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TALAT Lectures 2711


                          Design of A Helicopter Deck

                                        11 pages, 7 figures

                                         Advanced Level


          Prepared by Federico M. Mazzolani, University of Naples Federico II, Napoli

                                 Update from the TAS Project :


                TAS                   Leonardo da Vinci program
                                      Training in Aluminium Alloy Structural Design




Remark
The design of the main structural parts of an aluminium alloy helicopter deck is shown in this
document. The design of a bolted connection on the supporting structure is also presented. The
calculations carried out hereafter are based on the European Standard prENV 1999 (version April
1997).




Date of Issue: 1999
 EAA - European Aluminium Association
2711 Design of A Helicopter deck


Contents

2711 Design of A Helicopter deck ..........................................................................2
  1. INTRODUCTION ...................................................................................................2
  2. MATERIALS...........................................................................................................3
  3. LOADS .....................................................................................................................3
     3.1. Permanent loads .................................................................................................3
     3.2. Live loads ...........................................................................................................3
     3.3 Load combination................................................................................................4
  4. ANALYSIS OF THE DECK EXTRUSION .........................................................4
  5. ANALYSIS OF THE SUPPORT STRUCTURE .................................................7
  6. GIRDER CONNECTION ......................................................................................9




1. INTRODUCTION

The structure under consideration consists of a helideck to be built on an off-shore platform (fig. 1).
Its main bearing structure is made of three I-girders with welded built-up cross section (figs 2 and
3). The top deck is made with an extruded profile whose design has been performed in such a way
to give place to a continuous deck without welding (fig. 4). The span of the main girders, assumed
simply supported, is 8000mm. The upper deck may be considered as an orthotropic plate (having
two 3000mm long spans) simply supported to the girders.




TALAT 2711                                                         2
2. MATERIALS

The structure is entirely made of aluminium alloy members. The alloys used are listed in tab. 1.

                    Denomination  f0.2 (N/mm2)                ft (N/mm2)           Min. elong. (%)
Extrusions of       EN AW-6082 T6         255                        300                   8
support structure
Web plate of        EN AW-5083 H24                 240                340                   4
support structure
Deck extrusion       EN AW-6005 T6                 215                255                   8

Tab. 1 – Mechanical properties of alloys employed in the structure.

The design values of the basic properties assumed for all alloys are shown in Tab. 2. The partial
safety factor for material is assumed equal to γM = 1.10 for members and γM = 1.25 for bolted
connections.

Modulus of elasticity                                             E = 70 000 (N/mm2)
Shear modulus                                                     G = 27 000 (N/mm2)
Poisson’s ratio                                                         ν = 0.3
Coefficient of linear thermal expansion                           α = 23 × 10-6 per °C
Density                                                             ρ = 2 700 kg/m3

Tab. 2 – Design values of material coefficients.



3. LOADS


3.1. Permanent loads

Nominal values of permanent loads consist of structure selfweight. They are summarised in tab. 3.

Support structure                                               34.88 kg/m (H = 450 mm)
Deck extrusion                                                         10.55 kg/m

Tab. 3 – Selfweight of structural members.



3.2. Live loads

The live load is represented by the helicopter landing load, referred to in tab. 4. Distinction is made
between values for ultimate limit state and serviceability limit state, Elastic analysis is performed
for checking both limit states.




TALAT 2711                                     3
Ultimate limit state                Serviceability limit state
 Deck extrusion Fdeck = 116kN, distr. on 300 × 300 mm Fdeck = 70kN, distr. on 300 × 300 mm2
                                                     2

Support structure           Fsupp = 151 kN                         Fsupp = 91 kN

Tab. 4 – Live loads on deck extrusion and support structure.


3.3 Load combination

Rules provided in EC 1 have been followed for evaluating the partial safety factors γG and γQ. The
resulting values are shown in tab. 5. The value of γQ has been increased from 1.5 to 1.65 in order to
take into account a possible overload in emergency conditions.

                                           Ultimate limit state                    Serviceability limit state
                                         γG                   γQ                    γG                    γQ
Support structure                       1.35                 1.65                  1.00                 1.00
 Deck extrusion                         1.00                 1.65                  1.00                 1.00

Tab. 5 – List of the partial safety factors for applied loads.



    C                     B                       A




                                            3          8000                                  450



                                            2




                                            1

               3000                     3000
                                           F = 116kN (U.L.S.)
                                           F = 70kN (S.L.S.)                    3000               3000

         Points of application of external load


   Fig. 1 – Structural scheme of the helideck.                      Fig. 2 – Detail of the girder-to-deck assembly.


