Detailed Analysis of Slenderness Ratio

 

Buckling about Strong Axis

1. different moduli  (e.g. glulams)

E_x
E_y

2. different unbraced lengths  (e.g. sheathed stud walls)

(l_e/d)_x  -  for buckling about strong x axis (column movement in y direction)
(l_e/d)_y  -  for buckling about weak y axis (column movement in x direction)

3. end conditions

 

 

Inflection Points

l_e = distance between inflection points = K_e l

- reverse in curvature
- zero moment
- acts like a pinned end

mirror image is drawn when only one inflection point is shown

textbook image

Column Number	1	2	3	4	5	6
Theoretical effective length factors	0.5	0.7	1.0	1.0	2.0	2.0
Recommended design Ke (NDS appendix G)	0.65	0.8	1.0	1.2	2.1	2.4

↓ K_e, ↓ l_e, ↑ F_cr

F_cr = π²E / (l_e/r)²

 

 

End Conditions

braced frame & shearwall  =  no sidesway  (conservative to use K_e = 1)

- ends are assumed pinned
- but square-cut ends do prevent some rotation
- accidental eccentricity due to nonuniform bearing

moment frame  =  sidesway