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 *luy /(√(ly / Ag))
(k lu/r)z = k* luz/(√(Iz / Ag))
where
slenderness ratio = k*lu/r
k is an effective length factor
luy is the unsupported column length in respect of major axis (y axis)
luz is the unsupported column length in respect of minor axis (z axis)
ry is the radius of gyration of the column in the y-direction
rz is the radius of gyration of the column in the z-direction
Iy is the second moment of area of the stack section about the major axis (y axis)
Iz is the second moment of area of the stack section about the major axis (z axis)
Ag 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(Mtop), ABS(Mbot)]
M2 = the larger factored end moment on the column always taken as positive
= MAX [ABS(Mtop), ABS(Mbot)]