Table of Contents
Introduction ........................................................................................................... 1
Mission Statement ................................................................................................. 2
Product Design Specifications ................................................................................ 3
Top Level Design Concepts..................................................................................... 3
Final Design............................................................................................................ 7
Evaluations of the Prototype and Future Considerations ..................................... 10
Conclusion ........................................................................................................... 17
Appendix A: References ..................................................................................... 18
Appendix B: Product Design Specifications ........................................................ 19
Appendix C: Final Design Documentation .......................................................... 20
Appendix D: Identification of Customers ............................................................ 23
Appendix E: Internal Search (Includes: Top level designs) .................................. 25
Appendix F: Verification (Preliminary and Final Designs) .................................... 32
Appendix G: Three Point Bend Test Results ....................................................... 62
Appendix H: External Search .............................................................................. 64
Introduction
The Linde Group is a leader in the industrial gases market. Its gases are transported in a
variety of tanks and cylinders. They are transported on pallets specially designed to be shipped
on certain trailers, refer to Figure 1 below. The current pallets weigh approximately 200
pounds. The pallets are shipped on specially adapted trailers with a pallet capacity between 22
and 24 pallets. Often the pallets and tanks on the trailers exceed a 40,000 pound freight limit,
forcing truck drivers to leave empty spaces. Refer to appendix D of the report for figures on
what the freight trailer looks like and how the pallets are loaded. Leftover cylinders are
shipped via a common carrier with elevated costs. The Linde Group is looking to replace the old
pallets with a new, lighter weight pallet. A lighter pallet would allow for more cylinders to be
loaded onto the trailer, resulting in lower shipping costs for The Linde Group. The pallet must
restrain the tanks with two straps spaced apart as shown in Figure 2. The pallet must function
with multiple loading docks requiring certain pallet dimensions to remain the same as the
original with a visual of one method shown in figure 3.
Page 1
Mission Statement
The mission is to create a new pallet design that is half the weight of the current pallet
and at the same time performs as well or better. The Linde Group is the main customer of the
design team, along with the truck drivers and workers who engage with the pallets. Other
Page 2
companies who transport the same types of cylinders are potential customers. The target
pallet weight is 100 lbs with a safe load capacity of 5,500 lbs.
Product Design Specifications
The criterion for the design is based on customer given requirements and interviews.
The highest level criteria of the design include performance, cost, weight, and ergonomics. The
main objective of redesigning the pallets is to reduce the weight from approximately 200lbs to
100lbs. The cost of the pallet must remain comparable to the original (approximately 350
dollars). This price could be flexible if taking the money saved, by shipping more cylinders
without overloading, into account. The ease of fabrication is important due to its direct relation
to cost. It has been found that fabrication is likely to make up at least half the cost of
production. The other criteria are in place to insure that the pallet will function as well as the
original and conform to all other requirements.
The new pallets would be used along side of the original pallets; because of this the new
pallets must have the same:

footprint (depth and width)