4. ANALYSIS OF THE DECK EXTRUSION

The elastic analysis of the deck structure has been carried out by means of the F.E.M. code
ABAQUS. Specific allowance has been made for the effect of plate orthotropy due to the particular
arrangement of the extruded profiles. In order to investigate the structural behaviour for different
load conditions, the concentrated force shown in tab. 4 has been considered acting on the deck in

TALAT 2711                                                      4
three different points, as shown in fig. 1. Because of its very small value, the deck selfweight has
been neglected in this analysis.
For the above load conditions, the results in terms of transverse displacements and internal actions
are graphically shown in figs 1-6 of the Appendix for both serviceability and ultimate limit state.
The relevant numerical results are also provided in tabs 1-6 of the Appendix.
In order to check the ultimate limit state the cross section has to be classified. According to EC9
Part 1-1, Chapter 5.4.3, the slenderness parameter β must be evaluated. In the case of bending β =
0.40b/t for the extrusion webs, where the stress gradient results in a neutral axis at the section
center, and β = b/t for the compressed flange, b and t being the width and the thickness of the
section element, respectively.
                                200

                                                                                                                300
                                                                                    50              100                     100             50
    20


                      70                                                                                              t med =5mm
                                                                                                                                                 65.69

                                                                        125                                       G


                                                                                                                                                 59.31
                                                                               t med =3mm

                                                                                               55          45         45          55
                                                                       t med =6.5mm
                           12                                                                                   200
                                                                                         Original deck extrusion (schematic view)
      Fig. 3 – Detail of the girder extrusion
                                                                                                                300
                                                                               20              130                              130              20
                                                A
              q = 116kN/300x300 = 1.2889 N/mm
                                                                                                                                                 65.69
                                                                                                                       t med =5mm
                                                     t max = 6mm         125                                      G


                                                                                                                                                 59.31
                                                     101 N/mm                  t med =3mm

                                                                                          30              70               70          30
                                                                       t med =6.5mm
                                                18
                                                                                                                200

                                                A                                        Modified deck extrusion (schematic view)



 Fig. 5 – Calculation model for deck cantilever                        Fig. 4 – Deck extrusion (original and modified)
                    outstands.

For the assumed cross sections the values evaluated for β are summarised in tab. 6. Since the values
of the slenderness parameter β fall into the Class 1, 2 and 4 regions (see tab. 5.1 of EC9 Part 1-1,
ε = 250 / f 0.2 = 1.0783 ), a specific allowance for the effect of local buckling should be made. In
addition, the value of the shear forces evaluated by means of the F.E.M. analysis would be too
much high for the cantilever outstand of the original section (fig. 4). For this reason, it is convenient
to modify the original extruded profile according to fig. 4, where the relevant modifications of the
section are schematically indicated. Such modifications are intended in order to keep the same value
of the inertia moment of the original section (Ixc = 10 918 999 mm2). In this way, all the section
elements have a slenderness parameter β falling into Classes 1, 2 and 3, as shown in tab. 7. As a
consequence, the cross section is allowed for a value of the maximum bending moment
corresponding to the elastic limit moment Me = f0.2W/γM.


TALAT 2711                                                         5
Webs                  Upper flange          Lower flange internal    Lower flange outstand
  14.82 < β2 = 17.25         16 < β2 = 17.25         5.38 < β1 = 11.86         7.69 > β3 = 6.47
       Class 2                   Class 2                  Class 1                   Class 4

Tab. 6. – Values of the slenderness parameter β for the original deck extrusion.

        Webs                  Upper flange          Lower flange internal    Lower flange outstand
  14.82 < β2 = 17.25         22 < β3 = 23.72         9.23 < β1 = 11.86         3.85 < β2 = 4.85
       Class 2                   Class 3                  Class 1                   Class 2

Tab. 7. – Values of the slenderness parameter β for the modified deck extrusion.

Referring to fig. 4, for a value of the inertia moment Ixc = 10 918 999 mm4, one can obtain the value
of Wmin= Ixc / Cy = 10918999 mm4/ 65.69 = 166220 mm3. Hence:

       Me = f0.2W/γM = 215×166 220/1.10 = 32 488 Nm

This value is higher than the maximum bending moment evaluated in the numerical analysis for
ultimate limit state (M = 22 548 Nm, load condition 1, F = 116 kN, see tab. 1 in the Appendix).
The effect to shear forces can be evaluated approximately by means of the scheme shown in fig. 5,
where the calculation model assumed for the evaluation of the bending moment in the section A-A
is represented. This model is intended in order to provide an estimation of the maximum bending
action induced on the deck extrusion by a concentrated load applied on an area of 300 × 300 mm2.
Under the assumption of fig. 5, the design bending moment per unit length in the section A – A is
given by:

       Md = T × l − q × d2 /2 = 101 × 18 − 1.2889 × 182 /2 = 1818 – 219 = 1 609 Nmm/mm

Where (see fig. 5):

       T = 101 N/mm, is the maximum value of the design shear force
           (load condition 1, F = 116 kN, see tab. 1 in the Appendix);
       d = 18 mm, is the distance of the section A – A from the point of application of shear force;
       q = 1.2889 N/mm2, is the value of the distributed load on a deck area of 300 × 300 mm2.

