Sample Cal
description
Transcript of Sample Cal
-
DESIGN CALCULATION
DESIGN CALCULATION
PLATE HEAT EXCHANGER
(Fully Welded Hybrid Heat Exchanger Cryogenic Application)
FEED GAS/ RESIDUE GAS EXCHANGER
ITEM No: 3E-251 (New)
Location: BUHASA, Abu Dhabi
Rev: Date: Prepared: Issued for Approval
1 01.10.2013 Frank Betzold
-
Calculation
Finite Element Analysis
-
Report
Finite Element Analysis
of the
Hybrid Heat Exchanger Gasco02
Version 1.0
powered by
NX NASTRAN + FEMAP
SMART Engineering GmbH
Dipl.-Ing. Marco Solterbeck
Herrenheide 15a
D-21244 Buchholz
Phone: +49 4181/215900
Fax: +49 4181/215909
eMail: [email protected]
Internet: www.smart-fem.de
10-01-2013
-
SMART Engineering GmbH
2
Content
1. Project Definition ................................................................ 3
2. Regulations und design fundamentals ................................. 3
3. FE-Model ............................................................................. 3
4. Material Properties .............................................................. 5
5. Boundary Conditions ........................................................... 6
6. Verification of static strength due to test pressure ............. 7
6.1. Loadings ............................................................................... 7
6.2. Allowable stresses according to AD 2000 S4 .............................. 8
6.3. Analysis Results ..................................................................... 9
6.4. Verification according to AD 2000 S4 .......................................19
7. Verification of static strength due to operating pressure .. 19
7.1. Loadings ..............................................................................19
7.2. Allowable stresses according to AD 2000 S4 .............................21
7.3. Analysis Results ....................................................................22
7.4. Verification according to AD 2000 S4 .......................................31
8. Verification of the side lugs ............................................... 32
8.1. Loadings ..............................................................................32
8.2. Allowable stresses according to AD 2000 S4 .............................33 8.3. Analysis Results ....................................................................33
8.4. Verification according to AD 2000 S4 .......................................35
8.5. Reaction forces side lugs ........................................................36
-
SMART Engineering GmbH
3
1. Project Definition
For the housing of a hybrid heat exchanger the proof of the deformations and stresses based
on the finite element method shall be performed. Thereby has to be verified the strength of
the assembly due to test pressure and operating pressure.
For the side lugs the following load components are to be considered in different combina-
tions: dead weight of the structure, positive and negative nozzle loads, wind loads and earth-
quake loads.
The proofs will be carried out according to the rule type AD 2000 Guideline.
2. Regulations und design fundamentals
Used FEA-Software:
- Solver: NX Nastran, Release 8.5.1
- Pre-/Postprocessor: Femap, Release 11.0.1
Considered regulations and documents:
/ 1 / 2D-Drawing WH0887_sketch6.pdf 08-29-2013
/ 2 / 3D-Geometry data in Step-Format Gasco02_Bild_Step.stp
/ 3 / AD 2000 Guideline
/ 4 / Material data provided by SPX Flow Technology Rosista GmbH
/ 5 / Technical data provided by SPX Flow Technology Rosista GmbH
Table 1: Considered regulations and documents
3. FE-Model
The analysis model was created based on 3D-Geometry data in Step-Format. The discretiza-
tion of the model has been done almost exclusively with linear plate elements under consider-
ation of their corresponding wall thicknesses. The connections of the parts have been assumed
as ideal node couplings (merged coincident nodes). Welds and bolted connections have not been represented in detail. The modeling of the horizontal and vertical tie rods has been done
by beam elements with the corresponding cross sections. These beams have been connected
to the structure with rigid elements. The first inner rows of the vertical tie rods were meshed
in detail with brick elements.
Attached parts which are not relevant for stiffness were neglected. The same applies also for
the inner plate package, due to the soft connection to the structure. To keep the equilibrium
under pressure loads all nozzles have been closed.
