Buckling of s-ffened plates according to DNV RP C201
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Buckling of s-ffened plates according to DNV RP C201
Buckling of s-ffened plates
• Plates being part of a s-ffened panel are checked as effec-ve flange in the beam-‐column model. Addi-onal check of the plate alone is then not required
• Buckling checks of uns-ffened plates in are made according to the effec-ve width method
• Buckling check of plate not necessary if effec-ve width is ≈ s-ffener spacing i.e. σult ≈ σy
Buckling check not necessary Recommended Practice DNV–RP-C201, October 2002 Page 8
DET NORSKE VERITAS
Table 3-1 Reference table for buckling checks of plates
Description Load Sketch Clause reference
Limiting value
Unstiffened plate
Longitudinal compression
x,Sdx,Sd
- t -
l
s
! !
6.2 s < l Buckling check not necessary if
İ 42ts "
Unstiffened plate
Transverse compression
y,Sd
- t - s
l!
y,Sd!
6.3 s < l Buckling check not necessary if
5.4İts "
Unstiffened plate
Shear stress Sd
s - t -
l
#
6.4 s < l Buckling check not necessary if
İ70ts "
Unstiffened plate
Linear varying longitudinal compression
- t -
x,Sd!l
s
$ x,Sd!$
x,Sd! !x,Sd
6.6 s < l Buckling check not necessary if İ42
ts "
Unstiffened plate
Linear varying transverse compression
- t -
y,Sd!
l
sl1
6.8 s < l Buckling check not necessary if
5.4İts "
y235/fİ = İ = 1.0 for fy = 235 MPa İ = 0.814 for fy = 355 MPa
Recommended Practice DNV–RP-C201, October 2002 Page 8
DET NORSKE VERITAS
Table 3-1 Reference table for buckling checks of plates
Description Load Sketch Clause reference
Limiting value
Unstiffened plate
Longitudinal compression
x,Sdx,Sd
- t -
l
s
! !
6.2 s < l Buckling check not necessary if
İ 42ts "
Unstiffened plate
Transverse compression
y,Sd
- t - sl
!
y,Sd!
6.3 s < l Buckling check not necessary if
5.4İts "
Unstiffened plate
Shear stress Sd
s - t -
l
#
6.4 s < l Buckling check not necessary if
İ70ts "
Unstiffened plate
Linear varying longitudinal compression
- t -
x,Sd!l
s
$ x,Sd!$
x,Sd! !x,Sd
6.6 s < l Buckling check not necessary if İ42
ts "
Unstiffened plate
Linear varying transverse compression
- t -
y,Sd!
l
sl1
6.8 s < l Buckling check not necessary if
5.4İts "
y235/fİ = İ = 1.0 for fy = 235 MPa İ = 0.814 for fy = 355 MPa
Beam column model • S-ffener with associated effec-ve plate flange • Effec-ve width of plate flange accounts for biaxial
compression or compression-‐tension • Transverse stress and shear gives added lateral pressure
Tension field ac-on due to shear • Tension field allowed only if transverse stress is in tension
• The addi-onal strength has to be carried by the s-ffener-‐ hence added axial force
( )crgN stτ τ τ= −Buckling stress for plate without s4ffeners
Effective Width – long plate
ess= xuσ
yσ=
λ p − 0.22λ p
2 λ ≥ 0.673
1 λ ≤ 0.673
⎧
⎨⎪⎪
⎩⎪⎪
λ = 0.525 st
f y
E
Effective width, long plate
p
Effective Width – wide plate
l
Coulumn parts
Plate partσy
pyyy
Ry, kffEt3.11κ
fEt3.1 ⋅⋅
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟
⎠
⎞⎜⎜
⎝
⎛⋅⋅−⋅+⋅⋅=
llσ
0kbut ,st2
fp
h0.1k
otherwise
fst2p for 1.0 k
