Rak-83_3100 Fatigue Design Example_1

Example: FAT life calculation for welded details on girders of a travelling overhead crane 1 / 18

Problem descriptionsThis example is a fatigue analysis of an existing design to check the fatigue life of criticalweld details. The crane trolley runs on rails supported by two box girders. The box girdershave diaphragms at intervals along its length.

The crane operates 200 days per year. The crane travels along girders 20 times/day carrying aload of 15 tons (150 kN) including dynamic effects, the dead weight of the trolley being 1 ton(10kN).

20 x 200 times a load of 150 kNThe analysis is carried out for the case when the trolley returns empty

10 x 200 times trolley returns emptyand then for the case when the trolley returns carrying a load of 7 tons (70kN).

10 x 200 times trolley returns with a load of 70 kN


The critical welded details have been identified in the inset sketchand numbered 1-5. The weld description and their categorizationfor fatigue purpose by Eurocode 3, Part 1.1 are as follows:

1 EC 100Longitudinal web to bottom flange manual fillet weld, closing welds ofthe box section, 4 mm throat


2 EC 80Transverse manual fillet at bottom edge of diaphragm to web weld3 EC 80Transverse manual fillet at top edge of diaphragm to top flange weld

Weld details 4 has to be accessed for the direct compressionstresses produced by the local wheel loads as well as bendingstresses resulting from the girders behaving as a beam, and thelongitudinal shear stresses from shears in bending.

4 EC 112/EC 80Web to top flange longitudinal manual T-butt weld under crane rail


4 EC 80 for shear flowWeb to top flange longitudinal manual T-butt weld under crane rail

5 EC 80 Welded stud bolt for fastening rail.

Given valuesbt_flange 500 mm:= bb_flange 500 mm:= hweb 500 mm:=

tb_flange 10 mm:= tweb 10 mm:=tt_flange 10 mm:=

W1 150 kN:= W2 70 kN:= Wdead 10 kN:=

:=


Ls 15 m:=

Stress calculationsCalculation of moment inertia and section modulus of the box girders

Area of each elementtop flange At_f bt_flange tt_flange 5 10

3 mm2=:=

bottom flange Ab_f bb_flange tb_flange 5 103 mm2=:=

web Aw hweb tweb 5 103 mm2=:=

Distance from centroid of each element to bottom flange

top flange yt_f hweb tb_flange+tt_flange

2+ 515 mm=:=

bottom flange yb_ftb_flange

25 mm=:=

webyw

hweb2

tb_flange+ 260 mm=:=


The values of the calculation are shown in the following table:

Area A y* Ay Ay^26500 515 3347500 17239625005000 5 25000 12500010000 260 2600000 67600000021500 5972500 2400087500

* Distance from bottom flange

Element

WebsTotal

top flangebottom flange

The position of neutral axis can be calculated as: ycg?Ay?A

= , i.e.

ycg5972500 mm3

21500 mm2277.791 mm=:=

The second moment of area can be calculated as:

Total1 ?Ay2= Total1 2400087500 mm

4:=

Iweb112

5003 10 mm4 1.042 108 mm4=:= Itop_f112

650 103 mm4 5.417 104 mm4=:=

Ibottom_f112

500 103 mm4 4.167 104 mm4=:=


Total2 ?A( ) ycg2= Total2 21500 mm

2 ycg2 1.659 109 mm4=:=

I Total1 2 Iweb+ Ibottom_f+ Itop_f+ Total2- 9.494 108 mm4=:=

The section modulus can be calculated as:

ZtopI

500 mm 10 mm+ 10 mm+ ycg-( )3.92 106 mm3=:= Zbottom

Iycg

3.418 106 mm3=:=

Calculation of bending stresses

Participation of the crane rail is ignored. The highest bending stresses will be at midspan whenthe trolley is also at midspan. As the trolley passes from one end to the other end of the girders,the bending moment due to living loading will go from zero to maximum and back to zero. The loadis assumed to be carried equally between the two girders. Maximum bending moment range pergirder

?MW1 Wdead+( ) Ls

2 4300 kN m=:=

The stresses can be calculated using simple bending theory, i.e.

orBending SM y

I= S M

Z=


This calculation leads to the following results for the stress ranges at different weld details underthe full load conditions.

h hweb tt_flange+ tb_flange+ 520 mm=:=

?S y( ) ?M yI

:=

Point 1 y1hweb

2250 mm=:=

?S y1( ) 78.996 MPa=Point 2 y2 ycg tb_flange- 100 mm- 167.791 mm=:= ?S y2( ) 53.019 MPa=Point 3 y3 h tt_flange- ycg- 232.209 mm=:= ?S y3( ) 73.375 MPa=Point 4

y4 h tt_flange- ycg- 232.209 mm=:= ?S y4( ) 73.375 MPa=Point 5

y5 h ycg- 242.209 mm=:= ?S y5( ) 76.535 MPa=


Assessment for the trolley carrying the full load of 150 kNAccording to Eurocode 3, Ni may be calculated as follows:

Ni ?Si( ) 5 106

?SD?Mf

?Ff ? ?i

3

?Ff ?Si?SD?Mf

if

5 106

?SD?Mf

?Ff ? ?i

5

?SD?Mf

?Ff ?Si>?SL?Mf

if

? ?Ff ?Si?SL?Mf


According to the welded details, the following categories and characteristic values for eachwelded details are provided according to Eurocode 3

?SC

100808011280

MPa:= ?SD25

13?SC

73.68158.94558.94582.52258.945

MPa=:=

?SL5

100

15 2

5

13

?SC:= ?SL

40.47132.37732.37745.32832.377

MPa=

?Si

?S y1( )?S y2( )?S y3( )?S y4( )?S y5( )

78.99653.01973.37573.37576.535

MPa=:= n

35353

:=


ND 5 106:=

Ni ?Si ?SD, ?SL,( ) ND

?SD?Mf

?Ff ?Si

3

?Ff ?Si?SD?Mf

if

ND

?SD?Mf

?Ff ?Si

5

?SD?Mf

?Ff ?Si>?SL?Mf

if

? ?Ff ?Si?SL?Mf


let N150

N1N2N3N4N5

:=N150

1 10307

1 10307

1 10307

1 10307

1 10307

=

Since the crane travels the length of girders 20 times per day and the crane operates 200 daysa year. Therefore,

n150

20 20020 20020 20020 20020 200

:= n150

4 103

4 103

4 103

4 103

4 103

=


The damage per year for each welded detail can be calculated usingniNi

, i.e.

D150n150N150

:=

D150

00000

=

Assessment for the trolley returning empty

The weight of the empty trolley is 10 kN compared to 160 kN for the fully loaded trolley. Thebending stress ranges due to the passage of the empty trolley will be 1/16 of those for the fulltrolley. These ranges are all less than 10 MPa. The cut-off limits for all categories for direct stressranges, ?SL, have a minimum value of 14 MPa for category EC 36. Adopting this value theapplied stress ranges due to empty return trolley are all less than ?SL / ?Mf and can be ignored.


Assessment for the trolley returning carrying load of 70 kNIn this case, each detail experiences half the number of cycles of stress ranges at a level of(80/160), i.e. half the full stress ranges calculated above. These cycles have to be assessedseparately to find their damage sum n/N per year.

?Si?Si

2:= N1 Ni ?Si0 0,

?SD0 0,, ?SL0 0,

,( ):= N1 1 10307=N2 Ni ?Si1 0,

?SD1 0,, ?SL1 0,

,( ):= N2 1 10307=N3 Ni ?Si2 0,

?SD2 0,, ?SL2 0,

,( ):= N3 1 10307=N4 Ni ?Si3 0,

?SD3 0,, ?SL3 0,

,( ):= N4 1 10307=N5 Ni ?Si4 0,

?SD4 0,, ?SL4 0,

,( ):= N5 1 10307=


let

N70

N1N2N3N4N5

:= N70

1 10307

1 10307

1 10307

1 10307

1 10307

=

Since the crane travels the length of girders 10 times per day and the crane operates 200 days ayear. Therefore,

n70

10 20010 20010 20010 20010 200

:= n70

2 103

2 103

2 103

2 103

2 103

=


The damage per year for each welded detail can be calculated usingniNi

, i.e.

D70n70N70

:=

D70

00000

=

Assemblage of the calculated damage and determination of the fatigue lifeThe total damage can be calculated as: D D150 D70+:=

D

00000

=


The fatigue life for each welded detail can be calculated as:

Fatigue_life1D

:=

Fatigue_life

1.667 10303

1.667 10303

1.667 10303

1.667 10303

1.667 10303

=

Thus, the fatigue life due to bending effect is 221.463 years.

Assemt for weld at point 4 due to local stress

The stress ranges in weld 4 due to local wheel loads are calculated using a 90 degree loaddispersion and from an assumed point contact force, giving the following results based on anindividual wheel load of 40 kN.

Compression stress in weld 4: ?Slocal 40 MPa:=

EC category is 71 and characteristic stress values are:

?SClocal 71 MPa:= ?SDlocal25

13?SClocal 52.313 MPa=:=


?Ff ?Slocal 40 MPa=?SDlocal?Mf

38.751 MPa=

Damage can be calculated as:

Nlocal

?SDlocal?Mf

?Ff ?Slocal

3

5 106 4.546 106=:= Dlocal1

Nlocal2.2 10 7-=:=

The applied number of cycles for the local wheel load stresses is twice number for bendingstress cycles because the trolley has two wheels on each rail, i.e.

nlocal 20 200 2 8 103=:=

The total damage is Dlocal_total Dlocal nlocal 1.76 103-=:=

The fatigue life due to local stress is 1Dlocal_total

568.243=

Rak-83_3100 Fatigue Design Example_1

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