The ultimate bending moment per unit length is equal to:

       Mu = α0 × W × f0.2 /γM = 1.5 × 6 × 215 / 1.1 = 1 759 Nmm/mm

Where a geometrical shape factor α0 = 1.5 (rectangular section) has been considered. A section
depth t = 6mm has been assumed and the resistance modulus W has been evaluated accordingly.
From the above equations it results Md < Mu.
The analysis under serviceability conditions (Pdeck = 70kN) has provided values of the maximum
deflection umax for the deck ranging from 8.41 to 15.39, corresponding to L/357 and L/195,
respectively (see Figs 4-6 and Tabs 4-6 in the Appendix). These deflection values have been
calculated from the numerical results by subtracting to the displacements of the deck the
displacements of the girder on the corresponding alignment.




TALAT 2711                                     6
5. ANALYSIS OF THE SUPPORT STRUCTURE

The support structure consists of a welded built-up girder with I-section. The dimensions of the
extruded flanges, as well as the web thickness are given in fig. 3; the web depth has to be
determined according to the design limit state requirements. The solutions considered, different
from each other for the girder depth value, are shown in tab. 8, where the relevant geometrical and
mechanical properties are also shown for each solution. Even though built-up with two different
alloys, for the sake of simplicity the girder plastic modulus Z has been evaluated by assuming the
cross section as made of one alloy only, that of the flanges. This has been possible since both alloys
have a similar value of the proof stress f0.2 (255 and 240 N/mm2) and, in addition, the contribution
of the web to the ultimate resistance is very small.

Girder depth (mm)              I (mm4)                W (mm3)              Z (mm3)                α0
       400                   335 722 667              1 678 613           1 908 800             1.1371
       450                   438 987 667              1 951 056           2 224 300             1.1400
       500                   558 402 667              2 233 610           2 554 800             1.1438

Tab. 8 – Main geometrical properties of the examined solutions.

The most unconservative load condition is obtained when the helicopter landing load is applied in a
concentrated way at the beam midspan. The design value of the bending moment at beam midspan
is given by:

               γ G qL2       γ Q FL       1.35 × (34.88 + 10.55) × 9.81 × 8 2 1.65 × 91000 × 8
        Md =             +            =                                      +                 = 306811Nm
                  8            4                          8                           4

where γG = 1.35 and γQ = 1.65 are the partial safety factor for dead load and for live load,
respectively. The selfweight of the intermediate solution (H = 450mm, P = 342 N/m, see tab. 8) has
been considered, the differences with respect the other depth values being negligible. The deck
selfweight (10.55 N/m) has been also considered.
For the assumed cross sections the values evaluated for β are summarised in tab. 9. In all cases the
slenderness parameter β falls into the Class 1 or 2 region (see tab. 5.1 of EC9 Part 1-1,
ε = 250 / f 0.2 ≅ 1 ). As a consequence the cross section is allowed to withstand an ultimate bending
moment equal to the plastic moment Mp = f0.2Z/γM = α0 f0.2 W/ γM . The geometrical shape factor α0
may be evaluated through the relationship:
      α0 = Z/W

Z being the plastic resistance modulus of the cross section (see tab. 8).

       Girder depth (mm)                                Web                              Flanges
              400                              8.67 < β1 = 11 (Class 1)             4.5 = β2 (Class 2)
              450                             10.33 < β1 = 11 (Class 1)             4.5 = β2 (Class 2)
              500                             12.00 < β2 = 16 (Class 2)             4.5 = β2 (Class 2)

Tab. 9 – Values of the slenderness parameter β for the support structure.

Under the above assumption, the ultimate bending moment Mu is equal to:

Mu = Mp = f0.2Z/γm = α0 f0.2 W/ γm

TALAT 2711                                             7
in which the f0.2 value of the flanges has been considered f0.2 = 255 N/mm2. The values of the
ultimate bending moment Mu for the selected solutions are given in tab. 10, together with the ratio
Mu/Md, meaning the extra value of the safety coefficient at failure.

      Girder depth (mm)                       Mu (Nm)                            Mu/Md
             400                              439 578                            1.4327
             450                              512 226                            1.6695
             500                              588 362                            1.9177

Tab. 10 – Values of Mu and Mu/Md for the support structure.

Since Mu/Md > 1 for all solutions, all the analysed schemes are safe with regard to the structural
plastic collapse. The choice of the design solution is made on the basis of the serviceability
requirements. For this purpose, the serviceability limit states for the support structure are
investigated, namely the maximum deflection and the maximum stress values under the service
loads. A design value of the concentrated load equal to 91 kN is assumed. The maximum midspan
deflection is given by:

                  5 γ G ql 4 1 γ Q Fl
                                      3

       v max   =            +
                 384 EI       48 EI

where the partial safety value γG and γQ have been put equal to unity (see tab. 5). The values of vmax
are provided in tab. 11, together with the values of σmax and τmax evaluated via the expressions:

                 M
       σ max =     ;
                 W

                   T
       τ max =            ;
                 bw × t w

The design values M and T of the maximum bending moment and shear are evaluated as follows:

           qL2 FL
       M =    +   = 184737382 Nmm
            8   4

               qL F
       T=         + = 46869 N
                2  2

Girder depth (mm)             vmax (mm)         vmax/l          σmax (N/mm2)         τmax (N/mm2)
       400                     42.0805         1/190.1             110.05                10.85
       450                     32.1817         1/248.6              94.69                 9.53
       500                     25.2996         1/316.2              82.71                 8.49

Tab. 11 – Values of the relevant displacement and stresses for the support structure at serviceability
          limit state.




