FKT NiehII Statik GRP Stress

Ingenieurbüro für konstruktiven Ingenieurbau Dr.-Ing. Ingo Lukas

Am Krummen Morgen 1 67727 Lohnsfeld Tel. 06302 - 982844 Fax 06302 - 982846

Structural Analysis Power Plant Köln Niehl

Pipeline N3PAB50

Pipeline N3PAB09

Kom 1100/1150

Client: FKT Fassbender GmbH

Bonvitaweg 1-5

53424 Remagen-Kripp

Prepared : Lohnsfeld, 21. November 2013

Ingenieurbüro für konstruktiven Ingenieurbau

Dr.-Ing. Ingo Lukas

(Dr.-Ing. Ingo Lukas)

Project: Power Plant Köln Niehl Page 2 Pipeline N3PAB50 u. N3PAB09


Contents

1. GENERAL .................................................................................................................................................. 3

2. REDUCTION FACTORS AND REQUIRED SECURITIES ........................................................................ 3

3. PERMISSIBLE EXPANSIONS ................................................................................................................... 4

4. LOADING ................................................................................................................................................... 4

4.1 DEADWEIGHT ......................................................................................................................................... 4 4.2 PRESSURE ............................................................................................................................................. 4 4.3 FILLING .................................................................................................................................................. 5 4.4 TEMPERATURE ....................................................................................................................................... 5 4.5 HYDROSTATIC UPLIFT ............................................................................................................................. 5 4.6 LOADING DUE TO SOIL ............................................................................................................................. 6 4.7 TRAFFIC LOAD ........................................................................................................................................ 6 4.8 GROUNDWATER ..................................................................................................................................... 6 4.9 SETTLEMENT .......................................................................................................................................... 6 4.10 EARTHQUAKE ......................................................................................................................................... 7

5. PIPE DESIGN ............................................................................................................................................ 8

5.1 PROOF OF THE TENSIONS IN LENGTHWISE DIRECTION UNDERGROUND PIPELINES ..................................... 8 5.2 PROOF OF THE TENSIONS IN CIRCUMFERENTIAL DIRECTION UNDERGROUND PIPELINES ............................. 8 5.3 STABILITY ANALYSIS UNDERGROUND PIPELINES .................................................................................... 26

6. DETAIL PROOFS .................................................................................................................................... 31

6.1 JOINT LAMINATES ................................................................................................................................. 31 6.2 OPENINGS............................................................................................................................................ 32 6.3 FLANGE DESIGN ................................................................................................................................... 38 6.4 SUPPORT REACTIONS DUE TO LENGTHWISE LOADINGS .......................................................................... 45 6.5 WALL RING AT FIX POINTS .................................................................................................................... 47 6.6 HEAD DN 2000 .................................................................................................................................... 48

7. MATERIAL DATA ..................................................................................................................................... 50



1. General

Object of this analysis is the design for the underground cooling water lines N3PAB50 and N3PAB09 of the

Power Plant Köln-Niehl.

The substantial parts of the pipings are made in the winding mode method of a Winding-Laminat. With a

winding angle of 54°.The joint laminates are produced of mixed laminat. The connection of the single sec-

tions of the pipeline results from inner and outer joint laminates.

All parts receive a fleece layer on the inner side which serves as a protective layer.

The following materials are being used as amplifictaion material: Protection layer - C - or E - CR - glas - fleece Traglaminat - E - and E – CR respectively - glas The following matrix materials are used: Derakane 411 basis of calculation:

Spool Drawings FKT GmbH material: look at the paragraph material data

literature: [1] Berechnungsempfehlungen für stehende Behälter aus glasfaserverstärkten Kunstoffen,

- IfBt - Berlin, Oktober 1998

[2] AD-Merkblatt 2000

[3] DIN 18800 Teil 4

[4] DIN 1055

[5] DIN 18820

[6] DIN V2505

[7] DIN 1055

[8] mb-Software AG: Handbuch zum Programmsystem MicroFE; Hameln 2001 [9] Worksheet A 127 der ATV AD-N1.

2. Reduction Factors and Required Securities

Because the time of charge, the temperature and the filling medium of the Storage Tank have a great effect

on GRP, the loadings have to be increased by A-values and a global security factor S

stress analysis:

8,2 321 mBmB AAAA

stability analysis:

1,89 321 SAAASA II



Material safety m

m = 1,40 If there are no temperature or media impacts, the respective coefficients are not required.

The following applies to all laminates used on the seperator:

A2 = 1,10 (influence of the medium) A3 = 1,26 (influence of the temperature)

If there are no temperature or media impacts, the respective coefficients are not required.

Necessary safeties on the load side The necessary safeties on the load side can be taken from the load compilation of the component.

3. Permissible expansions

Underground Pipelines

All Laminate Types: zul = 0.50% Pipelines during Test

Winding laminates in circumferential direction during operation zul = 0.35%

Winding laminates in longitudinal direction during operation zul = 0.30%

Mixed laminates during operation zul = 0.35%

4. Loading

4.1 Deadweight

GF =18,00 kN/m³

tm ≤ ttr + SS

gE ≤ 2 .

. r

. 18

. tm

The consideration of the own weight of the laminate occurs intern of program by input of the shell thickness and the density of the laminate.

4.2 Pressure

Internal Design pressure pü = 500 kN/m

2

Internal Test pressure püT = 750 kN/m

2

Short time external Design pressure pu = 80 kN/m

2



4.3 Filling

W = 10,30 kN/m3

The following line loads set in the later calculation result from it

DN 2000 qw = 1,02 .

. 10,30 = 32,35 kN/m

4.4 Temperature

MCW piping downstream of the condenser

Design temperature TB = 50° C mit T = 30 K

Operation temperature TBO = 23° C mit T = 5,00 K

T = 2,0 . 10

-5

MCW piping upstream of the condenser

Design temperature TB = 30° C mit T = 10 K

Operation temperature TBO ≤ 20° C mit T ≈ 0,00 K

T = 2,0 . 10

-5

4.5 Hydrostatic uplift

W = 10,30 kN/m3

The following line loads set in the later calculation result from it

DN 2000 qw,lift = -1,02 .

. 10,30 = -32,35 kN/m

DN 1400 qw,lift = -0,72 .

. 10,30 = -15,85 kN/m



4.6 Loading due to soil

The load settings are defined by worksheet A-127 of ATV.

4.7 Traffic Load

SLW 60, Loading according to [9] –Chapter 52.2.1

4.8 Groundwater

Max. groundwater level above pipe invert : H = 4,37 m ( 200 year event) Min. groundwater level above pipe invert: H ≤ 0,00 If the groundwater levels exeeds H = 2,00 m the pipe must be flooded.

4.9 Settlement

Settlement s = -1,00 mm / m Differential settlements generate bending moments at a bend in the bending line. Due to continuous settle-ments resulting no bending moments

Covering Condition: A1 Embedding Condition: B1

Bedding Case 1: 2 = 180°



Example:

For the bending moment and l ≥ 3

. D in a conservative estimate, it is valid:

M = EI . s

. 3 / L

2 (smallest distance between supports)

DN 2000: M = EI . s / L

2 = 925911

. 0,006

. 3/ 6

2 = 462,96 kNm

DN 1800: M = EI . s / L

2 = 264546

. 0,0042

. 3/ 4,2

2 = 188,96 kNm

4.10 Earthquake

Earthquakes cause a horizontal acceleration of the construction. Free field acceleration ag = 0,40 m/s

2

Significance factor 1 = 1,20

Subsoil parameter S = 1,25 (Subsoil class C-T)

Structural behaviour factor q = 1,50

bound factor β0 = 2,50

The computation is done in a conservative estimate on the plateau of the design spectrum

Design field acceleration SD(T) = ag . S

. 1

. ßo /q = 0,40

. 1,25

. 1,2

. 2,50 /1,50 = 1,0 m/s

2

Horizontal force due to earthquake: VEQ = (1,00/9,81) . G = 0,10

. G

DN 2000 qEBx = qEBy = 0,10

. ( 2,47 + 31,42) = 3,39 kN/m

DN 1600 qEBx = qEBy = 0,10

. (1,78 + 20,11) = 2,19 kN/m

DN 1400 qEBx = qEBy = 0,10

. (1,47 + 15,40) = 1,69 kN/m

This loadings are small and can be neclected for the design.



5. Pipe Design

The design of the pipes results from the construction principle and the calculation references of the DIBt and

the worksheet A-127 of ATV.

5.1 Proof of the Tensions in lengthwise direction Underground Pipelines

Pipe DN 2000, t = 19,50 mm

Pressure: l,p = 0,50 . 500 /19,50 = 12,82 N/mm

2

Settlement: l,S = 492,96/ ( .19,50) = 8,04 N/mm

2

l = 1,5 . (1,5

. 12,82+ 8,04) = 40,91 N/mm

2 ≤ l,zul = 130/ ( 1,10

. 1,26

. 1,40) = 67,00 N/mm

2

l = 100

. (12,82+ 8,04)/(1,1

. 120000) = 0,19 % ≤ 0,25 %

Pipe DN 1400, t = 16,50 mm

Pressure: l,p = 0,35 . 500 /16,50 = 10,60 N/mm

2

Settlement: l,S = 188,96/ ( . 0,7

2 . 16,5) = 7,34 N/mm

2

l = 1,5 . (1,5

. 10,60 + 7,34 ) = 34,86 N/mm

2 ≤ l,zul = 130/ ( 1,10

. 1,26

. 1,40) = 67,00 N/mm

2

l = 100

. (10,60+ 7,34)/(1,1

. 120000) = 0,14 % ≤ 0,25 %

5.2 Proof of the Tensions in circumferential direction Underground Pipelines

The underground pipes are calculated with the worksheet A-127 of ATV. Condition for the approach is that

the pipes are grounded correspondent to the demands. It means that the support angle is ≥ 180°, the

grounding occurs in layers and a compaction of the ground ≥ 95 % Proctor is given.

For the pipeline with stiffening rings two proofs are carried out, the area of the ribs and the intermediate re-

gion. The area between the rips gets only the loading due to soil. The ring section takes the load of the soil

and an additional traffic load due to SLW 60.

When the pipe parts that are charged by the specified traffic load, the following approach for the determina-

tion of internal loads is chosen for the calculation of ring:

LR = t3ers

.

lR /12

ters =(12 . IR /LR )

1/ 3 . 0,75

LR : Distance between Stiffners

IR: Moment of inertia of the ringstffner

ters: Substitute thickness pipe in the area of the ribs

The following picture shows the used ringstiffner.



