Corrugated BHD

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Marine Structures 18 (2005) 548–565

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Buckling strength assessment of corrugated panelsin offshore structures

Hai-Hong Sun�, Jack Spencer

American Bureau of Shipping, 16855 Northchase Dr., Houston, TX 77060, USA

Received 1 July 2005; received in revised form 6 November 2005; accepted 8 December 2005

Abstract

There is an increasing trend of living quarters in offshore structures being constructed using

corrugated panels in order to save construction time and cost. Different from corrugated bulkheads

in ship structures, the corrugated panels used in the living quarters are designed in triangular or

trapezoidal profile with unequal flanges and with a corrugation angle between 451 and 901. Industry

needs have prompted the American Bureau of Shipping to develop design recommendations for the

buckling strength assessment of these corrugated panels. This paper describes the main features and

the principles of the recommendations based on ABS experience, along with the technical

background. The modeling uncertainty associated with the recommended criteria has been

established by comparing the predictions with laboratory tests and finite element analysis results.

Two design examples are provided to demonstrate the application of the recommendations.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Corrugated panels; Buckling strength; Structural design criteria; Finite element analysis

1. Introduction

Corrugated panels are self-stiffened and are usually corrugated in one direction. Theymay act as watertight bulkheads supported by stools in ship structures, or employed ascorrugated shear diaphragms in civil engineering structures when connected with fasteners.Recently, these structures have been applied to construct the living quarters in offshorestructures due to their advantages of easy acquisition and low construction cost. The

see front matter r 2006 Elsevier Ltd. All rights reserved.

.marstruc.2005.12.002

nding author. Tel.: +1 281 877 6317; fax: +1 281 877 5820.

dress: [email protected] (H.-H. Sun).

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z

y

x

B

l

b

a

Fig. 1. Typical corrugated panel in living quarters.

z0

t

t

c

a

d φ

b

z

y

s

Centroid

Fig. 2. Cross section profile.

H.-H. Sun, J. Spencer / Marine Structures 18 (2005) 548–565 549

geometry and cross section of a corrugated panel are depicted in Figs. 1 and 2. Thecorrugated panels are typically of triangular profile (a ¼ 0) or trapezoidal profile withunequal flanges (aab) and corrugation angle,f, between 451 and 901. The bucklingstrength assessment criteria for corrugated bulkheads in ship rules [1], which have thelimits of corrugation angle greater than 571 and trapezoidal profile with equal flangescannot be directly applied to the corrugated panels used in living quarters.

It has been recognized that the buckling failure modes of a stiffened panel can becategorized at three levels, which are (1) local face/web plate buckling, (2) unit corrugationbuckling, and (3) entire corrugation buckling. Unlike stiffened flat panels, corrugatedpanels will collapse immediately upon reaching any one of these three buckling levels.

This paper describes the main features and the principles of the ABS recommendationsand presents the technical background. The modeling errors associated with therecommended criteria have been established by comparing the predictions with laboratorytest and FE analysis results. Two design examples are provided to demonstrate theapplication of the ABS recommendations.

2. Technical background

The pioneering work on the buckling strength of corrugated panels subjected to lateralpressure was given by Caldwell [2]. He carried out an extensive theoretical and

ARTICLE IN PRESSH.-H. Sun, J. Spencer / Marine Structures 18 (2005) 548–565550

experimental study to develop a rational design formula, which can be written as

sEðBÞ ¼ kf

E

12ð1� n2Þtf

a

� �2¼ kw

E

12ð1� n2Þtw

c

� �2, (1)

where E and n are the elastic modulus and Poisson’s ratio; tf and tw are the thickness of theflange and web plates; a and c are the width of the flange and web plates. kf and kw are thebuckling coefficients of flange and web of unit corrugation, respectively, as given in Fig. 3.This equation was derived by replacing the web of width c by a reduced web of width gc

and treating the problem as one of uniform compression of both web and flange, where g isthe reduction factor determined by experiment.Caldwell [2] also performed three series of tests: corrugated panels under four points

bending, single corrugations under four points bending, and corrugated panels underlateral pressure. The corrugation angle of the test specimen was in the range from 41.51 to61.91. These tests indicated that the formulae developed for simple loading conditionscould safely be applied to practical bulkhead problems, and therefore constitute a usefulbasis for design. These tests also indicated that each trough of width s in a corrugatedbulkhead deforms similarly under a similar distribution of pressure, and so the behavior ofa single central corrugation can be taken as representative of the whole bulkhead, providedthat the end conditions of each trough are the same. In ABS SVR [1], the single centralcorrugation is called a ‘‘unit corrugation’’ for clarity.ABS SVR [1] adopted Caldwell’s equation to calculate the elastic bending buckling

stress of corrugated bulkheads and the buckling coefficient, kf , is analytically expressed by

kf ¼ ½7:65� 0:26ðc=aÞ2�2. (2)

