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Universitatea Politehnica TimioaraFacultatea de Construcii

Departamentul de Construcii Metalice i Mecanica Construciilor

PL CI CURBE SUBIRI

- CURS 10 -

- -

Proiectarea structurilor din oel

Rezistena i stabilitatea PCS (5)

Conf.dr.ing Adrian CIUTINA

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EN 1993-1-6 DESIGN CHECKING OF SHELLSANNEX C n Ex ressions for linear elastic

C1 General

membrane and bending stresses

Action effects and resistances: characteristic values of the action

effect or resistance are provided when characteristic values of the, .

Notations: specific for membrane theory shells.

Boundary conditions:

the boundary condition notations should be taken as detailed in 5.2.2.

The term clamped should be taken to refer to BC1r and the term

pinned to refer to BC2f.

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EN 1993-1-6 DESIGN CHECKING OF SHELLSANNEX C n membrane and bendin stresses

C2 Clamped base unstiffened cylindrical shells

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C2 Clamped base unstiffened cylindrical shells

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C3 Pinned base unstiffened cylindrical shells

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C4 Internal conditions in unstiffened cylindrical shells

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C4 Internal conditions in unstiffened cylindrical shells

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C5 Ring stiffener on cylindrical shell

C.5.1 Ring stiffened cylinder: radial force on ring

The stresses in the shell should be determined using the calculated

value of wfrom this clause introduced into the expressions given in C.2.5.ere ere s a c ange n e s e c ness a e r ng, e me o

set out in 8.2.2 of EN 1993-4-1 should be used.

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C.5.2 Ring stiffened cylinder: axial loading


value of wfrom this clause introduced into the expressions given in C.2.5. . .

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C.5.3 Ring stiffened cylinder: uniform internal pressure


value of wfrom this clause introduced into the expressions given in C.2.5. . .

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C6 Circular plates with axisymmetric boundary conditions

C.6.1 Plate with simply supported boundary: uniform load

C.6.2 Plate with local distributed load: simply supported boundary

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C6 Circular plates with axisymmetric boundary conditions

C.6.3 Plate with fixed boundary: uniform load

C.6.4 Plate with fixed boundary: local distributed load

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EN 1993-1-6 DESIGN CHECKING OF SHELLSANNEX D n Ex ressions for bucklin

D1 Unstiffened c lindrical shells of constant wall thickness

stress design

D.1.1 Notation and boundary

conditions

are set out in 2.3, 5.2.2 and 8.3.

D.1.2 Meridional axial com ression

Critical meridional bucklingstresses

with Cxfound in function of the length

of shell element:

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EN 1993-1-6 DESIGN CHECKING OF SHELLSANNEX D n bucklin stress desi n

D1 Unstiffened cylindrical shells of constant wall thickness


Meridional buckling parameters

The meridional elastic imperfection factor should be obtained from:

with wkthe characteristic

imperfection amplitude.

. .

Critical circumferential buckling stresses

with Cgiven in Table D4, function of the length of cylinder

Circumferential buckling parameters

e c rcum eren a e as c mper ec on ac or s ou e a en rom

table D.5 for the specified fabrication tolerance quality class.

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D.1.4 Shear

Critical shear buckling stresses

Shear buckling parameters

the specified fabrication tolerance quality class.

. . er ona ax a compress on w coex s en n erna pressure

Pressurised critical meridional buckling stress

, unaffected by the presence of internal pressure and may be obtained as

specified in D.1.2.1.

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D.1.5 Meridional axial com ression with coexistent internal ressure

Pressurised meridional buckling parameters

The pressurised meridional buckling stress should be verifiedana ogous y o e unpressur se mer ona uc ng s ress as spec e

in 8.5 and D.1.2.2. However, the unpressurised elastic imperfection factor

xmay be replaced by the pressurised elastic imperfection factor x .

The pressurised elastic imperfection factor xp should be taken as thesmaller of the two following values:

xpe -

xpp is a factor covering pressure-induced plastic destabilisation

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D.1.6 Combinations of meridional axial com ression circumferential

(hoop) compression and shear

The buckling interaction parameters are obtained from:

With x, , the buckling

reduction factors defined

. . .