method of attachment

deck height

fork spacing
The complete table of product design specifications can be found in appendix B. This
table includes all of the product design specifications, including medium and low priority
criteria. The table is color coded and has a descending order of priority. The requirement, basis,
metrics, targets, and verification methods are included
Top Level Design Concepts
Page 3
The capstone team developed four main pallet design concepts. We compiled a
Simplified Steel Pallet (SSP), a Mold Injected Plastic Pallet (MIPP), Fiber-reinforced Plastic Pallet
(FPP), and a Steel Frame with Plywood Insert Pallet (SPIP). In appendix E there is further
documentation of the preliminary and top level designs.
The SSP was derived from the current pallet design. The capstone team considered a
Figure 4) Simplified Steel Pallet (SSP)
very simple design configuration in an effort to save cost and weight. The objective of the
standard steel design was to take the current design and remove unneeded material. This
would result in thinner walled railings and taking away excess bracing. The SSP design is shown
in figure 4. The capstone team was not able to develop a configuration that was capable of
meeting the design criteria, due to the combination of cost, weight, and strength requirements.
Page 4
The MIPP was developed considering mass produced plastic pallets with high load
capacity and light weight, as the base material. The plastic pallets come in many different
shapes and sizes made for many different applications. Figure 5 shows this preliminary design
with a plastic base and steel rails attached. One of the critical design specifications of a 3” deck
height was not able to be met with this configuration. The pallet team was unable to discover a
currently manufactured unit under 5” thick, because a thinner design would not be able to
carry the payloads needed for industrial cylinders. The alternative was a mold injected base
Figure 5) Mold Injected Plastic Pallet design.
made specifically for this project for low volume production the mold injection process is
extremely expensive. The capstone team considered mold configurations and railing
attachment systems described further in appendix E.
The FPP design was attractive in the beginning because fiber-reinforced plastics
lightweight properties and long service life. The research information of FRP is given in
Page 5
appendix F. The pallet team conducted a three point bending test of FRP and Plywood to
gather information of their material properties. The results from the test are tabulated in
appendix G, the plywood could withstand higher loads than the FRP making it a better
candidate for the base. Plywood is considerably lighter than FRP and approximately a ¼ the
cost. In figure 6 the FRP grating extends across the entire deck of the pallet. This configuration
was changed because of a loading configuration discussed with the Linde Group. As shown in
Appendix E the fork slots must come within ½” of the top deck of the pallet. This design
parameter is the reason the pallet team concluded with steel plate over the fork slots. The
design concept was originally very promising, however due to cost and weight constraints was
found to be insufficient in meeting the design criteria.
Figure 6) Fiber Reinforced Plastic Grating pallet design.
Page 6
Final Design
The final pallet design is shown below in figure 7, it utilizes a simple steel frame and
base with a plywood insert. The frame is made of 1 ½” 14ga square tubing with only 90o and 45o
cuts. The base receives its strength from 3” channel on the front and back with 2” angle
running between. The final weight of the pallet was found to be 130 lbs. The pallet will be
painted to increase its resistance to corrosion. The plywood is used based on the three point
bend test results, the low cost, lightweight, and high availability of plywood.
Pallet Layout
Figure 7) Final pallet prototype
Page 7
Plywood Insert
The final design utilizes a ¾” piece of exterior grade plywood shown in figure 8, inserted
into the center of the pallet deck. Plywood has many advantages, it is very inexpensive,
lightweight, and can hold large amounts of weight. A disadvantage of plywood is its
susceptibility to decay from weather and the elements, due to the pallets outdoor use. The
plywood’s purpose is twofold: reduce weight and maintain strength. ¾” thickness was chosen
because it is readily available, very inexpensive and meets strength requirements. The exterior
grade makes the insert much less susceptible to decay and failure. The glue used to hold the
ply’s together is water resistant. This type of plywood was tested in a three point bend
configuration with results showing its superior strength compared to fiber-reinforced plastic
tabulated in appendix G of this report.
Figure 8) Plywood insert (refer to figure 7 for plywood placement)
Page 8
Frame
The frame of the pallet is comprised of primarily of 1 ½” 14 gage square tubing shown in figure
9 below. The frame is welded together with 90o and 45o cuts for simple manufacturability. The
45o cuts at the bottom where the frame mounts to the base are for alignment when the pallet is
placed onto the trailers. The strap mounts are evenly spaced for support of tall loads and for
restraining different tank sizes. A drawing of the strap mounts is shown in appendix C of this
report, the capstone team chose clevis pins for their strength and availability. The pin can also
be removed as apposed to the old pallet which used either a welded pin or bolt. The final
design will also have plastic caps installed in the open ends of the tubing to prevent the inside
of the members from corroding.
Figure 9) Final design of the frame
Page 9
Base
The base configuration is shown below in an exploded view without the plywood insert. The
spike support shown in the figure below is made of 3” x ¼” steel flatbar, its purpose is to hold
the pallet in place when on the trailer. Heavier gage steel was used on the spike support for
two reasons; the support holds the entire pallet in place while on the trailer and it is subject to
continuous abuse from loading and unloading from the trailer. 3/16” steel plate is used on top
of the fork slots, due to a design requirement established by the loading dock configuration.
The plywood insert is reinforced with two cross members made with 1/8” thick, 1” square
tubing and by 1” x 3/16” flat bar at the front and rear of the pallet.
Figure 10) Exploded view of the pallet frame design
Evaluations of the Prototype and Future Considerations
A thorough evaluation of the final design was conducted and all documentation of the analysis is
shown in appendix F of the report. This includes calculations made by the capstone team, finite element
Page 10
analysis (FEA), cost analysis, and SolidWorks figures. The sections mentioned below are high level
product design considerations.
Weight
The weight of the pallet has been verified to be approximately 130 pounds, this was
done by using SolidWorks, the primary modeling tool used throughout the project. When
modeling component of the assembly the material properties are chosen, which allows for the
calculation of the total weight of the assembly. The density of each member was chosen to be
slightly higher than the actual density of the material, this was done to account for extra weight
due to weld material, straps, errors in plywood density, and other factors not foreseen. The
Solidworks mass values were cross referenced and verified with tabulated values of weight
given on supplier’s websites
To definitively verify the weight of the design, the completed prototype must be
weighed. This is not possible due to the prototype not being completed. Due to the size of the
prototype, the way in which the team would weigh the pallet would be to use a 100 lb capacity
spring scale attached to one side of the pallet, lifting that side off the ground, recording the
weight and then doing the same thing for the other side. Theoretically the weight should be the
same for each side. When weighing the pallet in this manner, you are essentially weighing only
half the pallet at a time, because half the load is being supported by the side of the pallet on
the ground. The total weight of the pallet would be the sum of the weight of the two sides.
Cost
The cost criteria of the new pallet design is based on the production of 200 units.
Currently the capstone team does not have an accurate quote for producing 200 units. What
the team does have is a prototype quote of 600 dollars for a single pallet to be manufactured.
The capstone teams contact at Linde, Mike Dever, remarked that with his experience with
production manufacturing and a history with the shop building the prototype that the 600
dollar quote is reliable.
Page 11
The original design specification stated the new pallet be close to 350 dollars for the
manufacturing of 200 units. The 350 dollar cost constraint was developed for two different
reasons, the price of refurbished pallets which the Linde Group has been purchasing for use are
around 350 dollars and cost to manufacture one of their old design pallets is approximately 600
dollars. The company estimated the if 200 units were to be produced the manufacturing costs
would be close to the cost of refurbished pallets. The cost constraint has been verified by two
different methods. First the material cost was determined by pricing the material required to
build one pallet and estimating the expected fabrication time and multiplying that by a typical
manufacturing shop rate. The average shop rate for this type of product is around 65 dollars
per hour. Another way the cost requirement was verified was by getting an estimate from the
facility manufacturing the prototype, the estimate for the cost of the prototype was 600 dollars
including materials and construction. When 200 units are manufactured the new quote will be
less than 600 dollars and given the preliminary estimates and previous experience the cost
requirement is expected to be met.
Deck Height
The base of the pallet was required to be the same as the original pallet. This has been
verified by modeling the new pallet to have a deck height of 3 inches. The base of the original
pallet had a height of 3 and 3/16 inches. The difference of 3/16 of an inch was due to the
configuration of the material within the base. The new pallet uses 3 inch channel on the front
and back as the main supports of the base, to achieve the same height as the original, more
material would have to be added to the top or bottom of the base, which would have increased
the weight of the pallet. This difference in height was found to be small enough that the
purpose of the height restriction was not negatively effected. To verify that the deck height of
the prototype meets the criteria, a measurement of the base height would need to be made.
As talked about previously in the paper and shown in figure 3 in appendix E, the deck
height is important to the functionality of the new pallet. With the prototype, the design would
be verified by placing it on a fork lift and conducting normal loading and unloading of cylinders
and carts.
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Fork Spacing
The fork spacing design requirement insures that the new pallet can be used alongside
the old pallets. The forklifts currently in use must be able to pick up both types of pallets
without fork adjustments. The spacing has been verified by evaluating dimensions of the solid
assembly model. The second method is using a completed prototype and physically measuring
the slot spacing and conducting a test with a Linde Group fork lift.
Trailer Fitment
The new pallet was required to fit on the freight trailers in the same way as the original
pallet. This requirement primarily depends on the position and dimensions of the spike
extrusions on the trailer which restrains the pallets. This spike system is explained further in
appendix D and shown in figures 1 and 2. Also solid round stock is horizontally welded to the
trailer to restrain the front of the pallet on either side. The position, dimensions, and
orientation of these features were held constant when developing the new pallet model. When
the assembly was completed, the dimensions of interest were measured and verified again. The
final verification would be completed by loading the prototype on the freight trailer and
insuring proper fitment.
Loading
Analysis of various components of the pallet were performed to insure proper function,
strength, and safety of the pallet. First maximum stresses and loads on the components were
calculated based on the yield stresses of the material. Actual loads on these components were
calculated from the typical loading conditions given to the capstone team. Documentation of
the calculation procedures and derivation of typical loads can be found in appendix F. Factors of
safety were found for the individual components. Some components of the assembly were
evaluated using finite element analysis software because of the complexity of the required
