G Lee CK RSA Symposium

RSA Symposium, 28 Sept. 2011, NTU

ympos um on es gn o ee Structures using Eurocodes

Dynamic fatigue assessment and es gn o on a ner uay rane o Eurocode Eurocode 3 Presented by Associate Professor Lee Chi Kin Division of Structures and Mechanics School of Civil and Environmental Engineering, Nanyang Nanyang Technological echnological University University 28 September 2011 1


Topics of presentation Introduction ¾ Actions of fatigue Fatigue Design Philosophy of EN1993-1-9 ¾ Asse Assess ssme ment nt meth method ods s ¾ Partial factors ¾ S-N Curves Curves and and fatigu fatigue e assessm assessment ent Application example: Dynamic Fatigue Assessment of Container Quay Crane ¾ Introduction and structural form ¾ Operations and dynamic actions Conclusions

2 2


Introduction ¾ ¾

Actions of fatigue Everything you need to know about fati ue in ten minutes

3 3


Introduction

Actions of fatigue Fatigue “The process of initiation and propagation of fluctuating stress” (EN1993-1-9, stress” (EN1993-1-9, 1.3.1.1) Fatigue design and assessment could be one of the main criteria for ultimate limit states check for many structures subjected to cyclic loadings

“Cantilevered” Headquarters, Lamar Construction Corporation Hudsonville, Michigan 4 4


Introduction

Everything you need to know about fatigue in 10 minutes Basic actions, concept of fatigue failure

Constant amplitude stress range Q or σ

S‐N curves for different details

time

Q => Δσ welding

Δσ or “S” (log scale)

Δσ

1

Q => Δσ m=3

bolts

Q => Δσ

No. of cycles to failure or “N” (log scale)

Q => Δσ

Constant amplitude

‐ Higher stress and stress range =k Δσ , k>1 near connection => Modified nominal stress range

5 5


Introduction

Everything you need to know about fatigue in 10 minutes How to use the S-N curves for assessment and design? Q => Δσ

Δσ

For fatigue assessment: time Determine Q, then Δσ and N , ’ (FAT check in EC3)

Δσ or “S” (log scale)

Q or σ

Δσ

N No. of cycles to failure or “N” (log scale)

For fatigue design: Determine Q, select plate thickness and other details, com ute Δσ , and than N , check for client’s requirement (FAT check in EC3)

5%, 2.3%)

. .

6 6


Introduction

Everything you need to know about fatigue in 10 minutes Some important remarks Q => Δσ

Q => Δσ

k Δσ (depends on opening size) ¾ For a given values of Q, value of k Δσ depends on the geometry and details , . ¾ To help designers, many design guides (e.g. BS 7608 and EN1993-1-9)

provide tables for different standard construction details (“Detail Category” ) w c re a e e nom na s ress range Δσ o a g ven s an ar - curve S-N curve No.

7 7


Introduction

Everything you need to know about fatigue in 10 minutes Some important remarks ¾ S-N curve is a log-log curve => N quickly reduced as Δσ increases ¾ For any structural detail that is not included in the design guide or

non-uniform stress distribution occurred, designers should use other aids and tools e. . stress concentration formula charts and tables to obtain the modified nominal stress (Hot Spot Stress) ¾ Finite element analysis may be needed to estimate the value of hot

spo s ress ¾ Use of numerical methods implies that both global and local

structural anal ses are often needed => Fati ue desi n could be more demanding in both structural analysis and detail stress analysis than strength design

8 8


Introduction

Everything you need to know about fatigue in 10 minutes ar a e amp u e s ress range ¾ In practice, constant amplitude stress range is anything but exception range (or stress spectrum) ¾ The number of occurrences of different stress ranges can be counted

y us ng

e reservo r me o B

B

Δσ 1 Δσ 2

Δσ 1 Δσ A

Δσ 3

2

A C

Time

Cycles

9 9


Introduction

Everything you need to know about fatigue in 10 minutes a gue assessmen

or var a e amp u e s ress range

¾ For variable amplitude stress range

, contributed by different stress ranges is used or a g ven s ress range σ i e corresponding cycle to failure, N Ri is found from an appropriate S-N curve ¾ Damage factor: nEi / N Ri n n Ei ¾ Damage Dd = i =1 Ri