Caldwell Experiments

: kf : kw

0 1.0 2.0

4

8

12

16

kf

kw

k f, k

w

a/c

Fig. 3. Buckling coefficients.

ARTICLE IN PRESSH.-H. Sun, J. Spencer / Marine Structures 18 (2005) 548–565 551

The critical buckling stress is written by (Johnson–Ostenfeld plasticity correction)

sCðBÞ ¼

sEðBÞ for sEðBÞpPrs0;

s0 1� Prð1� PrÞs0

sEðBÞ

h ifor sEðBÞ4Prs0;

8<: (3)

where Pr is the proportional linear elastic limit of the structure, and s0is the specified

minimum yield point.A series of collapse tests on single corrugation models subjected to axial compression

and uniform water pressure was undertaken by Nagai [3] to examine the buckling behaviorof corrugated bulkheads under axial compression and hydrostatic pressure. He alsoderived the buckling strength formulations based on a simplified effective web widthapproach. The tests results agreed with the theoretical solutions.

Paik et al. [4] studied the collapse behavior of steel corrugated bulkheads. Theydeveloped a simple analytical formulation for ultimate bending strength used in the designof corrugated bulkheads under static lateral pressure, which is given by

Mu ¼ s0Af gþ s0Aw sin fg2

dþ suAw sin f

ðd � gÞ2

dþ suAf ðd � gÞ, (4)

where Af and Aw are the section area of corrugation flange and web plates, respectively; g

is the final neutral axis at ultimate limit state; su is the ultimate compressive stress of thecorrugation flange accounting for buckling. This formulation was based on the assumptionthat the entire material in compression of the corrugation reaches its ultimate strengthwhile the material in tension is in full yielding. They carried out collapse tests on nine mildsteel corrugated panels having five bays of corrugation. By comparing the theoreticalsolution with the experimental results, the proposed formula was confirmed to be withinengineering accuracy.

Caldwell’s formula is widely accepted by various classification societies for theassessment of corrugated bulkheads under lateral pressure. However, this formula islimited to a trapezoidal profile with equal flanges (i.e., a ¼ b). Caldwell’s formula shouldbe extended when corrugated panels with triangular (a ¼ 0) or trapezoidal profile withunequal flanges (aab) are analyzed, which is described in Section 4.

Bergmann and Reissner [5] calculated the buckling stress in shear of rectangularcorrugated panels, treating them as plates having different flexural rigidities in twoperpendicular directions. They proposed the formula

tE ¼ 4lD3=4

x D1=4y

tl2, (5)

where Dx and Dy are the equivalent bending stiffness per unit length of the panel. l is amultiplier dependent upon

y ¼ 2ðDxDyÞ

1=2

Dxy

and j ¼B

l

Dy

Dx

� �1=2

. (6)

The dependence of l on y and j is given in tabulated form of curves by Timoshenko andGere [6]

Easley [7] discussed the formulas for the elastic buckling loads of light-gage corrugatedpanels. He found that if Dx is much larger than Dy, and l/B is small, the coefficient 4l is


approximately equal to 3:65p2. This formula is in fair agreement with his experimentalresults and has also been verified by finite element analysis (FEA).

3. Design criteria

This section includes recommended design criteria for the corrugated panels.

