Parametric studies on the cutouts in moderately loaded aircraft beams

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Parametric studies on the cutouts in moderately loaded aircraft beams

PRIYA P

Department of Civil Engineering, GSKSJTI

Bangalore, Karnataka State, India

priyagopi23@gmail.com

SUBRAMANYA K G

Department of Civil Engineering, GSKSJTI

Bangalore, Karnataka, India

mail2subbu.kg@gmail.com

SUBRAMANYA SASTRY S S

AGM (Tech), Engineering Vertical, Infotech Enterprises Limited

Hyderabad, Karnataka, India

Subramanya.Sastry@Infotech-

Enterprises.com

http://Infotech-Enterprises.com

Abstract:

Cutouts or openings provided in the parts of the aircraft are grouped into two distinct groups. The first group is called the lightening cutouts, provided to reduce the weight of the components without compromising on the functionality and structural integrity of the component. The second group is called the functional cutouts, provided to serve the intended purpose of carrying the Environmental Control Systems, electrical wires etc., . This class of cutouts not only maintains the functionality but also reinforce the affected area adequately for proper load transfer. In this paper, a systematic study of the various the factors affecting the margin of safety of a typical beam with cutouts are presented. It is to be noted that the beams are assumed to be sufficiently stiff and stable so that the strength, stiffness and stability are accounted in the design. This paper concentrates the studies on the moderately loaded beams. Two Aluminum alloys 7075-T6 and 2024-T4 are selected for the studies.

Keywords: Moderately loaded beams, Cutout, Margin of Safety, Lightening holes

  1. INTRODUCTION

    The aircraft structure needs to be designed accommodating many cutouts of variable sizes. These cutouts are required to provide access to control rods / cables, hydraulic lines, electrical lines etc.

    The beams are classified into three classes namely, lightly loaded, medium load and heavily loaded beams. The definitions are as follows.

    Lightly loaded beams

    These beams are able to carry loads in their virgin form like I, ELL, TEE beams with 450 flange or dough nut doubler stiffeners around the cutouts.

    These cutouts are small to medium in size and their stress concentration effect is localized. The stresses in the immediate vicinity of the cutouts will be appreciably changed. Stresses in the far off region (beyond 2.5D, D is the diameter of the cutout) are less affected. This class of cutouts is reinforced with a doughnut doubler, forming a lip around the cutout [1]. Lightly loaded beams are also called very shallow beams. They mainly carry loads by the tension field created by the applied load. They are classified into two types as shown in Fig. 1 and Fig. 2 [2, 3].

    Fig.1: Cutout in the lightly loaded beams Type 1

    Fig.2: Cutout in the lightly loaded beams Type 2

    Moderately Loaded beams

    This is the second class of beams where the beam carrying shear characterized by a flanged hole with web stiffeners between the flanged holes. In this

    paper a detailed study of moderately loaded beam is resented (Fig. 3). The other two classes of beams are described for the sake of completeness only.

    Fig.3: Cutout in moderately loaded beams

    Heavily Loaded beams

    The large holes in the beams are generally not recommended, but if unavoidable they must be carefully reinforced. To properly reinforce holes in heavily loaded beams, the beam has to be framed. The increase in weight due to framing can be as high as 50% as the same beam without holes. Framing means providing flanged holes reinforced by vertical and horizontal stiffeners (Fig. 4, [2]).

    Fig.4: Cutout in heavily loaded beams

    The description of the problem and various parameters used in the mathematical modeling of the medium loaded beams are presented in the next section.

  2. ANALYTICAL MODELING

    The beam considered for the study at present is described below.

    Type of the beam: Simply supported beam Length of the beam: 39.37 inch (1 m)

    Shear flow in the web: 570 lb/in (99843.88 N/m)

    Height of the web: 12 in (0.3048 m)

    A list of parameters used in this study is provided below.

