Floor Beam Design Project

AER E 426 – Fall 2017

Eric Harper

Sean Mullen

Andrew Raudabaugh

Table of Contents

Executive Summary 2

1

Project Goals 3

Material Selection 3

Corrosion Resistance 4

Manufacturing 5

Cost Analysis 5

Beam Analysis 5

Loading 5

Fatigue 7

Joint Analysis 7

Buckling Analysis 15

Summary of Margins of Safety 17

Conclusion 18

References 20

2

Executive Summary

Within AER E 426, students are exposed to many different methods and tools which are

involved within the domain of aircraft structures. Learning application of the topics

covered is crucial for a greater understanding of how to implement them within industry

and product design.

The team was tasked to design an ideal floor beam for a 747-600 commercial jet. The

beam was to be optimized for weight but balanced by cost. Many crucial aspects have

gone into the design of the beam such as material selection, joint design, deflection

analysis, compression and shear buckling, and fatigue analysis.

Through this report the reader will be shown the design process which was gone

through to conceptualize, calculate, and design the ideal floor beam. The report will

cover strength analysis, manufacturing considerations, practicality, weight optimization

and cost analysis.

Figure 1 shows the layout of all floor beam components. All dimensions are in inches.

Figure 1: Floor Beam Drawing

3

Project Goals

Within the project, the group was given constraints to meet while designing the beam.

Maintaining structural integrity and limiting deflection are crucial for designing a

component within a high tolerance environment. Maintaining under an inch of deflection

at any point along the beam was set as a maximum value. After review of the load

profiles given to us, we discovered the largest loads are from a 3g Up (w/cargo) loading.

The group was able to use these loads and maintain a margin of safety greater than

0.5. As in any thorough component design, fatigue loads were to be considered. To

ensure a long life of the plan and the floor beams will not be the failure mode, a fatigue

life of 20,000 flights is used. Finally to balance all considerations, cost is to be explored.

A goal of 4,000 dollars was used.

The group also set more qualitative goals.

● Corrosion resistance

● Manufacturing simplicity

● Ease of repairability

Material Selection

When choosing a suitable material for the floor beam, many things were taken into

consideration. To make sure the best material was chosen, many materials were

compared against one another.

Within the realm of aluminums, three alloys are very prevalently used for structures

within industry; 7075-T6, 2024-T4, and 6061-T6. Aluminums are nearly half as dense as

steel which gives them a high strength to weight ratio. This makes them very desirable

in cases where both strength and weight are a priority. 7075-T6 is very unique with its

very high yield stress >70,000 [ksi]. This high yield stress is almost double that of the

other alloys considered. Due to the atomic structure and heat treating process,

aluminum alloys are very soft which allows them to be manufactured at a higher speed

with less energy. Unfortunately the ease of manufacturing comes at the expense of

durability. The hardness of all three alloys is very low. The HRC value for all three is

near the bottom of the chart. These hardness values will not deflect impacts leading to

pitting and fatigue. Of the three options selected, only 6061 has the ability to be welded.

The others will immediately crack and fail after welding, thus hampering their

repairability.

There is a plethora of steel alloys to choose from, but one stands out amongst the rest,

4130 (Chromoly) steel. Chromoly steel is a very suitable material for many reasons.

Due to its high chromium content, the yield stress sits >60,000 [psi]. The yield stress

4

alone is nothing special so looking a little deeper it is found how high of a Modulus of

elasticity 4130 has. This high value allows for an Ultimate tensile strength of 97,000

[psi]. Such a gap will allow for yielding to occur without catastrophically failing. When

comparing 4130 to the many other steels it is relatively easy to cut and extrude allowing

for a greater ease of manufacturing. Another feature is the receptivity to welding. Even

when heat treated, 4130 can be welded, further increasing its repairability.

Finally the group explored the material choice of using composites. Relatively new to

industry, composites have grown to be used in almost any situation. One of the main

reasons for their diverse use is the extremely high strength to weight ratio. It is higher

than any metal. Along with the high ratio, composites are also very stiff. Minimal

deflection is another point where composites shine. Honeycomb internal structures are

designed to resist bending loads, further decreasing deflection. These high marks come

at the trade off of extremely high cost. The production of carbon fibres is extremely

wasteful and labor intensive leading to higher material costs. Additionally, composites

do not yield, they catastrophically fail which limits the fatigue life and manufacturability

greatly. Fortunately composites are immune to rust and are mostly affected by acid

compounds when worrying about corrosion.

The team decided to go with 7075-T6 Aluminum for the floor beam.

Corrosion Resistance

To manage corrosion, a few methods were explored varying in complexity and cost. The

team first looked into anodizing components. After further research, anodizing was

considered unfeasible due to the massive cost and slow manufacturing time. Next we

looked into how surface finish effects corrosion. A better surface finish will reduce the

amount of cavities for fluids to sit in and corrode. Finally additive coatings were looked

at. If an option were to be used, additive coatings would be the most viable option.

