# 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,

` `

M_{min} = Pu*(0.6+0.03*h)] in

(US units)

` `

M_{min} = Pu*(15+0.03*h)] mm

(metric units)

` `

where

h = The major dimension of the column in the direction under consideration

P_{u} = 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,

` `

k_{ns} = 1 / (1 - (P_{u} / (0.75 * P_{c}))) ≥ zero

` `

where

P_{c} = The critical buckling load = π² * (EI) / (k*l_{u})²

EI can be computed by Eq. (10-14) or Eq (10-15)

## Step 5 - uniform moment factor

For lateral loads that are “not significant”,

` `

C_{m} = 0.6 + 0.4 *(M1 / M2)

(retaining moment signs)

` `

Else

C_{m} = 1.0

## Step 6 - moment magnifier

Calculate the moment magnifier from Equ. 10.12 as,

` `

d_{ns} = MAX [C_{m} * k_{ns}, 1.0]

## Step 7 - amplified minimum moment

Calculate the amplified minimum moment as,

` `

M_{min_amp} = M_{min} * k_{ns}

## 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”.