Pipe DN 2000, t = 19,50 mm

effective width of the Shell zR tRb **6.1 = 400 + 1,6 * (1000 . 19,5 ) = 623,4 mm

vorh IR ≥ 3139,3 cm4

ters =(12 . IR /lR )

1/ 3 . 0,75 = (12

. 3139,3/400)

1/ 3 . 0,75

. 10 = 34,12 mm

Pipe DN 1400, t = 14,50 mm


vorh IR ≥2757,7 cm

4


1/ 3 . 0,75 = (12

. 2757,7/400)

1/ 3 . 0,75

. 10 = 32,63 mm



DN 2000 Pipe Area between rips Data

Pipe DN 2000

Internal diameter di 2000 mm

External diameter da 2039 mm

Wall thickness(pipe material) t 19,5 mm

unit wt. Gravity pipe material R 22 kN/m3

Modulus of elasticity of pipe material( short-term characteristic) ERK 18000 N/mm2

Permitted vertical deformation of diameter(long-term) dv 6 %

Soil

Surrounding soil

Soil group G G3

Compactness DPr 95 %

Internal angle of friction j' 25 °

Groundwater present nein

Max. groundwater level above pipe invert max hW 0 m

Min. groundwater level below pipe invert min hW 0 m

Backfilling of pipeline zone

Soil group G G1

unit wt. Gravity pipe material B 14 kN/m3

Internal friction angle j' 35 °

Covering

Soil group G G3

Unti wt. B 20 kN/m3

Unit w. under buoyancy B' 10 kN/m3


Placement conditions

Covering high h 2,25 m

Trench width b 5 m

Embankment condition b 90 °

Covering condition A A1

Embedment condition B B1

Bedding case I

Bedding angle 2 180 °

Relative projection a 1 1

Trench walls retained long-term ja

Deformation moduli EB:

above the pipe E1 3 N/mm2

Tab 8

next to the pipe E2,0 16 N/mm2

Tab 8

surrounding soil next to the pipe E3 16 N/mm2

Tab1

Earth pressure ratio K1 0,5 1 Tab 4

Wall friction angle d 23,31 ° Tab 4

Loading

Standart vehicle konstruktiv

Traffic load p 5 kN/m2

Area load po 0 kN/m2

Water filling W 0 kN/m3

Internal pressure pi 0 kN/m2



1 (5.04)

pE 45,00 kN/m2 (5.01)

p 5 kN/m2 (5.07)

j 1 Tab. 6

pV 5 kN/m2 (5.11)

1 D5

f1 1 Tab. 1

f2 0,75 (6.01)

E2 16,00 N/mm2

Tab. 8, (6.02)

rm 1009,75 mm

ER 18000 N/mm2

I 617,91 mm4/mm (6.10e)

So 0,00135 N/mm2 (6.10b)

f 1,02 (6.18)

0,374 (6.17)

SBh 3,589 N/mm2 (6.16)

VRB 0,00301 (6.15)

K2 0,400 Tab.9

a' 0,260 (6.05)

max 1,020 6.3.1, (6.04)

SBv 16,00 N/mm2 (6.12)

Ch,qv 0,0833 Tab.10a

Ch,qh -0,0833 Tab. 10a

Ch,qh -0,0658 Tab. 10a

K* 1,2106 (6.14)

Cv,qv -0,0833 Tab.10a

Cv,qh 0,0833 Tab.10a

Cv,qh.

0,0640 Tab.10a

Cv* -0,00582 (6.13)

K` 1,000 (6.06b)

R 0,562 (6.06a)

RG 0,788 (6.21a)

fo 3,663 (6.23a)

1,146 (6.22)

qv 40,45 kN/m

2 (6.24)

qh 28,79 kN/m2 (7.01)

qh. 14,12 kN/m

2 (7.02a)

dv 0,63 % (8.17)



Internal Forces and Tensions Support angle 2 = 180° Internal Forces in kN Bending Moments in kNm Tensions in N/mm

2

Coefficients

mqv mqh mqh* mg mw

Crown 0,250 -0,250 -0,181 0,345 0,172 Haunch -0,250 0,250 0,208 -0,393 -0,196 Invert 0,250 -0,250 -0,181 0,441 0,220

nqv nqh nqh* ng mw

Crown 0,000 -1,000 -0,577 0,167 0,583 Haunch -1,000 0,000 0,000 -1,571 0,215 Invert 0,000 -1,000 -0,577 -0,167 1,417

Bending Moments and Normal forces

Mqv Mqh Mqh* Mg Mw Summe

Crown 10,311 -7,338 -2,606 0,123 1,771 2,262

Haunch -10,311 7,338 2,995 0,000 -2,018 -1,996

Invert 10,311 -7,338 -2,606 0,008 2,265 2,640

Nqv Nqh Nqh* Ng Nw Summe

Crown 0,000 -29,067 -8,228 0,030 5,944 -31,320

Haunch -40,846 0,000 0,000 0,000 2,192 -38,654

Invert 0,000 -29,067 -8,228 0,000 14,448 -22,847

mit

rm 1009,75 mm s 19,5 mm



Tensions in N/mm2

A 195,00 cm2

W 63,38 cm3

Vertical- loading

Lateral Pres-sure qh

Bedding Reaction

Pressure qh* Deadweight Waterfilling Sum

Crown 163,748 -118,015 -41,811 1,962 28,426 34,310

Haunch -165,842 116,525 47,563 0,000 -31,933 -33,688

Invert 163,748 -118,015 -41,811 0,129 36,710 40,761

Vertical- loading


Bedding Reaction


Crown -161,653 113,544 40,437 -1,934 -27,457 -37,063

Haunch 159,558 -115,034 -46,954 0,000 31,748 29,318

Invert -161,653 113,544 40,437 -0,128 -34,768 -42,568



DN 2000 Ring Area including Loading due to SLW Data

Pipe DN 2000


External diameter da 2068,24 mm





Soil

Surrounding soil

Soil group G G3







Soil group G G1



Covering

Soil group G G3

Unti wt. B 20 kN/m3





Trench width b 5 m




Bedding case I






Tab 8


Tab 8


Tab1



Loading

Standart vehicle SLW60

Traffic load p 22,45 kN/m2






1 (5.04)

pE 45,00 kN/m2 (5.01)

p 22,45 kN/m2 (5.07)

j 1,2 Tab. 6

pV 26,94 kN/m2 (5.11)

1 D5

f1 1 Tab. 1

f2 0,75 (6.01)

E2 16,00 N/mm2

Tab. 8, (6.02)

rm 1017,06 mm

ER 18000 N/mm2

I 3310,14 mm4/mm (6.10e)

So 0,00708 N/mm2 (6.10b)

f 1,01 (6.18)

0,368 (6.17)

SBh 3,531 N/mm2 (6.16)

VRB 0,01604 (6.15)

K2 0,400 Tab.9

a' 0,260 (6.05)

max 1,020 6.3.1, (6.04)

SBv 16,00 N/mm2 (6.12)


Ch,qh -0,0833 Tab. 10a

Ch,qh -0,0658 Tab. 10a

K* 1,0178 (6.14)

Cv,qv -0,0833 Tab.10a


Cv,qh.

0,0640 Tab.10a

Cv* -0,01816 (6.13)

K` 1,000 (6.06b)

R 0,609 (6.06a)

RG 0,815 (6.21a)

fo 3,663 (6.23a)

1,130 (6.22)

qv 63,63 kN/m

2 (6.24)

qh 28,62 kN/m2 (7.01)

qh. 35,63 kN/m

2 (7.02a)

dv 1,12 % (8.17)




2

Coefficients

mqv mqh mqh* mg mw


nqv nqh nqh* ng mw




Crown 16,454 -7,401 -6,671 0,219 1,810 4,411

Haunch -16,454 7,401 7,667 0,000 -2,062 -3,449

Invert 16,454 -7,401 -6,671 0,008 2,315 4,705


Crown 0,000 -29,107 -20,911 0,031 6,031 -43,957

Haunch -64,713 0,000 0,000 0,000 2,224 -62,489

Invert 0,000 -29,107 -20,911 0,000 14,658 -35,360

mit

rm 1017,06 mm s 34,12 mm



Tensions in N/mm2

A 341,20 cm2

W 194,03 cm3

Vertical- loading


Bedding Reaction


Crown 85,751 -39,423 -35,381 1,143 9,607 21,697

Haunch -87,648 38,570 39,955 0,000 -10,681 -19,804

Invert 85,751 -39,423 -35,381 0,043 12,492 23,482

Vertical- loading


Bedding Reaction


Crown -83,855 36,864 33,387 -1,116 -9,045 -23,766

Haunch 81,958 -37,717 -39,071 0,000 10,574 15,744

Invert -83,855 36,864 33,387 -0,042 -11,366 -25,013



DN 1400 Pipe Area between rips Data

Pipe DN 1400


External diameter da 1433 mm





Soil

Surrounding soil

Soil group G G3







Soil group G G1



Covering

Soil group G G3

Unti wt. B 20 kN/m3





Trench width b 5 m




Bedding case I






Tab 8


Tab 8


Tab1



Loading

Standart vehicle konstruktiv

Traffic load p 5 kN/m2






1 (5.04)

pE 51,00 kN/m2 (5.01)

p 5 kN/m2 (5.07)

j 1 Tab. 6

pV 5 kN/m2 (5.11)

1 D5

f1 1 Tab. 1

f2 0,75 (6.01)

E2 16,00 N/mm2

Tab. 8, (6.02)

rm 708,25 mm

ER 18000 N/mm2

I 374,34 mm4/mm (6.10e)

So 0,00237 N/mm2 (6.10b)

f 1,44 (6.18)

0,624 (6.17)

SBh 5,992 N/mm2 (6.16)

VRB 0,00317 (6.15)

K2 0,400 Tab.9

a' 0,260 (6.05)

max 1,026 6.3.1, (6.04)

SBv 16,00 N/mm2 (6.12)


Ch,qh -0,0833 Tab. 10a

Ch,qh -0,0658 Tab. 10a

K* 1,2079 (6.14)

Cv,qv -0,0833 Tab.10a


Cv,qh.