calculations. FEA software was also used to verify portions of the theoretical calculations. A
table of component factors of safety is shown below.
Page 13
Area of Interest
Property of Material
Pin Shear
Pin Tab Tensile Load
Weld with Tensile Load
Weld in Torsion
Load on Wood Insert
Loading on Metal Plate Span
Load on Rear Members
Load on Plywood Insert Supports
Sy=85,000 psi
Sy=30,000 psi
Sut=70ksi
Sy=57kpsi
Sy=30,000 psi
Sy=36,259 psi
Sy=36,259 psi
Factor of
Safety
60.23
52.5
52.5
55.8
3.79
1.53
1.92
3.91
Rear Members
The loading conditions of the rear members of the pallet were assumed to be
bending of a beam with fixed ends due to a uniform load. Each member was analyzed as
if it receiving the entire load due to the force from the straps. The factor of safety of the
weakest rear member was found to be 1.92, however the load due to the strapping of
the cylinders is actually distributed between three members instead of two so the actual
factor of safety is expected to be higher than the value given.
Plywood
The plywood insert was found to have a factor of safety of 3.79, based on a
calculation of a typical load applied to the largest span between the plywood supports.
Plywood Supports
Theoretical calculations and FEA models were used to verify the strength of the
plywood supports are sufficient when the maximum uniform load due to the loading of
cylinder is present. A factor of safety of 3.91 was found for the square tubing support.
Calculations on the front and rear supports were neglected due to thicker material
being used and attachment via welding the entire length. This would result in a much
higher load capacity of these members
Pin Attachment Points
Page 14
The pin attachments were analyzed in a variety of ways. Analysis of the pin in
shear, pin tab in tension, bearing stress of the pin tab, and the weld stresses in tension
and torsion, were considered. All the factors of safety for these attachment were found
to be larger than 50.
Corrosion Resistance
The resistance of the pallet to corrosion has been assured by the selection of a two part
urethane spray on coating. It is suitable for bare metal application even when small amounts of
rust are already present and requires no primer prior to application. The coating was
specifically designed to prevent corrosion to materials it has been applied. The specifications of
the coating can be found in appendix H.
The plywood insert was chose to be outdoor grade and water resistant. It is still
expected to decay over time but due to its water resistant properties, would likely last for more
than a year. Also the insert was made to be easily replaced and is low cost. Research of the
plywood was conducted with results shown in appendix H.
Documentation
The documentation required for production of the pallet includes dimensioned part and
assembly drawings, bill of materials, material cut sheet, and fabrication notes. Sufficient
documentation for the production of the prototype was verified by the fabrication facility
producing the prototype. The documentation needed for production is shown in appendix C.
DOT Requirements
The DOT requirements for the pallet must ultimately be verified by testing of the
prototype. The testing must be performed to assure that the pallet must withstand loading
incident to transportation of the pallet. Also the pallet must be able to withstand loading due to
minor vehicle accidents.
Page 15
Although the team does not have a prototype, preliminary verification of DOT
requirements has been performed by calculating factors of safety for specific members of the
assembly (as shown in the table above). The pin attachment points are considered the most
important factor in restraining the cylinder in case of an accident, the factors of safety for these
components are all larger than 50. The member and components were analyzed based on
typical loading conditions of the pallet. Factors of safety were calculated based on typical static
loading of a fully loaded pallet (max load conditions).
Maintenance
A design requirement of the new pallet was that it must be easily repaired if a
component or member of the pallet were to fail. The way the team assured this quality of the
pallet was the use of common and weldable material, so that if there is a failure of the
assembly or component of it, the portion that failed may be cut out and new member may be
welded in its place.
Also, because the plywood insert is expected to fail far sooner than the rest of the
structure, it must be easily replaceable. This criteria has been met by using a common material
(exterior grade plywood) and attaching it in such a way that it may be replaced as needed in a
relatively short amount of time (estimated to be less the 30 minutes). This is to be verified by
replacing the plywood insert of the prototype and recording the time that it takes to see if the
estimated time is correct.
Safety
The safety of the pallet is the result of many factors. Many of these factors are verified
by preceding methods such as DOT requirements and loading calculations. The primary safety
criteria not already covered is that the new pallet is to be free from sharp edges which may
injure those loading and unloading cylinders from the pallet The assembly was configured so
that no sharp edges are to be present. This is to be verified by visually inspecting the prototype.
Page 16
Conclusion
The capstone team is confident in the new pallet design and its capabilities as a lighter
weight unit than the old design. The new plywood insert is strong enough to accommodate all
the loading configurations currently used by the Linde Group. The manufacturing quote of
$600 for the prototype was a great indicator of the design simplicity and material selection.
The exact dollar amount for 200 units has not been assessed but an initial assessment by Mike
Dever from the Linde group said the cost reduction for 200 units is promising.
The capstone team realized early in the process that steel was the material most
capable to carry the load of the cylinders while maintaining the durability needed to withstand
loading and unloading onto freight trailers. The key to the design is the reduction of steel plate
area by using a plywood insert and analyzing common steel members (channel, angle) to cut
material where it was advantageous.
The capstone team had a meeting with an industry advisor about halfway through the
first term of the project. The team received excellent information regarding customer service.
The academic advisor coached the team on the importance of good communication throughout
the design process. The team took this information to heart and conducted more face to face
meetings with Mr. Dever. Greater communication resulted in the information regarding pallet
thickness above the fork slots being discovered early (further information in appendix C), and
corrections being implemented.
Page 17
Appendix A: References
A Ledford Steel Company. (2010, June 6). Metals Depot. Retrieved February 11, 2010, from
http://www.metalsdepot.com/
An RPM Company. (2010, June 6). High Performance FRP Composite Products. Retrieved February 11,
2010, from http://www.fibergrate.com/fileshare/ProductFiles/brochure/fibergrate.pdf
Budynas, R. G., & Nisbett, J. K. (2008). Mechanical Engineering Design (8th Edition ed.). New York:
McGraw-Hill.
DrillSpot. (2010). DrillSpot.com/Online Hardware Store. Retrieved May 20, 2010, from
http://www.drillspot.com/
eFunda, Inc. (2010). efunda. Retrieved June 2, 2010, from http://www.efunda.com/home.cfm
Engineers Edge, LLC. (2010). Engineers Edge. Retrieved May 15, 2010, from
http://www.engineersedge.com/material_science/moment-inertia-gyration-7.htm
EZwoodshop.com. (2010). Andy's EZ Wood Shop. Retrieved February 20, 2010, from
http://www.ezwoodshop.com/plywood/plywood-prices.html
Fastener SuperStore, Inc. (2010, June 6). Fastener Superstore. Retrieved May 20, 2010, from
http://www.fastenersuperstore.com/index2.cfm
Helium, Inc. (2010). Where Knowledge Rules. Retrieved February 20, 2010, from
http://www.helium.com/items/1124584-the-difference-between-marine-grade-and-pressure-treatedplywood
Homestead Inc. (2010). Marine Plywood by Homestead. Retrieved February 20, 2010, from
http://marine-plywood.us/
KTC Media Group. (2008). Grating Pacific. Retrieved February 12, 2010, from
http://www.gratingpacific.com/
NetPeers, Inc. (2005). Mr. Plywood. Retrieved February 20, 2010, from http://mrplywoodinc.com/
Stratis Plastic Pallets. (2008). Stratis Plastic Pallets. Retrieved February 10, 2010, from
http://www.pallets.com/
White Light Design, Inc. (2009). White Light Design. Retrieved February 10, 2010, from
http://www.whitelightdesign.com/services_Eng_ManufEIJ.htm
Page 18
Appendix B: Product Design Specifications
Product Design Specifications
Priority
High
Medium
Low
Criteria
Customer Requirements
Metrics
Targets
Basis
Verification
Performance
Linde
Same method of
attachment
inches
Factors of
safety
lbs
$ per 200
units
Time
$350
inches
no change
Mounting spike
and positioning
tabs on truck
Function and
safety
1/2 the weight of
current pallets
Similar to current
pallets
Cost and
production time
Easier loading
Modeling
Linde
Same as
the old
pallets
>2
Weight
Linde
Must hold
cylinders securely
Weight Reduction
Cost
Linde
Similar to Original
Linde
Linde
Simplicity of
construction
Fork Spacing
Linde
Deck Height
Inches
Life in Service
Linde
Life of the pallet
Years
3in (no
change)
≥20
Size and Shape
Linde
Key dimensions
must remain
unchanged
Inches
±1/4in
Quality and
Linde
Similar fit and
function
Compare
to old
pallets
≥Old
pallets
Customer
requirement
Comparison
Linde
Must survive
outdoor
environment
Corrosion
resistance
medium to
high
Pallets are abused
and subjected to
the elements
Analysis
Linde
Strength
≥current
Loading will
remain the same
Property Tables
Linde
Loading of pallet
on the truck
Sufficient
for typical
use
time
≤original
Productivity must
not be negatively
effected
Must have hard
copy of design
Testing new pallet
along with old
Ergonomics
Reliability
Materials
Testing
Documentation Linde
Sufficient for
production
100
< 5 hours
Completed Sufficient
documents for
production
Page 19
Curb height of
facilities
Life of the old
pallets
Must fit and
function same as
old pallet
Calculations
Analysis and
Testing
Analysis and
Documentation
Analysis and
Modeling
Analysis and
Measurement
Measurement and
Modeling
Analysis
Analysis and
Measurement
Discussion with
fabrication facility
Linde
Secure cylinders
safely for
transportation
Factors of
safety of
typical
loading
ME492
PDS report
Date
>10 for
strapping
points
>2 for non
crit. comp.
2/8/10
ME492
Progress Report
Date
3/8/10
ME493
Design Report
Date
6/3/10
Linde
Completed
Prototype
Date
6/1/10
Quantity
Linde
Production
Quantity
200
Aesthetics
Linde
Paintable
yes/no
yes
Maintenance
Linde
Weldable
yes/no
yes
Safety
Linde
yes/no
yes
DOT requirement
Linde
Safely secure
pallets under
normal driving
conditions
No Sharp Edges
yes/no
no
Cad
Format
NA
NA
Environment and
amount of use
NA
Modeling and
Prototyping
NA
NA
NA
NA
NA
NA
NA
NA
NA
Applicable
codes and
standards
Timelines
Company
DOT requirement
Analysis and
calculations
Course
Requirement
Course
Requirement
Course
Requirement
Customer and
course
requirement
Price target based
on 200 units
Protection against
corrosion and
visually pleasing
For repairs and
modifications
Grade
Grade
Grade
Customer
satisfaction
Analysis
Testing
Analysis and
Material
Properties
Analysis and
Testing
constraints and Drawing
procedures
Environment
NA
Disposal
NA
Outside
Environment
NA
Legal (Related
NA
NA
NA
NA
NA
NA
Shipping
NA
NA
NA
NA
NA
NA
Packaging
NA
NA
NA
NA
NA
NA
Installation
NA
NA
NA
NA
NA
NA
patents)
Appendix C: Final Design Documentation
Page 20
Figure 1) Pallet drawing formulated from SolidWorks.
Proposal
The capstone team discussed the prototype with Mike Dever when a final design was
reached. The capsone team formulated a prototype proposal consisting of the documents
shown in this appendix. The basic drawings, cut sheet call out drawings, and a detailed drawing
of the pin strap mount. The proposal was given to Mr. Dever and he used this information to
place the order for the prototype with a manufacturing facility used by the Linde Group. The
initial response for lead time on completion of the pallet suggested it would be completed
before the end of the term. The manufacturing shop was unable to complete the prototype
before the term ended.
Page 21
Figure 2) The drawing above has call outs to work with a cut sheet
shown below for ease of material ordering and manufacturing.
Cut Sheet and Bill of Materials (BOM)
The cut sheet is a manufacturing guide with a length column for each member needed for
assembly of the. The BOM is laid out for material acquisition, the material needed is listed with
a total length needed for the construction of one pallet
Page 22
Figure 3) Pin Strap configuration drawing
Appendix D: Identification of Customers
Internal Customers
Internal customers are the affiliates of Portland State University capstone program; they consist
of facility members, our assigned faculty team advisor, and team members.

