Design Report -ROV Hangar Deck-rev 1 - FINAL
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Content 1 2 3 4
5 6
7
Introduction: ........................................................................................................................................2 1.1 Design resume...............................................................................................................................2 Document References, Rules and Standards ..................................................................................2 Conclusions ........................................................................................................................................3 Design Basis .......................................................................................................................................3 4.1 Materials ........................................................................................................................................3 4.2 Stress .............................................................................................................................................4 4.3 Material Factors .............................................................................................................................4 4.4 Deflections .....................................................................................................................................5 4.5 Loads .............................................................................................................................................5 4.5.1 Environmental loads ..............................................................................................................5 4.5.2 Platform motions loads ..........................................................................................................5 4.5.3 Area load ...............................................................................................................................5 4.6 Accidental heel and trim ................................................................................................................5 4.7 Lifting and tranportation operations ...............................................................................................5 Design limit states ..............................................................................................................................6 5.1 Design factors ................................................................................................................................6 Analysis ...............................................................................................................................................7 6.1 Computer model ............................................................................................................................7 6.2 Load chart ......................................................................................................................................9 6.3 LC – Load combinations ............................................................................................................. 10 6.3.1 LC1: ULSa+b ...................................................................................................................... 10 6.3.2 LC2: ULS a+b ..................................................................................................................... 12 6.3.3 LC3: SLS ............................................................................................................................ 13 6.3.4 LC4: SLS ............................................................................................................................ 13 6.4 Reaction forces and moments (ULS) ......................................................................................... 13 6.5 Calculation results ULS .............................................................................................................. 14 6.5.1 Material ............................................................................................................................... 14 6.5.2 Middle Girder design .......................................................................................................... 15 6.5.3 Side girder design ............................................................................................................... 19 6.5.4 Stiffener design – L-profile stiffener: ................................................................................... 22 6.5.5 Stiffener design – UNP profile stiffener: ............................................................................. 25 6.6 Calculation results, SLS ............................................................................................................. 28 6.6.1 Main girders ........................................................................................................................ 29 6.6.2 Stiffeners ............................................................................................................................. 29 Hand calculations acc. to EN 1993-1-1 .......................................................................................... 30
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Introduction:
This report verifies the structural integrity of a new deck structure installed inside the existing ROV hangar onboard TO Barents. The verification is performed by use of computer program FEM software Autodesk Robot Strutural Analysis and by hand calculations where relevant. Completed with design brief and analysis of the new structure.
1.1 Design resume The structural scope includes the following activities covered in this report: Deck, Elevation 43.500: A new deck structure inside the hangar will be designed at same level as top of box-girder at EL.43.500, with 0.5 ton/m2 carrying capacity. The new deck is only to be supported by the walls/columns of the existing structure without internal columns down to the deck below. The existing deck at level 2 in ROV hangar will remain as a roof over existing rooms below. Upper level storage room shall be insulated and heated based on constant temperature (hot – dry storage). The storage room will be trafficked by a fork lift truck, ref type Toyota 8FBEKT18. Varyable loads are specified by Transocean. Ref /2/. Adjacent existing structure is controlled for the effects caused by the new deck only. In chapter 6 forces and moments transferred from the new deck to the adjacent structure are listed. In chapter 6 all new equipment (deck and office container) are listed with dead load. The design verification is performed for the Servicability limit state (SLS), Ultimate limit state (ULS) and Accidental limit state (ALS) as specified.