TALAT 2711                                     8
6. GIRDER CONNECTION

A connection between two semi-girders is designed, consisting of a lap joint with gusset plates, as
shown in fig. 5. Since it is placed at the girder midspan, the connection is conceived in order to
withstand the maximum design bending moment (Md = 305 695 Nm) with zero shear.
With reference to fig. 6, the moment of inertia of the gusset plates evaluated by accounting for holes
(∅21) is given by:

       I = 2×(200–42)×14×(225+7)2 + 4×(85–21)×14×(225-27)2 + 2×8×2803/12 - 4×21×8×1002 =

                      = 401 173 845 mm4

The maximum tensile stress at the outside gusset plate is equal to:

       σmax = M/I × H/2 = 305 695 000/401 173 845 × 478/2 = 182.12 N/mm2

By assuming for the gusset plate the same alloy as for the flange extrusion (f0.2 = 255 N/mm2, fu =
300 N/mm2), it results:

       σmax = 182.12 N/mm2 < f0.2/γM = 255/1.25 = 204 N/mm2

Similarly, the moment of inertia of the girder net section is given by:

       Inet = 438 987 667 - 4× 21 × 14 × 2152 – 2 × 21 × 12 × 1002 = 379 587 067 mm4

Hence, the resistance modulus:

       Wnet = Inet / (H/2) = 379 587 067 / 225 = 1 687 054 mm3

The ultimate bending moment is equal to:

       Mu = Mp = α0 f0.2 W/ γm = 1.14 × 255 × 1 687 054 / 1.25 = 392 341 Nm > Md = 306 811 Nm

The maximum tensile action transmitted by the extrusion flange may be conservatively calculated
by assuming that the bending moment acting on the joint is carried entirely by the flanges. Under
this assumption it follows that:

       Ttot = M/d’ = 305 695 000/430 = 710 919 N

d’ = 430mm being the distance between the flange centroids (fig. 6). By adopting M20 bolts, the
maximum shear stress in the flange bolts is evaluated as follows:

       τmax = Ttot / (2×n×Ab) = 710 919/(2×6×245) = 241.8 N/mm2

n and Ab being the number of bolts and the bolt net cross sectional area, respectively. By
considering a material partial factor γM = 1.25, the minimum shear ultimate resistance of the bolts
must be:

       τu = τmax × 1.25 = 241.8 × 1.25 = 302.2 N/mm2


TALAT 2711                                      9
A suitable bolt type is represented by Class 8.8 zinc coated steel bolts, having fd,v = 385 N/mm2.
The bearing resistance of the flange is evaluated through the formula:

       σb,Rd = 2.5 α fu / γM = 2.5 × .794 × 300 / 1.25 = 476.2 N

The factor α = .794 has been calculated according to Chapter 6, Table 6.4 of EC 9.
The maximum stress in the flange is equal to:

       σmax = Ttot / (n × d × t ) = 710 919/(6×20×14) = 423.2 N/mm2 < σb,Rd = 476.2 N/mm2.

n, d and t being the number of bolts, the bolt diameter and the flange thickness, respectively.
The check of the gusset plates bearing resistance may be neglected because their total thickness
(28mm) is greater than the flange thickness (20mm).
As far as the web gusset plates are concerned, the stress in the bolts is evaluated assuming that each
bolt is subjected to a force proportional to the distance from the central bolt (see detail of fig. 6).
The share of bending moment carried by the web gusset plates is evaluated as follows:

       Mweb = Md (Iweb/I) = 305 695 000 × 22 549 333 / 401 173 845 = 17 183 Nm

Under these assumptions, the shear force in the most stressed bolt is equal to:

                            M
        Fmax = F1 =                      = 20270 N
                      4d 1 + 4 d 2 / d 1
                                 2




from which the shear stress in the bolt is obtained:

       τmax = Fmax / (2×Ab) = 20270/(2×245) = 41.4 N/mm2 < fd,v = 385 N/mm2




TALAT 2711                                           10
50
                               20                                                                                       40
                               12
                                                                    100
                         450              310        430                                                                280
                                                                    100

                                                                                                                        40
                                8



                                    200
            bolts M20
            holes 21                                               40

                                                       14                         100    100       100   100   100      200
                                                                    120

                                                               40
                        F1
                               F2

                             d2                                         40
                        d1                                                                                              85
                                                              45
                                                                                                   600