Manufacturing

Extrusion is defined as the process of shaping material, in our case 7075-T6, by forcing

it to flow through a shaped opening in a die. Extruded material emerges as an

elongated piece with the same profile as the die opening. Extrusion allows for a rapid

production of beams from billet. With the reduced machining needed, manufacturing

time and cost will be low compared to casting and machining directly from billet.

Cost Analysis

After researching into the raw cost of aluminum and costs of using extrusion, the team

was able to make some estimates on the cost of manufacturing the designed floor

system. First the material cost for an ingot of 1000in^3 of aluminum approximately cost

450$ Then, from the material given on the project, we were to estimate the

manufacturing cost to be 500$. Through other suppliers, the fastener costs averaged

5

out to be 100$. Finally, the group approximated the costs of the other extruded

components to be 500$. These cost are not absolute and are flexible to change based

on demand for the beams and fluctuations of the material costs.

Beam Analysis

Loading

Any beam must be designed to safely carry the largest load it will encounter. The packet

provides eight specific Load Cases. Load Case 8 induces the largest stress on the

beams.The stress will be the greatest at the stanchions, centerline, and system

penetrations. The beam is designed to meet stress requirements at all three points

under Load Case 8.

The equation can be solved for second moment of inertia (I) to find a beam that meets

the requirements. Stress will be highest at the system penetration, so it is best to take

the stress concentration into account when solving for I. Solving the stress equation with

an additional concentration factor of 2.1 yields a minimum I of 25.18 [in4]. Aluminum

Association standard channel CS 7×4.72, shown in Figure 2, has an I of 33.8 [in4] and

produces a stress of 33,271 [psi].

6

Figure 2: Beam cross section drawing

This yields a margin of safety of 1, meeting the required margin of safety of 0.5. This is

for bending moment. There is no shear stress at the system penetration as indicated by

the FEA analysis and the axial stress is borne by the flanges.

The maximum stress outside of the system penetration is at the stanchion. Stress there

is a mere 16,555 [psi] with a margin of safety of 3. Shear stress in the beam at the

stanchion is only 1372 [psi] with a margin of safety of 27.

7

Fatigue

Fatigue is the final major concern. The system penetration will fatigue first, so stress

there is used in the fatigue analysis. Maximum stress for fatigue is 28,432 [psi], which

works out to 25,000 cycles before failure. Margin of safety for fatigue is 0.25.

Joint Analysis

For all of the joints, calculations were done in EES using the following Equations.

I=Moment of Inertia

d=rivet diameter

x

i=distance¿ joint edge¿rivet ∈x–direction

yi=distance ¿ joint edge ¿rivet∈ y–direction

¯x=center of rivet array∈x–direction

¯y=centerof rivet array∈ y–direction

I=∑

❑ ❑

d x

i

2

+∑

❑ ❑

d yi2–x∑

❑ ❑

d x

i-¯y∑

❑ ❑

d yi (1.1)

pi=load onrivet i

py=load on joint∈ y–direction

px=load on joint∈x–direction

m=moment

p¿dp¿d

¿ x/∑

❑ ❑

¿-(m( yi-¯y)/I)¿2}0.5

¿¿¿¿

pi=d{¿

(1.2)

t=webthickness of beam

n=factor of safety

strengt hmin=minimum strengththatrivet must withstand

d

bolt=bolt diameter

f bolt=bearing force onbolt

8

shearbol t

min=minimum shear that bolt must withstand

Figure 3 shows a table of various rivet strengths that were referenced to determine the

proper size and material for each rivet (MMPDS Handbook, Table 8.2.1).

Figure 3: Rivet Shear Strengths

Where the floor beam attaches to the zee frame, an array of eight rivets was necessary

to withstand the maximum forces with a margin of safety of 0.5. Figure 4 shows the

array dimensions in inches.

9

Figure 4: Zee frame joint drawing

Of the load cases provided, Load Case 8 had the greatest forces applied at this joint.

The force px was 2855 [lbf], py was 4318 [lbf], and moment was 28165 [lbf*in].

Figures 5 and 6 show the calculations that the team performed to discover that the

maximum force any rivet must withstand was 4090 [lbf].

10

Figure 5: Floor beam to zee frame joint calculations

Figure 6: Floor beam to zee frame joint solutions

Eight ⅜” diameter rivets made of 2017-T4 Aluminum were chosen to fasten this joint

because they can tolerate a shear force of 4445 [lbf], giving the joint a minimum margin

of safety of 0.63.

Where the floor beam attaches to the stanchion, a column of five rivets was necessary

to withstand the maximum forces with a margin of safety of 0.5. Figure 7 shows the

array dimensions in inches.

11

Figure 7: Stanchion joint drawing

Of the load cases provided, Load Case 8 had the greatest forces applied at this joint.

The force px was 2855 [lbf], py was 5408 [lbf], and moment was 0 [lbf*in] since

py acts directly in line with the rivets. Figures 8 and 9 show the calculations that the

team performed to discover that the maximum force any rivet must withstand was 1835

[lbf].

