design report -rov hangar deck-rev 1 - final

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Proj.code - supl.code - disc.code - SDDR code - Seq.nr

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Content 1 Introduction: ........................................................................................................................................2

1.1 Design resume...............................................................................................................................2 2 Document References, Rules and Standards ..................................................................................2 3 Conclusions ........................................................................................................................................3 4 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

5 Design limit states ..............................................................................................................................6 5.1 Design factors ................................................................................................................................6

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

7 Hand calculations acc. to EN 1993-1-1 .......................................................................................... 30

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1 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 Document References, Rules and Standards /1/ Document H600-AK-Z-FD-0001 H-6e Regulations /2/ Technical specification for purchase. ROV hangar modified to store /3/ NORSOK STANDARD N-001 Edition 7, June 2010 /4/ NORSOK STANDARD N-004 Rev.2, October 2004 /5/ NS-EN 1993-1-1/5:2005+NA:2008 /6/ NORSOK STANDARD M-120 Material Data Sheet for structural steel /7/ 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

3 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)

4 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/: Design Class: DC4 From table 5-2 ref. /4/, for DC4: Steel quality class: III (I) Minimum steel quality according to Norsok M-120: S355 Mpa From table 5-3 ref. /4/, for DC4 with moderate stresess: Inspection category for welds: C

4.1 Materials

Ref. /2/ The following linear structural steel materials were used [SI-units used]:

STEEL QUALITY

NORSOK GRADE

APPLICATION

(Min Yield Stress)

355 S355J2

Outfitting steel profiles, plates, etc., specified yield strength 355 MPa. (Standard EN10025)

355 S355J2H

RHS profiles, if delivered from stock,specified yield strength 355 MPa. (Standard EN10210)

Table4-1: Material types

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S355 J2 (acc. to NORSOK M-120, ref. /6/) Yield strength: fy = 355 N/mm2

Poisson number: ν = 0.3 Tensile strength: fu = 470N/mm2

Young’s modulus: E = 2.1 105 N/mm2

Shear modulus: G = E [2 (1 + v)]-1 = 8.077 104 N/mm2

Steel density: ρ = 7850 kg/m3

4.2 Stress

In general, according to NORSOK, the equivalent Von Mises design stress shall be less than:

sj < fd = fy / gm

where

fd = allowable design stress

fy = minimum yield stress

gm = material factor

The usage factor (U = sj / fd) for structural components is calculated in accordance with NS-

EN1993-1-1. 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

1

Cross –sections1-4, and

buckling

γM= 1.15

γM= 1.0

γM= 1.0

2 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

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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5 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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6 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 B1 C1 D1 E1 F1 A2 B2 C2 D2 E2 F2 A3 F3 A4 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 Loads / weights Unit ULS

factor Design load / weights for ULS foranalyses

Ref.

New deck

(EL.43.500)

Structural elements (self weight)

P 17000 Kg 1,3 22100

Overhanging

equipment P 3360 Kg 1,3 4368

Totalmass

deck ext. P 20360

Kg 1,3 26468

Office container

L 11600 kg 1,3 15080

Fork lift truck L 7030 Kg 1,3 9140

Deck live load L 5,0 kN/m2 1,3 7,5

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)


Local buckling analysis

Global buckling analysis

LC3

SLS Dead loads (OW)

Live loads (LL1)

Container load (CL)


Deflection check

LC4

SLS Dead loads (OW)

Live loads (LL1)

Container load (CL)


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) Container load (CL)

Fork lift load 1 (FLL1) 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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6.3.2 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 - 78.64 - 24.55 -

Table 4: Reaction Table

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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

[kNm]

Ved

[kN]

Ned

[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 29.10

Table 6-5: Design efforts for highest utilized structural members

6.5.1 Material

Table 6-6: Material S355J2 – all steel elements.