             M web                        M web



                                                                                  4000                               4000


                                          Fig. 6 – Detail of the girder connection



                                    120




                                                                                  100        200               100
                                                220x180
                                                    14

                                                  bolts M14
                                                  holes 15




                                                  bolts M20
                                                  holes 21                              14




                                    120                                           120




                                    200                                           300



                                      Fig. 7 – Detail of girder-to-deck connection

The representation of the deck-to-girder connection is shown in fig. 7, together with a possible
arrangement of the connection to the supporting structure. This connection is made by bolting the
girder bottom flange directly to a flush end plate welded to the support point. Because of the very
little resisting moment developed by this joint, it can be considered as nominally pinned. A 14mm
thick rectangular plate is placed between the top flange of the girder and each deck element in order
to compensate the overthickness introduced by the gusset plate of the midspan joint.



TALAT 2711                                                         11

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TALAT Lecture 2711: Design of a Helicopter Deck

  • 1. TALAT Lectures 2711 Design of A Helicopter Deck 11 pages, 7 figures Advanced Level Prepared by Federico M. Mazzolani, University of Naples Federico II, Napoli Update from the TAS Project : TAS Leonardo da Vinci program Training in Aluminium Alloy Structural Design Remark The design of the main structural parts of an aluminium alloy helicopter deck is shown in this document. The design of a bolted connection on the supporting structure is also presented. The calculations carried out hereafter are based on the European Standard prENV 1999 (version April 1997). Date of Issue: 1999  EAA - European Aluminium Association
  • 2. 2711 Design of A Helicopter deck Contents 2711 Design of A Helicopter deck ..........................................................................2 1. INTRODUCTION ...................................................................................................2 2. MATERIALS...........................................................................................................3 3. LOADS .....................................................................................................................3 3.1. Permanent loads .................................................................................................3 3.2. Live loads ...........................................................................................................3 3.3 Load combination................................................................................................4 4. ANALYSIS OF THE DECK EXTRUSION .........................................................4 5. ANALYSIS OF THE SUPPORT STRUCTURE .................................................7 6. GIRDER CONNECTION ......................................................................................9 1. INTRODUCTION The structure under consideration consists of a helideck to be built on an off-shore platform (fig. 1). Its main bearing structure is made of three I-girders with welded built-up cross section (figs 2 and 3). The top deck is made with an extruded profile whose design has been performed in such a way to give place to a continuous deck without welding (fig. 4). The span of the main girders, assumed simply supported, is 8000mm. The upper deck may be considered as an orthotropic plate (having two 3000mm long spans) simply supported to the girders. TALAT 2711 2
  • 3. 2. MATERIALS The structure is entirely made of aluminium alloy members. The alloys used are listed in tab. 1. Denomination f0.2 (N/mm2) ft (N/mm2) Min. elong. (%) Extrusions of EN AW-6082 T6 255 300 8 support structure Web plate of EN AW-5083 H24 240 340 4 support structure Deck extrusion EN AW-6005 T6 215 255 8 Tab. 1 – Mechanical properties of alloys employed in the structure. The design values of the basic properties assumed for all alloys are shown in Tab. 2. The partial safety factor for material is assumed equal to γM = 1.10 for members and γM = 1.25 for bolted connections. Modulus of elasticity E = 70 000 (N/mm2) Shear modulus G = 27 000 (N/mm2) Poisson’s ratio ν = 0.3 Coefficient of linear thermal expansion α = 23 × 10-6 per °C Density ρ = 2 700 kg/m3 Tab. 2 – Design values of material coefficients. 3. LOADS 3.1. Permanent loads Nominal values of permanent loads consist of structure selfweight. They are summarised in tab. 3. Support structure 34.88 kg/m (H = 450 mm) Deck extrusion 10.55 kg/m Tab. 3 – Selfweight of structural members. 3.2. Live loads The live load is represented by the helicopter landing load, referred to in tab. 4. Distinction is made between values for ultimate limit state and serviceability limit state, Elastic analysis is performed for checking both limit states. TALAT 2711 3