Figure 1 to Figure 3 show the analysis model which has following characteristics:
Number of elements 433,585
Number of nodes 465,773
Table 2: Characteristics of the FE-Model
-
SMART Engineering GmbH
4
Figure 1: FE-Model, exterior view
Figure 2: FE-Model, sectional view
-
SMART Engineering GmbH
5
Figure 3: FE-Model, detailed view, tie rod connection at first inner row
4. Material Properties
The used material was assumed to be linear-elastic according to Hookes law. As the stresses
and strains to be verified are associated with different temperature conditions, the considera-
tion of appropriate material properties was required. As base for all further examination the
following properties / 4 / have been considered:
Material
Temp. Youngs
Modulus
Poisson's
Ratio
Yield Strength
Rp0,2
Tensile Strength
Rm
[C] [N/mm2] [-] [N/mm] [N/mm2]
1.4404
20 200,000 0.29 260 530
85 195,125 0.29 210 -
1.4571
20 200,000 0.29 260 540
85 195,125 0.29 225 -
Table 3: Material Properties
The adjustment of the properties to AD 2000 is done in section 6.2, 7.2 and 8.2.
Welding seam
(brick elements)
Tie rod
(beam elements)
Tie rod
(brick elements)
End plate
(brick elements)
-
SMART Engineering GmbH
6
Figure 4: FE-Model, sectional view, used materials with different colors
5. Boundary Conditions
The housing was constrained with static definitions at the two lugs under consideration of
contact with the grounding plate. Additionally both bolts at each lug were fixed in all direc-
tions. The constraints of the model are shown in Figure 5.
1.4571 (green)
1.4404 (red)
-
SMART Engineering GmbH
7
Figure 5: FE-Model, supports (constraints)
6. Verification of static strength due to test pressure
6.1. Loadings
For the verification of static strength in the test case a test pressure of 41.5 bar was applied
to the entire housing. Figure 6 shows the pressure distribution in the FE-Model.
Contact considered
between lug and grounding plate (grey)
Grounding plate and bolts fixed in all directions
-
SMART Engineering GmbH
8
Figure 6: FE-Model, pressure distribution under test conditions
6.2. Allowable stresses according to AD 2000 S4
The determinations of the allowable stresses according to AD 2000 S4 are based on the
material properties from Table 3. The allowable stresses have been calculated based on the
following equations and are listed in Table 4:
f20C = K20C / S with K20C = Rp1,0, safety factor S = 1.05 and welding factor v
Primary global membrane stress:
Pm20C = 1.0 f20C v
Primary local membrane stress:
Pl20C = 1.5 f20C v
Primary membrane + bending stress:
Pm20C + Pb20C = Pm20C + Pl20C = 1.5 f20C v
Primary membrane + bending Stress + secondary stress
Pm20C + Pb20C + Q20C = Pm20C + Pl20C + Q20C = 3 f20C v
Material f20C Welding
factor
Pm20C
[N/mm2]
Pl20C
[N/mm2]
Pm+Pb(l)
[N/mm2]
Pm+Pb(l)+Q
[N/mm2]
1.4404 247 1,00 247 370 370 741
1.4571 247 1,00 247 370 370 741
0,85 210 315 315 630
Table 4: Allowable stresses according to AD 2000 S4, test situation
Test pressure 41.5 bar = 4.15 N/mm
Test temperature T = 20 C
-
SMART Engineering GmbH
9
6.3. Analysis Results
For result evaluation the established membrane stresses and von Mises equivalent stresses
have been used.
In Figure 7 to Figure 25 the stresses are given on the deformed structure. For clarification the
deflections are scaled by a factor of 50.
The stress legend of the first figures is limited to the maximum relevant stress value of the
shown model part. In further figures the legend was scaled to the allowable AD 2000 S4
values.