0,0640 Tab.10a

Cv* -0,00600 (6.13)

K` 1,000 (6.06b)

R 0,584 (6.06a)

RG 0,655 (6.21a)

fo 3,618 (6.23a)

1,139 (6.22)

qv 38,40 kN/m

2 (6.24)

qh 28,96 kN/m2 (7.01)

qh. 11,41 kN/m

2 (7.02a)

dv 0,30 % (8.17)




2

Coefficients

mqv mqh mqh* mg mw


nqv nqh nqh* ng mw




Crown 4,816 -3,632 -1,036 0,051 0,611 0,811

Haunch -4,816 3,632 1,190 0,000 -0,696 -0,690

Invert 4,816 -3,632 -1,036 0,004 0,782 0,934


Crown 0,000 -20,511 -4,661 0,021 2,924 -22,226

Haunch -27,199 0,000 0,000 0,000 1,078 -26,121

Invert 0,000 -20,511 -4,661 0,000 7,108 -18,064

mit

rm 708,25 mm s 16,5 mm



Tensions in N/mm2

A 165,00 cm2

W 45,38 cm3

Vertical- loading


Bedding Reaction


Crown 106,961 -81,902 -23,283 1,143 13,749 16,667

Haunch -108,609 80,659 26,432 0,000 -15,400 -16,919

Invert 106,961 -81,902 -23,283 0,089 17,790 19,655

Vertical- loading


Bedding Reaction


Crown -105,312 78,172 22,364 -1,123 -13,185 -19,084

Haunch 103,664 -79,416 -26,024 0,000 15,292 13,516

Invert -105,312 78,172 22,364 -0,088 -16,661 -21,524



DN 1400 Ring Area including Loading due to SLW Data

Pipe DN 1400


External diameter da 1465,26 mm





Soil

Surrounding soil

Soil group G G3







Soil group G G1



Covering

Soil group G G3

Unti wt. B 20 kN/m3





Trench width b 5 m




Bedding case I






Tab 8


Tab 8


Tab1



Loading

Standart vehicle SLW60

Traffic load 20,29 kN/m2






1 (5.04)

pE 51,00 kN/m2 (5.01)

p 20,29 kN/m2 (5.07)

j 1,2 Tab. 6

pV 24,348 kN/m2 (5.11)

1 D5

f1 1 Tab. 1

f2 0,75 (6.01)

E2 16,00 N/mm2

Tab. 8, (6.02)

rm 716,315 mm

ER 18000 N/mm2

I 2895,14 mm4/mm (6.10e)

So 0,01772 N/mm2 (6.10b)

f 1,41 (6.18)

0,599 (6.17)

SBh 5,755 N/mm2 (6.16)

VRB 0,02464 (6.15)

K2 0,400 Tab.9

a' 0,260 (6.05)

max 1,026 6.3.1, (6.04)

SBv 16,00 N/mm2 (6.12)


Ch,qh -0,0833 Tab. 10a

Ch,qh -0,0658 Tab. 10a

K* 0,9211 (6.14)

Cv,qv -0,0833 Tab.10a


Cv,qh.

0,0640 Tab.10a

Cv* -0,02435 (6.13)

K` 1,000 (6.06b)

R 0,650 (6.06a)

RG 0,719 (6.21a)

fo 3,618 (6.23a)

1,117 (6.22)

qv 61,01 kN/m

2 (6.24)

qh 28,64 kN/m2 (7.01)

qh. 29,81 kN/m

2 (7.02a)

dv 0,56 % (8.17)




2

Coefficients

mqv mqh mqh* mg mw


nqv nqh nqh* ng mw




Crown 7,826 -3,674 -2,769 0,104 0,632 2,119

Haunch -7,826 3,674 3,182 0,000 -0,720 -1,691

Invert 7,826 -3,674 -2,769 0,004 0,809 2,196


Crown 0,000 -20,514 -12,323 0,022 2,991 -29,824

Haunch -43,701 0,000 0,000 0,000 1,103 -42,598

Invert 0,000 -20,514 -12,323 0,000 7,271 -25,566

mit

rm 716,32 mm s 32,63 mm



Tensions in N/mm2

A 326,30 cm2

W 177,45 cm3

Vertical- loading


Bedding Reaction


Crown 44,771 -21,645 -16,218 0,595 3,708 11,211

Haunch -46,110 21,017 18,204 0,000 -4,087 -10,977

Invert 44,771 -21,645 -16,218 0,024 4,849 11,780

Vertical- loading


Bedding Reaction


Crown -43,432 19,759 14,989 -0,576 -3,417 -12,676

Haunch 42,092 -20,388 -17,659 0,000 4,032 8,077

Invert -43,432 19,759 14,989 -0,023 -4,265 -12,971

DN 2000 σu ≤ 500 . 1,00 / 19,50 + 40,98 = 66,62 N/mm²

AB . ≥ 350/ ( 1,50

. 1,10

. 1,26

. 1,40

. 1,50) = 80,16 N/mm²

u ≤ 66,62 / ( 1,10 . 18000) = 0,34 % < 0,50%

Deflections: δ ≤ 1,12 % < 2,00 % long term

DN 1400 σu ≤ 500 . 0,70 / 16,50 + 39,15 = 59,66 N/mm²

AB . ≥ 350/ ( 2,00

. 1,10

. 1,26

. 1,40

. 1,50) = 60,12 N/mm²

u ≤ 59,66 / ( 1,10 . 20000) = 0,27 % < 0,50%

Deflections: δ ≤ 0,60 % < 2,00 % long term



5.3 Stability Analysis Underground Pipelines

Due to the elastic support by the soil, shell and ringstiffners are able to accommodate a substantial higher

external pressure. The smallest known bedding factor is ß = 3

Decisive for the proof of stability get the √A1-f-times loading due to soil and shortime external pressure:

Pipe DN 2000, t = 19,50 mm

The stability analysis follows [1]. Reduction Factors and Required Securities: A1l,I = 1,50 A1l,u = 1,50 A2 = 1,10 A3 = 1,26

m = 1,40

- Pressure :

√A1 . f

. qv/b = (√1,50

. 1,50

. 40,45 + 1,50

. 80) / 3,00 = 64,77 kN/m

2

- Axial Forces :

In the worst case tensions in the lengthwise directions can occur due to a restrained thermal expansions of

the pipe.

Tensions due to restrained thermal expansion: L,T = -T . T

. (EU

. EL)

0,5 = 8,81 N/mm

2

EU = 18000 N/mm2

EL = 12000 N/mm2

T = 2,0 . 10

-5

T ≤ 30 K

√A1

. f

.nL = √1,50

. 1,00

. 19,5

. (8,81+ 8,04/1,2) + 80

. 1,5

. 0,50 = 430,42 kN/m

Critical axial loading: R = 1,00 m

Ev = lBuB EE

= 14696,9 N/mm²

EuB = 18000 N/mm² ElB = 12000 N/mm² ts = 19,50 mm



n k E Et

Rk E

t

Rkrit i uB lB

si V

s 2 2

kk

R

t

ir

Z i

1100 ,

ki = 0,34 nkrit = 1903,78 kN/m Critical circumferentiel loading:

5.2

4 385.0

R

t

l

REEp s

o

lBuBkrit

lo = 4000 mm pkrit = 183,52 kN/m² Stability analysis :

n

n

vorh

krit

= 430,42 . 1,1

. 1,26

. 1,40/1903,78 = 0,439 < 1

p

p

vorh

krit

= 64,77 . 1,1

. 1,26

. 1,40/183,52 = 0,68 < 1

( ) ( ). .n

n

p

p

vorh

krit

vorh

krit

125 125 = 0,439

1.25 + 0,68

1.25 = 0,975,00 1

Proof of the stiffening rings According to [1]:

pinst = 3

2

2222

2

44 3 )1(

)()2

1( RR

RRslBub

Rl

IEm

mmR

tEE

= . R / lz

ls = ∞

lR = 4000 mm

m = 2

For a ring gap of lR ≤ 4000 mm, an endless pipe length the following values count, if a stability analysis is

done:

= 0 m = 2



Erf ER

. IR ≥ 183,71 kNm²

erf IR ≥ 1837,1 cm4


Pipe DN 2000, t = 19,50 mm


vorh IR ≥ 3139,3 cm4

Pipe DN 1400, t = 16,50 mm

The stability analysis follows [1]. Reduction Factors and Required Securities: A1l,I = 1,50 A1l,u = 1,50 A2 = 1,10 A3 = 1,26

m = 1,40

- Pressure :

√A1 . f

. qv/b = (√1,50

. 1,50

. 38,40 + 1,50

. 80) / 3,00 = 63,51 kN/m

2



- Axial Forces :

In the worst case tensions in the lengthwise directions can occur due to a restrained thermal expansions of

the pipe.

Tensions due to restrained thermal expansion: L,T = -T . T

. (EU

. EL)

0,5 = 8,81 N/mm

2

EU = 18000 N/mm2

EL = 12000 N/mm2

T = 2,0 . 10

-5

T ≤ 30 K

√A1

. f

.nL = √1,50

. 1,00

. 16,5

. (8,81+ 7,34/1,2) + 80

. 1,5

. 0,35 = 343,64 kN/m

Critical axial loading: R = 0,70 m

Ev = lBuB EE

= 14696,9 N/mm²

EuB = 18000 N/mm² ElB = 12000 N/mm² ts = 16,50 mm

n k E Et

Rk E

t

Rkrit i uB lB

si V

s 2 2

kk

R

t

ir

Z i

1100 ,

ki = 0,35 nkrit = 2006,87 kN/m Critical circumferentiel loading:

5.2

4 385.0

R

t

l

REEp s

o

lBuBkrit

lo = 4000 mm pkrit = 275,18 kN/m²



Stability analysis :

n

n

vorh

krit

= 343,64 . 1,1

. 1,26

. 1,40/2006,87 = 0,33 < 1

p

p

vorh

krit

= 63,51 . 1,1

. 1,26

. 1,40/183,52 = 0,60 < 1

( ) ( ). .n

n

p

p

vorh

krit

vorh

krit

125 125 = 0,33

1.25 + 0,60

1.25 = 0,78 1

Proof of the stiffening rings According to [1]:

pinst = 3

2

2222

2

44 3 )1(

)()2

1( RR

RRslBub

Rl

IEm

mmR

tEE

= . R / lz

ls = ∞

lR = 4000 mm

m = 2

For a ring gap of lR ≤ 4000 mm, an endless pipe length the following values count, if a stability analysis is

done:

= 0 m = 2 Erf ER

. IR ≥ 62,05 kNm²

erf IR ≥ 620,51 cm4





vorh IR ≥2757,7 cm

4


1/ 3 . 0,75 = (12

. 2757,7/400)

1/ 3 . 0,75

. 10 = 32,63 mm

6. Detail Proofs

6.1 Joint laminates

chosen : mixed laminate tüi = tüa = 7,80 mm, lü = 125 mm

Pipe DN 2000, t = 19,50 mm

The maximum multiple A1-f-times cut load for the pipes is:

A1 . f

.nL = 1,50

. 1,50

. (19,5

. 8,04) + 500

. 0,50) = 915,26 kN/m

The maximum characteristic cut load for the pipes is: nlc = (19,5

. 8,04) + 500

. 0,50) = 406,78 kN/m

=915,26/ 15,60 = 58,67 N/mm2 ≤ zul = 130/ (1,1

. 1,26

. 1,40) = 67,01 N/mm

2

= 406,78 . 100 / (1,10

. 15,60

. 10000) = 0,24 % ≤ 0,30 %

KL =915,26/ (125 . 2 ) = 3,66 N/mm

2 ≤ zul = 8,00 (1,1

. 1,26

. 1,40) = 4,12 N/mm

2

Pipe DN 1700, t = 16,50 mm

The maximum multiple A1-f-times cut load for the pipes is:

A1 . f

.nL = 1,50

. 1,50

. (16,5

. 7,34) + 500

. 0,35) = 655,11 kN/m

The maximum characteristic cut load for the pipes is: nlc = (16,5

. 7,04) + 500

. 0,35) = 291,16 kN/m

=655,11/ 15,60 = 41,99 N/mm2 ≤ zul = 130/ (1,1

. 1,26

. 1,40) = 67,01 N/mm

2

= 291,16 . 100 / (1,10

. 15,60

. 10000) = 0,17 % ≤ 0,30 %

KL =655,11/ (125 . 2 ) = 2,62 N/mm

2 ≤ zul = 8,00 (1,1

. 1,26

. 1,40) = 4,12 N/mm

2



6.2 Openings

The proof is provided in accordance with the model calculation of the DIBt (civil engineering competence

centre). The respective proofs are provided in tables for the decisive sections. In these tables the following

abbreviations are used:

ts wall thickness of the shell laminate

tü wall thickness of the overlaminate

si ideal wall thickness; here the following applies: si = ts + tü . (Eoverlaminate/ Eshell laminate)

lü length of the overlaminate

va weakening coefficient

max n existing normal force in the area of the opening

SL tensions in the laminate of the shell

ÜL tensions in the overlaminate

zulSL permissible tensions in the laminate of the shell, zulSL = SAA

SL

32

zulÜL permissible tensions in the overlaminate, zulÜL = atÜberla

SchaleÜL

A

A

SAA min1

1

32

The following applies to the proof:

A2 = 1,1 A3 =1,26 M = 1,40 f = 1,50

Circumferential direction

A1,Schale = 1,50 A1,Überlaminat = 2,00

Lengthwise direction

A1,Schale = 1,50 A1,Überlaminat = 2,00

The following constructive stipulations have to be taken into consideration in accordance with [1]:

If tü > ts, the necessary strengthening laminate must be distributed across the inside and outside of

the shell.

Optimal: tüi = tüa

Possible: tüi = 0.33 tü and tüa = 0.67 tü



For the allowable tensions for A1 – times loadings it is valid:

Mixed Laminat

zul = 130/ (1,1 .1,26

. 1,40

. 1,50) = 44,66 N/mm

2

Winding Lamimat circumferential direction

zul = 350/ (1,1 .1,26

. 1,40

. 1,50) = 120,25 N/mm

2


zul = 130/ (1,1 .1,26

. 1,40

. 1,50) = 44,66 N/mm

2

For the allowable equivalent tensions due to deformations for characteristic loadings it is valid:

Mixed Laminat

,zul = 10000 . 1,1

. 0,003 = 33,0 N/mm

2 (operation)

,zul = 10000 . 1,1

. 0,0035 = 38,50 N/mm

2 (test)


,zul = 18000 . 1,1

. 0,003 = 59,40 N/mm

2 (operation)

,zul = 18000 . 1,1

. 0,0035 = 69,30 N/mm

2 (test)


,zul = 12000 . 1,1

. 0,0025 = 33,00 N/mm

2 (operation)

,zul = 12000 . 1,1

. 0,003 = 39,60 N/mm

2 (test)

Internal forces A1-times due to pressure

nu = 1,50 . 1,00

. 500 = 750 kN/m (operation)

nu = 1,00

. 750 = 750 kN/m (test)

nl = 1,50 . 1,00

. 500

. 0,5 = 375 kN/m (operation)

nl = 1,00

. 750

. 0,5 = 375 kN/m (test)

http://dict.leo.org/ende/index_de.html#/search=equivalent&searchLoc=0&resultOrder=basic&multiwordShowSingle=on



Shell section tensions in circumferential direction

Component Shell Ø DN opening Ø da Shell Eu Reinforcement Eu ts = szyl tü = sUE sa = ts+tü [mm] idealy thick. si

[mm] [mm] [N/mm

2] [N/mm

2] [mm] [mm] [mm]

1 2000 1400 18000 10000 19,5 62 81,5 53,94

2 2000 1620 18000 10000 19,5 66 85,5 56,17

Component max nud va Shell zul.Shell Jointlaminat zul.Jointaminat

[kN/m] [N/mm2] [N/mm

2] [N/mm

2] [N/mm

2]

1 750 0,213 65,30 69,30 36,28 38,50

2 750 0,195 68,44 69,30 38,02 38,50

Component erf. x1(Da*sa) erf. x2(da*sa) x1 x2

[mm] [mm] [mm] [mm]

1 403,7 337,8 410 350

2 413,5 372,2 420 380

Shell section tensions in lengthwise direction

Component Shell Ø DN opening Ø da Shell Eu Reinforcement Eu ts = szyl tü = sUE sa = ts+tü [mm] idealy thick. si

[mm] [mm] [N/mm

2] [N/mm

2] [mm] [mm] [mm]

1 2000 1400 12000 10000 19,5 62 81,5 71,17

2 2000 1620 12000 10000 19,5 66 85,5 74,50

Component max nld va Shell zul.Shell Jointlaminat zul.Jointaminat

[kN/m] [N/mm2] [N/mm

2] [N/mm

2] [N/mm

2]

1 375 0,233 22,57 39,60 18,81 38,50

2 375 0,215 23,39 39,60 19,50 38,50

Pos erf. x1(Da*sa) erf. x2(da*sa) x1 x2

[mm] [mm] [mm] [mm]

1 403,7 337,8 410 350

2 413,5 372,2 420 380

How the analysis points, the proof of the circumferential direction during the test filling is decisive for the de-

sign.

The tensions in the area of the openings during operation will be checked with the help of the FEM. For this

purpose the stiffners and the shell in the area of the openings are maped using shell elements.

The following pictures show the FEM-Models.



T-Stub DN 1400

Y-Stub DN 1400



Decisively for the design are the loadings due to deadweight, filling and pressure and the soil pressures. The

specification of the loadings is made by using Area loads. The consideration of the dead weight occur intern

of program by input of the thickness of the structural members and the density of the FRP.

The following pictures show the stresses. The tension peaks resulting from the FEM mesh must not be used

for design. As the following pictures show it is imperative

σmax ≤ 26,80 N/mm

2 ≤ 150,00/( 1,50

. 1,50

.1,10

. 1,26

. 1,40) = 34,35 N/mm

2 (flexural stress)

max ≤ 100 . 26,80/(1,10

. 10000) = 0,24 % ≤ 0,50 %





6.3 Flange design

The proofs of the flanges are done according to DIN V 2505. For the used mixed laminat it is valid:

d ,l = 150/(2,00 . 1,10

. 1,26

. 1,50

.1,40) = 25,76 N/mm

2 (long term loading)

d ,s = 150/( 1,10 . 1,26

. 1,50

.1,40) = 38,65 N/mm

2 (short term loading)

= 1,1 . 0,003

. 10000 = 33,00 N/mm

2 (operation)

= 1,1 . 0,0035

. 10000 = 38,50 N/mm

2 (operation)

pB = 500,0 kN/m2

pT = 750,00 kN/m2 Test pressure is authoritative for design



Flange DN 2000

Input data

Pressure 750 kN/m2

Axial force 0 kN

Bending Moment 0 kNm

Inner Diameter d 2000 mm

middle diameter of the gasket dd 2230 mm 2182

Witdh of gasket bd 162,5 mm

Type of gaket k1: xxxxxxxxxxxxxxxxxxxxxx

EPDM = 1 PTFE = 2 It = 3 1 Page 9 DIN V 2505

Specific value of the gaskett k0*KD Table 1 86

Diameter of bold circle dt 2230 mm

Shell thickness sr 19,5 mm

Outer diameter da 2325 mm

bolt hole diameter dL 47 mm

reduced bolt hole diameter dL´ 23,5 mm

height of the flange hF 250 mm

allowable Tension k/(A*S) 38,5 N/mm2

Wallthickness in the section A-A: sF 45 mm

Height of the conical attempt hF 250 mm

Analysis

PDV 602494,1302 N

k1 81,25

PRP 2356192,50 N

PRZ 0,00 N

PR 2356192,50 N

PF 573084,92 N

PDB 512295,15 N

ad 0,00 mm

aF 57,50 mm

aR 105,25 mm

M 280941643,57 Nmm

s1 9,65 mm

PSB 3441572,58 kN 3441,572575 0,18

PS0 602494,13 kN 602,4941302

M0 0 Nmm

Tensions in state of operating

Proof section A-A

W 11166173,80 mm3

section modulus

existing tension section A-A 25,16 N/mm2

< allow. sigma = 38,50 N/mm2

Proof section B-B

W 16928773,87 mm3

section modulus

existing tension section B-B 16,60 N/mm2


Proof section C-C

W 74547312,71 mm3

section modulus

existing tension section C-C 3,77 N/mm2


Tensions due to the predeformation of the flange

Proof section A-A

W 11166173,80 mm3

section modulus



Proof section B-B

W 16928773,87 mm3

section modulus



Proof section C-C

W 74547312,71 mm3

section modulus





Flange DN 1600

Input data

Pressure 750 kN/m2

Axial force 0 kN

















Analysis

PDV 1801073,547 N

k1 78,75

PRP 1507963,20 N

PRZ 0,00 N

PR 1507963,20 N

PF 443199,81 N

PDB 405241,55 N

ad 0,00 mm

aF 55,00 mm

aR 101,25 mm

M 177057263,51 Nmm

s1 7,71 mm

PSB 2356404,56 kN 2356,404557 0,76

PS0 1801073,55 kN 1801,073547

M0 0 Nmm


Proof section A-A

W 6610814,73 mm3

section modulus



Proof section B-B

W 9259165,91 mm3

section modulus



Proof section C-C

W 39123267,47 mm3

section modulus




Proof section A-A

W 6610814,73 mm3

section modulus



Proof section B-B

W 9259165,91 mm3

section modulus



Proof section C-C

W 39123267,47 mm3

section modulus





Flange DN 1400

Input data

Pressure 750 kN/m2

Axial force 0 kN

















Analysis

PDV 474537,1695 N

k1 68,75

PRP 1154534,33 N

PRZ 0,00 N

PR 1154534,33 N

PF 334638,24 N

PDB 309073,55 N

ad 0,00 mm

aF 47,50 mm

aR 86,75 mm

M 116051169,08 Nmm

s1 6,74 mm

PSB 1798246,12 kN 1798,246116 0,26

PS0 474537,17 kN 474,5371695

M0 0 Nmm


Proof section A-A

W 4677441,31 mm3

section modulus



Proof section B-B

W 6430680,69 mm3

section modulus



Proof section C-C

W 27787991,87 mm3

section modulus




Proof section A-A

W 4677441,31 mm3

section modulus



Proof section B-B

W 6430680,69 mm3

section modulus



Proof section C-C

W 27787991,87 mm3

section modulus





Flange DN 2000

Input Data

Pressure 750 kN/m2

Axial force 0 kN



middle diameter of the gasket dd 2087,5 mm 2107

Witdh of gasket bd 87 mm

Type of gaket k1:

Rubber = 1 Teflon = 2 It = 3 1 DIN 2505




Outer diameter da (coil) 2175 mm

Outer diameter da (loose flange) 2325 mm


reduced bolt hole diameter dL´ 24 mm


inner diameter steel ring 2110 mm

thickness steel ring 70

allowable tension FRP k/(A*S) 38,5 N/mm2

allowable tension steel k/(A*S) 145,45 N/mm2



Analysis

PDV 1.141.104

k1 43,5

PRP 2.356.193 N

PRZ 0,00 N

PR 2.356.193 N

PF 210.677 N

PDB 256.748 N

a 27,50

ad 71,25 mm

aF 65,63 mm

aR 77,75 mm

M 215.312.952 Nmm

s1 9,65 mm

PSB 2.823.618 N

PS0 1.141.104 N

M0 81.303.662 Nmm

Tensions in state of operating Proof section A-A

W 7.795.510 mm3

section modulus( Gl. 17 mit sr = sf)


< zul sigma = 38,50 N/mm2

Tensions due to the predeformation of the flangeProof section A-A

W 7.795.510 mm3 section modulus( Gl. 17 mit sr = sf)



Shear Stress

Shear 2.823.618 N

Shear Plane 1.641.482 mm2

Shear stress 1,72 N/mm2


Loose Flange

lever arm 27,50 mm

PSB 2.823.618 N

Moment 77.649.485 Nmm

W 642.691 mm3

section modulus(Gl. 16)

existing normal stress 120,82 N/mm2




Flange DN 1600

Input Data

Pressure 750 kN/m2

Axial force 0 kN



middle diameter of the gasket dd 1680 mm 1696,5

Witdh of gasket bd 80 mm

Type of gaket k1:
















Analysis

PDV 844.459

k1 40

PRP 1.507.963 N

PRZ 0,00 N

PR 1.507.963 N

PF 154.566 N

PDB 190.003 N

a 30,00

ad 70,00 mm

aF 60,00 mm

aR 71,75 mm

M 130.770.569 Nmm

s1 7,71 mm

PSB 1.852.533 N

PS0 844.459 N

M0 59.112.157 Nmm


W 4.068.379 mm3








Shear Stress

Shear 1.852.533 N

Shear Plane 1.043.009 mm2



Loose Flange

lever arm 30,00 mm

PSB 1.852.533 N


W 554.177 mm3






Flange DN 1400

Input Data

Pressure 750 kN/m2

Axial force 0 kN



middle diameter of the gasket dd 1467,5 mm 1484


Type of gaket k1:














Wallthickness in the section A-A: sF 28,5 mm


Analysis

PDV 345.771

k1 33,75

PRP 1.154.534 N

PRZ 57142,86 N

PR 1.211.677 N

PF 114.014 N

PDB 140.037 N

a 27,50

ad 61,25 mm

aF 50,63 mm

aR 59,25 mm

M 86.141.117 Nmm

s1 7,07 mm

PSB 1.465.728 N

PS0 402.914 N

M0 24.678.489 Nmm


W 2.860.339 mm3








Shear Stress

Shear 1.465.728 N

Shear Plane 823.914 mm2



Loose Flange

lever arm 27,50 mm

PSB 1.465.728 N


W 411.018 mm3






6.4 Support Reactions due to Lengthwise Loadings

Object of the following analysis are the support reactions of the fixed points of the pipelines according to the

next drawing.



Essential for the analysis are the bedding conditions of the pipe due to the soil.

The following assumptions:

Soil: Sand Compactness DPr = 95% Es ≤ 100000 kN/m2

kB ≤ 45454 kN/m3

With these Values the following bedding conditions are valid:

Transverse bedding to the axis of the pipe cs = ct = kB . D [kN/m/m]

Lengthwise bedding to the axis of the pipe cr = kB . ARing [kN/m]

by ringstiffners

The support reactions results from the loadings operation pressure and temperature. The calculation is done

with the help of the beam models in appendix 1.

For the support reactions it is valid:

N3PAB50:



6.5 Wall Ring at Fix Points

In a very conservative estimate the design of the support rings is done for the pressure and a strictly re-

strained thermal expansion .

L,T = T . T

. (EU

. EL)

0,5

( T = 10 K , MCW piping upstream of the condenser)

For the shearing force it is valid: nc = 500

. 0,50 + 2,0

. 10

-5 . (18000

. 12000)

0,5 . 10

. 19,5 = 307,31 kN/m

nd = 1,50

. 1,50

. 500

. 0,50 + 1,50

. 2,0

. 10

-5 . (18000

. 12000)

0,5 . 10

. 19,5 = 648,46 kN/m



= 648,5660 / 59 = 10,99 N/mm2

≤ 50/ ( 1,10 . 1,26

. 2,00) = 25,77 N/mm

2

kl = 648,46 / (2 . 150) = 2,16 N/mm

2 ≤ 8,0/ ( 1,10

. 1,26

. 2,00) = 4,12 N/mm

2

6.6 Head DN 2000

After doing the pressure test the head will be removed. The design is done according to [1]. Reductions and material values

A1* = 1,80 ( 1 year) A2 = 1,10 A3 = 1,26

M = 1,40 A2 · A3 · M = 1,10 1,26 1,40 = 1,94

The following values apply for mixed laminates: EZ = 10000,00 N/mm² EB = 10000,00 N/mm²

Z,d = 130,00 N/mm²

B,d = 150,00 N/mm²

Geometry

D = 2000,00 m tank diameter sB = 21,00 mm thickness sKr = 36,00 mm thickness of the brim rB = 308,00 mm radius of roof rBK = 1600,00 mm brim radius

The following loading is decisive for the tension proof: pB = 1,50

. 2,00

.. (500 + 2,00

. 10) =1560,00 kN/m

2

The following applies: A2 · A3 · M · pB = 1,94 · 1560 = 3026,40 kN/m2

(pB = A1 . F

. p)

The following characteristic loading is decisive for the proof of expansion: pG = 750 + 2,00

. 10 = 770,0 kN/m

2 (Test)



Proof of strength

pB · A2 · A3 · M =3026,40 kN/m²

pG =770,0 kN/m² C2k = 1,80

nk,B = pB

. R

. C2k / 2 = 3026,40

. 1,00

. 1,80 / 2 = 2723,76 kN/m

nk,G = pG

. R

. C2k / 2 = 770,00

. 1,00

. 1,80 / 2 = 693,00 kN/m

Proof of tension

= n

s

k B

B

, 2723,76/ 21,00 = 129,70 zul Z = 130,00 N/mm²

Proof of expansion

= n

s E

k G

B B

, *

* , *

100

11 693,00/ (21,00

. 1,1

. 10000) = 0,30 % grenz = 0,35 % (Test)

The following applies to the brim: C2kr = 3,50 mkr,B = pB

. R

. sk

. C2kr / 12 = 2723,736

. 1,00

. 0,036

. 3,50 / 12 = 31,78 kNm

mkr,G = pG

. R

. sk

. C2kr / 12 = 770

. 1,00

. 0,036

. 3,50 / 12 = 8,09 kNm

Proof of tension

= m

s

kr B

k

, * 6000

2 31,78

. 6000 / 36,0

2 = 147,12 zul = 150,00

Proof of expansion

= m

s E

kr G

k B

, * *

* , *

6000 100

112

= 8,09 . 6000 / (36

2 . 1,1

. 10000 )

. 100 = 0,34 % grenz = 0,35 % (Test)

For the stability of the head it is valid:

pkrit = 0,242 . EB

. (SB / rB)²

= 0,242 . 10000

. (21,00 / 1600,00)² * 1000 = 416,88 kN/m²

pvorh = pdI . A2

. A3

. S = (1,50

. 80 + √2,00

. 1,00

. 40,45)

. 1,10

. 1,26

. 1,40 = 343,98 kN/m²

pvorh / pkrit = 343,98 / 416,88 = 0,83 1.0



7. Material Data

values of the thermal value of streching:

T = 24 · 10-6

1/K mixed laminate and Winding laminate axial direction

Tu = 15 · 10-6

1/K Winding laminate circumferential direction

T = 30 · 10-6

1/K Sprayed laminate

Bruchwerte:

Lam = 50 N/mm² shear stress of the laminate

kl = 8 N/mm² shear stress in the laminate interface

= 4 N/mm² vertical stress

Loch = 150 N/mm² bearing stress

il = 15 N/mm² interlaminare shear stress

GFK-Stahl = 2 N/mm² shear stress in adhesive joint

stresses: (Index B = bending, Index Z = tension)

B [N/mm²] Z [N/mm²]

Mixed laminat 150 130

Winding laminat, axial 150 130

Winding laminat, radial 350 350

moduli of elasticity of annealed vessels t < 10,00 mm: (Index B = bending, Index Z = tension)

EB [N/mm²] EZ [N/mm²]

Mixed laminat 10000 10000

Winding laminat, axial 12000 12000

Winding laminat, radial 18000 18000

Reduction factor A1 of annealed vessels:

Resident Loading A1B A1G √A1I

Mixed laminat 2,00 2,00 1,41

Winding laminat, axial 1,5 1,5 1,22

Winding laminat, radial 1,5 1,5 1,22

short-term loading A1B,min A1G,min A1I,min

all kinds of laminate 1,00 1,00 1,00

Ingenieurbüro für konstruktiven Ingenieurbau Dr.-Ing. Ingo Lukas

Am Krummen Morgen 1 67727 Lohnsfeld Tel. 06302 - 982844 Fax 06302 - 982846

Appendix 1 FE-Analysis Pipes

Project: Power Plant Köln Niehl page 1

Dr.-Ing. Ingo Lukas Am Krummen Morgen 1 67727 Lohnsfeld

N3PAB30

Client:FKT Fassbender GmbH

Position scheme

Positions members - Geometry

beam xa ya za lType

xe ye ze

[m] [m] [m] [m]