The Portland State University Capstone Program
o Each capstone team is to research, design, prototype, and test their product.

Dr. Etesami, Mechanical Engineering Capstone Coordinator
o Dr. Etesami is the team member’s instructor that sets the requirements and
deadlines for the purpose of grading.
External Customers
Page 23
External customers are those who are setting the requirements that need to be met before
they will use the product. Below are some customers that we interviewed to see what their
thoughts and suggestions of the pallets were.

The Linde Group
o To reduce the weight of the current pallet by about half its weight while still
retaining the same performance as the current pallet allowing for more cylinders
to be loaded on the trucks at one time.
o Wants to reduce the shipment of overflow cylinders that are shipped by
common carrier due to exceeding the weight limit of the allowable payload.
o Retain the same fork locations and dimensions.
o Retain the same base height.
o Reduce the weight of the pallets to allow the trucks to be fully loaded and still be
under the 80,000 Lb gross weight requirement.
o Be in ODOT compliance.

Mike Dever
o Retain the same foot print dimensions.
o Needs to have two straps to allow for securing the load.
Initial Interview
The semi trucks and trailers are used to transport pallets with cylinders loaded on them. There
is a set max payload of 80,000 lbs set by ODOT. After accounting for the weight of the truck
and trailer there is about 40,000 lbs left for payload to be carried. When loading the truck the
max payload is reached before the pallet spaces on the trailer are filled. In figure 1 and 2 the
“spikes” for each pallet space are shown, there are a total of 22 to 24 pallet spaces on
depending on the trailer. The deck on the pallets must be level with a step of the trailer shown
in figure 2. All the pallets that don’t make it onto the truck must be shipped by common carrier
even though there are still empty spots left on the trailer.
Page 24
Our team meet with Mike Dever where he explained to us to solve the problem, a new pallet is
to be designed that weighs 100 lbs or less. With a new pallet, the trailers could be fully loaded
with cylinders. From there we were able to watch how the pallets were loaded with cylinders
and then see the pallets loaded on the trucks. While there we were able to talk to some
employees of the Linde Group that deal with the pallets on and everyday interaction; we talked
to two forklift operators, two truck drivers, and Mike Dever. There we concluded that the Linde
Group wants the new pallet to cost less than $350 and to manufacture approximately 200
pallets. This value was reached based on an estimate to refurbish the old pallets.
Figure 1) The image below is the trailer with
the pallets loaded.
Figure 2) The picture below is of the pallet
trailer with a visual of the “spikes.”
Appendix E: Internal Search (Includes: Top level designs)
Internal Search:
The Pallet Design Team came up with three different ideas; a mold injected plastic pallet
with steel rails, a standard steel design, and a steel frame pallet utilizing a wood, FRP, or plastic
deck insert.
The mold injected pallet met many of the material requirements, such as having a light
weight and low cost. The rails supporting the cylinders would be made of steel or aluminum
Page 25
attached to the base with fasteners or imbedding a material such as steel into the plastic for
the upper rails to attach.
The simple steel pallet is a takeoff of the current design with weight reduction the
primary task. The current pallet appears over built with excess material adding to the weight.
The current design has been in service for over 20 years with visible wear and tear but little
deformation from the actual cylinder load. The goal of creating a simple steel pallet based off
of the current pallet is to reduce excess material in the deck and bottom frame.
The current pallet has a 3/16 inch thick deck plate made of steel. This plate constitutes
a large portion of the pallet weight. The rails of the pallet experience a considerable amount of
side and frontal loads. With these two considerations the Pallet Design Team will replace the
deck with an alternative lighter material without compromising the strength of the rails intact.
The rails have two straps at different heights holding the pallets in place making the strength of
the rear frame important to cylinder stability. Different material considerations were wood and
a FRP deck. Both wood and FRP have a strength that could handle the side and frontal loads
and are much lighter than steel.
Table 1) Base selection decision matrix
Page 26
Breakdown of Each Top Level and Preliminary Design
Fiber Reinforced Plastic (FRP) Base Plate Insert
The design below is a flat grating covering the entire base of the pallet. This design is
advantagous because it meets weight requirements of 100 lbs and after initail probing meets
stress and load requirements. The information needed to verify these claims is a capstone
team group test including the grating shown in the figure 1 and figure 2. The grating has
empircal data published and shown in appendix H, on suppliers websites and using this data it
meets expectations. The capstone team group wants first hand data on each of the considered
materials. The data published has uniform load results and the capstone team group needs
some data on point loads. After meeting with Mike Dever a loading and unloading
configuration was determined to render the design below not functional and revisions were
considered shown in the next section and shown in figure 3.
Figure 1) Pallet Base Plate with Grating, the pallet above
utilizes a fiber reinforced plastic base plate.
Page 27
Figure 2) Bottom up view of Preliminary
FRP steel frame design.
Fiber-Reinforced Plastic (FRP) Base Plate with Increased Fork Height
During the designing of the pallet the team encountered an issue with forklift fork height. The
figure below shows a design addressing this issue. The forks will slide into the channel on the
pallet giving allmost 3” height as appose to a grading configuration above the fork slots.
Figure 3) Model of FRP deck reconfiguration for loading dock setup
The design in figure 4 is a base configuration of how the grating will only cover three separate
portions of the deck to increase fork slot spacing. The figure is only a prelimanary design and
not showing all product design specifications needed for a complete product. The fiberreinforced plastic pallet design was dropped after a testing of plywood and FRP was conducted
and plywood was chosen. The three point bend test information is shown in appendix G of the
report.
Figure 4) Pallet design (Channel) The pallet is using a greater fork spacing achieved by using channel
and splitting the grating into three separate pieces. No rails are shown for simplicity.
Page 28
DESIGN 4: FRP Grating (second frame consideration)
The proposed design contains the following design ideas:

Fiber-reinforced plastic grating insert

Angled sides

Perforated back plate

Steel frame: 1 ¼” Square tubing, 3/16” plate
This design weighs 146 lbs (25% of current design). Its frame is made of 1 ¼” Square steel
tubing and 3/16” steel plate. The supports for the FRP grating insert, seen in Figure 8, are steel
channels. Its sides are angled as compared to the square sides of the original to save material.
Lips are welded on the underside of the base plate for the outer edge of the insert to sit on, as
seen in Figure 8. The FRP insert is 1 inch thick. As seen in Figure 8, the inserts top face is 13/16”
above the surrounding steel plate. This is a design flaw that requires redesign because cylinders
need to be able to evenly sit on pallet.
Preliminary fiber-reinforced plastic pallet (FPP), and a steel frame with plywood
insert pallet (SPIP).
The following section is a more detailed look at the start of the final design shown in the
final design section of the paper. The first model shown in figure 5 is the original design with a
plywood insert, the second model shown through figures 6 – 10 is trials of the steel design with
insert configuration.
The design below was made with 2x2 steel square tubing frame and level sides. This
allows for easy fabrication due to similar material throughout and simple 90 degree angles. The
insert could be made of any material; however thickness is limited to 1 inch. This thickness limit
is due to height restriction and the fact that the forks of the fork lift must be able to easily slide
through the pallet. The current considerations for inserts are either plywood or fiberglass
reinforced plastic grating. Another significant change in the design is the repositioning to the
back frame over the mounting slot allowing for an additional 125 square inches of usable pallet
area.
Page 29
Figure 5) Pallet with Wood, the design above is an initial design
utilizing plywood for a base plate.
The design below in figures 6 – 10 shows further revisions to the steel frame design with an FRP
insert. The figures are not complete models because it was preliminary; these models were
generated to look at material mass and selection. The model was also used for installing
different insert materials and conducting weight reduction analysis.
Figure 6) Pallet, simple steel design
Figure 7) Pallet, with base plate insert (insert
material; FRP)
Page 30
Figure 8) Pallet top view (fiber reinforced
plastic base plate insert)
Figure 9) Pallet Rear View (notice holes in back
plate for reduced weight)
Figure 10) Pallet bottom view (bottom frame design
considerations labeled.)
Page 31
Figure 9) (Perforated) FRP insert, no back plate –
128 lbs (compared to figure 5 with back plate,
Weight – 146lbs
Figure 10) Wood insert with back plate – 147
lbs
Appendix F: Verification (Preliminary and Final Designs)
Verification Calculations of the Final Design
Strap Connection Stress Analysis
Summary:
The securing straps for the cylinders are secured to the pallet frame by a pin connection.
Tightening of the straps around the cylinders will put stresses on the pin connection. Stresses in the pin
connection caused by the strap load include shearing stresses in the pin itself, bearing stresses in the pin
and pin tabs, tensile stress in pin tab and stresses in the welds between the pin tabs and the frame. The
straps are rated for a maximum 10,000 lb load. The maximum load allowed on the straps (given the pin
connection material and dimensions) will be calculated. The maximum load will be the lowest maximum
load of any component of the pin connection.
Part 1: Stress in Pin and Pin Tabs
Given:
Page 32


𝐿 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑝𝑖𝑛 𝑎𝑟𝑒𝑎 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑝𝑖𝑛 𝑡𝑎𝑏𝑠 = 2𝑖𝑛
𝑡 = 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑝𝑖𝑛 𝑡𝑎𝑏𝑠 = .25𝑖𝑛

𝐷 = 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑝𝑖𝑛 = 8 𝑖𝑛 = .625𝑖𝑛



𝑃 = 𝑢𝑛𝑖𝑓𝑜𝑟𝑚 𝑙𝑜𝑎𝑑 𝑜𝑛 𝑝𝑖𝑛
𝑁 = 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦
𝑆𝑦 = 𝑌𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑝𝑖𝑛 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 85,000𝑝𝑠𝑖
5
Assumptions:


Load direction on pin puts pin tabs under direct tensile stress.
Assume actual loads on pins are half that of the load induced from the ratcheting strap. The
force from the ratchet strap is assumed to be 500 pounds. Therefore the load on each strapping
point would be 250 pounds. 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 = 250𝑙𝑏
Find:


The maximum load P that can be applied to the pins (as indicated in the problem diagram) in
terms of the pin shear stress and pin tab shear stress
Factor of Safety
Solution:
There are three stress components that are most important to understanding the stress in the pin.
These are pin shear stress, pin bearing stress and pin tab bearing stress.
Shear Stress in pin:
𝜏=
. 577𝑆𝑦
𝑃
=
𝐴𝑝𝑖𝑛
𝑛𝑑
𝐴𝑝𝑖𝑛 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒
Page 33
𝑃 = 𝐴𝑝𝑖𝑛 ∗ (. 577)𝑆𝑦 = (𝜋
𝑃=
𝐷2
) (. 577)𝑆𝑦
4
𝜋(. 625𝑖𝑛)2
(. 577)(85,000𝑝𝑠𝑖) = 15,057𝑙𝑏
4
𝑁=
𝑃𝑚𝑎𝑥
15,057𝑙𝑏
=
= 60.23
𝑃𝑎𝑐𝑡𝑢𝑎𝑙
250𝑙𝑏
Bearing stress of pin:
𝑅𝑝 = 𝑅𝑎𝑡𝑖𝑜 𝑜𝑓 𝑝𝑖𝑛 𝑡𝑜 𝑝𝑖𝑛 𝑡𝑎𝑏 𝑎𝑟𝑒𝑎
𝑅𝑝 =
𝐿
2𝑖𝑛
=
= .8
2𝑡 + 𝐿 (2 ∗ .25𝑖𝑛) + 2𝑖𝑛
𝜎𝑝𝑖𝑛 =
𝑃=(
𝑃𝑚𝑎𝑥 =
𝑃
𝑅
𝐿𝐷 𝑝
𝐿𝐷
)𝑆
𝑅𝑝 𝑦
2𝑖𝑛 ∗ .625𝑖𝑛
∗ (85,000𝑝𝑠𝑖) = 132,000𝑝𝑠𝑖
.8
Bearing stress of tabs:
𝑅𝑡𝑎𝑏 = 𝑅𝑎𝑡𝑖𝑜 𝑜𝑓 𝑝𝑖𝑛 𝑡𝑎𝑏 𝑡𝑜 𝑝𝑖𝑛 𝑎𝑟𝑒𝑎
𝑆𝑦 = 𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝑜𝑓 𝑝𝑖𝑛 𝑡𝑎𝑏 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 30𝑘𝑠𝑖
𝑅𝑝 =
2𝑡
2 ∗ (.25𝑖𝑛)
=
= .2
2𝑡 + 𝐿 (2 ∗ .25𝑖𝑛) + 2𝑖𝑛
𝑃
𝜎𝑡𝑎𝑏 = (
)𝑅
= 𝑆𝑦
2𝑡𝐷 𝑡𝑎𝑏
2𝑡𝐷
(𝑅 ) 𝑆𝑦
𝑃 = 𝑡𝑎𝑏
1
𝑃𝑚𝑎𝑥 =
(2 ∗ .25𝑖𝑛)(. 625𝑖𝑛)
∗ (30,000𝑝𝑠𝑖) = 46,875𝑙𝑏
.2
Tensile Stress of Tab:
𝑃 = 𝜎𝐴
Page 34
𝑃 = 𝑆𝑦 ((1.5𝑖𝑛 − .625𝑖𝑛) ∗ .25𝑖𝑛)
𝑃 = 6,562.5𝑙𝑏
2𝑃 = 13,125𝑙𝑏
𝑁=
13,125𝑙𝑏
= 52.5
250𝑙𝑏
Part 2: Stress in Welds
Given:


𝑊𝑒𝑙𝑑 𝑡ℎ𝑟𝑜𝑎𝑡 𝑤𝑖𝑑𝑡ℎ 𝑑 = 1.5 𝑖𝑛
𝑁 = 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦
Assumptions:





𝑊𝑒𝑙𝑑 𝑡ℎ𝑟𝑜𝑎𝑡 ℎ𝑒𝑖𝑔ℎ𝑡 ℎ = .3 𝑖𝑛
𝐴𝑛𝑔𝑙𝑒 𝑜𝑓 𝐿𝑜𝑎𝑑 𝑓𝑟𝑜𝑚 𝑛𝑜𝑟𝑚𝑎𝑙, 𝜃 = 90 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 (𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑙𝑜𝑎𝑑𝑖𝑛𝑔)
Assume actual loads on pins are (rating of straps/2pins per strap) 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 = 5,000𝑙𝑏
𝑆𝑢𝑡 𝑜𝑓 𝑤𝑒𝑙𝑑 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 70,000 𝑝𝑠𝑖 (𝐸70𝑥𝑥 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 𝑛𝑢𝑚𝑏𝑒𝑟), 𝑆𝑦 = 57,000𝑝𝑠𝑖
𝐹𝑖𝑙𝑙𝑒𝑡 𝑤𝑒𝑙𝑑 𝑜𝑛 𝑒𝑎𝑐ℎ 𝑠𝑖𝑑𝑒 𝑜𝑓 𝑚𝑒𝑚𝑏𝑒𝑟
Find:


The maximum load P that can be applied to the pins (as indicated in the problem diagram)
Factor of safety
Solution:
Page 35
If pallet has a full capacity of cylinders, the load on the pins will put the welds in shear only. If
there are smaller amounts of cylinders on the pallet, the load may not be tensile and the welds will be in
a combination of torsion and shear.
Welds in shear only (𝜃 = 90𝑑𝑒𝑔𝑟𝑒𝑒𝑠)
𝜏=
1.414𝑃
ℎ𝑑
𝜏 = .30𝑆𝑢𝑡
𝑃=
𝑃=
ℎ𝑑
(.30𝑆𝑢𝑡 )
1.44
. 3𝑖𝑛 ∗ 1.5𝑖𝑛
(. 30 ∗ 70,000𝑝𝑠𝑖) = 6563𝑙𝑏
1.44
𝑃 = 2𝑡𝑎𝑏𝑠 ∗ 6563𝑙𝑏 = 13,126𝑙𝑏
𝑁=
𝑃
𝑃𝑎𝑐𝑡𝑢𝑎𝑙
=
13,126𝑙𝑏
= 52.5
250𝑙𝑏
Welds in torsion and shear (0 < 𝜃 < 90):
𝜏 = 𝜏 ′ + 𝜏′′
𝜏′ =
𝑃
𝐴
𝐴 = 𝑡ℎ𝑟𝑜𝑎𝑡 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑤𝑒𝑙𝑑 = (. 707) ∗ ℎ ∗ 𝑑 = .318𝑖𝑛2
𝜏 ′′ =
𝑀∗𝑟
𝐽
𝑀 = 𝑚𝑜𝑚𝑒𝑛𝑡 𝑎𝑏𝑜𝑢𝑡 𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑 𝑜𝑓 𝑤𝑒𝑙𝑑 𝑔𝑟𝑜𝑢𝑝
𝑟 = 𝑓𝑢𝑟𝑡ℎ𝑒𝑠𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑚𝑜𝑚𝑒𝑛𝑡 𝑡𝑜 𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑜𝑓 𝑤𝑒𝑙𝑑
𝐽 = .707 ∗ ℎ ∗ 𝐽𝑢
Use Case 2 from Table 9-1 of Shigley’s2 for 𝐽𝑢 :
Assume load is 𝜃 = 45 𝑑𝑒𝑔𝑟𝑒𝑒𝑠:
𝐽𝑢 =
𝑑3 (1.5𝑖𝑛)3
=
= .5626𝑖𝑛3
6
6
𝑟 = √𝑥 2 + 𝑦 2 = √. 750𝑖𝑛2 +. 750𝑖𝑛2 = 1.06𝑖𝑛
Page 36
𝐽 = .707 ∗ ℎ ∗ 𝐽𝑢 = .707 ∗ .2𝑖𝑛 ∗ .281𝑖𝑛3 = .04𝑖𝑛4
𝜏 ′′ =
𝑃 ∗ 𝑦𝑐𝑜𝑠(𝜃) ∗ 𝑟
. 707 ∗ ℎ ∗ 𝐽𝑢
𝜏 = √𝑡′′2 + 𝑡′2
Assume 𝜏′ is very small and can be neglected because loading is at 45 degrees.
𝜏 = 𝜏′′
Distortion Energy Theory
𝜏=
𝑆𝑠𝑦 . 577𝑆𝑦
=
𝑁
𝑁
𝑆𝑦 = 57𝑘𝑝𝑠𝑖
𝑃 =. 577𝑆𝑦 ∗
𝐽
𝑦𝑐𝑜𝑠(𝜃)𝑟
Four welds per strap connection (2 weld groups)
2𝑃 = 13,952𝑙𝑏
𝑁=
13,952𝑙𝑏
= 55.8
250𝑙𝑏
1
Shigley’s Mechanical Engineering Design.
Wood Insert Allowable Span
Summary:
The wood insert sits in the middle of the pallet base. It is supported by square tubing supports and lip
supports from the sides. The maximum allowable load on the given span is to be calculated using
maximum bending stress data from the 3-point bend test experiment.
Given:
Page 37

𝑃𝑚𝑎𝑥 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑙𝑜𝑎𝑑 𝑤ℎ𝑒𝑛 𝑝𝑙𝑦𝑤𝑜𝑜𝑑 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑜𝑐𝑐𝑢𝑟𝑒𝑑 (𝑏𝑒𝑛𝑑 𝑡𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡) = 800𝑙𝑏
Assumption:
Use beam equations
Solution:
From the maximum load found in the 3-point bend test, a maximum stress can be determined that a
piece of plywood can stand under 3-point bending. A maximum load can be determined for the given
span in the pallet based on this data.
Finding the maximum bending stress from bend test experiment (pinned-pinned beam, point load):