Figure 7: FE-Model, full model, top view, Equivalent Stress [N/mm]
-
SMART Engineering GmbH
10
Figure 8: FE-Model, full model, bottom view, Equivalent Stress [N/mm]
Figure 9: FE-Model, top cover, Equivalent Stress [N/mm]
780 N/mm (surface tension)
1.210 N/mm (max. local stress peak)
-
SMART Engineering GmbH
11
Figure 10: FE-Model, bottom cover, Equivalent Stress [N/mm]
Figure 11: FE-Model, vertical tie rods, Equivalent Stress [N/mm]
290 N/mm
-
SMART Engineering GmbH
12
Figure 12: FE-Model, horizontal tie rods, Equivalent Stress [N/mm]
Figure 13: FE-Model, full model, top view, Equivalent Stress [N/mm]
Legend scaled to allowable
stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
193 N/mm
-
SMART Engineering GmbH
13
Figure 14: FE-Model, full model, bottom view, Equivalent Stress [N/mm]
Figure 15: FE-Model, welding seams (welding factor 0.85), Equivalent Stress [N/mm]
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Legend scaled to allowable stress
according AD2000 S4
blue: Pm = 1,0 f 0.85
yellow: Pm+P
b = 1,5 f 0.85
orange: Pm+P
b +Q = 3,0 f 0.85
red: > Pm+P
b +Q = 3,0 f 0.85
Welding seam
Welding seam
-
SMART Engineering GmbH
14
Figure 16: FE-Model, middle end plate, Equivalent Stress [N/mm]
Figure 17: FE-Model, top cover, Equivalent Stress [N/mm]
Legend scaled to allowable
stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Material 1.4404
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
-
SMART Engineering GmbH
15
Figure 18: FE-Model, bottom cover, Equivalent Stress [N/mm]
Figure 19: FE-Model, full model, top view, Membrane Stress [N/mm]
Legend scaled to allowable
stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Grey areas, no values available
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
-
SMART Engineering GmbH
16
Figure 20: FE-Model, full model, bottom view, Membrane Stress [N/mm]
Figure 21: FE-Model, welding seams (welding factor 0.85), Membrane Stress [N/mm]
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Grey areas, no values available
Legend scaled to allowable
stress according AD2000 S4
blue: Pm = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Welding seam
Welding seam
Legend scaled to allowable stress
according AD2000 S4
blue: Pm = 1,0 f 0.85
yellow: Pm+P
b = 1,5 f 0.85
orange: Pm+P
b +Q = 3,0 f 0.85
red: > Pm+P
b +Q = 3,0 f 0.85
Welding seam
Welding seam
-
SMART Engineering GmbH
17
Figure 22: FE-Model, middle end plate, Membrane Stress [N/mm]
Figure 23: FE-Model, top cover, Membrane Stress [N/mm]
Grey areas, no values available
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
589 N/mm (max. local stress peak)
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Material 1.4404
-
SMART Engineering GmbH
18
Figure 24: FE-Model, bottom cover, Membrane Stress [N/mm]
Figure 25: FE-Model, displacements [mm]
Grey areas, no values available
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
-
SMART Engineering GmbH
19
6.4. Verification according to AD 2000 S4
For result evaluation the established membrane stresses and von Mises equivalent stresses
have been used.
The proof of fatigue according to AD 2000 S4 is regarded as given under 6.3 when the calcu-
lated stresses are lower than the allowable stresses determined in 6.2.
The primary local membrane stresses are below the allowable value of 370 N/mm. Only at
the corners of the end plates the stresses locally exceeds this value.
Pl20C = 589 N/mm > 370 N/mm (Figure 23, upper end plate)
The Primary local membrane + bending stresses + secondary stresses are below the allowable
value of 370 N/mm. Only at the corners of the end plates and the welding seams of the tie
rods the stresses locally exceeds this value.
Pl20C + Pb20C + Q20C = 1.210 N/mm > 741 N/mm (Figure 9, upper end plate)
Pl20C + Pb20C + Q20C = 780 N/mm > 741 N/mm (Figure 9, welding seam tie rod)
Within the scope of the assumptions the strength proof of all components is regarded with the
exception of the end plate and the welding seams of the tie rods.
The stresses in these areas require a separate interpretation. The local stress distribution
allows the conclusion, that in these areas the material will yield causing a slight local plastic
deformation and thus the peak stresses will be reduced. Assuming that the pressure test is a
single event a failure of the structure is not to be expected
In the areas of the welding seams with the reduced welding factor of 0.85 the membrane and
equivalent stresses are below the allowable values (Figure 21 and Figure 15).