3.1. Local plate buckling

The following limit state is recommended for the buckling strength assessment forindividual flange or web plate [8]:

sxmax

ZsCx

� �2

þsymax

ZsCy

� �2

þt

ZtC

� �2

p1, (7)

where sxmax and symax are the maximum compressive stresses in corrugation and transversedirections, respectively; t is the in-plane shear stress; sCx and sCy are the critical bucklingstresses in corrugation and transverse directions; and tC is the critical buckling stress foredge shear. The critical buckling stresses are provided in Appendix A. Z is the allowablestrength utilization factor, which are defined based on load conditions representing alloperation modes of offshore structures. Two primary load conditions to be considered inoffshore structures are [9,10]:

(i)
Normal operations: Stresses due to operating environmental loading combined withdead and maximum live loads appropriate to the function and operations of thestructure. For this loading condition, the allowable strength utilization factor is takenas 0.6.
(ii)
Severe storm: Stresses due to design environmental loading combined with dead andlive loads appropriate to the function and operations of the structure during the designenvironmental condition. For this loading condition, the allowable strength utilizationfactor is taken as 0.8.
3.2. Unit corrugation buckling

The limit state recommended for unit corrugation is given by [8]

sa

ZsCðAÞ

þCmsb

ZsCðBÞ½1� sa=ðZsEðCÞÞ�p1, (8)

where sa is the axial compressive stress of the unit corrugation; Cm is the bending momentfactor determined by rational analysis, which may be taken as 1.5 for a panel whose endsare simply supported; Z is the allowable strength utilization factor as defined in Section 3.1;and sb is the bending stress along the unit corrugation due to lateral pressure, which iscalculated by

�
For the lateral pressure applied toward the upper flange as shown in Fig. 4, Case 1
sb ¼Mb=SMa, (9.1)

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c

Pressure

a

b

Pressure

a

b

Case 1

Case 2

c


Fig. 4. Lateral pressure direction.

�
For the lateral pressure applied toward the lower flange as shown in Fig. 4, Case 2
sb ¼Mb=SMb. (9.2)

The calculated bending moment, Mb is obtained by

Mb ¼qu þ q‘

2

� �sl2=12 (10)

SMa and SMb are the sectional modulus of upper flange and lower flange of unitcorrugation. qu and ql are the lateral pressure at the two ends of the corrugation. sCðAÞ isthe critical buckling stress of the unit corrugation under uniaxial compression, which iscalculated by

sCðAÞ ¼

sEðAÞ for sEðAÞpPrsCx;

s0 1� Prð1� PrÞsCx

sEðAÞ

h ifor sEðAÞ4PrsCx;

8<: (10.1)

where Pr is the proportional linear elastic limit of the structure and sC(A) is the critical localplate buckling stress in corrugation direction, which is taken as the lesser of local web bucklingstress and flange buckling stress. sEðAÞ is the Euler’s buckling stress as provided in Appendix B.

sC(B) is the critical buckling stress of the unit corrugation under lateral pressure, whichis obtained from Eq. (3). In order to assess the buckling strength of the corrugated panelswith the triangular profile and unequal flanges, Caldwell’s formula (1) for elastic bendingbuckling stress is extended, which is given by

�
For lateral pressure applied toward the upper flange as shown in Fig. 4, Case 1
sEðBÞ ¼ kcaE

12ð1� n2Þt

a

� �2. (11.1)


For lateral pressure applied toward the lower flange as shown in Fig. 4, Case 2
�
sEðBÞ ¼ kcb

E

12ð1� n2Þt

b

� �2, (11.2)

where

kca ¼ ½7:65� 0:26ðc=aÞ2�2 and kcb ¼ ½7:65� 0:26ðc=bÞ2�2. (12)

3.3. Entire corrugated panel buckling

The following limit state is recommended for the buckling strength assessment for entirecorrugated panels:

sx

ZsGx

� �2

þsy

ZsGy

� �2

þt

ZtG

� �2

p1, (13)

where sx and sy are the calculated average compressive stresses in the corrugation andtransverse directions, respectively; t is the in-plane shear stress; sGx and sGy are the overallcritical buckling stresses in the corrugation and transverse directions, respectively, as givenin Appendix C; Z is the allowable strength utilization factor as defined in Section 3.1; andtG is the overall critical buckling stress for edge shear as calculated by

tG ¼

tE for tEpPrt0;

t0 1� Prð1� PrÞt0tE

h ifor tE4Prt0;

8<: (14)

tE is the overall elastic buckling stress, as determined as follows (Easley [7])

tE ¼ 3:65p2D3=4

x D1=4y

tl2, (15)

where Dx and Dy are defined in Appendix C.

