# Column stack and wall panel classification (column and wall:ACI 318)

## Slenderness ratio

**For columns:** The slenderness
ratio, k lu/r, of the restrained length (note: not necessarily the stack length – it
will be longer if there is no restraint at either end of the stack) about each axis
is calculated as follows:

(k lu/r)_{y} = k *lu_{y} /(√(l_{y} / A_{g}))

(k lu/r)_{z} = k* lu_{z}/(√(I_{z} / A_{g}))

where

slenderness ratio = k*lu/r

k is an effective length factor

lu_{y} is the unsupported column length in respect of major axis (y axis)

lu_{z} is the unsupported column length in respect of minor axis (z axis)

r_{y} is the radius of gyration of the column in the y-direction

r_{z} is the radius of gyration of the column in the z-direction

I_{y} is the second moment of area of the stack section about the major axis
(y axis)

I_{z} is the second moment of area of the stack section about the major axis
(z axis)

A_{g} is the cross-sectional area of the stack section

For unbraced columns

IF (k lu/r)_{y} ≤ 22

THEN slenderness can be neglected and column can be designed as short column

ELSE, column is considered as slender

IF (k lu/r)_{z} ≤ 22

THEN slenderness can be neglected and column can be designed as short column

ELSE, column is considered as slender

For braced columns

IF (k lu/r)_{y} ≤ MIN((34-12*M1/M2), 40)

THEN slenderness can be neglected and column can be designed as short column

ELSE, column is considered as slender

IF (k lu/r)_{z} ≤ MIN((34-12*M1/M2), 40)

THEN slenderness can be neglected and column can be designed as short column

ELSE, column is considered as slender

where

M1 = the smaller factored end moment on the column, to be taken as positive if member is bent in single curvature and negative if bent in double curvature

= MIN [ABS(M_{top}), ABS(M_{bot})]

M2 = the larger factored end moment on the column always taken as positive

= MAX [ABS(M_{top}), ABS(M_{bot})]