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United Design Compilation: Final Design Report
SE 140
Dr. Van Den Einde
May 29th
, 2015
Team 1:
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Table of Contents
Acknowledgements:.................................................................................................................................. 4
1. Introduction and Project Purpose ....................................................................................................... 5
2. Company Mission & Team Responsibilities: ...................................................................................... 5
3. Conceptual Design ............................................................................................................................... 9
3.1 Structural System.............................................................................................................................. 9
3.1.1 Structural Deviations................................................................................................................ 14
3.2 Mechanical System ......................................................................................................................... 15
3.1.1 Mechanical Deviations............................................................................................................. 18
4. Theoretical and Computational Validation ...................................................................................... 21
4.1 Validation ....................................................................................................................................... 22
4.2 Mechanical System ......................................................................................................................... 25
5. Member and Connection Design........................................................................................................ 28
5.1. Member Design.............................................................................................................................. 28
5.2. Connection Design:........................................................................................................................ 37
6. Structural Performance...................................................................................................................... 41
6.1 Assumptions ................................................................................................................................... 41
6.2 Analysis .......................................................................................................................................... 41
6.3 Failure Modes ................................................................................................................................. 45
7. Predicted Final Test Results............................................................................................................... 46
8. Final Test Results................................................................................................................................ 47
9. RoboPro............................................................................................................................................... 49
10. Budget................................................................................................................................................ 51
11. Challenges.......................................................................................................................................... 53
12. Ethics ................................................................................................................................................. 54
13. Life Long Learning........................................................................................................................... 55
13.1. Musco Arts Center Lecture .......................................................................................................... 55
13.2 Integrated Design Lecture ............................................................................................................. 55
13.3 Temporary Structures Lecture....................................................................................................... 56
14. Conclusion ......................................................................................................................................... 57
References................................................................................................................................................ 57
Appendix A: ............................................................................................................................................ 58
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Project Schedule/Timeline: ................................................................................................................... 58
Team Hours: ......................................................................................................................................... 62
RoboPro Program: ................................................................................................................................ 63
Bill of Materials:................................................................................................................................... 63
Project Drawings: ................................................................................................................................. 66
Multi-Media:......................................................................................................................................... 70
Appendix B:............................................................................................................................................. 71
Hand Calculations Detail: ...................................................................................................................... 71
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Acknowledgements:
The team would like to thank Dr. Van Den Einde, Mr. Steve Porter and the SE 140 TAs for their
continued efforts in providing the skills and tools needed to complete the SE Senior Capstone
Project. A project that covers four years of curriculum and learning also needed time, effort and
patience to complete but it was ultimately doable due to your continued efforts and assistance,
and for that, you have our gratitude.
Thank You,
United Engineering (Team 1)
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1. Introduction and Project Purpose
The Port Authority for the City of San Diego has asked the firm to replace an aging crane that is
used to transfer cargo from docked ships at the port. They have also asked the assembled team to
build the stiffest possible crane, which will have limited deflection, and an efficient transfer time
for the cargo to go from the ships to warehouse.
The team started out with the goal of creating a crane that took into consideration the materials
properties, material cost, practicability and aesthetics all while having an efficient structural and
mechanical system. Ultimately the safety of the public was paramount, which is why the final
crane design was fabricated with the goal of carrying the cargo with the highest weight at a slow
but efficient time in order to ensure that all systems have a chance to dampen and lessen
unnecessary motion.
2. Company Mission & Team Responsibilities:
The team’s mission was to design and build a crane for the Port Authority of San Diego that was
able to pick up the heaviest cargo (the gold weights) while having a structural system with
minimum deflection and a slower paced mechanical system to ensure that the structural system
would not fatigue while in use. A well-paced and secure mechanical system ensures that the
operator has complete control of the crane; this limits swinging of the cargo and in turn secures
the safety of the public. Furthermore, the team also aimed to design a structural system that
carried the cargo over neighboring cruise ship terminal property.