(Palmgren-Miner’s summation)

n Ei y c n e q e r F

Stress range

Δσ i

Δσ i (Qk )

¾ Acceptable if Dd < 1.0

10 10


EN1993-1-9 ¾

Assessment methods

¾

S-N Curves and fatigue assessment

11 11


Fatigue design philosophy of EN1993-1-9

Assessment methods - ¾ The damage tolerance method  “Provide acceptable reliability so that a structure will perform satisfactorily

for its design life, provide that a prescribed inspection and maintenance regime for detecting and correcting fatigue is implemented” (EN1993-1-9) 9 Potential fatigue crack initiation size should be accessible 9 Checks on crack initiation 9 Specified minimum size of detectable fatigue crack 9 Specified maximum tolerable size of crack (using fracture mechanics) 9 Time taken for fatigue crack to grow from minimum to maximum size

(T1) 9 Inspection/out of service and repair/strengthening plans

12 12



Assessment methods - ¾ The safe life method  “Provide acceptable reliability so that a structure will perform satisfactorily

for its design life without the need for regular in-service inspection for fatigue damage. It should be applied in cases where local formation of cracks in one com onent could ra idl lead to failure of the element or structure” (EN1993-1-9)  The safe life method is recommended by BS and SS NA for new buildings

or c v eng neer ng s ruc ures  What are the differences in the design procedures for the damage

tolerance method and the safe life method?  Same assessment procedure but the damage tolerance method allows for higher stress range ( ≈17%) than the safe design method

an erent s cause method

ya

g er part a actor γ Mf va ue or t e sa e

e

13 13



The partial factors  The partial load factors γ Ff for safe life method  As usual, appears everywhere when stress ranges are used  Depends on how the characteristic loads are determined  Values given in BS and SS NA (only for safe life design)

No. of S.D. on load intensity 0 +1 +

S.D on intensity

No. of S.D. on no. of cycles 0 +2 1.5 1.4 1.3 1.2 . .

σ

r Δσ o Q

S.D on cycles

14 14



The partial factors  The partial material factors Mf  Appears whenever resistances/strengths (N ) are used  Depends on how the assessment method used  EN1993-1-9 suggested values (Clause 3.7 (b), Table 3.1)

Assessment method Damage tolerant Safe life

Unreasonable to use 1.15 >1.10 here. Hence 1.10

Consequence of failure Low High 1.00 1.15

1.15 1.35

BS and SS NA suggested a value .

 Remarks: If a value of γ Mf =1.10 is used throughout, no difference

between the dama e tolerant method and the safe life method

15 15



The S-N curves and fatigue assessment - . . ¾ Tri-linear log-log curves of

(life to failure) cycles

Δσ C at 2 million cycles (curve labels

¾ Based on 5% probability of

a ure

Constants amplitude fatigue limit

¾ Curves labeled by the

detail cate or nominal stress range corresponding to 2 million cycles, Δσ C

m=3

onstant amplitude atigue limit at 5 million cycles ¾ Cut-off limit at 100 million

cycles

m=5

Cut-off limit

16 16



The S-N curves and fatigue assessment 

The S-N curves used in EN1993-1-9 (Fig. 7.1)

¾ The nominal stress ran e corres ondin to 2 million constant

amplitude cycles, Δσ C , is used as the reference fatigue strength for the curve. It also labels the curve (detail category). , , nominal stress range of 100MPa will able to fail the detail in 2 million cycles ¾ The S-N curve can be written as