2 /1/ /2/ /3/ /4/ /5/ /6/ /7/
Document References, Rules and Standards
Document H600-AK-Z-FD-0001 H-6e Regulations Technical specification for purchase. ROV hangar modified to store NORSOK STANDARD N-001 Edition 7, June 2010 NORSOK STANDARD N-004 Rev.2, October 2004 NS-EN 1993-1-1/5:2005+NA:2008 NORSOK STANDARD M-120 Material Data Sheet for structural steel Det Norske Veritas DNV-OSS-101 Rules for Classification of Offshore Drilling and Support Units, October 2012 /8/ Det Norske Veritas DNV-OS-B101 Metallic Materials, October 2012 /9/ Det Norske Veritas DNV-OS-C101 Design of Offshore Steel Structures. General (LRFD Method), April 2011 /10/ Det Norske Veritas DNV-OS-C103 Structural design of Column Stabilised Units (LFRD Method), October 2012 /11/ Det Norske Veritas DNV OS-C401 Fabrication and Testing of Offshore Structures
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/12/ Det Norske Veritas DNV RP-C103 Column Stabilised Unit, April 2012 /13/ Det Norske Veritas DNV-RP-C201 Buckling Strength of Plated Structures, October 2010 /14/ Det Norske Veritas DNV-RP-C202 Buckling Strength of Shells, January 2013
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Conclusions
The analysis performed prove that the deck design fulfills the specified requirements. Maximum utilization for the ULS/ALS limit state is found to be 0,85. (Criterion 1,0) Maximum deflection for the SLS limit state is found to be 13 mm on a 3110 mm longitudinal span equals 1/250. (Criterion 1/250)
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Design Basis
Selection of steel quality and requirements for inspection of welds shall be based on a systematic classification of welded joints according to the structural significance and complexity of joints. The main criterion for decision of Design Class of welded joints is the significance with respect to consequences of failure of the joint. In addition the geometrical complexity of the joint will influence the DC selection. From table 5-1 ref. /4/: From table 5-2 ref. /4/, for DC4: Minimum steel quality according to Norsok M-120: From table 5-3 ref. /4/, for DC4 with moderate stresess:
Design Class: DC4 Steel quality class: III (I) S355 Mpa Inspection category for welds: C
4.1 Materials Ref. /2/ The following linear structural steel materials were used [SI-units used]: STEEL NORSOK QUALITY GRADE (Min Yield Stress) 355
355
S355J2
S355J2H
Table4-1: Material types
APPLICATION
Outfitting steel profiles, plates, etc., specified yield strength 355 MPa. (Standard EN10025) RHS profiles, if delivered from stock,specified yield strength 355 MPa. (Standard EN10210)
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S355 J2 (acc. to NORSOK M-120, ref. /6/) Yield strength: Poisson number: Tensile strength: Young’s modulus: Shear modulus: Steel density:
fy = 355 N/mm2 ν = 0.3 fu = 470N/mm2 E = 2.1 105 N/mm2 G = E [2 (1 + v)]-1 = 8.077 ρ = 7850 kg/m3
104 N/mm2
4.2 Stress In general, according to NORSOK, the equivalent Von Mises design stress shall be less than: sj
<
f d = f y / gm
fd
=
allowable design stress
fy
=
minimum yield stress
gm
=
material factor
where
The usage factor (U = sj / fd) for structural components is calculated in accordance with NSEN1993-1-1. The code admits a usage factor equal to 1, see NORSOK. FEM analysis will complete the manual calculations for the structural elements.
4.3 Material Factors According to table 6-1 ref./4/ the material factors will be taken:
Material factors γ
ULS
ALS
SLS
γM= 1.15
γM= 1.0
γM= 1.0
2
Cross –sections1-4, and buckling Boltedconnection
γMb=1.3
γMb=1.0
γMb=1.0
3
Netsection,bolts holes
γM2=1.3
γM2=1.0
γM2=1.0
4
Filletweld
γMw=1.3
γMw=1.0
γMw=1.0
1
Table4-2:Material factors
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4.4 Deflections Ref. /9/ For serviceability limit state the following maximum deflections will be considered: Item Maximum Deflection Deck plates
L/150
Deck beams supporting plaster or other brittle finish or non- flexible partitions
L/250
Table4-3:Maximum deflections
4.5 Loads 4.5.1
Environmental loads
N.A. 4.5.2
Platform motions loads
N.A. – hence the accidental accelerations due to static heel will be considered, see 4.11, the platform loads due of the environmental conditions which appear in the 100 years storm will not be considered. 4.5.3
Area load
Ref. /2/ Live load Deckload:
P1 = 5.0 kN/m2
Fork lift truck load – Toyota 8FBEKT18:
P2 = 70.3 kN
New office container – weight + furniture, weight 11.6 t:
P3 = 116 kN
Ref. /2/ Dead load Dead load new deck – weight 17.0 t
P4 = 170 kN
Overhanging equipment (HVAC, piping, EIT):
P2 = 0.3kN/m2
4.6 Accidental heel and trim Loads from accidental heel and trim is considered for a static angle of 17 deg. as specified in Ref. /10/.
