Documentation -sim sol.com LIMIT, Fatigue Strength Assessments According to Eurocode 3 page 11 Stresses and Section Forces Stresses and Section Forces Basic Procedure for generating

March 2014 www.cae-sim-sol.com

Fatigue Assessment with LIMIT According to Eurocode 3 Version LIMIT2014

Documentation

page 2 LIMIT, Fatigue Strength Assessments According to Eurocode 3 www.cae-sim-sol.com

Fatigue Assessment with LIMIT According to Eurocode 3

Motivation

Stresses and section forces

Stress spectra

Stress-relieved welded details in compression

FAT classes

S-N curves

Fatigue analysis

Results

Overview


Motivation

Example: Beam under bending load Cross section:

Height … h = 200mm

Width … w = 200mm

Distance between webs d = 160 mm

Thickness of all sheets t = 10mm

No displacement, no rotation

Vertical force


Motivation

FEA Analysis Results: FEA code Abaqus

Shell: 8 Node

Von Mises equivalent stress

Direct stress in local 2 direction

Direct stress in local 1 direction

Weld zone of interest


Aim of the Investigation: Weld between flange and web is highly loaded and critical

Proof of fatigue strength according to Eurocode 3

Motivation

Max. vonMises stress: 25,4 MPa


FAT Classes, Eurocode 3, Nominal Stress

Assessment of weld section

Table 8.1 to 8.10 in the Eurocode 3

Different permissible stresses depending on the loading direction:

parallel to weld

transverse to weld

shear

We need local stresses in weld section!

Motivation

Toe, transverse loading, EC3 Table 8.5

Root, transvers loading, EC3 Table 8.5

Toe/root, shear, EC3 Table 8.5


Local Shell Element Coordinate Systems Element coordinate systems not aligned with weld direction Abaqus default: local 1-axis in general parallel to global x-axis Ansys or Nastran default: local 1-axis depends on node numbering and interpolation functions

Direct usage of stress data for assessment not possible!

Motivation

Local weld direction

e.g. Abaqus


Motivation

Weld Analysis with LIMIT Basic features of LIMIT

Automated detection of elements along welds based on different shell properties for flange and web

Visualization of weld details relative to local weld direction


Motivation

n m

Weld Analysis with LIMIT Basic features of LIMIT

Checking all critical points (red circles)

Base material

Weld section

Toes and Roots


Overview


Motivation


Stress spectra


FAT classes

S-N curves

Fatigue analysis

Results


Stresses and Section Forces

Stresses and Section Forces Basic Procedure for generating stress quantities for

the fatigue analysis:

Transformation of stresses to local coordinate system of weld

Choosing the stress concept: Nominal stress Structural hot spot stress according to IIW

Finding section forces and section moments

Calculating the stresses in the weld section

Setting up the stress spectra

Example:

web element


transverse

longitudinal weld directions

Integration points Stress Data FE Stresses

in integration points

in local element system (Solver dependent, here ABAQUS)

extrapolation of stresses to the nodes

LIMIT Imported Data

stresses at nodes

in local element system

shells (2D-tensor): Bottom side (s11,SNEG, s22,SNEG, s12,SNEG)

Top side (s11,POS, s22,SPOS, s12,SPOS)

weld



transverse


Different Ways to Use Stresses Direct assessment

Stresses taken at weld line

Green points show stress positions

Stress are equal to Finite Element shell stresses

directions taken from weld orientation

Similar to nominal stress approach for reduced integrated elements and coarse meshes.

weld



transverse

longitudinal weld orientation

Different Ways to Use Stresses Offset by a certain distance (see i.e. DVS 1612)

for “nominal stress concepts”

taken at i.e. 1,5 x thickness

green points are stress extraction locations (can be visualized in LIMIT Viewer).