( Δσ R )mN R = ( Δσ c )m(2x10 6 ) ¾ Δσ R and N R are respectively the design strength and life of the

detail category

17 17



The S-N curves and fatigue assessment - . .  Some important remarks Ff

Mf

¾ Between the constant amplitude limit (5 million cycles) and the cut-

off limit, the slope of the curve is 1/m = 1/5 ¾ The 1/m=1/5 part is for stress spectrum that consists of stress

ranges both above and below the constant amplitude limit ress ranges a ove e cons an amp u e m w cause damage or growth of flaw => Reduce the constant amplitude limit  As time oes on, more stress ran es below the constant

amplitude limit shall contribute to crack growth (but at a lower rate with 1/m=1/5)

18 18



The S-N curves and fatigue assessment - ¾ Two approaches: the stress domain approach and the damage  The stress domain approach

- - , y u frequently used => They are mainly material properties ¾ However, “buckling strength, f buc ” does not exist (but

does)

¾ In EN1993-1-9, the reference fatigue strength Δσ C

corresponding to 2 million cycles of failure is used even it is not a ma er a proper y ¾ Δσ C is used in EN993-1-9 to (1) label the S-N curves and (2) for

19 19



The S-N curves and fatigue assessment - ¾ Damage equivalent factors

i k

constant stress range? ¾ Yes: Through the concept of equivalent damage 1

y c n e u q e r F

Stress range spectrum: Dd = n1 /N R1+ n2 /N R2

n2

N R1 and N R2 from SN curve 1

2

Stress range

ame amage or a cons an stress range Δσ E for n3 cycle Dd = (n3 )/N E . 3 2. Calculate N E 3. From S-N Curve => Δσ E

3

y c n e u q e r F

E

Stress range

Δσ E can be expressed as Δσ E =λ 1Δσ (Qk ), or in general for n stress range spectra

amplitude stress range

) factors Δσ E =λ 1 λ 2 ⋅⋅⋅⋅⋅⋅⋅⋅λ n Δσ (Qk

20 20



The S-N curves and fatigue assessment -  The stress domain approach i ,

i

i

3,

the detail category nor Δσ C ¾ If λ i are known and Δσ E is calculated, fatigue verification against, say 2

million cycles, is reduced to (EN1993-1-9, Clause 8(2)) Ff

Δ C

E , 2 Mf

≤ 1 . 0

Warning: Actual fatigue life required may be more than 2 million cycles

where Δσ E,2 is the equivalent constant amplitude stress range ¾ λ i are not given in EN1993-1-9 and should be specified in the relevant

parts of EN1993 (e.g. crane loading in EN1991-3) which generally are based on simplified loading model

21 21



The S-N curves and fatigue assessment -  The damage domain approach

, which is more representative of the loading expected ¾ Designer needs to obtain information on the loading ranges, frequencies an e r ac ons o e s ruc ures or s m ar s ruc ures  Steps for damage domain assessment i

, frequency, actions) on the structure (or similar structures) 2. Global Structural model: Create a global model of the structure 3. Global responses: Compute the responses of the global model (natural frequencies, nominal forces or stresses etc). If possible, verify the results based on in-situ measurements or scaled model test

22 22



The S-N curves and fatigue assessment -  Steps for damage domain approach (continued)

.

, at locations/details of interests and then their corresponding variable stress range spectra .

 Note that if the interested detail could not be found in the detail category of

EN1993 (or further stress concentration appears), local models (e.g. FE models) should be created to compute the stress range spectra (Δσ i )

5. Cycles to failure: Factor the stress range spectra to generate the design spectra ( γ Ff Δσ i ) and then check against the factored S-N curve 6. Damage verification: Compute damage due to different stress range and then the total damage by the Miner’s summation  For variable amplitude stress range, damage caused by both stress range

above and below the constant stress range limit must be computed

23 23



The S-N curves and fatigue assessment -  What to do if a given detail failed the verification?