4.7 Lifting and tranportation operations This report does not contain the lifting operations for the equipment. Separate reports will be made for lifting and handling when relevant.
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Design limit states
5.1 Design factors
Load Factors Condition
P(ermanent)
L(ive)
E(nvironm.) A(ccident.)
ULS-a
1.3
1.3
0.7
ULS-b
1.0
1.0
1.3
ULS-a+b *
1.3
1.3
1.3
SLS
1.0
1.0
1.0
ALS 1.0 1.0 1.0 1.0 Table 5-1: Design load and material factors according to NORSOK / DNV *ULS a+b is simplified concervative.
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Analysis
6.1 Computer model Figure 1: FEM Model – From Inventor
New deck structure
ROV Hangar - existing HEB 300 columns UPN 300 Side Girders
Steel plate t=8 mm
Figure 2:Top view of deck – girders and plates IPE 400 Middle Girders
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UPN 180 Stiffeners
Figure 3:Bottom view of deck – stiffeners L150x100x12 Stiffeners
Figure 4: Geometry of the deck supports (plan view) Support nodes are defined A1 to F4 A1 A2 A3 A4
B1 B2
C1 C2
D1 D2
E1 E2
F1 F2 F3 F4
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Deck girders will be fixed to the existing HEB columns of the ROV at one end and to the box girder at the other. Supports for the deck structure are showed in Figure 4.
6.2 Load chart Table 6-1: Load chart used in analysis Location Description Load P/L/E Structural elements P New deck (self weight) (EL.43.500) P Overhanging equipment Totalmass P deck ext. Office L container Fork lift truck L Deck live load
L
Loads / weights
Unit Kg
ULS factor 1,3
Design load / weights for ULS foranalyses 22100
17000 3360
Kg
1,3
4368
20360
Kg
1,3
26468
11600
kg
1,3
15080
7030
Kg
1,3
9140
5,0
kN/m2
1,3
7,5
Ref.
Table 6-2: Deck loadings in FEA Software Reference is given to each load combination below. Note: In the calculations, the following assumptions and simplifications, are done: 1. Masses are applied as net weight. 3. Live loads and environmental loads are applied as forces or pressure as shown in plots. 4. Utilization is based on maximum allowed stress: 355 N/mm2 / 1,15 =308,5 N/mm2 5. Utilization factor of 1.0 is allowed.