    Fs Ultimate allowable gross shear stress fs – Shear stress

    F0 Ultimate allowable web stress of beam without holes

    K2 – Correction factor for aluminum alloy webs with stiffeners and flanged lightening holes

    q Shear flow

    t Thickness of web MS Margin of safety n_h No of holes

    n_s No of stiffeners L Length of beam

    bs Spacing between stiffeners h Depth of beam

    D Diameter of cutout

    V(single) Area of single stiffener V(Tstiff) Total stiffener volume V(spar) Volume of beam V(uncut) – Volume of uncut sheet V(remain) – Volume removed V(reduct)- Volume reduction

    A typical drawing of the cutouts under study is shown in Fig. 5.

    Fig.5: Pictorial view of a problem under study

  3. Loads and Boundary Conditions

    The beam under study is assumed to be a simply supported beam. This beam represents typical beams like

    • Flap beams

    • Control surface beams

    • Ribs and formers

    • Floor supports beams

    The loading on the beam is assumed in the form of a shear flow (numerical value is given under Section 2). This shear flow is a typical characteristic of a class of beams called shear beams. Shear beams are short beams which fail primarily by shear than bending.

  4. MATERIALS

    The beam under study is assumed to be made of two different materials.

    1. Aluminium alloy 7075T6

    2. Aluminium alloy 2024T4

  5. ANALYSIS

    The steps of the analysis are summarized below

    1. The shear flow (q) and height (h) of the web are noted.

    2. The design process starts by considering a value of (D/bs) from the working range.

    3. By using the relationship between D, bs, h obtain the value of spacing between the stiffeners (bs ) i.e.,

      bs = (0.1 * h)/(0.85 (d/bs)

    4. Consider a value for web thickness from the working range and calculate the (bs/t) value.

    5. By using the (bs/t) value, obtain the value for ultimate allowable web stress of a beam without holes (Fo) from the graph as shown in Fig. 6.

      Fig.6: Allowable web stress without holes

    6. Calculate the diameter of hole (D) value by using the (D/bs) and bs values which were obtained earlier.

    7. Calculate the (D/h) value for a given h value of 12in.

    8. By using the value of (bs/t) and (D/h), obtain the K2 value from the graph shown in Fig. 7.

      Fig.7: Modification factor K2

    9. Calculate the ultimate allowable gross shear stress value (Fs) by using the formula, Fs = K2 * Fo.

    10. Calculate the value of shear stress (fs) in the web by using the formula, fs = q/t.

    11. Calculate the margin of safety by using the relation M.S= (Fs/fs)-1.

    The analysis is carried out for the following limiting conditions.

    1. Ratio of height of web to the thickness of web 115< (h/t) <1500

    2. Ratio of spacing between the stiffeners to the height of web 0.235< (bs/h) <1

    3. Ratio between the diameter of hole to the height of web 0.1< (d/h) <0.75

    4. Diameter of hole 1.2< D <9 in

  6. RESULTS AND DISCUSSIONS

    The results are presented in the form of graphs and tables. Table 1 and 2 show the margin of safety obtained for the two Aluminium allys under study. Figures 8 shows the variation of margin of safety with the variation of ratio (bs/t). Figures 9 shows the effect of correction factor K2, on the ultimate allowable gross shear stress Fo.

    Figures 10 shows the variation of margin of safety with the ultimate allowable gross shear stress Fo.

    q(lb/in) L(in) h/t D bs/t K2 F0 Fs=K2*F0 fs=q/t MS V(reduct)

    570 39.3701 210 4.2 49.387 0.58 21600 12528 9982.49 25.50% 29%

    570 39.3701 210 4.2 91.419 0.86 13100 11266 9982.49 12.86% 15%

    570 39.3701 210 4.2 133.450 1.14 9500 10830 9982.49 8.49% 11%

    570 39.3701 210 4.2 175.482 1.41 7400 10434 9982.49 4.52% 8%

    570 39.3701 210 4.2 210.158 1.59 6400 10176 9982.49 1.94% 7%

    Table 1: Table showing the various parameters with margin of safety (2024-T4)