United Engineering is qualified to perform the tasks for the crane project due to the team’s
competency in the pertinent engineering principles along with its diverse disciplinary focus. The
team having nearly completed UCSD’s SE program and with eight of the ten team members
having been accepted into graduate school programs, concepts surrounding structural analysis,
dynamics, modeling, and steel connection design are quite clear after years of practice. The
team’s mechanical engineer, Andrey Uvarov, is a top student in the Aerospace department and
has contributed his expertise to micro aspects of the project while those with focuses in Civil and
Geotechnical Engineering have concentrated on the macro aspects such as the structural system
of the crane.
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Table 1 below lists the team members and their contributions to the project.
Table 1: Member Contributions
Member Title Contribution
Farshad
Alimohamadi
Project
Engineer
As Project engineer, Mr. Alimohamadi had a hand in all three
phases: design, construction and testing. This included the
design of members and connections, aiding in fabrication as
well as helping on the Solidworks modeling and motion
simulations.
Documents Contributed To:
1. Conceptual Design Report
2. Water Jet DXF Submission
3. Solidworks Motion Study
4. Final Report and Presentation
Jorge
Balderrama
Integrated
Designer
As the integrated designer, Mr. Balderrama contributed to the
Solidworks modeling, steel connection design as well as
ensuring that the crane’s aesthetics were planned correctly by
having proper placement of members and proper wire
management.
Documents Contributed To:
1. Hand Calculations Report
2. Steel Member and Connection Design Report
3. Final Report and Presentation
Ryan
Bourdette
CEO/CFO Mr. Bourdette was the CEO during the project; this included
creating schedules as well as handling of any conflicts that
arose during the design, construction and testing phases. Mr.
Bourdette also kept in communication with the port authority
when questions or concerns arose. In a project that includes ten
members, it was important for everyone be aware of their
responsibilities and deadlines in order for the deliverables to be
turned in a timely and efficient manner.
Furthermore, as acting CFO Mr. Bourdette created an initial
estimation of the budget and then kept track of the accumulated
costs during construction and testing.
Documents Contributed To:
1. Conceptual Design Report
2. Analysis Validation Report
3. Final Report and Presentation
Javier Construction As the main construction engineer, Mr. Buenas was responsible
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Buenas Engineer for the fabrication of the crane as well as the installation of the
mechanical system. Having what is arguably the most
important part in the project, Mr. Buenas used his experience in
the construction industry to provide the team with state of the
art tools and techniques to ensure a structurally sound crane
would be built to the satisfaction of the design engineer. Mr.
Buenas was also responsible for the parts of the technical
documents that were related to his involvement.
Documents Contributed To:
1. Conceptual Design Report
2. Final Report and Presentation
Mohamed
Elgabaly
Structural
Designer
As the structural designer, Mr. Elgabaly provided the design
iterations needed to create a structure with minimum deflection
and proper rigidity. This includes the placement of diagonal
members on both the arm and the boom as well as the inclusion
of cables for increased stiffness. This process included
SAP2000 revisions as well as a sound grasp of engineering
principles in order to make the necessary changes.
Documents Contributed To:
1. Conceptual Design Report
2. Analysis Validation Report
3. Solidworks Motion Simulation
4. Final Report and Presentation
William
Fuentes
Structural
Analyst
As the structural analyst, Mr. Fuentes was responsible for
checking the designs provided by the structural designer and
mechanical engineer. This included a proper understanding of
the structure’s load path while identifying the critical members
and connections by using SAP2000, RISA and hand
calculations.
Documents Contributed To:
1. Hand Calculations Report
2. Steel Member and Connection Design Report
3. Final Report and Presentation
Sinan
Habeeb
Technical
Writer
Mr. Habeeb was responsible for all deliverables to the port
authority in a timely manner while also presenting explanations
provided by group members in a technical and professional
manner.
Documents Contributed To:
1. Conceptual Design Report
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2. Mechanical Systems Design Report
3. Analysis Validation Report
4. Steel Members and Connection Design Report
5. Pre-Test Report
6. Final Report and Presentation
Alan
Haduong
Control
Engineer
As the lead controls engineer, Mr. Haduong was responsible
for the creation of a Robo-Pro program that moved the crane in
the R, Theta and Z directions to the satisfaction of the
mechanical Engineer. Mr. Haduong also worked closely with
Mr. Uvarov in order to complete all schematics related to the
mechanical system as well as the Robo-Pro program.