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6.3 LC – Load combinations In the analysis 16 ULS and 16 SLS load cases were taken into consideration in accordance with the NORSOK standard. The structural elements were globaly and localy checked for buckling. The most unfavorable load combinations are presented in this report: LC1
ULS
Dead loads (OW)
Live loads (LL1)
Container load (CL)
Fork lift load 1 (FLL1)
Local buckling analysis
Global buckling analysis
LC2
ULS
Dead loads (OW)
Live loads (LL1)
Container load (CL)
Fork lift load 2 (FLL2)
Local buckling analysis
Global buckling analysis
LC3
SLS
Dead loads (OW)
Live loads (LL1)
Container load (CL)
Fork lift load 1 (FLL1)
Deflection check
LC4
SLS
Dead loads (OW)
Live loads (LL1)
Container load (CL)
Fork lift load 2 (FLL2)
Deflection check
Table6-3: Load combinations table For the ULS limit state, the conservative, simplified ULS a+b has been used. As specified in /2/ the ALS limit state should be controlled in accordance with DNV –OS-C103. This standard specifies an ALS check for a static accidental heel of 17 degrees. As the ALS does not include any additional loads or load impacts, the ULS calculations cover the ALS calculations and thus, ALS calculations are not required. 6.3.1
LC1: ULSa+b
The loads used in LC1 are the following:
Figure 5:LC1 combination
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Self weight (OW)
Fork lift load 1 (FLL1)
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Container load (CL)
Live load 1 (LL1)
The fork lift load (FLL1) was considered acting on the front wheels of the fork lift. The most unfovarable situation is achieved when 70% of the weight is unloading on one wheel (Fz=-44 kN) while 30% of the weight is unloading on the other wheel (Fz=-19 kN). FLL1 is applied on the L-stiffener at equal distances from the supporting ends. A 12.00 t container load (CL) was considered in the analysis to be positioned between A1-C1 and A2-C2 supports. The total weight was modeled as 4 point loads (Fz= -30kN). The above loads are without load factors. In the analysis material factors from table 4-1 and load factors from table 5-1 are used.
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LC2: ULS a+b
Figure 6:LC2 combination
Self weight (OW)
Container load (CL)
Fork lift load 1 (FLL2)
Live load 1 (LL1)
The fork lift load was considered acting on the front wheels of the fork lift. The most unfovarable situation is achieved when 70% of the weight is unloading on one wheel (Fz=-44 kN) while 30% of the weight is unloading on the other wheel (Fz=-19 kN). In LC2 the load is applied on the UPN-stiffener at equal distances from the supporting ends. A 12.00 t container load (CL) was considered in the analysis to be positioned between A1-C1 and A2-C2 supports. The total weight was modeled as 4 point loads (Fz= -30kN).
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The above loads are without load factors. In the analysis material factors from table 4-1 and load factors from table 5-1 are used. 6.3.3
LC3: SLS
LC3 is the equivalent of LC1 with SLS material and load factors given in tables 4-1 and 5-1.
6.3.4
LC4: SLS
LC3 is the equivalent of LC2 with SLS material and load factors given in tables 4-1 and 5-1.
6.4 Reaction forces and moments (ULS) Load case
Node
Fx [kN]
Fy [kN]
Fz [kN]
Mx [kNm]
My [kNm]
Mz [kNm]
LC1+LC2
A1
22.16
-
22.47
-
19.71
-
A2
21.99
-
20.27
-
14.16
-
A3
21.16
-
22.72
-
18.30
-
A4
22.66
-
30.03
-
15.08
-
B1
25.97
-
156.66
-
215.16
-
B2
21.61
-
141.41
-
151.27
-
C1
30.90
-
142.31
-
209.82
-
C2
25.68
-
122.88
-
150.97
-
D1
45.07
-
163.74
-
246.97
-
D2
50.60
-
188.08
-
192.08
-
E1
50.31
-
190.44
-
292.00
-
E2
55.31
-
191.03
-
199.87
-
F1
20.05
-
22.20
-
23.59
-
F2
17.97
-
74.41
-
18.59
-
F3
14.38
-
92.30
-
25.69
-
F4 17.97 Table 4: Reaction Table
-
78.64
-
24.55
-
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6.5 Calculation results ULS The main structural elements in the design are as shown above defined as:
Middle girders
Side girders
Stiffeners (L - stiffeners incl. effective flange)
Stiffeners (UPN180 - stiffeners)
The highest utilized elements, all load cases, are described below:
Structural Element
Governing Load comb.
Med
Ved
Ned
[kNm]
[kN]
[kN]
Middle girder
LC1
292.00
191.03
55.31
Side girder
LC1
27.96
92.30
22.58
Stiffener – L
LC1
42.46
44.09
31.35
Stiffener – UPN LC2 37.43 53.64 Table 6-5: Design efforts for highest utilized structural members
6.5.1
Material
Table 6-6: Material S355J2 – all steel elements.