12

Figure 8: Floor beam to stanchion joint calculations

Figure 9: Floor beam to stanchion joint solutions

Five ¼ ” diameter rivets made of 2017-T4 Aluminum were chosen to fasten this joint

because they can tolerate a shear force of 1970 [lbf], giving the joint a minimum margin

of safety of 0.61.

Where the floor beam attaches to the seat track, an extruded C-channel bracket was

used to connect the two. Where the bracket attaches to the floor beam, a column of five

rivets was necessary to withstand the maximum forces with a margin of safety of 0.5.

Figure 10 shows the array dimensions in inches.

13

Figure 10: Seat track joint drawing

Where the bracket attaches to the seat track, two bolts were needed as displayed in

Figure 11.

Figure 11: Seat track joint drawing side view

14

Of the load cases provided, Load Case 8 had the greatest forces applied at this joint.

The force px was 300 [lbf] to account for passengers that may force the seats to the

right or left while boarding the aircraft, py was 6000 [lbf]. Moment was calculated

separately since it varied for each rivet. Figures 12 and 13 show the calculations that

the team performed to discover that the maximum force any rivet must withstand was

1826 [lbf], and the bearing force that two ¼” diameter bolts must withstand was 90000

[lbf/in^2].

Figure 12: Floor beam to seat track joint calculations

15

Figure 13: Floor beam to seat track joint solutions

Five ¼ ” diameter rivets made of 2017-T4 Aluminum were chosen to fasten this joint

between the bracket and floor beam because they can tolerate a shear force of 1970

[lbf], giving the joint a minimum margin of safety of 0.62. Two 2” long, ¼” diameter bolts

made of Grade 8 Steel with a zinc coating were chosen to fasten this joint between the

bracket and seat track because they have a shear strength of 90,000 [lbf/in^2], giving

the joint a minimum margin of safety of 0.5. The zinc coating prevents corrosion

between the steel bolt and aluminum seat track.

Buckling Analysis

The team determined whether or not the beam and stanchion would buckle under the

anticipated loads using the following Equations.

b

n=sectionlength

t

n=sectionthickness

F

ccn=sectioncrippling stress

F

cc=crippling stress

F

cc=∑

❑ ❑

b

n∗tn∗Fccn/∑

❑ ❑

b

n∗tn (2.1)

I=second moment of inertia

A=crosssection area

ρ=radius of gyration

ρ=√❑ (2.2)

F

cr=maximum crippling stress

E=modulus of elasticity

L=length of beam

F

(¿¿cc/(4∗π2∗E))∗¿

1–¿

F

cr=Fcc∗¿

(2.3)

16

For the beam, the maximum axial load that it had to withstand was 6807 [lbf] from Load

Case 1. Figures 14 and 15 show the calculations, using EES, that were performed in

order to determine the maximum crippling stress that the beam could withstand.

Figure 14: Buckling of floor beam calculations

Figure 15: Buckling of floor beam solutions

Through these calculations, the maximum crippling stress was found to be 9648

[lbf/in^2]. The applied stress on the beam was 1698 [lbf/in^2]. This gave the beam a

buckling margin of safety of 4.68.

The stanchion underwent the same process to determine if it would buckle, as displayed

in Figures 16 and 17. The largest axial force on the stanchion was 5408 [lbf] from Load

Case 8.

17

Figure 16: Buckling of stanchion calculations

Figure 17: Buckling of stanchion solutions

Through these calculations, the maximum crippling stress was found to be 20317

[lbf/in^2]. The applied stress on the stanchion was 11696 [lbf/in^2]. This gave the

stanchion a buckling margin of safety of 0.74.

Summary of Margins of Safety

Bending stress

Floor beam: 1

Stanchion: 3

Shear stress

Stanchion: 27

Fatigue: 0.25

Joints

Floor beam to zee frame: 0.63

18

Floor beam to stanchion: 0.61

Floor beam to seat track (rivets): 0.62

Floor beam to seat track (bolts): 0.5

Buckling

Floor beam: 4.68

Stanchion: 0.74

Conclusion

Figure 18 shows the full assembly of the fuselage with the team’s floor beam.

Figure 18: Model of fuselage assembly

The floor beam that the team designed was sufficient in all aspects. It met all of the

criteria that was placed upon it. Margins of safety for all components of the beam were

greater than the required 0.5 except for the fatigue lifetime. However, the main concern

with fatigue was that the beam would last for 20,000 flights. The beam that the team

designed lasts for 25,000 flights, which meets that criteria. Through all of the decisions

and calculations detailed in this report, it is the belief of the team that this floor beam is

adequate for a 747-600 commercial jet.

19

References

Aluminum Association Standard channels, Table 4

<http://www.aluminum.org/sites/default/files/ADM2010Errata2.pdf>

Aluminum Extrusion Alloy Guide

<http://tri-stateal.com/resources/91>

Aluminum Extrusion Process

<https://www.bonlalum.com/education/aluminum_extrusion_process.shtml>

Floor Beam Design Project Packet

Metallic Materials Properties Development and Standardization (MMPDS) Handbook,

Table 8.2.1

<http://rivet-table-info.blogspot.com/2012/04/aeroteaching-aircraft-hardwarems20470.html>

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