ℎ = .75𝑖𝑛
𝑏 = 5𝑖𝑛
𝐿 = 16𝑖𝑛

𝑐 = 2 = .375𝑖𝑛

𝑃𝑚𝑎𝑥 = 800𝑙𝑏
ℎ
𝜎𝑚𝑎𝑥 =
𝑀𝑚𝑎𝑥 𝑐
𝐼
𝐼 = 𝐼𝑥 =
𝑏ℎ3
12
Page 38
𝑀𝑚𝑎𝑥 =
𝜎𝑚𝑎𝑥 =
𝜎𝑚𝑎𝑥 =
𝜎𝑚𝑎𝑥 =
𝑃𝐿
4
𝑃𝑚𝑎𝑥 𝐿 𝑐
∗
4
𝐼
𝑃𝑚𝑎𝑥 𝐿 12𝑐
∗ 3
4
𝑏ℎ
800𝑙𝑏 ∗ 16𝑖𝑛 12 ∗ .375𝑖𝑛
∗
= 6825𝑝𝑠𝑖
4
5𝑖𝑛 ∗ (.75𝑖𝑛)3
Maximum load for pallet wood insert span:




𝐿 = 8.5𝑖𝑛
ℎ = .75𝑖𝑛
𝑏 = 23𝑖𝑛
𝑐 = .375𝑖𝑛
𝑃=
𝑏ℎ3 4
( )𝜎
12 𝐿 𝑚𝑎𝑥
23𝑖𝑛 ∗ (. 75𝑖𝑛)3
4
6825𝑝𝑠𝑖
𝑃=
∗(
)(
) = 2861 𝑙𝑏
12
8.5𝑖𝑛
𝑖𝑛2
The load present on a single span of the plywood would be one third of the total load on the plywood:
𝑃𝑎𝑐𝑡𝑢𝑎𝑙 =
𝑃𝑎𝑐𝑡𝑢𝑎𝑙 =
𝑃𝑝𝑙𝑦𝑤𝑜𝑜𝑑 𝑤 ∗ 𝐴𝑖𝑛𝑠𝑒𝑟𝑡
=
3𝑠𝑝𝑎𝑛𝑠
3𝑠𝑝𝑎𝑛𝑠
3.5𝑝𝑠𝑖 ∗ 646.33𝑖𝑛2
= 755.56𝑙𝑏
3𝑠𝑝𝑎𝑛𝑠
𝑁=
2861𝑙𝑏
= 3.79
755.6𝑙𝑏
Stress and Deflection of Metal Plate
Summary:
A majority of the load is put onto metal plates that span the base of the pallet. Since a maximum pallet
weight is around 5000 lbs, an overestimate of the uniform load applied to a third of the pallet will be
2000 lbs. The maximum deflection and stress of the plate under loading is desired. The plate will be
assumed to be fixed on all sides because it is welded to the pallet base. Plate deflection and stress
equations can be found on eFunda.com and this website will be used to calculate the stress and
deflection of the given plate.
Page 39


𝐿𝑥 = 12𝑖𝑛
𝐿𝑦 = 30𝑖𝑛

ℎ = 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 16 𝑖𝑛 = .1875𝑖𝑛

Uniform load
3
Assumptions:


Clamped (fixed) plate
Uniform load of 2000 lbs placed downward on plate
Solution:
The following explanations of plate equations are given by eFunda.com1
The small transverse (out-of-plane) displacement w of a thin plate is governed by the Classical Plate
Equation,
where p is the distributed load (force per unit area) acting in the same direction as z(and w), and D is the
bending/flexural rigidity of the plate defined as follows,
Page 40
in which E is the Young's modulus,
the plate.
is the Poisson's ratio of the plate material, and is the thickness of
Furthermore, the differential operator
is called the Laplacian differential operator
,
If the bending rigidity D is constant throughout the plate, the plate equation can be simplified to,
where
is called the biharmonic differential operator.
1
eFunda: Plate Calculator. eFunda, Inc. June 5th, 2010.
<http://www.efunda.com/formulae/solid_mechanics/plates/calculators/CCCC_PUniform.cfm#Results >
We then arrive at the Classical Plate equation,
or a slimmer form
where w0 is replaced by w and pz replaced by p to be consistent with the notations in most published
literatures.
Page 41
Page 42
𝜎𝑚𝑎𝑥 = 11.3𝑘𝑠𝑖
𝑆𝑦 = 30,000𝑝𝑠𝑖 ∗ .577 = 17310𝑝𝑠𝑖
17.3𝑘𝑠𝑖
𝑁=
= 1.53
11.3𝑘𝑠𝑖
Stress Analysis of Cylinders On Rear Frame Members
Page 43
Summary:
The rear members of the pallet are subjected to bending due to the restraining of the cylinders with two
straps. The maximum load allowable on the back members needs to be calculated. One member is a box
cross-section while the other is an angle cross-section. The two members will share the full loading of
1000 lbs.
Region of Analysis
Given:
Page 44

𝑎 = 1.5𝑖𝑛

𝑡 = 16 𝑖𝑛 = .1875𝑖𝑛

𝐿 = 47.125𝑖𝑛

𝜎𝑦 = 𝑆𝑦 = 36,259 in2 = Yield strength of low carbon steel

𝐸 = 29,000,000 in2


Assumptions:
The supporting members loading are best described by a uniform loading on a beam with fixed
ends.
3
lbf
lbf
Find:
Maximum





Bending moment
Uniform load
Shear stress
Deflection
FOS of weakest member
Solution:
The load induced on the rear members of the pallet are best described by a uniform load on a beam
with fixed ends.
Starting with the stress equation for the bending of a beam and substituting the yield stress of steel, the
equation can be solved for M, the maximum moment the member can sustain before yielding. The area
moment of inertia, I, must be solved individually for different cross sections. The y in the equation is the
distance from the center of gravity of the cross section to the most extreme fiber or surface.
𝜎=
𝑀𝑦
𝐼
Page 45
𝜎𝑦 = 36,259
𝑀=
𝑀=
lbf
in2
𝜎𝐼
𝑦
𝑤
(6𝐿𝑥 − 𝐿2 – 6𝑥 2 )
12
X=distance along member from fixed end, w = distributed load.
𝑤=
12𝑀
(6𝐿𝑥 − 𝐿2 – 6𝑥 2 )
𝐿
𝑉 = 𝑤( − 𝑥 2 )
2
The equation may be simplified given that the magnitude of the shear stress is the greatest at each end
of the beam, as can be seen. The equation for shear stress becomes
𝑉=±
𝑤𝐿
2
With a uniform load, the deflection of the beam is given by the following equation. The modulus of
elasticity of steel is also given below. The value x need to get the maximum deflection is also given
below, this is because it is know the beam will deflect the most at the center of the beam.
𝛿=
𝑤𝑥 2
(𝐿 − 𝑥)2
24𝐸𝐼
𝐸 = 29,000,000
𝑥=
lbf
in2
𝐿
2
The following equations are used to calculate the area moment of inertia, distance from the center of
gravity to the outermost face, and the inside dimension, for a hollow square section.
𝑎4 − 𝑎𝑖 4
𝐼=
12
𝑎𝑖 = 𝑎 − 2𝑡
𝑦=
𝑎
2
The following equations are used to calculate the area moment of inertia and distance from the center
of gravity to the outermost edge, for an angle cross section.
Page 46
1
𝐼 = [𝑡𝑦 3 + 𝑎(𝑎 − 𝑦)3 − (𝑎 − 𝑡)(𝑎 − 𝑦 − 𝑡)3 ]
3
𝑦=𝑎−
𝑎2 + 𝑎𝑡 − 𝑡 2
2(2𝑎 − 𝑡)
Square Tubing Calculation:
𝑎𝑖 = 𝑎 − 2𝑡 → 1.5𝑖𝑛 − 2(.083𝑖𝑛) = 1.334in
𝑎4 − 𝑎𝑖 4 (1.5𝑖𝑛)4 − (1.334𝑖𝑛)4
𝐼=
→
= .158in4
12
12
𝑦=
𝑀=
𝑎 1.5𝑖𝑛
→
= .75
2
2
𝜎𝐼 36,259𝑝𝑠𝑖(.158in4 )
→
= 7638.6 𝑙𝑏 ∗ 𝑖𝑛
𝑦
0.75𝑖𝑛
𝑤=
12𝑀 12(7638.6𝑙𝑏 ∗ 𝑖𝑛)
𝑙𝑏𝑓
→
= 41.3
2
2
𝐿
(47.125𝑖𝑛)
𝑖𝑛
𝑉=
𝑤𝐿 41.3𝑙𝑏/𝑖𝑛 (47.125𝑖𝑛)
→
= 973.1𝑙𝑏
2
2
𝑤𝐿4
41.3𝑙𝑏/𝑖𝑛(47.125𝑖𝑛)4
𝛿=
→
= .1158𝑖𝑛
384𝐸𝐼 384(29,000,000psi)(.158in4 )
Angle Calculations:
1
𝐼 = [𝑡𝑦 3 + 𝑎(𝑎 − 𝑦)3 − (𝑎 − 𝑡)(𝑎 − 𝑦 − 𝑡)3 ]
3
1 3
3
3 3
[( )(1.05625)3 + 1.5(1.5 − 1.05625)3 − (1.5 − ( )) (1.5 − 1.05625 − ( )) ] = .10998
3 16
16
16
𝑦=𝑎−
1.5 −
𝑀=
𝑎2 + 𝑎𝑡 − 𝑡 2
2(2𝑎 − 𝑡)
3
3
1.52 + 1.5(16) − (16)2
3
2(2(1.5) − 16)
= 1.05625
𝜎𝐼 36,259𝑝𝑠𝑖(.10998𝑖𝑛4 )
→
= 3775.4𝑙𝑏 ∗ 𝑖𝑛
𝑦
1.05625
Page 47
𝑤=
12𝑀
12(3775.4𝑖𝑛 ∗ 𝑙𝑏)
→
= 20.4lb/in
2
𝐿
47.1252
𝑉=
𝛿=
𝑤𝐿 20.4(47.125𝑖𝑛)
→
= 480.7𝑙𝑏
2
2
𝑤𝐿4
20.4(47.125)4
→
= .08215𝑖𝑛
384𝐸𝐼 384(29,000,000)(.10998)
𝐴𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝐿𝑜𝑎𝑑 𝑜𝑛 𝑤ℎ𝑜𝑙𝑒 𝑚𝑒𝑚𝑏𝑒𝑟 = 𝑤 ∗ 47.125 = 961𝑙𝑏
𝑃𝑎𝑐𝑡𝑢𝑎𝑙 = 500𝑙𝑏
𝑁=
961𝑙𝑏
= 1.92
500𝑙𝑏
Plywood Supports Analysis
Summary:
The plywood is supported as shown below. The maximum load that the supports can hold needs to be
calculated. The supports are square tubing as indicated below.
Given:
Page 48
lbf

