Advanced Package Training Scaffolding 2011.1 - Scia-Software GbR

Buckling Ratio
For the calculation of the buckling ratios, some approximate formulas are used. These formulas are
treated in the Theoretical Background (Ref.[32]).
The e following formulas are used for the buckling ratios:
• for a non sway structure :
( ρ1
ρ2
+ 5ρ1
+ 5ρ2
+ 24)( ρ1
ρ2
+ 4ρ1
+ 4 ρ2
+ 12)2
l/L =
(2ρ
ρ + 11ρ
+ 5ρ
+ 24)(2ρ
ρ + 5ρ
+ 11ρ
+ 24)
1
2
• for a sway structure :
l/L = x
1
π
+ 4
ρ x
1
2
with L the system length
2
E the modulus of Young
I the moment of inertia
Ci the stiffness in node I
Mi the moment in node I
Fi the rotation in node I
2
4ρ1
ρ2
+ π
x =
2
π ( ρ1
+ ρ2)
+ 8
C L
=
EI
i
ρ1
8ρ1
ρ
ρ i
Mi
Ci
=
φi The values for Mi and φi are approximately determined by the internal forces and the deformations,
calculated by load cases s which generate deformation forms, having an affinity with the buckling form.
The following load cases are considered :
- load case 1 : on the beams, the local distributed loads qy=1 N/m and qz= qz=-100 N/m are used,
on the columns the global distributed load loads s Qx = 10000 N/m and Qy =10000 N/m are used.
- load case 2 : on the beams, the local distributed loads qy= qy=-1 1 N/m and qz= qz=-100 N/m are used,
on the columns the global distributed loads Qx = -10000 10000 N/m and Qy= -10000 N/m are used.
The used approach gives good d results for frame structures with perpendicular rigid or semi semi-rigid beam
connections. For other cases, the user has to evaluate the presented bucking ratios.
Stability Check in Scia Engineer
Example
Scaffolding.esa
2
1
2
1
30
2
Advanced Training