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)]