Documents Contributed To:
1. Robo-Pro Submission
2. Mechanical Design Report
3. Final Report and Presentation
Ata Mohseni Integrated
Designer
As the second integrated designer, Mr. Mohseni communicated
with the structural designer and mechanical designer to ensure
that the final design can accommodate structural loads and
mechanical systems. Mr. Mohseni was also responsible for
ensuring that proper assumptions were made for the validation
reports as well as the steel connection report. Furthermore, he
was also responsible for the final report drawings.
Documents Contributed To:
1. Conceptual Design Report
2. Analysis Validation Report
3. Final Report and Presentation
Andrey
Uvarov
Mechanical
Engineer
As the lead mechanical engineer, Mr. Uvarov was responsible
for the design and fabrication of the mechanical system
including placement of pulleys, winches, sensors and other
related portions. Furthermore, Mr. Uvarov was responsible for
the corresponding calculations related to the mechanical system
such as dynamic response, friction, swinging as well as load
balancing. Lastly, Mr. Uvarov worked closely with Mr.
Haduong in order to finish the Robo-Pro and mechanical
collaboration.
1. Robo-Pro Submission
2. Mechanical Design Report
3. Final Report and Presentation
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3. Conceptual Design
3.1 Structural System
The team wanted to focus on providing the client with a crane that had an emphasis on structural
rigidity, aesthetics and of course cost effectiveness. The firm has also hired a mechanical
engineer for the design of the mechanical system components, ensuring the safe transfer of cargo
at the port at an efficient rate. The structure is also focused on constructability, featuring 0.75”
long L-channel brackets for the outer members on the base of the arm and 0.25” diameter tubes
for the internal bracing as well as the outer bracing for the arm.
The first initial design was focused on stiffness to limit deflection at the highest load while also
having sufficient room for the mechanical component. The first design, shown in Figure 1, had
no x-bracing in the tower in order to reduce material consumption. The design also had a cable
system connected at the arm of the crane in order to limit compression at the bottom of the
structure. The plan was to pre-tension the cables to relieve the loads on the critical members of
the structure.
Figure 1: First Design Iteration
However, since analysis of the first model yielded very high compression loads in the tower, the
decision was made to add x-bracing members, as shown in Figure 2. This would ensure that base
of the crane had enough support and bracing to resist buckling loads.
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Figure 2: Second Design Iteration
A third design iteration was done with an added pulley on the top of the tower instead of having
the cables tied to the structural members. This was done to allow for the moment to be
transferred to the end of the crane, acting as a counter-weight. Unnecessary zero-force members
that were connected to the end of the arm were also removed. Furthermore, the decision was
made to add JB weld epoxy to the connections to ensure structural rigidity, as shown in Figure 3.
However, the final design did not feature epoxy on the members as the bolts and washers were
deemed satisfactory in holding and distributing the maximum 10 lbs of force (gold weights) on
the structure.
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Figure 3: Third Design Iteration with Added Pulley
After doing three different iterations, the location of the critical sections were known and where
axial forces needed to be decreased and the members that were not critical in load reduction.
Reinforcement was added for torsional and lateral loading at the tip of the boom. The pre-
tensioned cables were also expanded to the bottom of the base to further transfer the loading to
the crane’s foundation. The boom also features straight track members that were added to
support against torsion and other lateral forces, as shown in Figure 4.
Figure 4: Added Lateral Support
These changes also aid in creating an easy installation platform for the mechanical system. The
final design keeps the L-brackets, cross bracing and extended cables from previous iterations as
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shown below in Figure 5. Figure 6 shows relevant dimensions of the crane while Figure 7
display a 2D and 3D views generated from solidworks.
Figure 5: Final Design with Dimensions
Figure 6: Relevant Dimensions
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Figure 7: 2D and 3D Views of Final Design
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3.1.1 Structural Deviations
As with any other large-scale project, there were some deviations between the final design
documents and the actual fabricated design. For starters, it was realized that the water-jet
members would be better used for the mechanical system rather than the top members of the
crane’s arm. Thus, 0.25” diameter rods were used for the top of the crane’s arm during
construction and subsequent testing. Additionally, the worm drive that was needed for the
mechanical system to function would occasionally pull off of motor when heavy weights were
applied. The construction engineer circumvented this issue by adding an extra member at the end
of the boom that pushed against the worm-drive and hold it in place, as shown below in Figure 8.