𝜎𝑦 = 36,259 in2

𝐸 = 29,000,000 in2


𝐿 = 22.357𝑖𝑛
𝑎 = 1𝑖𝑛
lbf
Assumptions:
The supporting members loading are best described by a uniform loading on a beam with fixed ends.
Find:
Maximum




Bending moment
Uniform load
Shear stress
Deflection
Solution:
𝐼=
𝑎4 − 𝑎𝑖 4 14 − (0.75)4
→
= 0.057in4
12
12
1
𝑎𝑖 = 𝑎 − 2𝑡 → 1 − 2( ) = 0.75in
8
𝑦=
𝑀=
𝑎 1
→ = 0.5𝑖𝑛
2 2
𝜎𝐼 36,259𝑝𝑠𝑖(0.057in4 )
→
= 4133.5𝑖𝑛 ∗ 𝑙𝑏
𝑦
0.5
𝑤=
12𝑀 12(4133.5𝑖𝑛 ∗ 𝑙𝑏)
𝑙𝑏𝑓
→
= 99.1 2
2
2
𝐿
(22.375𝑖𝑛)
𝑖𝑛
𝑉=
𝑤𝐿 99.1(22.375𝑖𝑛)
→
= 1108.4𝑙𝑏
2
2
𝑤𝐿4
99.1(22.375𝑖𝑛)4
𝛿=
→
= .039𝑖𝑛
384𝐸𝐼 384(29,000,000psi)(0.057in4 )
𝐴𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝐿𝑜𝑎𝑑 𝑜𝑛 𝑤ℎ𝑜𝑙𝑒 𝑚𝑒𝑚𝑏𝑒𝑟 = 𝑤 ∗ 22.375 = 2217.4𝑙𝑏
Page 49
The load on one member is a quarter of the entire load on the plywood insert, because the plywood is
supported by four equally spaced members. The load on the plywood insert is the uniform load on the
base multiplied by the area of the insert.
1
𝑃𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑃𝑖𝑛𝑠𝑒𝑟𝑡 = 566.7𝑙𝑏
4
For both square tubing plywood supports:
𝑁=
2217.4𝑙𝑏
= 3.91
566.7𝑙𝑏
Area of Interest
Property of Material
Pin Shear
Pin Tab Tensile Load
Weld with Tensile Load
Weld in Torsion
Load on Wood Insert
Loading on Metal Plate Span
Load on Rear Members
Load on Plywood Insert Supports
Sy=85,000 psi
Sy=30,000 psi
Sut=70ksi
Sy=57kpsi
Sy=30,000 psi
Sy=36,259 psi
Sy=36,259 psi
Factor of
Safety
60.23
52.5
52.5
55.8
3.79
1.53
1.92
3.91
Cost Analysis
Cost of Old Pallet
The cost refurbish or buy a used pallet of the original design is approximately 350 dollars. The
cost to build a single pallet of the new design was estimated to be around 600 dollars. Our industry
advisor estimated that if 200 pallets were produced, the cost per pallet could be reduced to 350 dollars.
Shipping Costs
Because the freight limit of the trailer is often exceeded Linde is often forced to ship the extra
cylinders using a common carrier. The average shipping costs due to the excess load of 2200 pounds is
850 dollars per week.
New Pallet
Fabrication Costs
Page 50
The fabrication facility manufacturing the prototype gave an estimate of 600 dollar to make the
first one. This is in line with the cost to make one of the original pallets, so it is reasonable to expect that
the per pallet price of the new pallet would be similar to that of the original.
Shipping Costs
The new pallet has been verified to be 70 pounds lighter than the pallet currently in use. If the
entire trailer was to be loaded with pallets of the new design, 1540 to 1680 pounds would be freed up
for additional cylinders. This would reduce the excess load from 2200 pounds per week to 520 to 660
pounds per week. Average shipping cost per week would be reduced to 200 to 255 dollars. This would
allow for a weekly savings of 595 to 650 dollars per week.
Finite Element Analysis of Final Design
Finite Element Analysis was done for verification of calculations. It was performed with
AbaqusTM on the following sections of the pallet:



Pallet Base
Pin Tab
Frame
Understanding AbaqusTM contour plots: Deflection (U) is magnitude of deflection and is in units
of Inches. S, Mises is the Von Mises Stress magnitude and is in units of PSI.
Basic plate span:
To determine what type of modeling would be the most accurate, a basic plate was modeled
with shell modeling and 3d modeling, where results were compared with results of manual
calculations. The plate span is the same dimensions as the top of the base (12 in x 30 in) and
clamped on all sides. Uniform loading of 2000 lbf was administered.
Page 51
Deflection results of Abaqus (Inches) from 2000lb uniform load, clamped sides
The results for shell modeling matched very similarly with manual calculations:
Maximum deflection (w)= .0158 inches
Pallet Base Analysis:
This portion of the base of the pallet contains a metal plate span that is subjected much of the
cylinder load. Since it is the same on both sides only one side needs to be modeled. Analysis
was done with Shell Modeling. Boundary Conditions include pinning of bottom faces. Multiple
loading schemes were conducted:
Page 52
Summary of Results:
Analysis
Max. Deflection (In.)
1000 lb Point Load in Center
0.13
2000 lb Uniform Load
0.05
Loading Cart
0.02
800 lb Load Over Fork Slot
0.03
Point Load of 1000 lbs in Center
(Units of Inches)
1,000lb point load near center: (U) Deflection is in Inches. Maximum global deflection
represented as red
Uniform Load of 2000 lb
Page 53
(Units of Inches)
(Units of PSI)
2,000lb uniform load over surface: (U) Deflection is in Inches. Maximum global deflection
represented as red. Von Mises Stresses in PSI. Highest stress in red at power portions of modelat stress concentrations.
Wheels of Loading Cart:
Transport carts roll onto pallets. Four caster wheels transfer the cart weight to the pallet. Half
of the cart lies on the part analyzed (two wheels). Each wheel is a point load of 500 lbs.
Page 54
(Units of Inches)
Two 500 lb point loads. (U) Deflection is in Inches. Maximum global deflection represented as
red.
800 lb Load Over Fork Slot
(Units of Inches)
(U) Deflection is in Inches. Maximum global deflection represented as red.
Load of Forklift
Page 55
(PSI)
Bottom face where forklift fork would push up was pinned and the uniform load of 2,000 lbs
was applied to the top surface. Von Mises Stresses in PSI
Frame:
Load of 10,000 lbs on each loading strap in the forward direction. Frame is fixed at all bottom
areas as if it were connected to the pallet base.
Page 56
Pin Tab:
Model of pin being pulled by loading straps: 250 lb force is applied to right-half of inner surface
of pin tab part as if the pin was being pulled against the surface by the force of the straps. Force
on strap would be 500 lbs. Analysis should verify stresses from bearing stress and tensile
loading.
250 lb force is applied to right-half of inner surface (directed to the right), fixed on left side.
Page 57
Load support analysis of FRP
Figure 3) Part of FRP brochure for Fiberglass Molded Plastic from
Fibergrate.com
The max load
that pallets see is 5,500 lbs. If FRP (Fiber-reinforced plastic) is desired as a supporting material,
the maximum span of that material can be calculated using tables provided by the
manufacturer. Generally a uniform pressure load can be used for analysis since pallets are
often fully loaded, but sometimes significant point loads are present when carts with casters sit
on pallets. This point loading by casters will be analyzed. The results of the analysis make the
FRP a good candidate for the base material. The FRP is strong enough to support point loads up
to 500 lbs. If the pallet design needs supports configured to relieve some stresses from high
loads the test planned will address this issue.
Given: Pallet load: 5,500 lbs (maximum load)
Pallet loading area: Width = 48” Span ≈ 24”
Material: FRP Grating: 1.5 in2 square mesh, 1 in depth
Find: The maximum span length that can be used
on a pallet using the specified FRP material
without failure or excessive deflection.
Page 58
Calculate maximum span length with two types of loading.