7. Verification of static strength due to operating pressure
7.1. Loadings
For the verification of static strength in the operating case an allowable pressure of 29.0 bar
was applied to the entire housing. Furthermore the nozzle loads in positive (Figure 27) and
negative (Figure 28) directions have been considered. Figure 26 shows the pressure distribu-
tion in the FE-Model.
-
SMART Engineering GmbH
20
Figure 26: FE-Model, pressure distribution under operating conditions
Figure 27: FE-Model, positive nozzle loads (nozzle 1 to 4)
Operating pressure 29.0 bar = 2.9 N/mm
Operating temperature T = 85 C
Forces [N] Moments [Nmm]
N1 N1
N4
N2 N2
N3 N3 N4
Resulting positive nozzle forces: Fx = -57.0 kN; Fy = 66.0 kN; Fz = 58.5 kN
-
SMART Engineering GmbH
21
Figure 28: FE-Model, negative nozzle loads (nozzle 1 to 4)
7.2. Allowable stresses according to AD 2000 S4
The determinations of the allowable stresses according to AD 2000 S4 are based on the
material properties from Table 3. The allowable stresses have been calculated based on the
following equations and are listed in Table 5:
f85C = K85C / S with K85C = Rp1,0, safety factor S = 1.50 and welding factor v
Primary global membrane stress:
Pm85C = 1.0 f85C v
Primary local membrane stress:
Pl85C = 1.5 f85C v
Primary membrane + bending stress:
Pm85C + Pb85C = Pm85C + Pl85C = 1.5 f85C v
Primary membrane + bending Stress + secondary stress
Pm85C + Pb85C + Q85C = Pm85C + Pl85C + Q85C = 3 f85C v
Material f85C Welding
factor
Pm85C
[N/mm2]
Pl85C
[N/mm2]
Pm+Pb(l)
[N/mm2]
Pm+Pb(l)+Q
[N/mm2]
1.4404 140 1,00 140 210 210 420
1.4571 150 1,00 150 225 225 450
0,85 127 191 191 382
Table 5: Allowable stresses according to AD 2000 S4, operating situation
N1 N1
N4
N2 N2
N3 N3 N4
Forces [N] Moments [Nmm]
Resulting negative nozzle forces: Fx = 57.0 kN; Fy = -66.0 kN; Fz = -58.5 kN
-
SMART Engineering GmbH
22
7.3. Analysis Results
For result evaluation the established membrane stresses and von Mises equivalent stresses
have been used. Relevant for the stress evaluation is the load case with negative nozzle loads.
At this load case the maximum stress appears in the structure.
In Figure 29 to Figure 46 the stresses are given on the deformed structure. For clarification
the deflections are scaled by a factor of 50.
The stress legend of the first figures is limited to the maximum relevant stress value of the
shown model part. In further figures the legend was scaled to the allowable AD 2000 S4
values.
Figure 29: FE-Model, full model, top view, Equivalent Stress [N/mm]
-
SMART Engineering GmbH
23
Figure 30: FE-Model, full model, bottom view, Equivalent Stress [N/mm]
Figure 31: FE-Model, top cover, Equivalent Stress [N/mm]
549 N/mm (surface tension)
858 N/mm (max. local stress peak)
-
SMART Engineering GmbH
24
Figure 32: FE-Model, bottom cover, Equivalent Stress [N/mm]
Figure 33: FE-Model, vertical tie rods, Equivalent Stress [N/mm]
204 N/mm
-
SMART Engineering GmbH
25
Figure 34: FE-Model, horizontal tie rods, Equivalent Stress [N/mm]
Figure 35: FE-Model, full model, top view, Equivalent Stress [N/mm]
Legend scaled to allowable
stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
136 N/mm
-
SMART Engineering GmbH
26
Figure 36: FE-Model, full model, bottom view, Equivalent Stress [N/mm]
Figure 37: FE-Model, welding seams (welding factor 0.85), Equivalent Stress [N/mm]
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Legend scaled to allowable stress
according AD2000 S4
blue: Pm = 1,0 f 0.85
yellow: Pm+P
b = 1,5 f 0.85
orange: Pm+P
b +Q = 3,0 f 0.85
red: > Pm+P
b +Q = 3,0 f 0.85
Welding seam
Welding seam
-
SMART Engineering GmbH
27
Figure 38: FE-Model, middle end plate, Equivalent Stress [N/mm]
Figure 39: FE-Model, top cover, Equivalent Stress [N/mm]
Legend scaled to allowable
stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Material 1.4404
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
-
SMART Engineering GmbH
28
Figure 40: FE-Model, full model, top view, Membrane Stress [N/mm]
Figure 41: FE-Model, full model, bottom view, Membrane Stress [N/mm]
Legend scaled to allowable
stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Grey areas, no values available
Grey areas, no values available
-
SMART Engineering GmbH
29
Figure 42: FE-Model, welding seams (welding factor 0.85), Membrane Stress [N/mm]
Figure 43: FE-Model, middle end plate, Membrane Stress [N/mm]
Legend scaled to allowable stress according AD2000 S4
blue: Pm = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Welding seam
Welding seam
Legend scaled to allowable stress according AD2000 S4
blue: Pm = 1,0 f 0.85
yellow: Pm+P
b = 1,5 f 0.85
orange: Pm+P
b +Q = 3,0 f 0.85
red: > Pm+P
b +Q = 3,0 f 0.85
Welding seam
Welding seam
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
Material 1.4404
-
SMART Engineering GmbH
30
Figure 44: FE-Model, top cover, Membrane Stress [N/mm]
Figure 45: FE-Model, bottom cover, Membrane Stress [N/mm]
Grey areas, no values available
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
418 N/mm (max. local stress peak)
Grey areas, no values available
Legend scaled to allowable stress according AD2000 S4
S4 blue: P
m = 1,0 f
yellow: Pm+P
b = 1,5 f
orange: Pm+P
b +Q = 3,0 f
red: > Pm+P
b +Q = 3,0 f
-
SMART Engineering GmbH
31
Figure 46: FE-Model, displacements [mm]
7.4. Verification according to AD 2000 S4
For result evaluation the established membrane stresses and von Mises equivalent stresses
have been used.
The proof of fatigue according to AD 2000 S4 is regarded as given under 7.3 when the calcu-
lated stresses are lower than the allowable stresses determined in 7.2.
The primary local membrane stresses are below the allowable value of 370 N/mm. Only at
the corners of the end plates the stresses locally exceeds this value.
Pl20C = 418 N/mm > 225 N/mm (Figure 44, upper end plate)
The Primary local membrane + bending stresses + secondary stresses are below the allowable
value of 370 N/mm. Only at the corners of the end plates and at the welding seams of the tie
rods the stresses locally exceeds this value.
Pl20C + Pb20C + Q20C = 859 N/mm > 450 N/mm (Figure 31, upper end plate)
Pl20C + Pb20C + Q20C = 549 N/mm > 450 N/mm (Figure 31, welding seam tie rod)
Within the scope of the assumptions the strength proof of all components is regarded with the exception of the end plate and the welding seams of the tie rods.
The stresses in these areas require a separate interpretation. The local stress distribution
allows the conclusion, that in these areas the material will yield causing a slight local plastic
deformation and thus the peak stresses will be reduced. Assuming that the pressure test is a
single event a failure of the structure is not to be expected
In the areas of the welding seams with the reduced welding factor of 0.85 the membrane and
equivalent stresses are below the allowable values (Figure 42 and Figure 37).
-
SMART Engineering GmbH
32
8. Verification of the side lugs
8.1. Loadings
For the verification of the side lugs the load cases listed in Table 6 have been considered. The
pressure was neglected.
Load case 3a 3b 4 5a 5b
Self-weight, operation, full mop,full = 40.268 t / 5 / x x - x x
Self-weight, testing, full mtest,full= 67.740 t / 5 / - - x - -
Nozzle loads, positive direction (Figure 27) / 1 / x - - x -
Nozzle loads, negative direction (Figure 28) / 1 / - x - - x
Wind load, full (Figure 47) / 5 / x x - - -
Wind load, half / 5 / - - x - -
Earthquake loads (Figure 47) / 5 / - - - x x
Table 6: Load cases for verification of the lugs
The wind and earthquake loads were applied to the center of gravity of the heat exchanger.
