AE 462 , SPRING 2014

DESIGN OF AEROSPACE STRUCTURES

TERM PROJECT

MINIMUM WEIGHT FIGHTER WING DESIGN AND ANALYSIS

1-Project Description

In the project, the students are asked to design F-16 fighter wing structure. The internal spar and rib configuration of the aircraft is provided. Students are expected to size the structural members (wing skin, spar web, spar flanges, rib web/flanges) based on the 9g loading distribution. Therefore, as the first step you need to obtain the internal loads using the Schrenk distribution for the 9g limit load case. Factor of safety of 1.5 should be included in the material allowables not on the limit load.

Use integral method (not the strip method) to obtain your internal loads. This way you will have freedom to calculate the internal loads whereever you desire without using strips. Your units must be SI units.

The design will be judged based on the total structural weight, design with the least weight being considered the winner from a competitive standpoint. You should make sure that you do not have any calculation mistake in your analyses. Additional considerations affecting the project grade are:

Credibility of your design from a manufacturing standpoint The technical approach taken Structural solutions developed to meet the various design constraints How general your code is. A general code means that the user can enter the

number of spar and ribs and the required dimensions so that it can also be used for other wing configurations. Therefore, try to write a general code which does not just solve the wing configuration given in the assigned project.

The class will be divided into two or at most three-member design teams, with each member being responsible for different tasks. It is the responsibility of the team to divide the work load evenly. The team members are jointly responsible for the overall design. It is important that each member of your team participates fully for your design to be successful.

The final report is due to the June 13, Friday until 17.00. Project presentations will be on June 14 Saturday. The exact time will be announced later on. Final report should be submitted as a complete document with the team members identified on the cover page of the report. The report should be organized into sections according to the main analysis and design tasks performed as required by the project specifications. Reports should be typed, no handwritten reports will be accepted. Reports should be submitted in pdf format. No hardcopy is required !!.

2-Analysis Tools

Each team is responsible for performing load calculation and structural analysis to carry out the calculations in order to substantiate that the wing has the sufficient structural integrity with minimum weight. It is strongly recommended that the programs be written such that design iterations can be carried out without requiring laborious hand calculations.

3-Design Objective

The objective is to design a suitable primary structure of least possible weight for the uniform cantilever F-16 wing shown in Figure 1. Figure 1(a) shows the spar/rib layout and the torque box of the actual wing, and Fig. 1(b) shows the simplified spar/rib layout and the torque box of the F-16 wing. In the simplified wing structure, the root region which contains the tension fittings for the wing root joints is not included. Figure 2 shows the detailed internal structural lay-out of the F-16 wing which shows the tension fittings clearly.

Region which contains tension fittings for the wing root joints

(a) Actual wing structure (b) Simplified wing structure

Figure 1 Spar/rib structural lay-out of the F-16 wing

Section 4

Section 3

Section 2

Section 1

Torque box

Leading edge

Trailing edgeSpars

Figure 2 Detailed internal structural lay-out of the F-16 wing

4-Design Specifications and Materials

The proposed primary structure consists of multi-cell box beams, as shown in Figure 1(b). Due to the tapered nature of the wing, the number of cells in each section increase as you go from wing tip to wing root. In this project, spar and rib locations are fixed as shown in Figure 1(b). The goal is to size the four sections shown in Fig. 1(b).

The design variables are:

- Flange areas of the spars in each section (You can size them according to the spar heights so that they more or less have equal stresses. Note that the flange areas must be reasonable.)

- Upper and lower skin thicknesses in each section- Spar web thicknesses in each section- Rib web thicknesses, rib flange areas and vertical member at the intersection of the

spars and the ribs (see the note for rib sizing)

You can keep the flange areas and thicknesses constant in each section and increase them discretely from section 1 to section 4. Structural analysis of the wing can be carried out in discrete sections, as shown by the dash lines in Figure 3. At the inboard station of each rib section, you should make strength calculations. However, you should calculate shear flows at the inboard and outboard stations of each rib section.

In the sizing calculations, try to use minimum dimensions to get minimum margin of safety. For the minimum margin of safety, you can take 0.01. Since 1.5 factor of safety is already included in the material allowables, for minimum weight you have to aim for minimum margin of safety.

Tension fittings for root joint connection

For strength calculations, use a factor of safety of 1.5 on the ultimate strength values of the materials used in the wing. For skin buckling calculations do not use a factor of safety on the elastic modulus of the material.

Figure 3 Sections where structural analysis (shear flow and bending stress) must be performed

Materials:Materials used in the F-16 wing are given below.