Stress interpolation within the target element using stresses at corners

directions taken from weld orientation

See also additional Information in document: LIMIT-Defining_Offset_Endings_Directions.pdf

i.e. 1,5 x t

weld



transverse


Different Ways to Use Stresses Stress extrapolation

for “IIW structural hot spot stress”

IIW reference points at distance of IIW, IIW_A: 0,5 x thickness and 1,5 x thickness or

IIW_B: 5mm and 15mm

Local stresses defined relative to extrapolation direction

Extrapolation direction = transverse

Longitudinal = transverse to extrapolation dir.

1,5 x t

0,5 x t

0,5 x t

1,5 x t

structural hot spot stress type IIW_A

IIW reference points

weld



… transverse

lI…parallel

Section Forces Transformation from s11, s22, t12 to sll, s, tlI

For bottom and top side of shell

Integration over shell thickness Linear distribution across thickness assumed Section forces (s…shear force):

nII, n, sII ……. [N/mm] Section moments (t…torsion):

mll, m, tII …… [N mm/mm]

Orientations: Weld system

IIW

1

1

1 1 2

2

2

2

m, tII

nll, slI

mII, tII

n, sII

weld



Assessment Points within LIMIT Are used to perform the fatigue analysis

for potential areas of crack initiation

Are defined relative to shell normal

P1 to P4 …. Weld Section

P1, P4 … toe

P2, P3 … root

P5 and P6 …. Base Material

Weld dimensions

A-Bot … welded from bottom side

A-Top … welded from top side

Root Position (midplane to root)

D-Bot … welded from bottom side

D-Top … welded from top side



Assessment Points and Stresses One sided full penetration weld

Thickness = a (weld section)

Stresses for base material and weld section equal!


(sll, s, tII )Bottom,P5

Bottom Top

Shell normal

(sll, s, tII )Top,P4,P5


Assessment Points and Stresses Double sided fillet weld

a = t/2

P5, P6 … shell stresses transformed to local directions (II, )

P1-P4 … next slide


(sll, s, tII)Bottom,P5

Bottom Top

Shell normal

(sll, s, tII)Top,P6

(sll, s, tII)P1

(sll, s, tII)P2

(sll, s, tII)P4

(sll, s, tII)P3


Double sided fillet weld, Stresses in P1 to P4 a = t/2 ….t = sheet thickness

continously welded


Stress longitudinal to weld direction: sll,P1,2 = sll,Bot, sll,P3,4 = sll,Top

Stress lateral to weld direction: i = 1 to 4

s,Pi = ntt / (ABot+ATop) + m ePi/Jweld

Shear in weld (in plane): tII,Pi = sIl / (ABot+ATop)

with Jweld = (t+ABot+ATop)³/12 - t³/12

Bottom Top

ABot ATop

eP4 eP1

eP2 eP3

P4 P3 P1 P2

e.g.: eP1 = - t/2 - Abot

t/2 t/2

n m


Assessment Points and Stresses Single sided fillet weld

a = 0.7 t


Bottom Top

Shell normal

(sll, s, tII)P6

(sll, s, tII)P4

(sll, s, tII)P3


Single sided fillet weld, Stresses in P3 and P4 t … sheet thickness

continously welded


Stress longitudinal to weld direction: sll,P3,4 = sll,Top

Stress lateral to weld direction: i = 3 and 4

s,Pi = n / ATop + (m - n eEXC) ePi/Jweld

eEXC = eSSW …free (FKM, FAT71)

eEXC = eSSW /2…constrained

Shear in weld (in plane): tIl,Pi = sIl / ATop

with Jweld = ATop³/12

Bottom Top

ATop

P4 P3 eP3 = -Atop/2

eP4 = Atop/2

eSSW = t/2 + Atop/2

(SSW…Single Sided

Weld)

t/2 t/2

n m

eP4 eP3

eSSW


Single sided fillet weld, Stresses in P6 t … sheet thickness

continously welded

P6 … stresses caculated for sheet thickness


Stress longitudinal to weld direction: sll, 6 = sll,Top

Stress lateral to weld direction: s,P6 = n / t + (m + n eEXC) / (t²/6)