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6.5.2 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 : IPE 400

Element No. : 4

Length : 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 sX min | t | max si max

Stresses 261.35 MPa -248.40 MPa 66.69 MPa 261.35 MPa

Relative position 0.00 0.00 0.03 0.81

Absolute position 0.0 mm 0.0 mm 8200.0 mm 0.0 mm

Forces applied

Fx = 54.67 kN Mx = 0.00 kN*m

Fy = 2.75 kN My = -292.00 kN*m

Fz = 190.44 kN Mz = 0.35 kN*m

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Figure 12: 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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6.5.3 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


STRESS ANALYSIS IN THE UPN300 BAR – EXTERIOR GIRDER

Section : UPN 300

Element No. : 12

Length : 8350 mm

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CROSS SECTION


Load case : "LC1"


Internal forces taken into account : Fx Fy Fz Mx My Mz






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


U = sj / fd= 208,62Mpa / 308,0 Mpa = 0,68 < 1 OK !

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6.5.4 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 : UPLL 300x150x100

Element No. : 75

Length : 3110 mm

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CROSS SECTION


Load case : "LC1"


Internal forces takenintoaccount: Fx Fy Fz Mx My Mz







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


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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:


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 : UNP 180

Element No. : 76

Length : 3110 mm

CROSS SECTION

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Load case : "LC2"


Internal forces takenintoaccount: Fx Fy Fz Mx My Mz







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


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Figure 32: von Mises equivalent stresses XY plane 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 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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Iy

b h3

b tw h 2 tf 3

120.03r

4 0.2146r

2 h 2 tf 0.4468r 2 2.313 10

4 cm

4Iz

2 tf b3

h 2 tf tw3

120.03r

4 0.2146r

2 tw 0.4468r 2 1.318 10

3 cm

4

VEd 191.02kNMyEd 292kNm

1. Efforts:

2. Geometry:

3. Safety factors:

4. Geometric characteristics:

IPE 400

Height of web:

Section Area

Maximum inertia moment y-y

Minimum inertia moment z-z

L 8225mm

M0 1.15

M1 1.15

h 400mm

b 180mm

tf 13.5mm

r 21mm

tw 8.6mm

hw h 2 tf 2 r 331mm

Aa 2 tf b h 2 tf tw 4 ( ) r2

84.464cm2

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G E 2 1 ( )[ ]1

G 8.077 104

N

mm2

Torsional moment

Sectorial moment

Elastic strength modulus y-y

Elastic strengt modulus z-z

Plastic strength modulus y-y

Plastic strength modulus z-z

Giration radius y-y

Giration radius z-z

5. Material properties

Elastic modulus

Poisson coefficient

Shear modulus

It

2 b 0.63 tf tf3

3

h 2 tf 3

tw3

2tw

tf

0.145 0.1r

tf

rtw

2

2

r tf 2 r2

2 r tf

4

51.075cm4

Iw

tf b3

24h tf 2 4.9 10

5 cm

6

Wely

2Iy

h1.156 10

3 cm

3

Welz

2Iz

b146.425cm

3

Wply

tw h2

4b tw h tf tf

4

2r2

h 2 tf 3 10( ) r

3

3 1.307 10

3 cm

3

Wplz

b2

tf

2

h 2 tf

4tw

2 r

3 10

3

2

2

tw r2

229 cm3

iy

Iy

A15.208

m

A0.5

mm

iz

Iz

A3.63

m

A0.5

mm

fyk 355MPa fy

fyk

M0

308.696MPa

E 210000N

mm2

0.3

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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

Web sujected to bending acc. to EN 1993-1-1 Tabel 5.2

cf

b tw 2 r

264.7mm

cf

tf

4.793

235N mm

2

fy

0.873

flangeclass 1cf

tf

9 if

2 9 cf

tf

10 if

3 10 cf

tf

14 if

4 14 cf

tf

if

"not good" otherwise

flangeclass 1

cw h tf 2 r 344.5mmcw

tw

40.058

webclass 1cw

tw

72 if

2 72 cw

tw

83 if

3 83 cw

tw

124 if

4 124 cw

tw

if

"not good " otherwise

webclass 1

sectionclass maxflangeclass webclass( ) 1

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7. Bending verification acc. to EN 1993-1-1 (6.13)