29.10
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Middle Girder design
The girders are considered to be fixed at both ends (see figure 4), transferring bending, shear and axial efforts to the existing structures. IPE 400 profiles are chosen.
IPE 400 section properties
Figure 7: Girder section properties
Figure 8: Bending moment diagrams for all girders (only girders are shown)
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Figure 9: Shear force diagrams for all girders (only girders are shown)
From figures 7 & 8, we find out the most stressed girder (girder no 4 supported between E1 and E2) from the deck structure, mainly the one which overstakes half of the biggest plate span on which the office container will be placed (3100 mm x 4400 mm).
Figure 10: Effort diagrams for the most stressed girder
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STRESS ANALYSIS IN THE IPE 400 BAR – Middle Girder Section Element No. Length
: IPE 400 : 4 : 8225 mm
CROSS SECTION
Figure 11: von Mises equivalent stresses – cross section Load case : "LC1" Stress analysis type (hypothesis) : von Mises
Internal forces taken into account : Fx Fy Fz Mx My Mz Extreme stresses in the beam sX max Stresses 261.35 MPa Relative position 0.00 Absolute position 0.0 mm Forces applied Fx = 54.67 kN Fy = 2.75 kN Fz = 190.44 kN
sX min
| t | max
si max
-248.40 MPa 0.00 0.0 mm
66.69 MPa 0.03 8200.0 mm
261.35 MPa 0.81 0.0 mm
Mx = 0.00 kN*m My = -292.00 kN*m Mz = 0.35 kN*m
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Figure 12: von Mises equivalent stresses XZ plane view
Figure 13: von Mises equivalent stresses XZ plane view
Figure 14: von Mises equivalent stresses 3D view U = sj / fd= 261,35 Mpa / 308,0 Mpa = 0,85 < 1 OK !
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Side girder design
The exterior girders were considered to be fixed on the ROV hangar HEB columns, respectively in points A1 to A4 and F1 to F4. UPN 300 sections are chosen. UPN 300 section properties
Figure 15: Exterior girder section properties
Figure 16: von Mises equivalent stresses – cross section STRESS ANALYSIS IN THE UPN300 BAR – EXTERIOR GIRDER Section Element No. Length
: UPN 300 : 12 : 8350 mm
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CROSS SECTION
Figure 17: von Mises equivalent stresses – cross section
Load case : "LC1" Stress analysis type (hypothesis) : von Mises
Internal forces taken into account : Fx Fy Fz Mx My Mz Extreme stresses in the beam sX max Stresses 207.99 MPa Relative position 0.06 Absolute position 150.0 mm
sX min
| t | max
si max
-129.40 MPa 0.06 150.0 mm
93.17 MPa 0.56 0.0 mm
208.62 MPa 0.76 700.0 mm
Forces applied to the section Fx = -13.44 kN Mx = 0.58 kN*m Fy = -37.20 kN My = -27.96 kN*m Fz = -92.30 kN Mz = 3.43 kN*m
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Figure 18:von Mises equivalent stresses XZ plane view
Figure 19:von Mises equivalent stresses XY plane view
Figure 20: von Mises equivalent stresses 3D view
U = sj / fd= 208,62Mpa / 308,0 Mpa = 0,68 < 1 OK !