Upper skin material: 2024 Al T851Lower skin material: 7475 Al T7651Spar materials: 2124 Al T851 and 7475 Al T7351Rib materials: 2124 Al T851 , 7475 Al T7351 and 7075 Forging T73

5-General Requirements

Structural idealization:

Assume that spar flanges and stiffeners take axial load only. Spar webs and skin panels are effective in shear and axial load. Therefore, in your calculations you should include the inertia of the panels (skin panels and spar webs) in the bending stress calculations only. Explanation about the sizing of the structural members of the wing is given under two separate headings. The first group is the spar flange, spar web thickness and skin thicknesses. The second group is the sizing of the rib web thickness, rib flange area and vertical rib members at the rib/spar intersections.

Design material:Materials used in the F-16 wing are repeated below.

Upper skin material: 2024 Al T851Lower skin material: 7475 Al T7651Spar materials: 2124 Al T851 and 7475 Al T7351 (Find out where these two materials are used)Rib materials: 2124 Al T851 , 7475 Al T7351 and 7075 Forging T73 (Find out where these three materials are used)

Prepare a table and compare the material properties of the materials used in the F-16 wing. Use MIL-HDBK-5H to get the material properties. Give the tension allowables for L, LT and ST. Explain L, LT and ST values. What are they? Besides the tension allowables give the elastic moduli of the materials used in the F-16 wing and compare all in a Table. Discuss on the different choice of materials in different parts of the F-16 wing.

In the project, in order for the project groups to compete in achieving minimum weight design, use the following materials and material properties in your design.

Upper skin material: 2024 Al T851Tension allowable: Xtu=462 MPa, Modulus of elasticity= 72.4 GPa, Poisson’s ratio: 0.33Density: 2767.99 kg/m3

Lower skin material: 7475 Al T7651Tension allowable: Xtu=479 MPa, Modulus of elasticity= 71 GPa, Poisson’s ratio: 0.33Density: 2795.67 kg/m3

Rib material: 7475 Al T7351Tension allowable: Xtu=482.6 MPa, Modulus of elasticity= 70.3 GPa, Poisson’s ratio: 0.33Density: 2795.67 kg/m3

Spar web and flange: 7475 Al T7351Tension allowable: Xtu=482.6 MPa, Modulus of elasticity= 70.3 GPa, Poisson’s ratio: 0.33Density: 2795.67 kg/m3

For strength calculations, use a factor of safety of 1.5 on the ultimate strength values of the materials used in the wing. In the strength calculations, use the elastic moduli given above. Do not apply factor of satety on the elastic moduli in strength calculations.

5.1. Sizing of spar flange, spar web thickness, skin thicknesses

Shear Flow Calculations:In the shear flow equations, include only the inertia of the flanges in the calculation of the first moments. This way, we can get constant shear flow webs.

ex: q2=q1-VQ/I

In this equation, consider the first moment Q for flanges and for the total moment of inertia (I)include the inertia of the flanges only in the shear flow calculations. This is our classical approach except for the fact that for the bending stress calculations, use the total moment of inertia including the inertia of the flanges and web/skin panels. This is the second idealization that you practiced in the take home part of the midterm examination.

Buckling Checks:In this project, we will assume that we have buckling resistant panels (skin and spar web). Therefore, we will not permit buckling at the limit load. However, in this case to have a minimum weight wing structure, you need to size the panels such that you will have minimum positive margin of safety such as 0.01 (Note: Bruhn has margin of safety relations for combined buckling cases). Panel buckling (skin and spar web) will be due to combined buckling:

For the upper skin panels: combined shear + compression loadingFor the lower skin panels: combined shear + tension loadingFor the spar webs: combined shear + in-plane bending loading

root

Rib iRib i+1

In the buckling calculations, for the fighter wing, you can assume clamped edge conditions for the skin panels and spar webs.

Note that although the wing section is unsymmetric, you can use the symmetric bending formula in the calculation of axial stresses due to bending and in writing the shear flow equations.

Change the sizing discretely between the rib stations.

For buckling check of the panels (skins and spar webs) use the average stresses (or stresses in the middle of each rib section) in each rib section as shown in the figure below. Note that F-16 wing does not have many ribs since there are many spars. Panel lengths of section 3 are high. So be careful !.

Note on buckling checks:

When checking the buckling design constraint remember that:

You need to use interactive equations for buckling checks under combined loading of the panels since we assume that panels also carry axial stress.

As for the panels, check upper and lower skin panels, spar webs and ribs. In the buckling calculations, assume that spars, ribs and stringers provide clamped support conditions.

Also note that in this project, we do not consider the buckling of spar flanges. This is because the spanwise flanges are supported by the wing skin on one side and by the spar webs on the other side.