Moment resistance check:

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: :

For the strenth of beams which do not have transversal stiffeners local shear buckling check is not necessary if the condition above is fullfilled:

MplRd

Wply fy

M0

350.879kN m

MelRd

Wely fy

M0

310.418kN m McRd MplRd sectionclass 2if

MelRd 2 sectionclass 3if

MeffRd 3 sectionclass 4if

MeffRdMeffRd

Weffy fy

M0

Weffy

McRd MplRd 350.879kNm

ufM

MyEd

McRd

0.832

Moment_resistance "OK" ufM 1if

"Choose another section" ufM 1if

Moment_resistance "OK"

Av Aa 2 b tf tf tw 2 r 42.695cm2

VplRd

Av fy

M0 3661.675kN ufV

VEd

VplRd

0.289

Shear_resistance "OK" ufV 1if

"Choose another section" ufV 1if

Shear_resistance "OK"

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f

Ifc Ift

Ifc Ift

Ifc

9. Lateral torsional buckling strenth

Elastoc critical moment for lateral torsional buckling:

for double simmetrical sections

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:

1

strength "compulsory"hw

tw

72

if

"not compulsory"hw

tw

72

if

strength "not compulsory"

Mcr

C1 2

E Iz

kz L 2kz

kw

2Iw

Iz

kz L 2 G It

2

E Iz

C2 zg C3 Zj 2 C2 zg C3 zj

C1

zj zsA

A

Az y2

z2

d

2 Iy zi zs

zj 0

Mcr

C1 2

E Iz

kz L 2kz

kw

2Iw

Iz

kz L 2 G It

2

E Iz

C2 zg C3 Zj 2 C2 zg

C1

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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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Mcr

C1 2

E Iz

kz L 2kz

kw

2Iw

Iz

kz L 2 G It

2

E Iz

C2 zg 2 C2 zg

14.74 103

kN m

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:

distance form the loading plane to C

Tabel 4.2

zg za zs za

zj zs 0.5 Ay2

z2

z

Iy

d

zs

kz 1

kw 1

zgh

2200 mm

C1 1 L 0.6m

C2 0

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Reducted slenderness for lateral tosional buckling:

EN 1993-1-1 § 6.3.2.2 (1)

For laminated profiles:

bLT

Wply fy

Mcr

0.165

LT0 0.4

"the lateral torsional buckling effects can not be neglected" bLT LT0if

"the lateral torsional buckling effects can be neglected" otherwise

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c_flamb "b" section 1h

b2if

"c" section 1h

b2if

"c" section 0h

b2if

"d" section 0h

b2if

Reduction Factor:

(1 for laminated, 0 for welded) section 1

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LT 0.21 c_flamb "a"if

0.34 c_flamb "b"if

0.49 c_flamb "c"if

0.76 c_flamb "d"if

LT0 0.4

0.75

LT 0.5 1 LT bLT LT0 bLT2

0.453

LT min1

LT LT2

bLT2

1

bLT2

1

1

EN 1993-1-1 Tabel 6.5, Tabel 6.3

Recommended values for λLT0, β acc. to EN 1993-1-1 § 6.3.2.3(1)

LT 0.49

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BeamLTB "OK"

BeamLTB "OK"MyEd

Mb.Rd

1if

"Girder not OK" otherwise

MyEd

Mb.Rd

0.832

f' 1 0.5 1 kc 1 2 bLT 0.8 2

1

f min f' 1( ) 1

LT.mod

LT

f1

Mb.Rd LT.mod

Wply fy

M1

350.879kN m

kc 1

10. Design buckling resistance moment :

11. Lateral torsional buckling verification:

design report -rov hangar deck-rev 1 - final

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