ncrease e c ness o mem ers e a s no re- es gn needed) 9 Reduce nominal stress ran e 9 Thickness correction factor for some details with thickness > 25mm ¾ Upgrade the details to next details category ( ≈12% increase in stress range) => local re-design (e.g. connection details) ¾ Re-design of global structural form (e.g. damping, members

arrangement and sizes) => Improve overall responses of structure, reduce forces in members

24 24



Comparison with BS 7608 BS5950 steel structures

a gue es gn and assessment of steel structures n orma ve annexes and references

BS5400 Steel, concrete and composite bridges

Structural Dynamic Fracture mechanics In general: BS more comprehensive Easier to use Less iterations in reading More designer friendly But (perhaps) similar results

Other EN: EN1991, EN1993, NCCI and PD EN1993-1-9 Design of steel structures: Fatigue “Minimum” Annexes NA to EN1993-1-9: Choices of parameters

Similar details given

 Partial factors in EN  More complete detail category in EN

,  Shear and combine stress failure in some EN details  Thickness correction: BS >16mm, EN >25mm

PD6695-1-9-2008 Recommendations, information for design and use

.

25 25


pp ca on examp e: ynam c Fatigue Assessment of Container Quay Crane ¾

Introduction and structural form

¾

Quay crane fatigue assessment

26 26


Dynamic Fatigue assessment of Container Quay Crane

Introduction and structural form  Container Quay Crane (CQC) ¾

A special from of gantry crane

¾

Key machinery for efficient port operations

¾

Main functions: load and unload container to/from ships

¾

Special lifting device called a spreader for loading and discharging of containers

¾

Horizontal gantry rails for quayside movement

¾

Driven by an operator that sits in a cabin suspend from the trolley runs along rails (hoist block )

¾

Lorries/straddle-carriers move underneath the base of t e quay crane

27 27



Introduction and structural form ¾ Typical dimensions:  Boom level: +44m  Overall height: 75m  Boom length: 55m

A-frame

Backstay

Forestay Support beams Boom

 Leg spacing: 30m ¾ Outreach:18 containers ¾ Self Weight: up to 2000

tons ¾ Trolley, machine and

Trolley

Landside upper leg

Spreader container

Landside lower leg

spreader (Hoist block) we g t: tons Portal girders Sill beams 28

28



Introduction and structural form 

Structural form

¾

“Machine-on-trolley” design => Crane machinery moves with trolley for

¾

Designed as a “structure” of thin-plate box girder (plate thickness≤22mm) with many longitudinal and transverse stiffeners

¾

Low stress level in STR limit state: Typical stress level < 50MPa ( f y of steel = 420MPa). For EQU limit: Only 4 legs provide no redundancy

¾

oom ra

es gn ase on

e cons era on o crane ac ons

¾

FAT limit state is critical in design and services: Owner may prefer to s ecific the FAT limit state in terms of the numbers of c cles of operations instead of years of service

¾

Frequent maintenance and services check (4-6 days per year)

¾

Dynamic fatigue analysis is deemed to be compulsory

30 30



Operations and dynamic actions 

Operations

¾ Hoist block load and unloading container to ship and truck

Ship-to-Truck (S-T) and Truck-to-Ship (T-S) 

Dynamic loadings

¾

Movement of crane along wharf-line railway (gantry movement)  Slow and relativity low frequency of occurrence: not critical Wind loading  More severe when the forestay is stowed  Not critical for Singapore terminals but critical for places like HK due to t hoon Dynamic loadings due to S-T and T-S movements of hoist block  High frequency operations (S-T and T-S Cycles)