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Stiffener design – L-profile stiffener:
In the model, stiffeners are defined as «specially designed element» consicting of the L-profile itself and an effective flange as shown in figure 23. Effective flange calculation ref. /5/, /13/:
Figure 21: Effective length Le of plate for stiffeners acc. to EN1993-1-5, ref. /5/
Figure 22: Effective width principle for stiffeners acc. to DNV-RP-C201, ref./13/ Le1 = Le2 = 600 mm - spacing between the stiffeners The condition in EN 1993-1-1-5 is more restrictive that the one in DNV-RP-C201, thus the effective flange width for the middle stiffeners will be : S=1/2 (Le1+ Le2) = 300 mm
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Resulting the following composed cross section:
Figure 23:Stiffener + plate section properties
Figure 24: Bending moment and shear force diagrams for stiffener
STRESS ANALYSIS IN THE BAR Section Element No. Length
: UPLL 300x150x100 : 75 : 3110 mm
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CROSS SECTION
Figure 25: von Mises equivalent stresses – cross section Load case : "LC1" Stress analysis type (hypothesis) : von Mises Internal forces takenintoaccount: Fx Fy Fz Mx My Mz Extreme stresses in the beam sX max Stresses 230.89 MPa Relative position 0.31 Absolute position 962.4 mm
sX min
| t | max
si max
-269.07 MPa 0.31 962.4 mm
32.65 MPa 0.31 0.0 mm
269.12 MPa 1.00 962.4 mm
Forces applied to the section Fx = 51.76 kN Mx = 0.01 kN*m Fy = -8.43 kN My = 42,46 kN*m Fz = -44.09 kN Mz = -51.76 kN*m
Figure 26: von Mises equivalent stresses XZ plane view
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Figure 27: von Mises equivalent stresses XY plane view
As we see both in top and bottom flange the equivalent stresses are under the yield strength of the material:
Figure 28: von Mises equivalent stresses 3D view U = sj / fd= 269,12Mpa / 308,0 Mpa = 0,874< 1 OK ! NB ! The plate between stiffeners will normally be checked implicitly by the stiffener check since plate buckling is accounted for by the effective width method.
6.5.5
Stiffener design – UNP profile stiffener:
Due to the deck’s erection method, some deck stiffeners are chosen UNP 180 profiles. These profiles are checked without the contribution of an effective flange (conservative).
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UPN 180 section properties
Figure 29: Channel stiffener section properties
Figure 30:Bending moment and shear force diagrams for stiffener
STRESS ANALYSIS IN THE BAR Section Element No. Length
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: UNP 180 : 76 : 3110 mm
CROSS SECTION
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Load case : "LC2" Stress analysis type (hypothesis) : von Mises
Internal forces takenintoaccount: Fx Fy Fz Mx My Mz
Extreme stresses in the beam sX max Stresses 256.92 MPa Relative position 0.31 Absolute position 962.4 mm
sX min
| t | max
si max
-238.62 MPa 0.31 962.4 mm
35.36 MPa 0.00 0.0 mm
256.92 MPa 0.86 962.4 mm
Forces applied to the section Fx = 26.26 kN Mx = 0.00 kN*m Fy = 0.02 kN My = 37.43 kN*m Fz = -42,49 kN Mz = 0.02 kN*m
Figure 31: von Mises equivalent stresses XZ plane view
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Figure 32: von Mises equivalent stresses XY plane view
Figure 33: von Mises equivalent stresses 3D view U = sj / fd= 256,92 Mpa / 308,0 Mpa = 0,834 < 1 OK !
6.6 Calculation results, SLS Acc. to ref. /9/ Serviceability limit states for offshore steel structures are associated with: — deflections which may prevent the intended operation of equipment; — deflections which may be detrimental to finishes or non-structural elements; — vibrations which may cause discomfort to personnel; — deformations and deflections which may spoil the aesthetic appearance of the structure. For calculations in the serviceability limit states ym = 1.0 For serviceability limit state the following maximum deflections will be considered Ref. /9/:
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Item
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Maximum Deflection
Deck plates
L/150
Deck beams supporting plaster or other brittle finish or non- flexible partitions
L/250
Table6-7:Maximum deflections 6.6.1
Main girders
The main girders are fixed to the box girder in one end and to the existing ROV HEB300 columns in the other end. Based on survey meassurements, maximum span of the girders are 8225 mm.