4. Calibration

The calibration approach is provided in this subsection, and the accuracy fordetermining buckling strength predictions obtained from the application of the abovecriteria is established by comparing its results against an extensive database of tests andalso from the results of FEA. In the FEA, the boundary conditions are assumed as simplysupported.

4.1. Axial compression

One of three types of failure modes (local plate buckling, column buckling of unitcorrugation and overall corrugated panel buckling) may occur for a corrugated panelsubjected to single axial compression.Local buckling of flange and web plates may not be a critical failure mode if the section

of a corrugated panel is compact, as defined in Appendix B. By the review of existingdesign of corrugated panels in ships and offshore structures, it is found that most

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Test & FEA, �x/�0

AB

S Pr

edic

tion,

�x/�

0

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

FEATest

Fig. 5. Comparison of corrugated panels in axial compression.


corrugated panel sections are not compact and, consequently, the local buckling may bemore crucial than column buckling and overall buckling, and should be considered in thebuckling strength assessment.

Column buckling or overall buckling may occur for corrugated panels with shallowtrough (small d, as specified in Fig. 2). A deep trough in thin plating is more efficient than ashallow trough of equal section modulus in resisting column buckling or overall buckling.Therefore, the most efficient way to increase the column buckling or overall bucklingstrength is to increase the trough depth.

Due to the lack of sufficient experimental data, FEAs of the buckling strength for 40actual corrugated panels were conducted. Fig. 5 compares the solutions of bucklingstrength with the finite element results and test results by Paik et al. [4], where the allowablestrength utilization factor is excluded. In the analysis, the least critical buckling stress ofsCx, sCðAÞ and sGx as given in Section 3 is used to compare with that from FEA. The meanand COV of modeling uncertainty are 1.11 and 8.35%, respectively.

4.2. Lateral pressure

Experiments and numerical analyses [2,4] demonstrate that corrugated panels subjectedto lateral pressure exhibit bending collapse due to local buckling of the compressed flangeand part of web in the 1/3 middle region of the corrugation span, as shown in Fig. 6.Caldwell [2] pointed out that there are two ways to reach maximum economy of material incorrugated panel design:

(i)
The corrugation angle should be as large as possible, e.g., a rectangular trough profileis more efficient than a trapezoidal or triangle profile of equal section modulus.
(ii)
A deep trough in thin plating is more efficient than a shallow trough of equal sectionmodulus.

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Fig. 6. Collapse mode of a corrugated panel in lateral pressure.

H.-H. Sun, J. Spencer / Marine Structures 18 (2005) 548–565556

Fig. 7 compares the solutions of buckling strength with the experimental results andFEA results available for 30 Caldwell’s and Paik’s test models and 18 FE models, wherethe allowable strength utilization factor is excluded. The predicted critical buckling stress,sCðBÞ, as given in Section 3.2 is conservative and the mean and COV of modelinguncertainty are 1.13 and 17.64%, respectively. The collapse mode from the present FEA isfairly consistent with the existing knowledge.

4.3. Edge shear

A corrugated panel subjected to single edge shear exhibits overall buckling when it failsas shown in Fig. 8. Edge shear stress is the most significant load effect that the corrugatedpanel used in living quarters should resist.Fig. 9 presents the comparison of recommended solutions of buckling strength with the

experimental results and FEA results for Easley’s models [7], where the allowable strengthutilization factor is excluded. The FE models are constructed with the same overall lengthand width of the actual test specimens. The recommended formula (14) produces the meanand COV of modeling uncertainty of 1.10 and 12.62%, respectively. All models exhibitoverall shear buckling failure, and statement (ii) in Section 4.2 from Caldwell [2] is alsoapplicable for the corrugation panel subjected to edge shear based on the modelexperiments and FEA results.

4.4. Combined axial compression and edge shear

Corrugated panels used in living quarters of offshore structures should be designed tomainly withstand combined axial compression and edge shear. The normal transversestress should be negligibly small, because the panel stiffness in the transverse direction is

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Fig. 8. Collapse mode of a corrugated panel in edge shear.

