Placi Curbe - 7 [Compatibility Mode]

8/13/2019 Placi Curbe - 7 [Compatibility Mode]

1/13


2/13

EN 1993-1-6 DESIGN CHECKING OF SHELLS5. Stress resultants and stresses in shells

Stress resultants in the shellThe ei ht stress resultants in the shell wall at an oint should becalculated with respect to each limit state.

The shear stresses xn , n due to the transverse shear forces q xn, q n

almost all practical cases, so they may be neglected in design.

made using only the six stress resultantsin the shell wall n x , n , n x , m x , m , m x .Where the structure is axisymmetric andsubject only to axisymmetric loading andsupport, only n x , n , m x , and m .

If uncertainties arises concerning the stress to be used in limit stateverifications, the von Mises e uivalent stress on the shell surface

should be used.


3/13


Modelling of the shell for analysisThe shell shall be re resented b its middle surface.

The radius of curvature shall be taken as the nominal radius of

curvature.mper ect ons s a e neg ecte , except as set out n sect on .

An assembly of shell segments shall not be subdivided into separatese ments for anal sis unless the boundar conditions for each

segment are chosen in such as way as to represent interactionsbetween them in a conservative manner.

in the analysis model.

A shell that is corrugated (vertically or horizontally) may be treatedas an orthotropic uniform shell provided that the corrugationwavelength is less than 0,5(rt) 0.5 .

largest dimension is smaller than 0,5(rt) 0.5 .


4/13


Boundary conditionsThe a ro riate boundar conditions should be used in anal ses forthe assessment of limit states according to the conditions shown in

following table.

conditioncode

term displacements displacements rotation

radially restrained meridionally

condition

code

term displacements displacements rotation

radially restrained meridionally res ra ne ro a on res ra ne

BC1fradially restrained meridionallyrestrained rotation free w = 0 u = 0 0

res ra ne ro a on res ra ne

BC1fradially restrained meridionallyrestrained rotation free w = 0 u = 0 0

BC2rradially restrained meridionally freerotation restrained w = 0 u 0 = 0BC2rradially restrained meridionally freerotation restrained w = 0 u 0 = 0

BC2f Pinnedradially restrained meridionally freerotation free w = 0 u 0 0

Free edge radially free meridionally free

BC2f Pinnedradially restrained meridionally freerotation free w = 0 u 0 0

Free edge radially free meridionally freerotation free

NOTE: The circumferential displacement v is closely linked to the displacement w normal to the surface so separate boundary conditions are not identified in paragraph (3) for these two parameters.

rotation free

NOTE: The circumferential displacement v is closely linked to the displacement w normal to the surface so separate boundary conditions are not identified in paragraph (3) for these two parameters.


5/13


Boundary conditionsSupport boundary conditions should be checked to ensure that theydo not cause excessive non-uniformity of transmitted forces or

introduced forces that are eccentric to the shell middle surface. ,the normal displacement w should also be used for the circumferentialdisplacement v .

Actions shall all be assumed to act at the shell middle surface.Local actions and local patches of action shall not be represented byequivalent uniform loads.The modelling should account for different influences, such as: local

, , ,connections to other structures, conditions during erection etc.

Stress resultants and stresses min ,

recommended value is 25) the curvature of the shell may be ignoredwhen calculating the stress resultants in the shell wall


6/13


Types of analysisThe design should be based on one or more of the types of analysisgiven below

T e of anal sis Shell theor Material law Shell eometr Membrane theory of shells membrane equilibrium not applicable perfectLinear elastic shell analysis (LA) linear bending and

stretchinglinear perfect

near e as c urca on ana ys s near en ng anstretching

near per ec

Geometrically non-linear elastic analysis(GNA)

non-linear linear perfect

Materially non-linear analysis (MNA) linear non-linear perfectGeometrically and materially non-linear

analysis (GMNA)

non-linear non-linear perfect

- - with imperfections (GNIA)Geometrically and materially non-linearanalysis with imperfections (GMNIA)

non-linear non-linear imperfect


7/13

EN 1993-1-6 DESIGN CHECKING OF SHELLS6. Plastic limit state LS1

Design values of actionsThe design values of the actions shall be based on the most adverserelevant load combination