Strength Checks: For strength checks, determine the maximum direct stresses on the spar flanges and the skin/web panels based on the in-board values of the stresses for each rib station. For the panels (skin/spar web), calculate the Von-Misses stresses using the maximum shear and axial stresses due to bending at the in-board location of each rib station. For spar flanges calculate the axial stress at the in-board station of each rib section, as shown in Figure 3.

Note that in sizing the spar flanges, you have to make sure that spar flanges possess sufficient stiffness to enforce boundary conditions for local buckling of wing skins. You need to come up with reasonable flange areas so that they provide the required edge conditions.

in-board values of stress for strength check

Average stresses at the mid station for buckling check

Therefore, try to minimize skin thicknesses so that flange areas do not turn out to be very small. Remember, because you are also taking the spar web and skin inertias into account, wing bending load will also be carried by the skin also. Therefore, if you increase the wing skin thicknesses, you may come up with small flange areas and thicker wing skins with possible weight penalty. You should make a research on the required spar flange sizes such that spar flange areas provide the required stiffness for an edge constraint between simply supported edge and clamped edge.

As an example, you can follow a design strategy such as the one given below. This design strategy is only given to explain a typical methodology. You are expected to come up with your design strategy. Groups who come up with design strategies that allow minimum weight at the lowest computational cost will get bonus point.

0- Start your design from the tip section and proceed inboard. Make your design section by section. Once you finish the outboard section, you will have idea about what flange area or what thickness to use in the initial iterations for the inboard sections.

1- First size the spar flanges assuming that all the bending load is carried by the spar flanges with all the inertia calculated based on spar flanges. When determining the spar flange areas try to go down to the lowest margin of safety possible (such as 0.01). Perform iterations to optimize flange areas.

2- Then, assuming that spar flanges provide the necessary edge conditions for the wing skins and spar webs, size the skin and web thicknesses against buckling. At this step, you can size the skin and the spar webs based on shear buckling only. Again, try to obtain lowest margins of safety possible. Perform iterations to optimize thicknesses.

3- In the third step, include the inertia of skin and spar webs in the inertia you determined in step one and re-size the spar cap areas. After resizing, check if spar flanges provide the required stiffness for edge constraint between simply supported edge and clamped edge.

4- After re-sizing the spar flanges, do strength and buckling checks for the spar webs and skins. In this step, allow skins and spar webs to carry axial load. You need to check for strength and buckling for the wing skins and spar webs. Everytime you make changes in thickness values, you need to update the inertia and check your spar flange sizing again. You may have to perform sub-iterations in this step.

5- Once you are done with a section, make a weight break down for that section and keep it.

6- Go to the next section and perform steps 1-5.7- Once you complete spar flange, wing skin and spar web sizing, do your rib sizing

as explained in Section 5.2.

In this part, you also need to introduce the calculations performed by presenting one sample calculation in your report.

Margin of safety calculation for one of the spar flange at a certain wing span location for the final minimum weight configuration that you obtained.

Calculation of shear flows in the skin and webs at a certain spanwise station for the final minimum weight configuration that you obtained. Here you also have to show the margin of safety based on the Von-Misses stress acting on the particular skin or web panel.

Buckling constraint calculation of skin or web panels and buckling margin of safety.

Simplifications:

- Ignore the contribution of the leading and the trailing edge of the wing behind rear spar to the structural stiffness. Consider only the torque box shown in Fig. 1(b).

- For the inertia and buckling calculations, you can approximate wing as composed of straight panels between the wing spars. You can ignore the curvature for simplification.

- Since the internal loads are calculated for the limit load factor of 9g, you have to use a factor of safety of 1.5 on the ultimate strength allowable of wing material. For buckling calculations, do not use a factor of safety on the elastic modulus.

- Select the final skin thicknesses, spar caps and other longitudinals from standard available sizes. You may refer to Bruhn, or other references such as aircraftspruce.

- You may change skin thicknesses, flange and stiffener areas discretely between the wing ribs. Do not change skin thicknesses chordwise, but you can change the flange areas and spar web thicknesses chordwise.

- The rib spacing is already given in the Project_igs_Modified.igs.01 file. Use the simplified drawing given in Fig. 1(b). Thickness must maintain the basic airfoil shape, without local or global buckling of the rib and the skin longitudinal stringers.

5.2. Sizing of rib web thickness and rib flange areas

Rib web thicknesses:

Size the inter-spar rib webs based on the rib web shear stresses and the compressive stress due to Brazier loading acting on them. In this project, we assume that ribs are composed of rib web, rib flanges and vertical members at the intersection of the ribs with spar flanges. Vertical members are assumed to provide support for the spar webs.

a) Inter-spar rib web shear stresses

Determine the inter-spar rib web shear stresses by finding the reactive shear stresses coming from the outboard and inboard sections of the ribs as shown in the figure given below. Since the skin and spar web thicknesses are different in the outboard and in the inboard sections of the wing, there will be net reacting shear stress on the rib coming from wing skins and spar webs. Note the maximum shear stress in the inter-spar rib webs at the rib station. You can use the maximum stress in sizing the rib web thickness, as described below.

root

Rib i

in-board stationout-board station

b) Compressive stress due to Brazier loading while wing bends

The explanation for the Brazier loading is given in the class. Calculate the compressive load on the rib using the following formula we have derived in class. More explanations are given during the project discussion hour.