¾

¾

 Effect could be highly localized

31 31



Operations and dynamic actions ¾ Cycle counting: one cycle per every S-

T (or T-S) operation operations ms: mass of spreader mt : mass o ro ey w mac ne mc : mass of container (variable) av : vertical acceleration of spreader aH : horizontal acceleration of trolley With container Vertical : F = m +m a Horizontal : F H = (ms+mt +mc )( aH ) Without container = Horizontal : F H = (ms+m )( ) t aH

av

18 rows for the CQC studied, row 1 nearest to dock

aH

p Sea-to-truck Truck-to-sea

32 32



Quay crane fatigue assessment 

Overall assessment procedure rea e mo e for global dynamic analysis

Identify fatigue prone oca ons and obtain the stress range s ectrum

Some could only be

Global dynamic

Could be obtained

measurements

wireframe models

measurements or by detailed 3D solid FE modelling

data (aV , aH , mt , mc , ms and frequencies)

assessment by using suitable rules

Butt weld

Fillet weld

33

Backstay tip

33




Global dynamic analysis

¾ Governin

e uation of the s stem in term of dis lacement u

&& + C u& + Ku = F (mg, oper(t), T(t), env(t)) u Self-weight

Operations Temperature Environmental

¾ Wireframe model for dynamic analysis ¾ Dimensions and sections details from

cons ruc on raw ngs ¾ 430 joints, 353 beam-column elements, approx. 2600 DOF ¾ Hoist block modelled as point mass and point load while other utilities as distributed loads ¾ Lump mass matrix, single damping factor

34 34




Global dynamic analysis

¾ To predict the following structural properties of

the CQC under dynamic loading 9 Natural frequencies and mode shapes (1st horizontal 0.64Hz, 1st vertical 1.16Hz) 9 Member forces and force ranges 9 Fatigue prone location(s) = Design spectra due to different operations ¾ Key parameters to be calibrated: shape (for different locations of hoist block) 9 Ground support conditions (spring stiffness for 9 Damping factors

35 35




In situ measurements

¾ Two different tests done with real time

¾ 9

9 9

Extreme land position

Row 18

measuremen s: on ro es an Operation test Control test Separated horizontal hoisting and veridical lifting operations with maximum container weight followed by free vibration Provide specific excitations Responses monitored:  Deflection at sea side boom end by HD video  Accelerations: Two accelerometers  Member forces: Strain au es at two levels, on the four side walls of one of the lower land side legs

36 36




Control test results and calibrations

¾ “Stiff” (150kN/mm) ground support condition

gave best modelling results ¾ Natural frequencies correctly predicted by the model ¾ There is a small change in natural frequencies when the hoist block moved from extreme sea side to extreme land side (≈5%) ¾ Deflections and strain gauges readings compared well with the model  Under static loading deflection range at sea side boom end ≈ 240mm ≈1/460 of boom+ girder

,

=

¾ Damping factors obtained by tracing the peak

res onse deca rate durin free vibration ¾ Horizontal actions: 1%, vertical actions: 0.25% of critical damping ratio

37 37



Quay Crane fatigue assessment 

Critical locations and key parameters

¾ From the control test and global model,

the stiffener ends of sea facing walls of the lower land side legs ¾ The horizontal motions of the hoist block is more critical (≈3-5 times higher in stress range) than vertical lifting of container ¾ Other critical parameters that affecting  Loading and unloading rows  Weight of container

or zon a an ver ca acce era ons o e hoist block and container during operation => operator’s “style” 38 38




Operation test

¾ To obtain magnitudes, distributions and frequency of critical parameters:

, containers  Loading/unloading times a a o a ne rom oa ng an un oa ng opera ons “ uns” on a sma container ship (operation rows 1 to 6), 7 runs from ship-to-truck and 28 runs from truck-to-ship v eo recor s or o s oc or zon a mo ons an con a ner ver ca motions ¾ Accelerometers (on trolley) and strain gauges measurements (side walls of ower an s e eg ¾ In addition, the starting/ending rows distributions during loading/unloading operations from 10 years record (0.85 million operations) from crane owner

39 39




Motions paths for hoist block and container

¾ The horizontal acceleration of the hoist block and the vertical acceleration of the

container are the two most important parameters that affect the dynamic forces applied and stress range induced

Motion path of

h Position S

S m

hm

S d os

on

h s

S

40 40




Motions paths for hoist block and container

Operator accelerated/braked whenever he/she felt necessary for operations or to achieve a minimum time of travel

Motion plot

Velocity and acceleration for a typical cycle

41 41




Motions equations

¾

Velocity and acceleration limits of hoist block and container: max =

¾



.

