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>