taking into account if lateral loads are “significant”, or “not significant”.