Buckling of Stiffened Panels 1
overall buckling vs plate buckling
PCCB Panel Collapse Combined Buckling
Various estimates have been developed to determine the minimum size
stiffener to insure the plate buckles while the stiffener remains straight. this
is equivalent to insuring that plate buckling occurs before overall buckling.
Timoshenko does so by calculating k in
σ
cr
k
π
2
D
⋅
b
2
t
⋅
⋅
:=
and observing the
value of
γ
which results in a critical stress above that which will cause plate
buckling alone.
where;
γ
flexural_rigidity_of_combined_section
flexural_rigidity_of_plate
:=
γ
EI
x
⋅
Db
⋅
:=
where;
I
x
is the inertia of the plate with the attached plate associated with individual
stiffener.
Bleich pg 365, 367, for plates with longitudinal stiffness determines minimum
γ
to insure the plate
buckles before the stiffener (overall buckling). unfortunately Bleich uses different ratios than
Hughes. Bleich uses B where Hughes uses b.
for the following:
α
a
B
:=
δ
A
x
Bt
⋅
:=
γ
x
⋅
DB
⋅
:=
α
0.1 0.2
,
10
..
:=
δ
0.1
:=
κ
1
α
n
,
()
n
π
α
⋅
4
α
⋅
n
1
+
⋅
:=
κ
2
α
n
,
n
π
α
⋅
4
α
⋅
n
1
−
⋅
:=
γ
o
αδ
,
n
,
16
π
2
α
n
3
⋅
1
κ
1
α
n
,
tanh
κ
1
α
n
,
2
⋅
1
κ
2
α
n
,
tan
κ
2
α
n
,
2
⋅
−
16
α
n
2
⋅δ
⋅
+
:=
γ
omax
,
max
γ
o
,
1
,
γ
o
,
2
,
γ
o
,
3
,
:=
05
1
0
0
20
40
γ
o
,
1
,
γ
o
,
2
,
γ
o
,
3
,
α
1
0
0
20
40
γ
omax
,
α
1