  • 4. Ultimate limit state Serviceability limit state Deck extrusion Fdeck = 116kN, distr. on 300 × 300 mm Fdeck = 70kN, distr. on 300 × 300 mm2 2 Support structure Fsupp = 151 kN Fsupp = 91 kN Tab. 4 – Live loads on deck extrusion and support structure. 3.3 Load combination Rules provided in EC 1 have been followed for evaluating the partial safety factors γG and γQ. The resulting values are shown in tab. 5. The value of γQ has been increased from 1.5 to 1.65 in order to take into account a possible overload in emergency conditions. Ultimate limit state Serviceability limit state γG γQ γG γQ Support structure 1.35 1.65 1.00 1.00 Deck extrusion 1.00 1.65 1.00 1.00 Tab. 5 – List of the partial safety factors for applied loads. C B A 3 8000 450 2 1 3000 3000 F = 116kN (U.L.S.) F = 70kN (S.L.S.) 3000 3000 Points of application of external load Fig. 1 – Structural scheme of the helideck. Fig. 2 – Detail of the girder-to-deck assembly. 4. ANALYSIS OF THE DECK EXTRUSION The elastic analysis of the deck structure has been carried out by means of the F.E.M. code ABAQUS. Specific allowance has been made for the effect of plate orthotropy due to the particular arrangement of the extruded profiles. In order to investigate the structural behaviour for different load conditions, the concentrated force shown in tab. 4 has been considered acting on the deck in TALAT 2711 4
  • 5. three different points, as shown in fig. 1. Because of its very small value, the deck selfweight has been neglected in this analysis. For the above load conditions, the results in terms of transverse displacements and internal actions are graphically shown in figs 1-6 of the Appendix for both serviceability and ultimate limit state. The relevant numerical results are also provided in tabs 1-6 of the Appendix. In order to check the ultimate limit state the cross section has to be classified. According to EC9 Part 1-1, Chapter 5.4.3, the slenderness parameter β must be evaluated. In the case of bending β = 0.40b/t for the extrusion webs, where the stress gradient results in a neutral axis at the section center, and β = b/t for the compressed flange, b and t being the width and the thickness of the section element, respectively. 200 300 50 100 100 50 20 70 t med =5mm 65.69 125 G 59.31 t med =3mm 55 45 45 55 t med =6.5mm 12 200 Original deck extrusion (schematic view) Fig. 3 – Detail of the girder extrusion 300 20 130 130 20 A q = 116kN/300x300 = 1.2889 N/mm 65.69 t med =5mm t max = 6mm 125 G 59.31 101 N/mm t med =3mm 30 70 70 30 t med =6.5mm 18 200 A Modified deck extrusion (schematic view) Fig. 5 – Calculation model for deck cantilever Fig. 4 – Deck extrusion (original and modified) outstands. For the assumed cross sections the values evaluated for β are summarised in tab. 6. Since the values of the slenderness parameter β fall into the Class 1, 2 and 4 regions (see tab. 5.1 of EC9 Part 1-1, ε = 250 / f 0.2 = 1.0783 ), a specific allowance for the effect of local buckling should be made. In addition, the value of the shear forces evaluated by means of the F.E.M. analysis would be too much high for the cantilever outstand of the original section (fig. 4). For this reason, it is convenient to modify the original extruded profile according to fig. 4, where the relevant modifications of the section are schematically indicated. Such modifications are intended in order to keep the same value of the inertia moment of the original section (Ixc = 10 918 999 mm2). In this way, all the section elements have a slenderness parameter β falling into Classes 1, 2 and 3, as shown in tab. 7. As a consequence, the cross section is allowed for a value of the maximum bending moment corresponding to the elastic limit moment Me = f0.2W/γM. TALAT 2711 5
  • 6. Webs Upper flange Lower flange internal Lower flange outstand 14.82 < β2 = 17.25 16 < β2 = 17.25 5.38 < β1 = 11.86 7.69 > β3 = 6.47 Class 2 Class 2 Class 1 Class 4 Tab. 6. – Values of the slenderness parameter β for the original deck extrusion. Webs Upper flange Lower flange internal Lower flange outstand 14.82 < β2 = 17.25 22 < β3 = 23.72 9.23 < β1 = 11.86 3.85 < β2 = 4.85 Class 2 Class 3 Class 1 Class 2 Tab. 7. – Values of the slenderness parameter β for the modified deck extrusion. Referring to fig. 4, for a value of the inertia moment Ixc = 10 918 999 mm4, one can obtain the value of Wmin= Ixc / Cy = 10918999 mm4/ 65.69 = 166220 mm3. Hence: Me = f0.2W/γM = 215×166 220/1.10 = 32 488 Nm This value is higher than the maximum bending moment evaluated in the numerical analysis for ultimate limit state (M = 22 548 Nm, load condition 1, F = 116 kN, see tab. 