Stress design

accurately predict the plastic limit state. It provides a conservativeassessment of the plastic collapse resistance.

eac po n n e s ruc ure e es gn va ue o e s ress eq,Ed should be taken as the highest primary stress determined in a

structural analysis that considers the laws of equil ibrium betweenimposed design load and internal forces and moments.Where a membrane theory analysis is used, the result ing two

x, , , x ,represented by the equivalent design stress eq,Ed obtained from:


8/13


Where an LA or GNA analysis is used, the resulting two dimensionalfield of r imar stresses ma be re resented b the von Misesequivalent design stress:

with:

OBS: these expressions give asimplified conservative

equivalent stress

OBS: The values of xn,Ed and n,Ed are usuallyvery small and do not affect the plastic

resistance, (they may generally be ignored)

Stress limitationThe design stresses should satisfy the condition:

with: the von Misses design strength factor.


9/13


Design by global numerical MNA or GMNA analysisThe design plastic limit resistance shall be determined as a load factorR applied to the design values of the combination of actions for the

relevant load case. load combinations.In an MNA or GMNA analysis based on the design yield strength f yd ,

the shell should be subject to the design values of the load casesdetailed in (2), progressively increased by the load ratio R until theplastic limit condition is reached.Where an MNA analysis is used, the load ratio R MNA may be taken asthe largest value attained in the analysis, ignoring the effect of strain

.Where a GMNA analysis is used, if the analysis predicts a maximumload followed by a descending path, the maximum value should beuse o e erm ne e oa ra o GMNA . The result of the analysis should

produce a load ratio R greater than 1,0.


10/13


Direct designFor each shell segment in the structure represented by a basicloading case as given by Annex A, the highest von Mises membrane

stress

eq,Ed determined under the design values of the actions F Ed Where net section failure at a bolted joint is a design criterion, thedesign value of the actions F ed should be determined for each joint .

ere e s ress can e represen e y a as c oa case as g ven n Annex A, and where the resulting stress state involves onlymembrane stresses, F Ed should not exceed the load resistance F Rd based on the design ultimate strength f ud .


11/13

EN 1993-1-6 DESIGN CHECKING OF SHELLS7. C clic lasticit limit state LS2

Design values of actionsThe design values of the actions for each load case should be chosenas the characteristic values of those parts of the total actions that areexpected to be applied and removed more than three times in the

Stress designThe shell should be analysed using an LA or GNA analysis of the

Ed .For each extreme load condition in the cyclic process, the stresscomponents should be evaluated. From adjacent extremes in thecyclic process, the design values of the change in each stresscomponent x,Ed , ,Ed , x ,Ed on each shell surface and at any pointin the structure should be determined.From these changes in stress, the design value of the von Misesequivalent stress change on each surface eq,Ed,i should be found


12/13


The design value of the stress range eq,Ed should be taken as thelargest change in the von Mises equivalent stress changes eq,Ed,i ,considering each shell surface in turn.

Stress range limitation

the design stress range should satisfy:with: the von Misses equivalent stress range resistance.Design by global numerical MNA or GMNA analysis (total accumulated

The total accumulated von Mises equivalent plastic strain p,eq.Ed at theend of the design life of the structure should be assessed.Unless a more refined analysis is carried out , the total accumulatedvon Mises equivalent plastic strain p,eq.Ed may be determined from:

with: n - the number of cycles of loading in the design l ife of the structure

p,eq,Ed

during one complete load cycle at any point in the structure,occurring after the third cycle.


13/13


Unless a more sophisticated low cycle fatigue assessment isundertaken, the design value of the total accumulated von Misesequivalent plastic strain p,eq,Ed should satisfy the condition:

The value n p,eq = 5 is recommended.

Direct designFor each shell segment in the structure, represented by a basic

,stress range eq,Ed considering both shell surfaces under the designvalues of the actions F Ed should be determined using the relevantexpress ons g ven n nnex .

Placi Curbe - 7 [Compatibility Mode]

Documents

Transcript of Placi Curbe - 7 [Compatibility Mode]