The connection between the load point and the meshed structure was done with a non-
stiffening interpolation element.
Figure 47: FE-Model, wind and earthquake loads
Wind loads [N]
Center of gravity
Earthquake loads [N]
Center of gravity
-
SMART Engineering GmbH
33
8.2. Allowable stresses according to AD 2000 S4
The determinations of the allowable stresses according to AD 2000 S4 are based on the
material properties from Table 3. The allowable stresses have been calculated based on the
following equations and are listed in Table 7:
f85C = K85C / S with K85C = Rp1,0, safety factor S = 1.50 and welding factor v
Primary global membrane stress:
Pm85C = 1.0 f85C v
Primary local membrane stress:
Pl85C = 1.5 f85C v
Primary membrane + bending stress:
Pm85C + Pb85C = Pm85C + Pl85C = 1.5 f85C v
Primary membrane + bending Stress + secondary stress
Pm85C + Pb85C + Q85C = Pm85C + Pl85C + Q85C = 3 f85C v
Material f85C Welding
factor
Pm85C
[N/mm2]
Pl85C
[N/mm2]
Pm+Pb(l)
[N/mm2]
Pm+Pb(l)+Q
[N/mm2]
1.4571 150 1,00 150 225 225 450
Table 7: Allowable stresses according to AD 2000 S4, operating situation
8.3. Analysis Results
For result evaluation the established membrane stresses and von Mises equivalent stresses
have been used. The maximum stresses and deformations of the considered load cases are
listed in Table 8.
Load case Membrane Stress
[N/mm]
Equivalent Stress
[N/mm]
Displacement
[mm]
3a 36 49 1.03
3b 42 58 1.15
4 33 45 0.59
5a 39 85 1.05
5b 62 87 1.50
Table 8: Stresses and displacements of the lugs
In Figure 48 to Figure 50 only the stresses of the load case with the maximum stress value
are given on the deformed structure. For clarification the deflections are scaled by a factor of
50.
The stress legend of the following figures is limited to the maximum relevant stress value of
the shown model part.
-
SMART Engineering GmbH
34
Figure 48: FE-Model, side lug, Equivalent Stress [N/mm]
Figure 49: FE-Model, side lug, Membrane Stress [N/mm]
87 N/mm
62 N/mm
-
SMART Engineering GmbH
35
Figure 50: FE-Model, side lug, displacements [mm]
8.4. Verification according to AD 2000 S4
For result evaluation the established membrane stresses and von Mises equivalent stresses
have been used.
The proof of fatigue according to AD 2000 S4 is regarded as given under 8.3 when the calcu-
lated stresses are lower than the allowable stresses determined in 8.2.
The primary local membrane stresses are below the allowable value of 225 N/mm.
Pl20C = 62 N/mm < 225 N/mm (Figure 49)
The Primary local membrane + bending stresses + secondary stresses are below the allowable
value of 225 N/mm.
Pl20C + Pb20C + Q20C = 87 N/mm < 450 N/mm (Figure 48)
Within the scope of the assumptions the strength proof of the side lugs is regarded.
-
SMART Engineering GmbH
36
8.5. Reaction forces side lugs
The calculated values for the reaction forces of the both side lugs named in Figure 51 are
listed in Table 9.
Figure 51: FE-Model, side lug positions for reaction loads
Load case
Side lug A Side lug B
FRx [kN]
FRy [kN]
FRz [kN]
FRx [kN]
FRy [kN]
FRz [kN]
3a 64,0 250,6 -51,3 -30,3 78,5 -19,8
3b 29,5 135,4 38,3 -109,8 325,6 7,5
4 90,5 332,4 -3,3 -102,2 332,1 -3,1
5a 13,9 212,3 -78,8 -80,4 116,8 -46,9
5b -21,8 98,1 11,1 -158,7 362,9 -19,7
Table 9: Reaction forces side lugs
Side lug A Side lug B