eEXC = eSSW …free (FKM, FAT71)

eEXC = eSSW /2…constrained

Shear in weld (in plane): tIl,P6 = sIl / t

Bottom Top

ATop

e = Atop/2

eSSW = t/2 + Atop/2

(SSW…Single Sided

Weld)

t/2 t/2

n m

e e

eSSW

P6


Overview


Motivation


Stress spectra


FAT classes

S-N curves

Fatigue analysis

Results


Stress Spectrum

Assessment Points P1 to P4:

1. Setting up the local weld coordinate system (longitudinal, transverse)

2. Scanning through all load cases of a spectrum

3. According to EC3 relevant stresses are s and tlI.

4. Saving maxima and minima stresses for all components: (s, tlI ) Pi

5. Calculating stress range of each component and point: Ds = smax - smin

6. Assembly of stress spectrum for transverse stress s and shear tlI

Stress Spectra

Ds,1

Ds,2 Ds,3

Number of cycles

Ds,4

Ds

Example shown with four stress blocks:


Stress Spectrum

Assessment Points P5 and P6:

1. Cutting plane algorithm in order to find direction of maximum stress range Angle increment of 15 , starting point: 0 … parallel to weld

Normal stress is calculated using plain stress tensor (sll, s, tlI ) Pi

2. Scanning through all load cases of a spectrum at one angle j

3. Saving maxima and minima stresses for all components: sjj

4. Calculating stress range of each component and point: Ds = smax - smin

5. Assembly of stress spectrum for sjj

Stress Spectra

Dsjj,1

Dsjj,2 Dsjj,3

Number of cycles

Dsjj,4

Ds

Example shown with four stress blocks:


Overview


Motivation


Stress spectra


FAT classes

S-N curves

Fatigue analysis

Results



60% of the compression is used to calculate a reduced effective stress range

Can be activated in the JobManager in Keywords: *EC3_REDUCED_EFFECTIVE_STRESS_RANGE

Output to the .txt-file: SPECTRUM DATA: BLOCK: 1, PER ROW ONE STRESS COMPONENT (11,22,33,12)

COMP., STRESS RANGE, MEAN STRESS, EFF.RANGE, CYCLES, RELEVANT LOAD CASES)

S11 5.0888 0.0000 4.07104 0.50000E+07 1 2

Eurocode 3


Overview


Motivation


Stress spectra


FAT classes

S-N curves

Fatigue analysis

Results


Fatigue Assessment according to Eurocode 3

Basic Procedure:

Selecting FAT classes for the assessment point

Definition of relevant S-N curve

Proof of strength

Calculation of damage

Calculation of degree of utilization in terms of stress range

Eurocode 3


FAT Classes, Eurocode 3

Assessment points P1 to P4

Stresses used for weld section: s and tlI

Out of plane shear is not resolved over shell stresses and in general negligible

Stress in longitudinal direction is not taken into account in the weld section

FAT Classes

Relevant stresses


FAT Classes, Eurocode 3

Assessment points P1 to P4, nominal stress approach

Table 8.1 to 8.10 in the Eurocode 3

Typical values for transverse loading are : Toe: FAT71 to FAT80

Root: FAT36

Typical values for shear loading are :

Toe or root: FAT80

FAT Classes


Root, transvers loading, EC3 Table 8.5

Toe/root, shear, EC3 Table 8.5


Fat Classes

Assessment points P5 and P6

Toe points

Cutting plane algorithm in increments of 15 (0 …parallel to weld, 90 is transverse to weld)

Only the direct stress in the cutting plane is used.