( N rib )i=2 N xi

2

Etdi( L1+L2

2 )Nxi=Mxi/di

Mxi = (M/∑ wi)*(wi/∑ wi)

where

M: Bending moment acting at the sectionMxi: Bending moment per unit width for the ith inter-spar rib(Nrib)i: Crushing load on the ith inter-spar rib per unit widthNxi: is the axial force per unit width for the itof the wing skin.di: Height of the ith inter-spar ribt: Skin thickness of the wing (Take the lower value, outboard skin thickness)wi: Inter-spar distance (width of the ith inter-spar rib)E: Young’s modulus of the wing material (take the lowest elastic modulus given for the wing material)(L1 + L2)/2: Average rib spacing – defined in Figure 4 below.

Spar web i Spar web i+1

Reacting shear stresses on the rib coming from in-board and out-board sections

Figure 4 Brazier loads due to wing bending

For wing rib sizing, use Figure 5 which shows the shear and compressive stress acting on the wing rib.

σ ( comp . rib )i=Nxi /t i

Figure 5 Combined loading acting on the wing rib

Having determined the shear stress and compressive stress acting on the rib size the rib web by making the following strength buckling checks

- Calculate the maximum Von Misses stress on the rib and make strength check- Check the buckling of the rib web assuming that rib web is under compression and

shear loading. Therefore, you need to use interaction equations to check buckling of the rib web. In the buckling calculations you can assume clamped edge conditions in the connection of the wing rib to wing skins and spar webs.

Make sure that you make the sizing to determine minimum positive margin of safety such as 0.01.

Rib web flange:

Normally, rib web flanges must be sized based on rib bending and concentrated loads acting on the rib flange. However, in this project we will size the rib flanges such that they possess sufficient stiffness to enforce boundary conditions for local buckling of wing skins.

σ ( comp . rib )i=Nxi /t i

Maximum reacting shear stress in the inter-spar rib at the rib station

In this project you can approximate the rib flange area as the average of spar flange areas at the rib station. This would be a reasonable assumption.

Vertical members at the rib/spar intersection:

You can approximate the area of the vertical members at the rib/spar intersection as the rib flange area.

6. Submission Documents

1. Wing loading calculation document.

Summarize the internal loads due to 9g limit load case. This is what you have done in first part of your project. Use Schrenk’s integration method to calculate the internal loads at the stations where you will do sizing.

2- Wing structural design and analysis document

The overall sizing should be decided based on the calculations that you have to report within the content of this document.

You can perform the analysis with a computer program or using excel or Matlab etc. Based on internal loads you have determined, you have to carry out iterations until you satisfy the design constraints and obtain a wing structural lay-out with minimum weight. Do not forget that you success is directly proportional to:

Your design strategy to achieve minimum weight design Manufacturability and the use of standard size material How general your code is. A general code means that the user can enter the

number of spar and ribs and the required dimensions so that it can also be used for other wing configurations. Therefore, try to write a general code which does not just solve the wing configuration given in the assigned project.

Discussion of your results:

The final section of this part should include a table summarizing the structural elements and cross-sectional areas and thicknesses etc. along with a weight break down resulting in the final weight of the wing. This part should give the summary of the structural layout calculated for the 9g load case. Your summary tables should be easy to understand. Readers should not have to guess what you have done. You should have clear headings, explanations for all the information that you want to convey.

In the discussion of your results, stress on the design weight and the iterations performed to reach the minimum design weight. Explain your design strategy. Out a flowchart of your design strategy in your report. Make some comparisons such as spar flange area, skin thicknesses for the design you performed using the 9g limit load case. Comment on your results and see if they make sense or not.

From internet or TAI try to find the weight of one half F-16 wing. Compare your design weight with that. Remember in your design, you do not consider the wing-fuselage attachment fittings and leading and trailing edge sections. Therefore, your design weight should be lower than the weight that you may find.

3- Project Presentation

Each team will prepare a presentation and present the key points reported in documents 1-4. The presentation of each group will be maximum 20 minutes. In their presentation the groups should stress:

Design weight and the iterations performed to reach the minimum design weight How general their code is Weight break down and minimum weight design you achived Manufacturability and the use of standard size material