Figure 34: IPE girders deflections for LC3 and LC4 Figure 35: Maximum displacement for girder no. 4
uz = 11 mm < 8225 mm / 250 = 32,9 mm OK ! 6.6.2
Stiffeners
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Figure 36: Stiffener deflections for LC3 and LC4
Figure 37: Maximum stiffener deflections for LC3 and LC4 uz = 13 mm < 3110 mm / 250 = 12,42 mm = 13 mm OK ! Considering that the upper flange of the stiffeners is the plate, the admissible deformation for the plate will be : uz = 13 mm < 3110 mm / 150 = 20,73 mm OK !
7
Hand calculations acc. to EN 1993-1-1
In order to verify the results from the computer model, hand calculations are performed to the most critical elements and sections.
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VEd 191.02kN
MyEd 292kN m
1. Efforts: 2. Geometry: L 8225mm
3. Safety factors:
M0 1.15 M1 1.15
4. Geometric characteristics:
IPE 400 h 400mm
b 180mm tf 13.5mm
r 21mm tw 8.6mm
Height of web:
hw h 2tf 2r 331mm
Section Area
Aa 2 tf b h 2 tf tw (4 ) r 84.464cm
2
2
Maximum inertia moment y-y 3
3
2 tbf bh 3 hb 2t tf htw 2 t 3 4 2 2 w f 0.2146r 4 2 3 cm4 4 4 Iz I 0.03r tw 20.4468r 1.318 10 0.03r 0.2146r h 2 tf 0.4468r 2.313 10 cm y 12 12
Minimum inertia moment z-z
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Torsional moment 4
2 tw 2 2 3 r r t r f 2 b 0.63 tf tf h 2 tf 3 tw r 2 4 It tw 2 0.145 0.1 51.075cm 3 3 tf tf 2 r tf
tf b
3
h tf 24
2 4.9 105cm6
Sectorial moment
Iw
Elastic strength modulus y-y
2Iy 3 3 Wely 1.156 10 cm h
Elastic strengt modulus z-z
2Iz 3 Welz 146.425cm b
Plastic strength modulus y-y Wply
tw h 4
2
b tw h tf tf 2
Plastic strength modulus z-z
Wplz
Giration radius y-y
iy
Giration radius z-z
iz
5. Material properties fyk 355MPa
Elastic modulus
Poisson coefficient
4
b tf 2
2
h 2 tf
4
2
r h 2 tf
tw r 2
3
10
3
( 3 10) r
3
3
2
3
3
1.307 10 cm
2 3 tw r 229 cm 2
Iy
m 15.208 mm A 0.5 A Iz A
m
3.63
A
0.5
mm
fyk fy 308.696MPa M0 N E 210000 2 mm
0.3
G E [2 (1 )]
Shear modulus 4
G 8.077 10
N 2
mm
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6. Section classification EN 1993-1-1, tab. 5.2 Compression on the top flange acc. to EN 1993-1-1 Tabel 5.2 cf
b tw 2 r 2
cf
64.7mm
tf
4.793
2
235N mm
0.873
fy
flangeclass
1 if
cf tf
9
2 if 9
cf
4 if 14 "not good"
10
tf
3 if 10
cf tf
flangeclass 1
14
cf tf otherwise
Web sujected to bending acc. to EN 1993-1-1 Tabel 5.2 cw
cw h tf 2r 344.5mm webclass
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Laurentiu Gavrila
1 if
cw tw
tw
40.058
72
2 if 72
3 if 83
cw tw cw
4 if 124
tw
83
webclass 1 124
cw tw
"not good " otherwise
sectionclass max(flangeclass webclass ) 1
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34
7. Bending verification acc. to EN 1993-1-1 (6.13) MplRd
M elR d
MeffRd
W ply fy
350.879kN m
M0 W ely fy M0
310.418kN m
McRd
MplRd if sectionclass 2 MelRd if 2 sectionclass 3
W effy fy
MeffRd if 3 sectionclass 4
M0
McRd MplRd 350.879kN m
u fM
Moment resistance check:
Moment_resistance
M yEd M cR d
0.832
"OK" if ufM 1
Moment_resistance "OK"
"Choose another section"
if ufM 1
EN 1993-1-1 § 6.3.2.1
8. Shear resistance acc. to EN 1993-1-1, 6.2.6 The plastic shear resistance not taking into account the torsion depends on the shear area which is calculated: :
2
Av Aa 2 b tf tf tw 2 r 42.695cm VplRd