101 -89.75 -1.46 0.00 17.10 ST

-89.75 -18.57 0.00

102 -89.75 -1.46 0.00 1.07 ST

-89.21 -0.54 0.00

103 -89.21 -0.54 0.00 1.07 ST

-88.29 0.00 0.00

104 -1.46 0.00 0.00 86.82 ST

-88.29 0.00 0.00

105 -0.54 0.54 0.00 1.07 ST

-1.46 0.00 0.00

106 0.00 1.46 0.00 1.07 ST

-0.54 0.54 0.00

107 0.00 1.46 0.00 11.24 ST

0.00 12.70 0.00

108 0.00 12.70 0.00 1.13 ST

0.00 13.83 0.00

109 0.00 13.83 0.00 2.21 ST

0.00 16.05 0.00

110 0.00 16.05 0.00 1.50 ST

0.00 17.55 0.00

201 0.00 13.83 0.00 2.68 ST

-2.32 15.17 0.00

202 -2.32 15.17 0.00 0.49 ST

-2.64 15.55 0.00

203 -2.64 15.55 0.00 0.49 ST

-2.81 16.01 0.00

204 -2.81 16.01 0.00 1.95 ST

-2.81 17.97 0.00

205 -2.81 17.97 0.00 0.75 ST

-2.81 18.62 0.38

206 -2.81 18.62 0.38 0.75 ST

-2.81 18.99 1.02

207 -2.81 18.99 1.02 2.88 ST

-2.81 18.99 3.90

208 0.00 17.55 0.00 0.42 ST

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beam xa ya za lType

xe ye ze

[m] [m] [m] [m]

0.00 17.97 0.00

209 0.00 17.97 0.00 0.75 ST

0.00 18.62 0.38

210 0.00 18.62 0.38 0.75 ST

0.00 18.99 1.02

211 0.00 18.99 1.02 2.88 ST

0.00 18.99 3.90

ST member (N, V, M)

DS compr. member(-N)

ZS Tension member (+N)

ZD ZD = tension/compr. member (N)

Positions members - Coordinate system

beam Alpha Beta Gamma

[°] [°] [°]

101 -90.00 0.00 0.00

102 60.00 0.00 0.00

103 30.00 0.00 0.00

104 180.00 0.00 0.00

105 -150.00 0.00 0.00

106 -120.00 0.00 0.00

107 90.00 0.00 0.00

108 89.97 0.00 0.00

109 90.00 0.00 0.00

110 90.02 0.00 0.00

201 150.01 0.00 0.00

202 130.00 0.00 0.00

203 110.00 0.00 0.00

204 90.00 0.00 0.00

205 90.00 -30.00 90.00

206 90.00 -60.00 90.00

207 0.00 -90.00 180.00

208 90.00 0.00 0.00

209 90.00 -30.00 90.00

210 90.00 -60.00 90.00

211 0.00 -90.00 180.00

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Positions members - Material and cross sections

beam material E-Modulus Rho Cross section Haunch Type HA

G-Modulus angle/mirror

[N/mm²] [t/m

3

]

101 S FKT 14697 2.00ROHRS 2000-19.5 keine SP fix

8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°

110 S FKT 14697 0.00ROHRS 2000-19.5 zentr SP fix

8000 0°

201 S FKT 14697 0.00ROHRS 1400-16,5 keine SP fix

8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°

NP Norm section (standard steel and standard profile)

SP Special section (special steel and/or special profile)

KP complex section (generated section)

MP multipart profile

HA principal axis

haunch definition

110Sonderprofil ROHRS 2000-19.5, angle = 0 deg.

centric haunched

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Start End

[mm] [mm]

D 2039.00 1530.00

t 19.50 15.00

cross section values - special profiles

profile Sonderprofil ROHRS 1400-16,5

M 1:13

717

717

Y

Z

material properties

dead weight g = 146.85 kg/m

yield stress fy = 70.34 N/mm2

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sectional values (elastic)

width b = 1433.00 mm

heigth h = 1433.00 mm

area A = 734.26 cm2

pos. of main axles Alfa = -0.00 °

centroid ys = 71.7 cm

zs = 71.7 cm

shear force area Ay = 367.22 cm2

Az = 367.22 cm2

2nd pol. mom. of area Iy = 1841842.50 cm4

Iz = 1841842.50 cm4

static moment Sy = 16554.14 cm3

Sz = 16466.55 cm3

mod. of resistance Wy = 25706.11 cm3

Wz = 25706.11 cm3

radius of inertia iy,g = 50.1 cm

iz,g = 50.1 cm

torsional constant

It = 3683642.18 cm4

distance of shear centroid

from centroid dym = 0.0 cm

dzm = 0.0 cm

sectional values (plastic)

mod. of resistance Wpl,y = 33108.29 cm3

Wpl,z = 33046.58 cm3

moments Mpl,y = 2328.84 kNm

Mpl,z = 2324.50 kNm

normal force Npl = 5164.79 kN

shear forces Vpl,y = 1491.31 kN

Vpl,z = 1491.31 kN

profile Sonderprofil ROHRS 2000-19.5

M 1:18

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1020

1020

Y

Z

material properties






area A = 1237.17 cm2



zs = 102.0 cm


Az = 618.69 cm2


Iz = 6307635.07 cm4


Sz = 39762.39 cm3


Wz = 61869.89 cm3


iz,g = 71.4 cm

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torsional constant

It = 12615170.08 cm4



dzm = 0.0 cm



Wpl,z = 79402.96 cm3


Mpl,z = 5585.20 kNm



Vpl,z = 2512.54 kN

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Pos. A1 - Point support

systemx = 0.00 m y = 12.70 m z = 0.00 m

SupportCompr./Tens.spr. Transl. in x-direction =

1.00e+009 kN/m

Compr./Tens.spr. Transl. in y-direction =

7.20e+005 kN/m

Compr./Tens.spr. Transl. in z-direction =

1.00e+009 kN/m

Pos. L1 - Line support

systemx = -2.81 -2.81 m

y = 18.99 18.99 m

z = 3.90 1.02 m

SupportCompr./Tens.spr. Transl. in r-direct. = 5.35e+003

kN/m²

Compr./Tens.spr. Transl. in s-Direction =

6.36e+004 kN/m²

Compr./Tens.spr. Transl. in t-Direction =

6.36e+004 kN/m²

(l = 2.88 m)


systemx = 0.00 0.00 m

y = 18.99 18.99 m

z = 3.90 1.02 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 2.88 m)


systemx = -2.81 -2.81 m

y = 18.99 18.62 m

z = 1.02 0.38 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 0.75 m)


systemx = 0.00 0.00 m

y = 18.99 18.62 m

z = 1.02 0.38 m


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kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 0.75 m)


systemx = 0.00 0.00 m

y = 18.62 17.97 m

z = 0.38 0.00 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 0.75 m)


systemx = -2.81 -2.81 m

y = 18.62 17.97 m

z = 0.38 0.00 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 0.75 m)


systemx = -2.81 -2.81 m

y = 17.97 16.01 m

level = 0.00 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 1.95 m)


systemx = 0.00 0.00 m

y = 17.97 1.46 m

level = 0.00 m


kN/m²


9.09e+004 kN/m²


9.09e+004 kN/m²

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(l = 16.50 m)


systemx = -2.81 -2.64 m

y = 16.01 15.55 m

level = 0.00 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 0.49 m)


systemx = -2.64 -2.32 m

y = 15.55 15.17 m

level = 0.00 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 0.49 m)


systemx = -2.32 0.00 m

y = 15.17 13.83 m

level = 0.00 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 2.68 m)


systemx = 0.00 -0.54 m

y = 1.46 0.54 m

level = 0.00 m


kN/m²


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 1.07 m)


systemx = -0.54 -1.46 m

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y = 0.54 0.00 m

level = 0.00 m


kN/m²


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 1.07 m)


systemx = -1.46 -88.29 m

y = 0.00 0.00 m

level = 0.00 m


kN/m²


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 86.82 m)


systemx = -88.29 -89.21 m

y = 0.00 -0.54 m

level = 0.00 m


kN/m²


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 1.07 m)


systemx = -89.21 -89.75 m

y = -0.54 -1.46 m

level = 0.00 m


kN/m²


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 1.07 m)


systemx = -89.75 -89.75 m

y = -1.46 -18.57 m

level = 0.00 m


kN/m²

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9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 17.10 m)

Load scheme (for each loading case)

position based loads

dead weight reinf.-steel-members

beam Profile length SurfaceUn.weight Load

[m] [cm

2

] [kN/m

3

] [kN/m]

101 ROHRS 2000-19.5 17.10 1237.17 20.00 -2.47

102 ROHRS 2000-19.5 1.07 1237.17 20.00 -2.47

103 ROHRS 2000-19.5 1.07 1237.17 20.00 -2.47

104 ROHRS 2000-19.5 86.82 1237.17 20.00 -2.47

105 ROHRS 2000-19.5 1.07 1237.17 20.00 -2.47

106 ROHRS 2000-19.5 1.07 1237.17 20.00 -2.47

107 ROHRS 2000-19.5 11.24 1237.17 0.00 0.00

108 ROHRS 2000-19.5 1.13 1237.17 0.00 0.00

109 ROHRS 2000-19.5 2.21 1237.17 0.00 0.00

110 ROHRS 2000-19.5 1.50 957.72 0.00 0.00

201 ROHRS 1400-16,5 2.68 734.26 0.00 0.00

202 ROHRS 1400-16,5 0.49 734.26 0.00 0.00

203 ROHRS 1400-16,5 0.49 734.26 0.00 0.00

204 ROHRS 1400-16,5 1.95 734.26 0.00 0.00

205 ROHRS 1400-16,5 0.75 734.26 0.00 0.00

206 ROHRS 1400-16,5 0.75 734.26 0.00 0.00

207 ROHRS 1400-16,5 2.88 734.26 0.00 0.00

208 ROHRS 1400-16,5 0.42 734.26 0.00 0.00

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[m] [cm

2

] [kN/m

3

] [kN/m]

209 ROHRS 1400-16,5 0.75 734.26 0.00 0.00

210 ROHRS 1400-16,5 0.75 734.26 0.00 0.00

211 ROHRS 1400-16,5 2.88 734.26 0.00 0.00

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Loading case LF-2 (Lastfall)

single loads - loading case LF-2

position Type Load x y z Description

[kN]/[kNm] [m] [m] [m]