    Table 2: Table showing the various parameters with margin of safety (7075-T6)

    60%

    50%

    M.S %

    40%

    30%

    20%

    10%

    0%

    For H/T =210 and D=4.2in

    M.S % v/s Bs/T

    0 50 100 150 200 250

    2024 T4

    7075 T6

    because corrected ultimate allowable stress decreases.

    q(lb/in) L(in) h/t D bs /t K2 F0 Fs=K2*F0 fs =q/t MS V(reduct)

    570 39.3701 210 4.2 49.4 0.58 25500 14790 9982.49 48.16% 29%

    570 39.3701 210 4.2 91.4 0.86 15600 13416 9982.49 34.40% 15%

    570 39.3701 210 4.2 133.5 1.14 11000 12540 9982.49 25.62% 11%

    570 39.3701 210 4.2 175.5 1.41 8600 12126 9982.49 21.47% 8%

    570 39.3701 210 4.2 210.2 1.59 7400 11766 9982.49 17.87% 7%

    1. As the (bs/t) decreases, the stiffness of the beam increases because the number of stiffeners increases. This will also increase the weight of the beam.

    2. It is observed that in general for short shear web applications, such as that under study, 7075-T6 gives higher margin safety as compared to 2024-T4.

  7. Conclusions

    1. In moderately loaded (short shear) beams

      Ratio of spacing between the stiffeners to the thickness of web bs / t

      Fig. 8: Graph showing the comparison of margin of safety between 2024-T4 and 7075-T6

      For H/T =210 and ALUMINIUM 2024 T4

      Fo (psi) v/s K2

      30000

      25000

      for aircraft applications, it is recommended to use 7075-T4 for moderately loaded beams.

    2. Proposed procedure in literature gives acceptable results which show significant reduction in weight of the structure. Hence this procedure is adopted in the design of short beams in aircraft parts.

Allowable web stress Fo (psi)

20000

15000

10000

5000

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Correction factor K2 for aluminium alloy webs with stiffeners and flanged lightening holes

2024 T4

7075 T6

ACKNOWLEDGMENT

We sincerely thank and acknowledge the support and encouragement provided by Mr. M. Lakshmana Rao, VP, Engineering Vertical, Infotech Enterprises Limited, Hyderabad and Dr.

Fig. 9: Graph showing the comparison of

correction factor K2 between 2024-T4 and 7075-T6

For H/T =210 and D=4.2in

M.S % v/s Fo(psi)

    1. Patil, Professor and Head, Department of Civil Engineering, GSKSJTI, Bangalore in bringing out this work in the form of a technical paper.

      60%

      50%

      M.S %

      40%

      30%

      20%

      10%

      0%

      0 5000 10000 15000 20000 25000 30000

      ultimate allowable web stress of a beam without holes (Fo)

      2024 T4

      7075 T6

      REFERENCES

      1. King K. M., Rings used for shear web hole reinforcement, Aero Digest, Aug 1955

      2. Niu, Airframe stress analysis and sizing, Second edition 1999.

        Fig. 10: Graph showing the comparison of ultimate

        allowable web stress without holes between 2024- T4 and 7075-T6

        The detailed study of results presented in Table 1 are presented below

        1. The study is presented for a constant diameter of the cutout of 4.2 in (106.68 mm).

        2. From Table 1 and 2, it is observed that as (bs/t) increases correction factor K2, increases. But, Fo(ultimate allowable web stress without hole) decreases.

        3. Product of K2 and F0 also reduces. This means that as the cutout size increases, the corrected ultimate allowable stress decreases.

        4. The induced stress in the web remains constant. Hence margin of safety decreases

      3. Paul Kuhn, The strength and stiffness of shear webs with round lightening holes having 450 flanges.

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