0.00

0.05

0.10

0.15

0.20

0.00 0.05 0.10 0.15 0.20

Test & FEA, MPa

AB

S Pr

edic

tion,

MPa

TestFEA

Fig. 7. Comparison of corrugated panels in lateral pressure.


very small. It is widely accepted that a corrugated panel can be treated as plates havingdifferent flexural rigidities in two perpendicular directions; and the buckling limit states forthe local and entire panels can be expressed as spherical interaction surfaces from thedesign point of view [8,11], as described in Sections 3.1 and 3.3. Other forms of interaction

ARTICLE IN PRESS

0

5

10

15

20

0 5 10 15 20Test & FEA, MPa

AB

S Pr

edic

tion,

MPa

TestFEA

Fig. 9. Comparison of corrugated panels subjected in edge shear.


surfaces as discussed in Galambos [12] and Paik and Thayambali [13] are not adopted dueto their inconsistency in dealing with uniform axial compression or in-plane bendingcombined with edge shear.Fig. 10 presents verifications for local plate buckling in a corrugated panel by comparing

the local buckling limit state with the FEA results, in which the allowable strengthutilization factor is excluded. It can be seen that the recommended limit state in Section 3.1gives very reasonable predictions.Fig. 11 presents verifications for the overall buckling of corrugated panels with two

different types of profiles that are used in living quarters by comparing the overall bucklinglimit state with the FEA results, in which the allowable strength utilization factor isexcluded. It can be seen that the recommended limit state in Section 3.3 providesconservative predictions compared to the FEA results.

4.5. Combined axial compression and lateral pressure

In addition to considering combined axial compression and edge shear, the loadcombination of axial compression and lateral pressure is also important in the bucklingstrength assessment of corrugated panels used in living quarters. It is well recognized thatthe buckling strength of corrugated panels in such a load combination can be calculated bya beam-column buckling limit state, as described in Section 3.2, in which the local bucklingeffect due to axial compression is incorporated in the case where the section is non-compact.Fig. 12 demonstrates the verification by comparing the beam-column buckling limit

state with the FEA results, in which the allowable strength utilization factor is excluded. Itcan be seen that the recommended limit state provides very reasonable predictions.

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Local Buckling, Eq. (7)FEA

� = 15, � = 1.48

�/� C

�x /�Cx

Fig. 10. Local buckling interaction.

Profile-I

Profile-IIOverall Buckling, Eq. (13)

FEA-Profile-IFEA-Profile-II

0.00.0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1.0

1.0

1.2

1.2

1.4

1.4

�/� G

�x /�Cx

Fig. 11. Overall buckling interaction.


5. Design examples

Two design examples are provided based on the above design criteria, which are takenfrom two living quarters on offshore platforms. The stresses in the buckling strengthassessment are obtained from the general structural analysis computer system (SACS) [14].

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Cm� b

/�C

(B)

�a/�C (A)

0.00.0

0.2

0.2

0.4

0.4

0.6

0.6 0.8

0.8

1.0

1.0 1.2

1.2Beam-Column Buckling, Eq. (8)

FEA

Fig. 12. Beam-column buckling interaction.


SACS is a comprehensive design and analysis package used to the offshore and civilstructure design industries.

5.1. Corrugated panel with triangular profile

Fig. 13 shows the sectional geometry of the panel with triangular profile. The totalheight and breadth are 3.35m and 4.88m, respectively. The modulus of elasticity andminimum yield point are 2.1� 105MPa and 248MPa, respectively.The maximum membrane stresses from SACS in the operational condition are

sx ¼ 16:55MPa; sy ¼ 0MPa; t ¼ 30:34MPa:

The wind velocity in the operational condition is 76 km/h and the wind pressure is5.36� 10�4MPa.Based on the above design criteria, the buckling assessment results are given in Table 1.The corrugation panel satisfies all design criteria and therefore the design is acceptable.

5.2. Corrugated panel with trapezoidal profile

Fig. 14 shows the sectional geometry of the panel with trapezoidal profile. The totalheight and breadth are 3.05m and 4.27m, respectively. The modulus of elasticity andminimum yield point are 2.1� 105MPa and 248MPa, respectively.The maximum membrane stresses from SACS in the severe storm condition are

sx ¼ 68:95MPa; sy ¼ 0MPa and t ¼ 86:87MPa:

The wind velocity in the severe storm condition is 185 km/h and the wind pressure is2.15� 10�3MPa.