Permissible FAT values from EC3

If FAT values for loading parallel and transverse to weld orientation differ, LIMIT will interpolate for intermediate cutting angles (ellyptic interpolation)

FAT Classes

e.g. But-Weld

FAT parallel

FAT transverse


FAT Classes

Assessment points P5 and P6, nominal stress approach:

Direct stress,

FAT class interpolated depending on angle

Typical values for transverse loading are: Toe: FAT71 to FAT80

Typical values for parallel loading is: Toe: FAT100

FAT Classes


Toe, parallel loading, EC3 Table 8.2

FAT parallel FAT transverse


FAT Classes

Assessment points P5 and P6, structural hot spot stress approach:

According to IIW s found by extrapolation

Direct stress and FAT class depending on angle of cutting plane

Typical value for transverse loading is: Toe: FAT100

Typical values for parallel loading is: Toe: FAT100

FAT Classes

Toe, transverse loading, EC3 Table B.1

Toe, parallel loading, EC3 Table 8.2

FAT parallel

FAT transverse


Overview


Motivation


Stress Spectra


FAT classes

S-N curves

Fatigue analysis

Results


S-N-Curve

Characteristic values for direct stress

FAT class at 2 mio. cycles: DsC

Fatigue strenght 5 mio. cycles: DsD = (2/5)1/3 DsC

Cutoff at 100 mio. cycles: DsL = (5/100) 1/5 DsD

S-N Curves

Ds

DsC

DsD

DsL

Number of cycles

Direct Stress


S-N-Curve

Characteristic values for shear stress

FAT class at 2 mio. cycles DtC

Cutoff at 100 mio. cycles DsL = (2/100) 1/5 x DtC

S-N Curves

Dt DtC

DtL

Number of cycles

Shear Stress


Overview


Motivation


Stress Spectra


FAT classes

S-N curves

Fatigue analysis

Results


Proof of Fatigue Strength According to Eurocode 3

Two possibilities for proof

1. Damage criteria

2. Calculation of the equivalent constant amplitude stress range for 2 million cycles

In case of no damage, the actual margin of safety in terms of stress is not clear!

Implementation of the Eurocode 3 in LIMIT

Two modes available

1. Direct damage calculation with damage as the result quantity The stress spectra are taken directly for damage calculation

2. Degree of utilization in terms of stress range A load multiplier LF is calculated

Stress spectra are multiplied by LF

Since the SN-curve may change its shape depending on LF, an iterative procedure is used

Iteration ends when damage is equal or changes from lower 1.0 to values higher than 1.0

Fatigue Analysis


Direct Damage

Procedure

Scaling spectra by: gFf

Reducing SN-curve with: gMf

Fatigue Analysis

Ds1 gFf

Ds2 gFf Ds3 gFf

Number of cycles

Ds4 gFf

Ds

Ds1 gFf

Ds2 gFf

Ds3 gFf

Ds4 gFf

DsD =(2/5)1/3 DsC / gMf

DsL = (5/100) 1/5 DsD


Degree of utilization in terms of stress range

Search for the margin of safety against a damage above 1.0 with respect to stress range!

Damage calculation

Scaling spectra by: gFf and LF

Reducing SN-curve with: gMf

Iterative procedure

First iteration: LF = 1.0

Last iteration: LF = margin of safety

1/LF = degree of utilization

Fatigue Analysis

Ds1 gFf LF

Ds2 gFf LF

Ds3 gFf LF

Ds4 gFf LF

DsD =(2/5)1/3 DsC / gMf

DsL = (5/100) 1/5 DsD

= 1.0


Interaction of Direct Stress and Shear Stress Direct Damage In assessment points P1 to P4: Damage due to transverse direct stress and shear stress are added. In assessment points P5 and P6: Always in cutting plane mode only using direct stress in combination with angle dependent FAT-class. No interaction necessary.