p
2
y
Sdαp
y
2
Sdp
≥⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞⎜
⎝⎛⋅−⋅−=
⋅⎟⎠⎞⎜
⎝⎛⋅≤=
The kp factor accounts for reduction in strength due to lateral load
8
Effect of lateral pressure on buckling strength
• Since the deformation from lateral load is in the general case different from the buckling shape for longitudinal compression the interaction effect from lateral load is negligible
• Lateral load continuous over several plate-fields will lead to clamped condition and the effect on transverse compression strength will therefore only be of significance for large lateral load
Effective Width – bi-axial compression
se
σ 'xuxuσ
⎛⎝⎜
⎞⎠⎟2
− c1σ 'xu
xuσyσyuσ+ yσ
yuσ⎛⎝⎜
⎞⎠⎟+ τ
τY
⎛⎝⎜
⎞⎠⎟
2
≤1c1 =1−
s / t120
c1 = 0 for s / t >120
e1sse
=σ xu1
σ xu
⎛
⎝⎜⎞
⎠⎟= 1−
σ y
σ yu
⎛
⎝⎜
⎞
⎠⎟
2
+ c1
σ x
σ xu
⎛
⎝⎜⎞
⎠⎟σ y
σ yu
⎛
⎝⎜
⎞
⎠⎟ −
Solve for effec-ve width
Lateral pressure due to transverse stress
• Elas-c buckling of transversely s-ffened panels
• Bending stress for uniform lateral pressure
• Calibrate bending stress so that it is equal to yield stress when transverse stress equal to buckling stress
2 22
2G G
syEG
L LD mit L m m
πσ⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥= + +⎜ ⎟ ⎜ ⎟⎝ ⎠⎢ ⎥⎝ ⎠⎣ ⎦
ll ll
2
3 222 1 1
/12(1 )s
yEI sD
t tπσ
ν⎛ ⎞
= + +⎜ ⎟⎜ ⎟−⎝ ⎠l
2
2
1212
s bb
s
Wps pW s
σσ = ⇒ =ll
2
12y
s Yy
yE
Wpsσσ σσ
=l
23
13.310.92 1 1
y
s Yy
s
WpI Et s
t s
σσ σ=
⎛ ⎞+ +⎜ ⎟
⎝ ⎠
Column buckling • Perry Robertson ini-al yield formula
• Solve for cri-cal stress
• Equivalent imperfec-on to match w0=0.0015"
xcrσYσ+ xcrσ
1− xcrσEσ
eqw AYσ W
= 1
crσYσ=
1+ µ + λ 2 − 1+ µ + λ 2( )2 − 4λ 2
2λ 2
µ = eqw A
W= 0.34 + 0.08
zp
ie
⎛
⎝⎜
⎞
⎠⎟ λ − 0.2( )
µ = eqw A
W= 0.34 + 0.08
zt
ie
⎛
⎝⎜⎞
⎠⎟λ − 0.2( )
Column buckling
• Buckling length con-nuous func-on of lateral pressure
• Fully clamped when lateral pressure gives yield at support
1 0.5eY
pp
⎛ ⎞= −⎜ ⎟
⎝ ⎠l l
2
12 YY
Wpsσ=
l
Failure of s-ffened panel
• Two modes – Combined axial compression and bending on the compression side (Here: 1 and 4)
– Combined axial compression and bending failure on the tension side (Here 2 and 3)
Failure of s-ffened panel • Combined axial compression and bending on the compression
side (Here: 1 and 4) 2*
11cr u
crE
N M NzN NM
N
ττ⎛ ⎞±+ + =⎜ ⎟⎛ ⎞ ⎝ ⎠−⎜ ⎟
⎝ ⎠
2
2
1 stiffner supports121 mid span24
M q
M q
=
=
l
l
Shear term omi[ed if tension field allowed
Failure of s-ffened panel – Combined axial compression and bending failure on the tension side (Here 2 and 3)
2
2
1 stiffner supports121 mid span24
M q
M q
=
=
l
l
NNcr
− NNY
⎛
⎝⎜⎞
⎠⎟
utilizatio wrt buckling
+ M ± Nz*
Mcr 1− NNE
⎛
⎝⎜⎞
⎠⎟
− NNY
⎡
⎣
⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥
utilization wrt yielding
+ ττ u
⎛
⎝⎜⎞
⎠⎟
2
=1
Shear term omi[ed if tension field allowed
Failure of s-ffened panel – U-lisa-on depends on the z* factor. The op-mal u-lisa-on is the minimum value of the maximum all UF
– The op-mum is typically obtained when the failure criterion is met at support and mid span simultaneously
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