ARTICLE IN PRESS

508mm

76m

m

90°

4.8mm

Wind pressure

Fig. 13. Geometry of triangular corrugation.

Table 1

Buckling assessment results for the corrugated panel with triangular profile

Design criteria Unity check

Flange buckling 0.48

Web buckling 0.38

Unit corrugation buckling 0.46

Entire corrugation buckling 0.65

Maximum 0.65

394mm

51.8

mm

67.6mm

Wind pressure

203mm

4.76mm

102mm

Fig. 14. Geometry of unequal flanged corrugation.


Based on the above design criteria, the buckling assessment results for the design aregiven in Table 2. As shown in the ‘‘Original’’ column of the unity check, the corrugationpanel does not satisfy buckling criteria for unit corrugation and the entire corrugatedpanel. The panel must be redesigned.

As mentioned before, the most efficient way to increase the buckling strength ofcorrugated panels is to increase the trough depth. In this example, if the trough depth isincreased to 96mm, the buckling assessment results are shown in the last column, Table 2.It can be seen that the redesign is acceptable.

6. Conclusions

There is an increasing demand for living quarters built of corrugated panels in offshorestructures, which led the American Bureau of Shipping to develop design recommenda-tions for buckling strength assessment. This paper describes the main features and theprinciples of the recommendations based on ABS experience, which includes buckling

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Table 2

Buckling assessment results for the corrugated panel with trapezoidal profile

Buckling mode Unity check

Original Improved

Flange buckling 0.91 0.91

Web buckling 0.84 0.85

Unit corrugation buckling 1.61 0.57

Entire corrugation buckling 1.44 0.97

Maximum 1.61 0.97


strength assessment for all relevant failure modes. The technical background of therecommendations is provided and the modeling uncertainty is established by comparingthe proposed design criteria with extensive laboratory tests and FE analysis results.The recommended criteria are applicable for corrugated panels with triangular profile or

unequal-flanges trapezoidal profile subjected to axial compression, shear and lateralpressure and their combinations. The comparisons to laboratory tests and FE analysisdemonstrate that the recommendations have suitable conservatisms for the bucklingstrength assessment. Two design examples were provided to demonstrate the application ofthe design criteria.

Acknowledgements

The authors wish to express their appreciation and gratitude to the management of theAmerican Bureau of Shipping. Special thanks Pao-Lin Tan and Kuan-Tao Chang for theirtechnical reviews. The authors are indebted to Jana Palfy and Jim Speed for editing themanuscript.

Appendix A. Critical buckling stresses of local panels

The critical buckling stresses, sCiði ¼ x; yÞ and tC , for flange and web plates may beobtained from the following equations, with respect to uniaxial compression, bending andedge shear, respectively.

sCi ¼

sEi for sEipPrs0;

s0 1� Prð1� PrÞs0sEi

h iforsEi4Prs0:

8<:

tC ¼

tE for tEpPrt0;

t0 1� Prð1� PrÞt0tE

h ifor tE4Prt0;

8<:

where Pr is the proportional linear elastic limit of the structure, which may be taken as 0.6

for steel, sEi the elastic buckling stress ¼ ksp2E

12ð1�n2Þts

� �2� �.


For loading applied along the short edge of the plating (long plate):

ks ¼

8:4kþ1:1 for 0pkp1;

7:6� 6:4kþ 10k2 for � 1pko0:

(

For loading applied along the long edge of the plating (wide plate):

ks ¼

1:0875 1þ 1a2

� �2� 18 1

a2

h ið1þ kÞ þ 24 1

a2 for ko 13

and 1pap2;

1:0875 1þ 1a2

� �2� 9 1

a

h ið1þ kÞ þ 12 1

a for ko 13

and a42;

1þ 1a2

� �2ð1:675� 0:675kÞ for kX 1

3:

8>>>><>>>>:

For edge shear

ks ¼ 4:0s

l

� �2þ 5:34

� �,

where a is the aspect ratio ( ¼ l/s), k the ratio of edge stresses, which can be varied from �1(pure bending) to +1 (pure compression) ( ¼ simin=simax), s0 the specified minimum yieldpoint of plate, t0 the shear strength of plate ( ¼ s0=

ffiffiffi3p

), E the modulus of elasticity, n thePoisson’s ratio, 0.3 for steel, l the length of long plate edge, s the length of short plate edge,and t the thickness of plate.