Degree of utilization in terms of stress range In assessment points P1 to P4: LF is calculated taking interaction into account according to: with: gFf DsE,2 = Ddirect

1/3 DsC / gMf and Ddirect … Damage from direct stress

gFf DtE,2 = Dshear1/5 DtC / gMf and Dshear … Damage from shear stress

Interaction becomes again summation of damages for transverse stress and shear: Ddirect + Dshear ≤ 1.0

In assessment points P5 and P6: Always in cutting plane mode only using direct stress in combination with angle dependent FAT-class. No interaction necessary.

Fatigue Analysis


Overview


Motivation


Stress spectra


FAT classes

S-N curves

Fatigue analysis

Results


Results

In the following section results are compared and documented for different weld types :

a.) One sided full penetration weld

b.) Double sided fillet weld

c.) One sided fillet weld

Results

a.) b.) c.)


Loads / Spectra

Picture shows LoadManager of LIMIT

FE Result Defines which time steps should be imported

Names the Step 1: Load_1

Loads Is used to generate linear combinations of FE results

Loads generated for fatigue analysis: » Force_1 = 4 x Load_1 » Force_2 = 3 x Load_1 » Force_3 = 2 x Load_1 » Force_4 = 1 x Load_1 » Zero = 0 x Load_1

Spectra Four blocks (BL1 to BL4) are defined each cycling

between Zero and either Force_1,2,3, or 4

Each block has its own cycle number, decreasing with load height

Results


Comparison for different geometries

Degree of Utilization (DoU)

Results

DoU = 4,88 DoU = 0,71 DoU = 0,85


Full penetration weld, details

Critical assessment Point P3 (root)

FAT classes:

Parallel: FAT100

Transverse: FAT36 (conservative setting)

Shear: FAT80

Results

Root


Results: Full penetration weld: LIMIT Text output

no damage for shear at LF = 1

damage for direct stress at LF = 1

no damage for shear at LF = 1.17

damage = 1 for direct stress at LF = 1.17

DoU = 0.85

EC3-VALUES:

Rp02 = 235.000 , Yield stress

gff = 1.00000 , Partial safety factor fatigue load

gfm = 1.00000 , Partial safety factor fatigue strength

FAT-VALUES (2 Mio Cycles):

DSCL = 100.000 , 1. direction resp. parallel to weld

DSCQ = 36.0000 , 2. direction resp. lateral to weld

DSCS = 80.0000 , Shear in weld section

FAT-VALUES (2 Mio Cycles) / gfm :




DIMENSIONS:

t = 10.0000 , Sheet thickness

au = 0.00000 , A-dimension, shell bottom side

ao = 10.0000 , A-dimension, shell top side

dau = 0.00000 , Root position, shell bottom side

dao = -5.00000 , Root position, shell top side

IEX = 2, Exzentricity: constrained (50%)

ALFA = 0.00000 , Angle between cutting plane and weld

(only valid for weld toes: Positions 5 and 6)

SPECTRUM DATA:

BLOCK: 1, PER ROW ONE STRESS COMPONENT (11,22,33,12)

COMP., STRESS RANGE, MEAN STRESS, CYCLES, RELEVANT LOAD CASES)

S11 76.284 38.142 0.10000E+06 1 2

S22 60.824 30.412 0.10000E+06 1 2

S33 0.0000 0.0000 0.0000 0 0

S12 13.200 6.6000 0.10000E+06 1 2



S11 57.213 28.607 0.20000E+06 3 2

S22 45.618 22.809 0.20000E+06 3 2

S33 0.0000 0.0000 0.0000 0 0

S12 9.9000 4.9500 0.20000E+06 3 2



S11 38.142 19.071 0.50000E+06 4 2

S22 30.412 15.206 0.50000E+06 4 2

S33 0.0000 0.0000 0.0000 0 0

S12 6.6000 3.3000 0.50000E+06 4 2



S11 19.071 9.5355 0.10000E+07 5 2

S22 15.206 7.6029 0.10000E+07 5 2

S33 0.0000 0.0000 0.0000 0 0

S12 3.3000 1.6500 0.10000E+07 5 2

FATIGUE STRENGTH and CUTOFF:

DSDQ = 26.5320 , Fatigue strength, lateral to weld direction

DSLQ = 14.5735 , Cutoff lateral to weld direction

DSLT = 36.5600 , Cutoff shear

------------------------------------------------

RESULT OF FIRST ITERATION: LF=1

DST ... SHEAR STRESS WELD SECTION

STEP DST*gff DST*gff*LF N_D=1 N_given DAM

1 13.200 13.200 0.10000E+06

2 9.9000 9.9000 0.20000E+06

3 6.6000 6.6000 0.50000E+06

4 3.3000 3.3000 0.10000E+07

DSQ ... STRESS IN WELD SECTION (LATERAL)

DAMAGE AT DSQ*gff*LF:

STEP DSQ*gff DSQ*gff*LF N_D=1 N_given DAM

1 60.824 60.824 0.41469E+06 0.10000E+06 0.24114

2 45.618 45.618 0.98297E+06 0.20000E+06 0.20347

3 30.412 30.412 0.33175E+07 0.50000E+06 0.15072

4 15.206 15.206 0.80865E+08 0.10000E+07 0.12366E-01

------------------------------------------------

RESULT OF LAST ITERATION: LF= 1.17859

(STRESS RANGES ARE MULTIPLIED WITH MARGIN OF SAFETY)

DAMAGE AT DST*gff*LF:


1 13.200 15.557 0.10000E+06

2 9.9000 11.668 0.20000E+06

3 6.6000 7.7787 0.50000E+06

4 3.3000 3.8893 0.10000E+07

DAMAGE EQUIVALENT STRESS RANGE:

DSTEQ2 = 0.00000 , Damage equivalent range DS, 2 mio cycles


1 60.824 71.686 0.25330E+06 0.10000E+06 0.39479

2 45.618 53.764 0.60041E+06 0.20000E+06 0.33310

3 30.412 35.843 0.20264E+07 0.50000E+06 0.24674

4 15.206 17.921 0.35559E+08 0.10000E+07 0.28122E-01


DSQEQ2 = 36.0331 , Damage equivalent range DS, 2 mio cycles

------------------------------------------------

DEGREE OF UTILIZATION (INVERSE MARGIN OF SAFETY)

ALGQ = 0.848472 , Degree of utilization lateral to weld

ALGQPL = 0.172549 , Degree of utilization lateral to weld, yielding

ALGT = 0.848472E-06, Degree of utilization shear

ALGTPL = 0.648595E-01, Degree of utilization shear, yielding

ALGKMB = 0.848472 , Combined degree of utilization


Double sided fillet weld, details


FAT classes:

Parallel: FAT100

Transverse: FAT36 (conservative setting)

Shear: FAT80

Results

Root


Results: Double sided fillet weld: LIMIT Text output





DoU = 0.71

EC3-VALUES:












DIMENSIONS:





dao = 5.00000 , Root position, shell top side




SPECTRUM DATA:



S11 76.284 38.142 0.10000E+06 1 2

S22 50.830 25.415 0.10000E+06 1 2

S33 0.0000 0.0000 0.0000 1 2

S12 13.243 6.6217 0.10000E+06 1 2



S11 57.213 28.607 0.20000E+06 3 2

S22 38.123 19.061 0.20000E+06 3 2

S33 0.0000 0.0000 0.0000 0 0

S12 9.9326 4.9663 0.20000E+06 3 2



S11 38.142 19.071 0.50000E+06 4 2

S22 25.415 12.708 0.50000E+06 4 2

S33 0.0000 0.0000 0.0000 0 0

S12 6.6217 3.3109 0.50000E+06 4 2



S11 19.071 9.5355 0.10000E+07 5 2

S22 12.708 6.3538 0.10000E+07 5 2

S33 0.0000 0.0000 0.0000 0 0

S12 3.3109 1.6554 0.10000E+07 5 2





------------------------------------------------




1 13.243 13.243 0.10000E+06

2 9.9326 9.9326 0.20000E+06

3 6.6217 6.6217 0.50000E+06

4 3.3109 3.3109 0.10000E+07




1 50.830 50.830 0.71051E+06 0.10000E+06 0.14074

2 38.123 38.123 0.16842E+07 0.20000E+06 0.11875

3 25.415 25.415 0.61994E+07 0.50000E+06 0.80652E-01

4 12.708 12.708 0.10000E+07

------------------------------------------------

RESULT OF LAST ITERATION: LF= 1.41052




1 13.243 18.680 0.10000E+06

2 9.9326 14.010 0.20000E+06

3 6.6217 9.3401 0.50000E+06

4 3.3109 4.6700 0.10000E+07




1 50.830 71.697 0.25318E+06 0.10000E+06 0.39498

2 38.123 53.773 0.60013E+06 0.20000E+06 0.33326

3 25.415 35.849 0.20254E+07 0.50000E+06 0.24686

4 12.708 17.924 0.35531E+08 0.10000E+07 0.28145E-01



------------------------------------------------








One sided fillet weld, details


FAT classes:

Parallel: FAT100

Transverse: FAT36

Shear: FAT80

Results

Root

Bending moment due to excentricity was taken into account (half excentricity with FAT36).


Results: One sided fillet weld: LIMIT Text output





DoU = 4.88

EC3-VALUES:












DIMENSIONS:





dao = 5.00000 , Root position, shell top side




SPECTRUM DATA:



S11 76.284 38.142 0.10000E+06 1 2

S22 349.89 174.94 0.10000E+06 1 2

S33 0.0000 0.0000 0.0000 0 0

S12 18.826 9.4130 0.10000E+06 1 2



S11 57.213 28.607 0.20000E+06 3 2

S22 262.42 131.21 0.20000E+06 3 2

S33 0.0000 0.0000 0.0000 0 0

S12 14.120 7.0598 0.20000E+06 3 2



S11 38.142 19.071 0.50000E+06 4 2

S22 174.94 87.472 0.50000E+06 4 2

S33 0.0000 0.0000 0.0000 0 0

S12 9.4130 4.7065 0.50000E+06 4 2



S11 19.071 9.5355 0.10000E+07 5 2

S22 87.472 43.736 0.10000E+07 5 2

S33 0.0000 0.0000 0.0000 0 0

S12 4.7065 2.3533 0.10000E+07 5 2





------------------------------------------------




1 18.826 18.826 0.10000E+06

2 14.120 14.120 0.20000E+06

3 9.4130 9.4130 0.50000E+06

4 4.7065 4.7065 0.10000E+07




1 349.89 349.89 2178.5 0.10000E+06 45.903

2 262.42 262.42 5163.8 0.20000E+06 38.731

3 174.94 174.94 17428. 0.50000E+06 28.690

4 87.472 87.472 0.13942E+06 0.10000E+07 7.1724

------------------------------------------------

RESULT OF LAST ITERATION: LF=0.205078




1 18.826 3.8608 0.10000E+06

2 14.120 2.8956 0.20000E+06

3 9.4130 1.9304 0.50000E+06

4 4.7065 0.96520 0.10000E+07




1 349.89 71.754 0.25258E+06 0.10000E+06 0.39592

2 262.42 53.816 0.59871E+06 0.20000E+06 0.33405

3 174.94 35.877 0.20206E+07 0.50000E+06 0.24745

4 87.472 17.939 0.35390E+08 0.10000E+07 0.28256E-01



------------------------------------------------








Last slide!

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Documentation -sim sol.com LIMIT, Fatigue Strength Assessments According to Eurocode 3 page 11 Stresses and Section Forces Stresses and Section Forces Basic Procedure for generating