Examples of

interaction-relevant

stress components

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D2 Unstiffened cylindrical shells of stepwise variable wall thickness

D.2.1 General

Notation and boundary conditions

L - overall cylinder length

r- radius of cylinder middle surface

jan integer index denoting the individual cylinder sections

tjthe constant wall thickness of sectionjof the cylinder

j

The expressions may only be used for shells with boundary conditionsBC1 or BC2 at both edges, with no distinction made between them.

Geometry and joint offsets

It is considered that the wall thickness of the

top to bottom.

The intended offsets e0between plates of

by the following expressions:

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For long equivalent cylinders, the parameter Cxb should be conservatively

taken Cxb=1, unless a better value is justified by more rigorous analysis.D.2.3 Meridional (axial) compression

Critical circumferential buckling stresses

. . ,

D.1 should be applied.For cylinder sections of moderate or short length, the critical

c rcum eren a uc ng s ress o eac cy n er sec on o e or g na

cylinder of stepwise variable wall thickness should be determined from:

For long cylinder, with the critical circumferential buckling

stress should be determined from:

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Buckling strength verification for circumferential compression

For each cylinder sectionj, the following check should be carried out:

Where Ed is the key value of the circumferential compressive membrane stress;

,Rd,j is the design circumferential buckling stress, as derived from thecritical circumferential buckling stress (D.1.3.2).

D.2.4 Shear

Critical shear buckling stresses

If no specific rule for evaluating an equivalent single cylinder of uniformwall thickness is available, the expressions of D.2.3.1 may be applied.

Buckling strength verification for shear

. . . ,

compression expressions by the relevant shear expressions.

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D3 Unstiffened lap jointed cylindrical shells

D.3.1 General

Definitions

D.3.2 Meridional (axial) compression

shell

Where a lap jointed cylinder is subject to meridional compression, with

meridional lap joints, the buckling resistance may be evaluated as for a

- , ,

resistance reduced by the factor 0,70.D.3.3 Circumferential (hoop) compression

Where a lap jointed cylinder is subject to circumferential compression

across meridional lap joints, the design buckling resistance may be

evaluated as for a uniform or ste ed-wall c linder as a ro riate butwith a reduction factor of 0,90.

D.3.4 Shear

,

resistance may be evaluated as for a uniform or stepped-wall cylinder.

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D4 Unstiffened complete and truncated conical shells

D.4.2 Desi n bucklin stresses

Uniform external pressure

the equivalent cylinder of length le is the minimum between

and the equivalent cylinder radius re is:

- for short cones:- for long cones:

e uc ng s reng ver ca on s ase on mem rane s ress:

Shear

Uniform torsion

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D.4.3 Bucklin stren th verification

Meridional compression

The buckling design check should be carried out at that point of the cone where

most critical.

The design buckling stress should be determined for the equivalent cylinder

accor ng o . . .

Circumferential (hoop) compression and uniform external pressure

,

the buckling design check should be carried out using the acting design

circumferential stress E,ddetermined using expression D.77 and the design

R,d . . . . . . .

Where the circumferential compression is caused by actions other than uniform

external pressure, the calculated stress distribution E(x) should be replaced by a

E,env ,

which would arise from a fictitious uniform external pressure. The bucklingdesign check is carried out as above, but using E,env instead of E.

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D.4.3 Bucklin stren th verification

Shear and uniform torsion

In the case of shear caused by a constant global torque on the cone, the bucklingE,d

point with r=recos and the design buckling stress R,daccording to D.3.2.1 and

D.3.2.4.

ere e s ear s cause y ac ons o er an a cons an g o a orque suc

as a global shear force on the cone), the calculated stress distribution E(x) shouldbe replaced by a fictitious stress distribution E,env(x) that everywhere exceeds the

, .

buckling design check should then be carried out as above, but using E,env instead

of E.

R,d

according to D.1.4.

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