,

max =

.

2 ,

vmax =

.

,

max =

2

.

All operators would try to minimize the time needed for each operation (within safety limits). Actual travel time depends on the skill and style of operator Different “forms” of motion equations were employed to represent the style and skill of operator 

Six variables (Initial and final positions, velocities and accelerations) are required to define the initial and final conditions of the hoist block

 Assuming

the position of the hoist block is a fifth order polynomial of time =

 Acceleration

2

3

4

5

is then a cubic polynomial: aH =2c 3 + 6c 4t+ 12c 5 t 2 + 20c 6 t 3

42 42




Motions equations

¾

From the maximum velocity and acceleration, the minimum time of travel T (cubic) could be obtained

¾

The cubic acceleration form is corresponding to a “gentle” operator who tries to achieve a gentle acceleration/deceleration throughout the operation “ ” the order and “smoothness” of the acceleration equation to 1. Linear acceleration form => T min(linear) 2. Constant acceleration form=> T min(const)

¾

The constant acceleration form is corresponding to a “swift” operator who alwa s able to use the hoist block en ine u to its mechanical limit so that T min(cubic) > T min(linear) > T min(const)

¾

The main function of motion equations is not to reproduce the measured acceleration forces)

43 43




Motions equations

¾

Checking with actual travel time from HD video records confirmed that the constant acceleration form could give a lower bound of the travel time => maximum dynamic forces

¾

For vertical motions of spreader, similar approach was used and it was found that a linear form is appropriate

50

Cubic form

45

40

) 35 s ( e m i t

Linear form

30 m u m i n i M25

Constant form

20

15

10 30

40 With container

50 Tmin(Con)

60

70

Sm(m) without container

Tmin(Lin)

80 Tmin(Cubic)

44 44




Dynamic loading on quay crane

¾

The final dynamic loading is the combination of horizontal and vertical . , were not synchronized as the operator needed to avoid obstacles (other containers in ship) during operation

¾

The dynamic loadings were applied with the following combinations to obtained the member force ranges 7 6  Rows 1 to 18 s n o i t 5 a  S-T and T-S operations r e 0, 20, 40 tons =>Totally 108 analyses

p o 4 f o e g 3 a t n e c 2 e r P

1 0 1

2

3

4

5

6

7

8

9 ow

10 11 12 13 14 15 16 17 18 um er

45 45




Damage assessment

¾

No special treatment on resonance since period of operations >> > => -

¾

Lower land side leg walls nominal stress ranges: 

From operation test measurement (Rows 1-6): 22MPa to 40MPa



Predicted from dynamic models (Rows 1-6): 31MPa to 55MPa



Higher stress ranges from S-T operations



Maximum stress range from S-T operation with 40 ton container, Row 18 operation => 83MPa (c.f. static range = 37MPa) = .

¾

For other parts such as backstay and addition bracing, FE analysis needed to calculate stress range from member force ranges

46 46




Damage assessment Butt weld

Fillet weld

Backstay tip

47 47



Quay crane fatigue assessment ¾

From nominal/Hot spot stress, perform fatigue design/check by using the appropriate S-N curves  2.3 % failure probability curve was used (or 5% failure probability curve with γ Mf =1.10)  Lower land side leg wall details shall be safe for at least 20 years’ services  Damage contributions from different rows’ operations 12

n o 10 i t u b i r t n 8 o c e g a m 6 a d f o e g 4 a t n e c e r P 2

0 1

2

3

4

5

6

7

8

9

10

Row Number

11

12

13

14

15

16

17

18

48 48

G Lee CK RSA Symposium

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