1 in the Appendix). The effect to shear forces can be evaluated approximately by means of the scheme shown in fig. 5, where the calculation model assumed for the evaluation of the bending moment in the section A-A is represented. This model is intended in order to provide an estimation of the maximum bending action induced on the deck extrusion by a concentrated load applied on an area of 300 × 300 mm2. Under the assumption of fig. 5, the design bending moment per unit length in the section A – A is given by: Md = T × l − q × d2 /2 = 101 × 18 − 1.2889 × 182 /2 = 1818 – 219 = 1 609 Nmm/mm Where (see fig. 5): T = 101 N/mm, is the maximum value of the design shear force (load condition 1, F = 116 kN, see tab. 1 in the Appendix); d = 18 mm, is the distance of the section A – A from the point of application of shear force; q = 1.2889 N/mm2, is the value of the distributed load on a deck area of 300 × 300 mm2. The ultimate bending moment per unit length is equal to: Mu = α0 × W × f0.2 /γM = 1.5 × 6 × 215 / 1.1 = 1 759 Nmm/mm Where a geometrical shape factor α0 = 1.5 (rectangular section) has been considered. A section depth t = 6mm has been assumed and the resistance modulus W has been evaluated accordingly. From the above equations it results Md < Mu. The analysis under serviceability conditions (Pdeck = 70kN) has provided values of the maximum deflection umax for the deck ranging from 8.41 to 15.39, corresponding to L/357 and L/195, respectively (see Figs 4-6 and Tabs 4-6 in the Appendix). These deflection values have been calculated from the numerical results by subtracting to the displacements of the deck the displacements of the girder on the corresponding alignment. TALAT 2711 6
  • 7. 5. ANALYSIS OF THE SUPPORT STRUCTURE The support structure consists of a welded built-up girder with I-section. The dimensions of the extruded flanges, as well as the web thickness are given in fig. 3; the web depth has to be determined according to the design limit state requirements. The solutions considered, different from each other for the girder depth value, are shown in tab. 8, where the relevant geometrical and mechanical properties are also shown for each solution. Even though built-up with two different alloys, for the sake of simplicity the girder plastic modulus Z has been evaluated by assuming the cross section as made of one alloy only, that of the flanges. This has been possible since both alloys have a similar value of the proof stress f0.2 (255 and 240 N/mm2) and, in addition, the contribution of the web to the ultimate resistance is very small. Girder depth (mm) I (mm4) W (mm3) Z (mm3) α0 400 335 722 667 1 678 613 1 908 800 1.1371 450 438 987 667 1 951 056 2 224 300 1.1400 500 558 402 667 2 233 610 2 554 800 1.1438 Tab. 8 – Main geometrical properties of the examined solutions. The most unconservative load condition is obtained when the helicopter landing load is applied in a concentrated way at the beam midspan. The design value of the bending moment at beam midspan is given by: γ G qL2 γ Q FL 1.35 × (34.88 + 10.55) × 9.81 × 8 2 1.65 × 91000 × 8 Md = + = + = 306811Nm 8 4 8 4 where γG = 1.35 and γQ = 1.65 are the partial safety factor for dead load and for live load, respectively. The selfweight of the intermediate solution (H = 450mm, P = 342 N/m, see tab. 8) has been considered, the differences with respect the other depth values being negligible. The deck selfweight (10.55 N/m) has been also considered. For the assumed cross sections the values evaluated for β are summarised in tab. 9. In all cases the slenderness parameter β falls into the Class 1 or 2 region (see tab. 5.1 of EC9 Part 1-1, ε = 250 / f 0.2 ≅ 1 ). As a consequence the cross section is allowed to withstand an ultimate bending moment equal to the plastic moment Mp = f0.2Z/γM = α0 f0.2 W/ γM . The geometrical shape factor α0 may be evaluated through the relationship: α0 = Z/W Z being the plastic resistance modulus of the cross section (see tab. 8). Girder depth (mm) Web Flanges 400 8.67 < β1 = 11 (Class 1) 4.5 = β2 (Class 2) 450 10.33 < β1 = 11 (Class 1) 4.5 = β2 (Class 2) 500 12.00 < β2 = 16 (Class 2) 4.5 = β2 (Class 2) Tab. 9 – Values of the slenderness parameter β for the support structure. Under the above assumption, the ultimate bending moment Mu is equal to: Mu = Mp = f0.2Z/γm = α0 f0.2 W/ γm TALAT 2711 7