P1 Pr -1570.800 0.00 1.46 0.00 Punktlast

P2 Pr 1570.800 0.00 16.05 0.00 Punktlast

P3 Pr 769.700 0.00 17.55 0.00 Punktlast

P4 Pr 769.700 0.00 17.97 0.00 Punktlast

P5 Pr -1570.800 0.00 16.05 0.00 Punktlast

P6 Pr -769.700 0.00 17.55 0.00 Punktlast

P7 Pr -769.700 0.00 13.83 0.00 Punktlast

P8 Pr 769.700 -2.32 15.17 0.00 Punktlast

P9 Pr 769.700 -2.64 15.55 0.00 Punktlast

P10 Pr 769.700 -2.81 16.01 0.00 Punktlast

P11 Pr 769.700 -2.81 17.97 0.00 Punktlast

P12 Pr -769.700 -2.32 15.17 0.00 Punktlast

P13 Pr -769.700 -2.65 15.58 0.00 Punktlast

P14 Pr -769.700 -2.81 16.01 0.00 Punktlast

P15 Pr 1570.800 -0.54 0.54 0.00 Punktlast

P16 Pr -1570.800 0.00 1.46 0.00 Punktlast

P17 Pr -1570.800 -0.54 0.54 0.00 Punktlast

P18 Pr 1570.800 -1.46 0.00 0.00 Punktlast

P19 Pr -1570.800 -1.46 0.00 0.00 Punktlast

P20 Pr 1570.800 -88.29 0.00 0.00 Punktlast

P21 Pr 1570.800 -88.29 0.00 0.00 Punktlast

P22 Pr 1570.800 -89.21 -0.54 0.00 Punktlast

P23 Pr 1570.800 -89.75 -18.57 0.00 Punktlast

P24 Pr -1570.800 -89.75 -1.46 0.00 Punktlast

P25 Pr -1570.800 -89.75 -1.46 0.00 Punktlast

P26 Pr -1570.800 -89.21 -0.54 0.00 Punktlast

P27 Pr 769.700 -2.81 18.62 0.38 Punktlast

P28 Pr 769.700 -2.81 18.99 1.02 Punktlast

P29 Pr 769.700 -2.81 18.99 3.90 Punktlast

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[kN]/[kNm] [m] [m] [m]

P30 Pr -769.700 -2.81 17.97 0.00 Punktlast

P31 Pr -769.700 -2.81 18.62 0.38 Punktlast

P32 Pr -769.700 -2.81 18.99 1.02 Punktlast

P33 Pr 769.700 0.00 18.62 0.38 Punktlast

P34 Pr 769.700 0.00 18.99 1.02 Punktlast

P35 Pr -769.700 0.00 18.62 0.38 Punktlast

P36 Pr -769.700 0.00 18.99 1.02 Punktlast

P37 Pr -769.700 0.00 17.97 0.00 Punktlast

P38 Pr 769.700 0.00 18.99 3.90 Punktlast

line loads - loading case LF-2


[.../m] [m] [m] [m]

LILA-1 pr/l 534.07 0.00 16.05 0.00 Linienlast

534.07 0.00 17.55 0.00

Type l: Load direction local, r-axis is

load axis

g: Load direction global

p: Load direction global projected

Load [.../m]: line load (p) -> [kN/m] line

moments (m) -> [kNm/m]

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temperature loads - loading case LF-3

TMLA-1 (member load Temperaturlast

)

x = -2.81 -2.81 m

y = 16.01 17.97 m

z = 0.00 0.00 m

Coeff. of thermal exp. = 2.000000e-005 1/K

dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


)

x = -2.64 -2.81 m

y = 15.55 16.01 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


)

x = -2.32 -2.64 m

y = 15.17 15.55 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr

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)

x = 0.00 -2.32 m

y = 13.83 15.17 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


)

x = 0.00 0.00 m

y = 17.55 17.97 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


)

x = 0.00 0.00 m

y = 16.05 17.55 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


)

x = 0.00 0.00 m

y = 13.83 16.05 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


)

x = 0.00 0.00 m

y = 12.70 13.83 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


)

x = 0.00 0.00 m

y = 1.46 12.70 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr

TMLA-10 (member Temperaturlast

load)

x = 0.00 -0.54 m

y = 1.46 0.54 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr

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load)

x = -0.54 -1.46 m

y = 0.54 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = -1.46 -88.29 m

y = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = -89.21 -88.29 m

y = -0.54 0.00 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = -89.75 -89.21 m

y = -1.46 -0.54 m

z = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = -89.75 -89.75 m

y = -1.46 -18.57 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = -2.81 -2.81 m

y = 17.97 18.62 m

z = 0.00 0.38 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = -2.81 -2.81 m

y = 18.62 18.99 m

z = 0.38 1.02 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr

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load)

x = -2.81 -2.81 m

y = 18.99 18.99 m

z = 1.02 3.90 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = 0.00 0.00 m

y = 17.97 18.62 m

z = 0.00 0.38 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = 0.00 0.00 m

y = 18.62 18.99 m

z = 0.38 1.02 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr


load)

x = 0.00 0.00 m

y = 18.99 18.99 m

z = 1.02 3.90 m


dTs = 0.00 K, dTt = 0.00 K

T = 30.00 degr

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point support evaluation

system

evaluation witout MIN/MAX-superposition

A1 x/y/z = 0.00/12.70/0.00 [m], globale Definition

Lcn Fx Fy Fz Mx My Mz

[kN] [kNm]

1 -110.58 -532.72 35.31 - - -

2 -93.74 -350.07 24.98 - - -

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Position scheme

Positions members - Geometry

beam xa ya za lType

xe ye ze

[m] [m] [m] [m]

101 0.00 61.49 0.00 20.80 ST

0.00 40.69 0.00

102 0.00 40.69 0.00 0.95 ST

0.43 39.85 0.00

103 0.43 39.85 0.00 0.95 ST

1.19 39.28 0.00

104 1.19 39.28 0.00 16.28 ST

17.22 36.45 0.00

105 17.22 36.45 0.00 0.71 ST

17.83 36.10 0.00

106 17.83 36.10 0.00 0.71 ST

18.29 35.56 0.00

107 18.29 35.56 0.00 5.21 ST

20.07 30.66 0.00

108 20.07 30.66 0.00 2.42 ST

20.90 28.39 0.00

109 20.90 28.39 0.00 13.86 ST

25.64 15.36 0.00

110 25.64 15.36 0.00 3.31 ST

25.64 12.05 0.00

111 25.64 12.05 0.00 6.13 ST

25.64 5.92 0.00

112 25.64 5.92 0.00 1.00 ST

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beam xa ya za lType

xe ye ze

[m] [m] [m] [m]

201 25.64 4.92 0.00 0.68 ST

25.64 4.24 0.00

202 25.64 4.24 0.00 3.07 ST

25.64 1.17 0.00

203 25.64 1.17 0.00 0.86 ST

26.07 0.43 0.00

204 26.07 0.43 0.00 0.86 ST

26.81 0.00 0.00

205 26.81 0.00 0.00 6.73 ST

33.54 0.00 0.00

206 33.54 0.00 0.00 1.15 ST

34.69 0.00 0.00

207 25.64 9.34 0.00 3.35 ST

28.01 6.97 0.00

208 28.01 6.97 0.00 0.64 ST

28.60 6.73 0.00

209 28.60 6.73 0.00 4.94 ST

33.54 6.73 0.00

210 33.54 6.73 0.00 1.15 ST

34.69 6.73 0.00

301 0.00 56.38 0.00 3.90 ST

0.00 56.38 3.90

302 0.00 59.38 0.00 3.90 ST

0.00 59.38 3.90

ST member (N, V, M)

DS compr. member(-N)

ZS Tension member (+N)

ZD ZD = tension/compr. member (N)

Positions members - Coordinate system


[°] [°] [°]

101 -90.00 0.00 0.00

102 -62.67 0.00 0.00

103 -37.33 0.00 0.00

104 -10.00 0.00 0.00

105 -30.00 0.00 0.00

106 -50.00 0.00 0.00

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[°] [°] [°]

107 -70.00 0.00 0.00

108 -70.00 0.00 0.00

109 -70.00 0.00 0.00

110 -90.00 0.00 0.00

111 -89.99 0.00 0.00

112 -89.99 0.00 0.00

201 -89.99 0.00 0.00

202 -90.00 0.00 0.00

203 -60.00 0.00 0.00

204 -30.00 0.00 0.00

205 0.00 0.00 0.00

206 0.00 0.00 0.00

207 -44.99 0.00 0.00

208 -22.73 0.00 0.00

209 0.00 0.00 0.00

210 0.00 0.00 0.00

301 0.00 -90.00 180.00

302 0.00 -90.00 180.00

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Positions members - Material and cross sections

beam material E-Modulus Rho Cross section Haunch Type HA

G-Modulus angle/mirror

[N/mm²] [t/m

3

]


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°

112 S FKT 14697 2.00ROHRS 2000-19.5 zentr SP fix

8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°


8000 0°

NP Norm section (standard steel and standard profile)

SP Special section (special steel and/or special profile)

KP complex section (generated section)

MP multipart profile

HA principal axis

haunch definition

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112Sonderprofil ROHRS 2000-19.5, angle = 0 deg.

centric haunched

Start End

[mm] [mm]

D 2039.00 1635.00

t 19.50 17.50

cross section values - special profiles

profile Sonderprofil ROHRS 1400-16,5

M 1:13

717

717

Y

Z

material properties



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area A = 734.26 cm2



zs = 71.7 cm


Az = 367.22 cm2


Iz = 1841842.50 cm4


Sz = 16466.55 cm3


Wz = 25706.11 cm3


iz,g = 50.1 cm

torsional constant

It = 3683642.18 cm4



dzm = 0.0 cm



Wpl,z = 33046.58 cm3


Mpl,z = 2324.50 kNm



Vpl,z = 1491.31 kN


M 1:14

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818

818

Y

Z

material properties






area A = 889.27 cm2



zs = 81.8 cm


Az = 444.73 cm2


Iz = 2908584.17 cm4


Sz = 198367.32 cm3


Wz = 35579.01 cm3

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iz,g = 57.2 cm

torsional constant

It = 5817110.25 cm4



dzm = 0.0 cm



Wpl,z = 45787.15 cm3


Mpl,z = 3220.67 kNm



Vpl,z = 1806.08 kN


M 1:18

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1020

1020

Y

Z

material properties






area A = 1237.17 cm2



zs = 102.0 cm


Az = 618.69 cm2


Iz = 6307635.07 cm4


Sz = 39762.39 cm3


Wz = 61869.89 cm3


iz,g = 71.4 cm

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torsional constant

It = 12615170.08 cm4



dzm = 0.0 cm



Wpl,z = 79402.96 cm3


Mpl,z = 5585.20 kNm



Vpl,z = 2512.54 kN

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systemx = 0.00 m y = 52.16 m z = 0.00 m


1.00e+009 kN/m


1.00e+009 kN/m


1.00e+009 kN/m


systemx = 25.64 m y = 12.03 m z = 0.00 m


1.00e+009 kN/m


1.00e+009 kN/m

Pos. B1 - Point support

systemx = 0.00 m y = 60.54 m z = 0.00 m


kN/m

Additional angle transformations:

- Axis gyration about local t-axis: Alpha =

-90.00°


systemx = 0.00 m y = 57.86 m z = 0.00 m


kN/m



-90.00°


systemx = 0.00 m y = 53.92 m z = 0.00 m


kN/m



-90.00°

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systemx = 0.00 m y = 48.21 m z = 0.00 m


kN/m



-90.00°


systemx = 0.00 m y = 43.71 m z = 0.00 m


kN/m



-90.00°


systemx = 2.92 m y = 38.97 m z = 0.00 m


kN/m



-10.00°


systemx = 6.86 m y = 38.28 m z = 0.00 m


kN/m



-10.00°


systemx = 10.80 m y = 37.58 m z = 0.00 m


kN/m



-10.00°

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systemx = 14.73 m y = 36.89 m z = 0.00 m


kN/m



-10.00°


systemx = 19.05 m y = 33.46 m z = 0.00 m


kN/m



-70.00°


systemx = 21.83 m y = 25.82 m z = 0.00 m


kN/m



-70.00°


systemx = 23.20 m y = 22.06 m z = 0.00 m


kN/m



-70.00°


systemx = 24.59 m y = 18.25 m z = 0.00 m


kN/m



-70.00°

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systemx = 0.00 m y = 61.49 m z = 0.00 m

SupportTens.spring Transl. in y-direction = 1.43e+005

kN/m

Pos. C1 - Point support

systemx = 25.64 m y = 10.32 m z = 0.00 m

SupportCompr./Tens.spr. Transl. in z-direction = rigid


systemx = 25.64 m y = 6.52 m z = 0.00 m

SupportCompr./Tens.spr. Transl. in z-direction =

1.00e+009 kN/m


systemx = 25.64 m y = 2.81 m z = 0.00 m

SupportCompr./Tens.spr. Transl. in x-direction = rigid


1.00e+009 kN/m


systemx = 28.08 m y = 0.00 m z = 0.00 m


1.00e+009 kN/m


systemx = 33.54 m y = 0.00 m z = 0.00 m

SupportCompr./Tens.spr. Transl. in y-direction = rigid


1.00e+009 kN/m


systemx = 29.44 m y = 6.72 m z = 0.00 m


1.00e+009 kN/m

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systemx = 33.54 m y = 6.72 m z = 0.00 m

SupportCompr./Tens.spr. Transl. in y-direction = rigid


1.00e+009 kN/m


systemx = 0.00 0.00 m

y = 61.49 40.69 m

level = 0.00 m

SupportCompr./Tens.spr. Transl. in s-Direction =

9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 20.80 m)


systemx = 0.00 0.43 m

y = 40.69 39.85 m

level = 0.00 m


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 0.95 m)


systemx = 0.43 1.19 m

y = 39.85 39.28 m

level = 0.00 m


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 0.95 m)


systemx = 1.19 17.22 m

y = 39.28 36.45 m

level = 0.00 m


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 16.28 m)


systemx = 17.22 17.83 m

y = 36.45 36.10 m

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level = 0.00 m


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 0.71 m)


systemx = 17.83 18.29 m

y = 36.10 35.56 m

level = 0.00 m


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 0.71 m)


systemx = 18.29 20.07 m

y = 35.56 30.66 m

level = 0.00 m


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 5.21 m)


systemx = 20.90 25.64 m

y = 28.39 15.36 m

level = 0.00 m


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 13.86 m)


systemx = 25.64 25.64 m

y = 15.36 12.05 m

level = 0.00 m


9.09e+004 kN/m²


9.09e+004 kN/m²

(l = 3.31 m)

Pos. LIRB-9 - Line support

systemx = 0.00 0.00 m

y = 56.38 56.38 m

z = 0.00 3.90 m

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kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 3.90 m)

Pos. LIRB-10 - Line support

systemx = 0.00 0.00 m

y = 59.38 59.38 m

z = 0.00 3.90 m


kN/m²


6.36e+004 kN/m²


6.36e+004 kN/m²

(l = 3.90 m)

Load scheme (for each loading case)

position based loads

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dead weight reinf.-steel-members


[m] [cm

2

] [kN/m

3

] [kN/m]

101 ROHRS 2000-19.5 20.80 1237.17 20.00 -2.47

102 ROHRS 2000-19.5 0.95 1237.17 20.00 -2.47

103 ROHRS 2000-19.5 0.95 1237.17 20.00 -2.47

104 ROHRS 2000-19.5 16.28 1237.17 20.00 -2.47

105 ROHRS 2000-19.5 0.71 1237.17 20.00 -2.47

106 ROHRS 2000-19.5 0.71 1237.17 20.00 -2.47

107 ROHRS 2000-19.5 5.21 1237.17 20.00 -2.47

108 ROHRS 2000-19.5 2.42 1237.17 20.00 -2.47

109 ROHRS 2000-19.5 13.86 1237.17 20.00 -2.47

110 ROHRS 2000-19.5 3.31 1237.17 20.00 -2.47

111 ROHRS 2000-19.5 6.13 1237.17 20.00 -2.47

112 ROHRS 2000-19.5 1.00 1056.90 20.00 -2.11

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[m] [cm

2

] [kN/m

3

] [kN/m]

201 ROHRS 1600-17.5 0.68 889.27 20.00 -1.78

202 ROHRS 1600-17.5 3.07 889.27 20.00 -1.78

203 ROHRS 1600-17.5 0.86 889.27 20.00 -1.78

204 ROHRS 1600-17.5 0.86 889.27 20.00 -1.78

205 ROHRS 1600-17.5 6.73 889.27 20.00 -1.78

206 ROHRS 1600-17.5 1.15 889.27 20.00 -1.78

207 ROHRS 1600-17.5 3.35 889.27 20.00 -1.78

208 ROHRS 1600-17.5 0.64 889.27 20.00 -1.78

209 ROHRS 1600-17.5 4.94 889.27 20.00 -1.78

210 ROHRS 1600-17.5 1.15 889.27 20.00 -1.78

301 ROHRS 1400-16,5 3.90 734.26 20.00 -1.47

302 ROHRS 1400-16,5 3.90 734.26 20.00 -1.47

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single loads - loading case LF-2


[kN]/[kNm] [m] [m] [m]

P1 Pr -1570.800 0.00 61.49 0.00 Punktlast

P2 Pr 1570.800 0.00 40.69 0.00 Punktlast

P3 Pr -1570.800 0.00 40.69 0.00 Punktlast

P4 Pr 1570.800 0.43 39.85 0.00 Punktlast

P5 Pr -1570.800 0.43 39.85 0.00 Punktlast

P6 Pr 1570.800 1.19 39.28 0.00 Punktlast

P7 Pr -1570.800 1.19 39.28 0.00 Punktlast

P8 Pr 1570.800 17.22 36.45 0.00 Punktlast

P9 Pr -1570.800 17.22 36.45 0.00 Punktlast

P10 Pr 1570.800 17.83 36.10 0.00 Punktlast

P11 Pr -1570.800 17.83 36.10 0.00 Punktlast

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[kN]/[kNm] [m] [m] [m]

P12 Pr -1005.300 25.64 9.34 0.00 Punktlast

P13 Pr 1570.800 18.29 35.56 0.00 Punktlast

P14 Pr -1570.800 18.29 35.56 0.00 Punktlast

P15 Pr 1570.800 25.64 15.36 0.00 Punktlast

P16 Pr -1570.800 25.64 15.36 0.00 Punktlast

P17 Pr 1005.300 28.01 6.97 0.00 Punktlast

P18 Pr -1005.300 28.01 6.97 0.00 Punktlast

P19 Pr 1005.300 28.60 6.73 0.00 Punktlast

P20 Pr -1005.300 28.60 6.73 0.00 Punktlast

P21 Pr 1005.300 34.69 6.73 0.00 Punktlast

P22 Pr 1005.300 25.64 1.17 0.00 Punktlast

P23 Pr -1005.300 25.64 1.17 0.00 Punktlast

P24 Pr 1005.300 26.07 0.43 0.00 Punktlast

P25 Pr -1005.300 26.07 0.43 0.00 Punktlast

P26 Pr 1005.300 26.81 0.00 0.00 Punktlast

P27 Pr -1005.300 26.81 0.00 0.00 Punktlast

P28 Pr 1005.300 34.69 0.00 0.00 Punktlast

P29 Pr 769.700 0.00 56.38 3.90 Punktlast

P30 Pr 769.700 0.00 59.38 3.90 Punktlast

P31 Pr -769.700 0.00 59.38 0.00 Punktlast

P32 Pr -769.700 0.00 56.38 0.00 Punktlast

P33 Pr 1570.800 25.64 5.92 0.00 Punktlast

P34 Pr -1570.800 25.64 5.92 0.00 Punktlast

P35 Pr 1005.300 25.64 4.92 0.00 Punktlast

P36 Pr -1005.300 25.64 4.92 0.00 Punktlast

line loads - loading case LF-2


[.../m] [m] [m] [m]

LILA-1 pr/l -565.50 25.64 4.92 0.00 Linienlast

-565.50 25.64 5.92 0.00

Type l: Load direction local, r-axis is

load axis

g: Load direction global

p: Load direction global projected

Load [.../m]: line load (p) -> [kN/m] line

moments (m) -> [kNm/m]

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temperature loads - loading case LF-3


)

x = 0.00 0.00 m

y = 59.38 59.38 m

z = 0.00 3.90 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr

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)

x = 0.00 0.00 m

y = 56.38 56.38 m

z = 0.00 3.90 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


)

x = 33.54 34.69 m

y = 6.72 6.72 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


)

x = 28.60 33.54 m

y = 6.72 6.72 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


)

x = 28.01 28.60 m

y = 6.97 6.72 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


)

x = 25.64 28.01 m

y = 9.34 6.97 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


)

x = 33.54 34.69 m

y = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


)

x = 26.81 33.54 m

y = 0.00 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr

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)

x = 26.07 26.81 m

y = 0.43 0.00 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 25.64 26.07 m

y = 1.17 0.43 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 25.64 25.64 m

y = 4.24 1.17 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 25.64 25.64 m

y = 12.05 9.34 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 25.64 25.64 m

y = 15.36 12.05 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 20.90 25.64 m

y = 28.39 15.36 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 20.07 20.90 m

y = 30.66 28.39 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr

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load)

x = 18.29 20.07 m

y = 35.56 30.66 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 17.83 18.29 m

y = 36.10 35.56 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 17.22 17.83 m

y = 36.45 36.10 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 1.19 17.22 m

y = 39.28 36.45 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 0.43 1.19 m

y = 39.85 39.28 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = -0.00 0.43 m

y = 40.69 39.85 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr


load)

x = 0.00 -0.00 m

y = 61.49 40.69 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr

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load)

x = 25.64 25.64 m

y = 9.34 4.24 m


dTs = 0.00 K, dTt = 0.00 K

T = 10.00 degr

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point support evaluation

system

evaluation witout MIN/MAX-superposition



[kN] [kNm]

1 -5.94 -172.09 26.27 - - -

2 -1.37 -39.76 6.53 - - -



[kN] [kNm]

1 -39.68 1377.19 - - - -

2 -8.88 318.60 - - - -

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Date post:	30-May-2017
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FKT NiehII Statik GRP Stress

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