Av fy M0 3
Shear_resistance
661.675kN
VEd ufV 0.289 VplRd
"OK" if ufV 1 "Choose another section"
if ufV 1
Shear_resistance "OK"
For the strenth of beams which do not have transversal stiffeners local shear buckling check is not necessary if the condition above is fullfilled:
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1 strength
"compulsory" if
hw tw
"not compulsory" if
72 hw tw
72
strength "not compulsory"
9. Lateral torsional buckling strenth Elastoc critical moment for lateral torsional buckling: 2
Mcr
C1 E Iz
kz L2
zj zs
zj 0
2
A
2
z y z d A
A
2 Iy
zi
for double simmetrical sections
2
Mcr
2 k 2 I z w kz L G It 2 C2 zg C3 Zj C2 zg C3 zj 2 kw Iz E Iz
C1 E Iz
kzL2
2 k 2 I z w kz L G It 2 C2 zg C3 Zj C2 zg kw Iz 2 E Iz
Th coeff. C1, C2, C3 depend of the loading scheme and of the suporting conditions at the ends of the bar. The values are determined below: Ifc Ift f Ifc Ift
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Ifc si Ift are the inertial moments of the compressed and the tensioned flenge calculated with respect to the minimum inertia axis z. Tables 4.1 and 4.2 can be used only if the condition below is fulfiled: 0.9 f 0.9
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zg za zs
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za si zs are the coordinates where the loading is applied with respect to C, the center of gravity of the section. Values are positive when the application point and C are both in the compressed area, and negative when they are in the tensioned area of the transversal cross section of the bar.
Factor zj from Mcr formula takes into account the unsimetry of the cross section with respect to the maximum inertia axis y:
zj zs 0.5
y2 z2 z dA Iy
kz 1 kw 1 h zg 200 mm 2
C1 1
distance form the loading plane to C Tabel 4.2
L 0.6m
C2 0
2
Mcr
C1 E Iz
kzL2
2 k 2 I z w kz L G It 2 3 C2 zg C2 zg 14.74 10 kN m 2 kw Iz E Iz
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Reducted slenderness for lateral tosional buckling: bLT
Wply fy Mcr
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0.165
EN 1993-1-1 § 6.3.2.2 (1)
For laminated profiles: LT0 0.4 "the lateral torsional buckling effects can not be neglected" "the lateral torsional buckling effects can be neglected"
if bLT LT0
otherwise
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Reduction Factor:
section 1
(1 for laminated, 0 for welded) c_flamb
"b" if section
1
h
"c" if section
1
h
"c" if section
0
h
"d" if section
0
h
b b b b
2 2 2 2
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LT
0.21 if c_flamb
"a"
0.34 if c_flamb
"b"
0.49 if c_flamb
"c"
0.76 if c_flamb
"d"
EN 1993-1-1 Tabel 6.5, Tabel 6.3
LT 0.49
Recommended values for λLT0, β acc. to EN 1993-1-1 § 6.3.2.3(1) LT0 0.4
0.75 LT 0.5 1 LT bLT LT0 bLT 0.453
LT min
LT
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1 1 1 2 2 2 LT bLT bLT 1
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kc 1
f' 1 0.5 1 kc 1 2 bLT 0.8
2 1
f min(f' 1) 1
LT.mod
LT f
1
10. Design buckling resistance moment : Mb.Rd LT.mod
W ply fy M1
350.879kN m
11. Lateral torsional buckling verification: MyEd Mb.Rd
0.832
BeamLTB
"OK" if
MyEd Mb.Rd
1
"Girder not OK" otherwise
BeamLTB "OK"
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