Pressure load

Point load (individual caster wheels from rolling carts)
Figure 1) Pressure loading
Figure 2) Point loading
Solution:
Calculating total load area: Width = (48 in)/( 12 in/ft) = 4 ft
Span = (24 in)/(12 in/ft) = 2 ft
Total Area = Width x Span = 4 ft x 2 ft = 8 ft2
Max Load = 5,500 lb
Calculating maximum pressure that will be applied to pallet:
Max Pressure = Max Load / Total Area = 5,500 lb / 8 ft2 = 687.5 psf
PRESSURE LOADING:
Page 59
Table 1 ) Uniform pressure loading and deflection for span lengths, provided
by FiberGrate.com
Load
Area
Pressure
Span (in)
5500 lb
8 ft^2
687.5 psf
Deflection*
24 Not acceptable
12 .05 in
18 0.25 in
ANSWER: Largest span for max pressure ≈ 18 in
POINT LOADING (Cart Casters):
≈2,000 lb per cart
4 casters per cart
1 in2 contact area per caster
Page 60
Point loading table is done in PSF loads:
(2,000 lb/cart)/(4 casters/cart)/(1 in2 per caster) = 500 psi at one point
One caster sitting in a ft2 area would be 500 psf.
Table 2 ) Point loading and deflection for span lengths, provided by
FiberGrate.com
As seen from Table 2, a 42 inch span is too wide to support 500 psf. The next lowest span in the
table that supports 500 psf is 36 inches.
Page 61
Appendix G: Three Point Bend Test Results
Figure 1) Image of FRP being loaded in a 3 point
configuration.
A full report was written documenting the 3 point bend test of both the Fiber-reinforced plastic and
plywood. Figure 8 below shows the stress vs. strain curve for each member tested. Table 1 below gives
tabulated results of the test. From the tests and other information obtained about each specimen
plywood was chosen as the material in the final design.
Page 62
6000
5000
PLYWOOD 01
4000
STRESS (PSI)
PLYWOOD 03
PLYWOOD 4
Plywood
3000
PLYWOOD 5
PLASTIC (1) 1"
6"WIDE
PLASTIC (2) 1"
6"WIDE
PLASTIC (3) 1" 6"
WIDE
PLASTIC (4) 1" 3"
WIDE
PLASTIC (1) 1.5"
3" WIDE
2000
Fiber Reinforced Plastic
1000
0
0
0.005
0.01
0.015
0.02
STRAIN (in/in)
Figure 8) Stress vs. strain curve for each of the materials tested. The plywood tested was ¾” samples
6” wide and loaded over a span of 16”. The Fiber Reinforced Plastic (FRP) was tested in 4 different
configurations; 1” thick by 6” wide, 1” thick by 3” wide, 1.5” thick by 3” wide, and 1.5” thick by 6”
wide. Modulus of Elasticity values are calculated from the slope of each curve and listed in table 1.
Table 1: Results from the 3 point bend test
Page 63
Appendix H: External Search
External Search
The external search consists of identifying
correct material for the pallet design. The first thing
we looked at was a mold injected plastic pallet. The
mold injected pallets, seen in figure 1, have good
strength characteristics but the pallets were too big
in size. Mold injected pallets have a low price due to
Figure 1) Mass produced mold injected
them being mass produced with a generic size and
plastic pallet.
shape. Mass produced mold injected pallets on
average have a deck height of five inches; we have a constraint of three inches. The cost to
modify an existing pallet to meet specifications, like deck height, would cost too much. The cost
of a specially made pallet is much higher with a low production run making cost too high.
The current pallet is made entirely out of steel, shown in figure 1 on page 1, and was
found to be overbuilt. The all steel design is desirable due to the strength, durability, and
longevity of steel. By modifying the original pallet design the total weight of the pallet was
reduced by 26 pounds. The all steel design has all the qualities to make a good pallet but
exceeds the weight limit.
Figure 2) from left to right: Channel, Square Tubing, Flat Plate, and Angle are the different types
of steel used in making the current pallet.
The Capstone team found that choosing plywood
or fiber reinforced plastic for the pallet deck instead of
steel saved a total of 50 pounds weight. The steel frame
would allow the pallet to have strength and durability of
the original pallet while the different decking would
allow the pallet to be within the weight limit.
A fiber reinforced plastic grating (FRP) shown in
figure 3, was being considered due to its weather
resistance. The advantage to FRP is it is much more
Figure 3) Fiber-reinforced plastic
ridged that plywood while the disadvantage is the
walkway.
strength falls just short of plywood while being heavier;
plywood weighs two pounds per square foot and FRP weighs two and a half pounds per square
foot. FRP is a material having many of the characteristics needed for the pallet. The FRP is very
Page 64
durable, appearing to be a good candidate as the base plate. FRP’s service life would be only
dependant on the mechanical breakage by the forklifts; service life for plywood is around three
years and is still subject to mechanical breakage. The cost of the FRP is about $9 per square foot
making it much more than the cost of untreated plywood which is $1 per square foot; the cost
per square foot of plywood would increase if coatings were to be applied.
Plywood, seen in figure 4, has many advantages; it is light weight, readily available, has a
low cost, and strong. The disadvantage to using plywood is it decays when exposed to ultraviolet light and precipitation. The pallets are transported on both open and closed trailers from
Phoenix to Vancouver and see all types of weather conditions. We looked into two different
types of plywood; pressure treated and marine plywood.
Pressure treated and marine plywood have better
characteristics when exposed to the elements; we are also
looked into coating the untreated plywood to enhance its
characteristics but the cost of plywood increases by 150%.
Exterior grade plywood was chosen to be the decking
material because of its cost and durability to weather
elements.
Figure 4) ¾” exterior grade plywood
Page 65
Pallet Hardware
Name: Clevis Pin
System: Strap mounting
Description: 5/8” X 2-1/4” grade 5 Low carbon steel 1010 used to
retain the straps to the pallet.
Name: Cotter Pin
System: Strap mounting
Description: 1/8” X 1-1/2” Low carbon steel 1010 used to retain the
clevis pin in its location.
Name: Carriage Bolt
System: Plywood mounting
Description: 1/2”/13 X 2-1/2” Low carbon with a yield strength of
36,000 psi used to secure the plywood to the pallet.
Name: Washer
System: Plywood mounting
Description: 1/2” inner and 1” outer diameter used to spread the
force from the carriage bolt on the cross member to help secure the
plywood.
Name: Split Lock Washer
System: Plywood mounting
Description: 1/2” heavy split lock washer used to keep tension on the
nut of the carriage bolt to keep from vibrating lose over time.
Name: Nut
System: Plywood mounting
Description: 1/2”-13 heavy hex nuts used to tighten and create a
clamping force to secure the plywood to supporting cross members.
Page 66
Finish
The pallet will be painted with a two component acrylic urethane finish. The urethane
finish is formulated for direct-to-metal applications which cut down on the application time due
to no need to primer before painting. The urethane finish has superior gloss and color
retention and excellent UV stability while having a good resilience to impact as well as solvents,
oils, acids, and alkalis. The urethane finish can be applied by spraying, brushing, and/or rolling.
Acrylic urethane specifications and preparation/application can be found bellow.
Page 67
Project Plan
The three timeline tables are shown below; starting with the initial table at the
beginning of the project and two subsequent tables made current as the project progressed.
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Table 2) Project timeline Jan - June
Table 2) Project timeline March - June
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Table 3) Project timeline May - June
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House of Quality
This House of Quality is defines the relationship between customer desires and the
firm/product capabilities.
Table 2) The * symbol is a representation of how much the Demanded Quality and
Quality Characteristics correlate with each other. The symbol is read as (*) meaning
little correlation up to (*****) representing significant correlation.
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