  • 8. in which the f0.2 value of the flanges has been considered f0.2 = 255 N/mm2. The values of the ultimate bending moment Mu for the selected solutions are given in tab. 10, together with the ratio Mu/Md, meaning the extra value of the safety coefficient at failure. Girder depth (mm) Mu (Nm) Mu/Md 400 439 578 1.4327 450 512 226 1.6695 500 588 362 1.9177 Tab. 10 – Values of Mu and Mu/Md for the support structure. Since Mu/Md > 1 for all solutions, all the analysed schemes are safe with regard to the structural plastic collapse. The choice of the design solution is made on the basis of the serviceability requirements. For this purpose, the serviceability limit states for the support structure are investigated, namely the maximum deflection and the maximum stress values under the service loads. A design value of the concentrated load equal to 91 kN is assumed. The maximum midspan deflection is given by: 5 γ G ql 4 1 γ Q Fl 3 v max = + 384 EI 48 EI where the partial safety value γG and γQ have been put equal to unity (see tab. 5). The values of vmax are provided in tab. 11, together with the values of σmax and τmax evaluated via the expressions: M σ max = ; W T τ max = ; bw × t w The design values M and T of the maximum bending moment and shear are evaluated as follows: qL2 FL M = + = 184737382 Nmm 8 4 qL F T= + = 46869 N 2 2 Girder depth (mm) vmax (mm) vmax/l σmax (N/mm2) τmax (N/mm2) 400 42.0805 1/190.1 110.05 10.85 450 32.1817 1/248.6 94.69 9.53 500 25.2996 1/316.2 82.71 8.49 Tab. 11 – Values of the relevant displacement and stresses for the support structure at serviceability limit state. TALAT 2711 8
  • 9. 6. GIRDER CONNECTION A connection between two semi-girders is designed, consisting of a lap joint with gusset plates, as shown in fig. 5. Since it is placed at the girder midspan, the connection is conceived in order to withstand the maximum design bending moment (Md = 305 695 Nm) with zero shear. With reference to fig. 6, the moment of inertia of the gusset plates evaluated by accounting for holes (∅21) is given by: I = 2×(200–42)×14×(225+7)2 + 4×(85–21)×14×(225-27)2 + 2×8×2803/12 - 4×21×8×1002 = = 401 173 845 mm4 The maximum tensile stress at the outside gusset plate is equal to: σmax = M/I × H/2 = 305 695 000/401 173 845 × 478/2 = 182.12 N/mm2 By assuming for the gusset plate the same alloy as for the flange extrusion (f0.2 = 255 N/mm2, fu = 300 N/mm2), it results: σmax = 182.12 N/mm2 < f0.2/γM = 255/1.25 = 204 N/mm2 Similarly, the moment of inertia of the girder net section is given by: Inet = 438 987 667 - 4× 21 × 14 × 2152 – 2 × 21 × 12 × 1002 = 379 587 067 mm4 Hence, the resistance modulus: Wnet = Inet / (H/2) = 379 587 067 / 225 = 1 687 054 mm3 The ultimate bending moment is equal to: Mu = Mp = α0 f0.2 W/ γm = 1.14 × 255 × 1 687 054 / 1.25 = 392 341 Nm > Md = 306 811 Nm The maximum tensile action transmitted by the extrusion flange may be conservatively calculated by assuming that the bending moment acting on the joint is carried entirely by the flanges. Under this assumption it follows that: Ttot = M/d’ = 305 695 000/430 = 710 919 N d’ = 430mm being the distance between the flange centroids (fig. 6). By adopting M20 bolts, the maximum shear stress in the flange bolts is evaluated as follows: τmax = Ttot / (2×n×Ab) = 710 919/(2×6×245) = 241.8 N/mm2 n and Ab being the number of bolts and the bolt net cross sectional area, respectively. By considering a material partial factor γM = 1.25, the minimum shear ultimate resistance of the bolts must be: τu = τmax × 1.25 = 241.8 × 1.25 = 302.2 N/mm2 TALAT 2711 9
  • 10. A suitable bolt type is represented by Class 8.8 zinc coated steel bolts, having fd,v = 385 N/mm2. The bearing resistance of the flange is evaluated through the formula: σb,Rd = 2.5 α fu / γM = 2.5 × .794 × 300 / 1.25 = 476.2 N The factor α = .794 has been calculated according to Chapter 6, Table 6.4 of EC 9. The maximum stress in the flange is equal to: σmax = Ttot / (n × d × t ) = 710 919/(6×20×14) = 423.2 N/mm2 < σb,Rd = 476.2 N/mm2. n, d and t being the number of bolts, the bolt diameter and the flange thickness, respectively. The check of the gusset plates bearing resistance may be neglected because their total thickness (28mm) is greater than the flange thickness (20mm). As far as the web gusset plates are concerned, the stress in the bolts is evaluated assuming that each bolt is subjected to a force proportional to the distance from the central bolt (see detail of fig. 6). The share of bending moment carried by the web gusset plates is evaluated as follows: Mweb = Md (Iweb/I) = 305 695 000 × 22 549 333 / 401 173 845 = 17 183 Nm Under these assumptions, the shear force in the most stressed bolt is equal to: M Fmax = F1 = = 20270 N 4d 1 + 4 d 2 / d 1 2 from which the shear stress in the bolt is obtained: τmax = Fmax / (2×Ab) = 20270/(2×245) = 41.4 N/mm2 < fd,v = 385 N/mm2 TALAT 2711 10
  • 11. 50 20 40 12 100 450 310 430 280 100 40 8 200 bolts M20 holes 21 40 14 100 100 100 100 100 200 120 40 F1 F2 d2 40 d1 85 45 600 M web M web 4000 4000 Fig. 6 – Detail of the girder connection 120 100 200 100 220x180 14 bolts M14 holes 15 bolts M20 holes 21 14 120 120 200 300 Fig. 7 – Detail of girder-to-deck connection The representation of the deck-to-girder connection is shown in fig. 7, together with a possible arrangement of the connection to the supporting structure. This connection is made by bolting the girder bottom flange directly to a flush end plate welded to the support point. Because of the very little resisting moment developed by this joint, it can be considered as nominally pinned. A 14mm thick rectangular plate is placed between the top flange of the girder and each deck element in order to compensate the overthickness introduced by the gusset plate of the midspan joint. TALAT 2711 11