Appendix B. Critical buckling stress of unit corrugation

A cross section is compact if the web and flange plates satisfy the following requirement[1,8]:

a

t;b

t;c

tp1:5

ffiffiffiffiffiE

s0

r

where a, b, c and t are defined in Fig. 2.The critical buckling stress for a unit corrugation may be obtained from the following

equation:

sCðAÞ ¼

sEðCÞ for sEðCÞpPrsF ;

sF 1� Prð1� PrÞsF

sEðCÞ

h ifor sEðCÞ4PrsF ;

8<:

where sEðCÞ is the elastic buckling stress, N/cm2 (kgf/cm2, lbf/in2) ð¼ p2Er2=l2Þ, r the radiusof gyration of area A of unit corrugation ¼

ffiffiffiffiffiffiffiffiffiffiffiIy=A

p� �, E the modulus of elasticity, A, Iy the

area and moment of inertia of unit corrugation, Pr the proportional linear elastic limit ofthe structure, which may be taken as 0.6 for steel, s0 the specified minimum yield point,sCx the critical local buckling stress, as specified in Appendix A, l the length of unitcorrugation, and

sF ¼s0 if the cross section is compact;

sCx if the cross section is non�compact:

(


Appendix C. Critical buckling stress of entire corrugated panels

The critical buckling stress sGiði ¼ x; yÞ for entire corrugated panels may be obtainedfrom the following equation:

sGi ¼

sEi for sEipPrs0;

s0 1� Prð1� PrÞs0sEi

h ifor sEi4Prs0;

8<:

where

sEx ¼kxp2ðDxDyÞ

1=2

txB2,

sEy ¼kyp2ðDxDyÞ

1=2

tl2,

kx ¼

4 for l=BX1;1f2

x

þ f2x for l=Bo1;

(

ky ¼

4 for B=lX1;1f2

y

þ f2y for B=Lo1;

8<:

l, B length and width of corrugated panel,tx equivalent thickness of the corrugation in the corrugation direction the

ðstþ AsxÞ=s,t thickness of the corrugation,fx (l/B)(Dy/Dx)

1/4,fy (B/l)(Dx/Dy)

1/4,Dx EIy/s,Dy s/(a+b+2c)Et3/12(1–n2),Iy moment of inertia of unit corrugation,Asx 2ct sinf,a, b, c width of flanges and web plating, respectively, as defined in Fig. 2,s width of unit corrugation, as defined in Fig. 2,E modulus of elasticity,n Poisson’s ratio, 0.3 for steel,s0 specified minimum yield point of the material.

References

[1] ABS. Rules for building and classing steel vessels, 2005.

[2] Caldwell JB. The strength of corrugated plating for ships’ bulkheads. Trans RINA 1955;97:495–522.

[3] Nagai T. On the buckling phenomena of corrugated bulkheads. J Naval Archit Japan 1964;116:50–7.


[4] Paik JK, Thayamballi AK, Chun MS. Theoretical and experimental study on ultimate strength of corrugated

bulkheads. J Ship Res 1997;41:301–17.

[5] Bergmann VS, Reissner H. Neuere probleme aus der flugzeugstatik. Z Flugtech Mororluftsch 1929:20.

[6] Timoshenko SP, Gere JN. Theory of elastic stability, 2nd ed. New York: McGraw-Hill Book Co; 1961.

[7] Easley JT. Buckling formulas for corrugated metal shear diaphragms. J Struct Div ASCE 1975;101:1403–17.

[8] ABS. Guide for buckling and ultimate strength assessment for offshore structures, 2004.

[9] ABS. Rules for building and classing offshore installations, 1997.

[10] ABS. Guide for building and classing floating production installations, 2004.

[11] American Petroleum Institute. API bulletin 2V, Design of flat plate structures, 2nd ed., 2000.

[12] Galambos TV. Guide to stability design criteria for metal structures, 5th ed. New York: Wiley; 1998.

[13] Paik JK, Thayamballi AK. Ultimate limit state design of steel-plated structures. New York: Wiley; 2003.

[14] EDI. Structural analysis computer system (SACS). Engineering Dynamics, Inc., 2005.

Documents

Corrugated BHD