Figure 8: Added Plate to Support Worm Drive
Furthermore, since the winch for the pulley used in the mechanical system would occasionally
become unspooled and the mounting bracket would rotate around the bottom member, an
additional diagonal member was added at the top to ensure that the winch remained in place, as
shown below in Figure 9.
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Figure 9: Members Added to Stabilize Winch
Lastly, the worm drive needed stabilization as it spun. At times it would come unhinged at its
connection to the motor and also encounter large deflections due to the cargo. So a flattened tube
was wrapped around the worm drive to support it. This is shown below in Figure 10.
Figure 10: Added Worm-drive Support
3.2 Mechanical System
The mechanical system design that the team used was externally mounted. It features H-plate
panels that house four stabilization bars and a plate assembly suspended with cables. This design
was chosen because of its robustness. Since the goal was to lift the largest amount of weight, the
design has a large cross section and multiple mechanisms to prevent shaking and rotations. 2D
and 3D image of the mechanical system are presented below in Figure 11.
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Figure 11: 2D and 3D View of Mechanical System
In order to move the cargo from its initial position to the target destination, three degrees of
motion were considered. The first degree of motion, here forth referred to as β€œTheta”, is the
degree of rotation about the turntable. For the next degree of freedom, the distance along the
crane’s boom is to be considered and will be referred to as the β€œRadial Distance”. The final
degree of motion is the vertical distance from the table surface and will be referred to as the
β€œHeight”. By bolting the crane’s base to the rotating turntable provided, Theta is controlled
simply through the use of a Robopro script. However, there is potential for the cargo load to
oscillate during the transit, which will cause a different Theta than that of the crane’s boom. In
order to resist this additional motion, four force-stabilization rods were attached to the lift
platform that will be used to stabilize the load and prevent swinging (Figure 12).
Figure 12: Four Added Stabilization Rods
The radial distance is controlled through the use of a worm drive and nut attached (Figure 13) to
a cart. This cart uses a set of wheels (Figure 14) to traverse along a track attached to the exterior
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of the crane’s boom. With a motor mounted within the crane to rotate the worm drive, the cart
will be able to adjust its radial distance to accurately drop the cargo onto the target location,
which is set to a different radial distance than that of its starting location.
Figure 13: Worm-drive Attached to Cart
Figure 14: Wheels Used By Mechanical System Transfer Cargo
Finally, in order to pick up the cargo from its initial cradle and traverse over the wall, a motor
controlled winch will be used to adjust the lift platform’s height (Figure 15). The winch will be
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mounted to the turntable, and a system of pulleys will be used to redirect the line to the correct
position and to allow the platform to raise and lower.
Figure 15: Lift Platform
Previous iterations of the design had a total of two wheels on each side being used, but in order
to reduce force concentration two additional wheels were added to each side. There was also a
matter of only two pulleys being used to lift the weights on the platform, which only gave the
design a 1:1 mechanical advantage. This was corrected by adding a third pulley for a more
advantageous 2:1 mechanical operation. Figure 16 below shows this early design.
Figure 16: Early Iteration of Mechanical System
3.1.1 Mechanical Deviations
As with the structural system, the mechanical system also had deviations during construction
than the original planned drawings. For starters, the team original planned for only a single rail,
the team later decided to add a top rail as well in order to add additional stability for the cart
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system. If the weights shook or shifted, the top rail would provide some resistance. Furthermore,
some lubrication was added in order to allow the wheels to translate with very little friction. This
is shown below in Figure 17A.
Figure 17A: Double Rail System
There was also an issue with the force stabilizing bars being too long, thus the decision was
made to use a telescoping design. The goal was to have the larger tube fixed to the β€œH-panels”
and allow the smaller tube to slide in and out freely. Because the fixed rod was extended below
the β€œH-panel”, the smaller tube did not have to be as long as the original design. This design is
shown below in Figure 17B.
Figure 17B: Telescoping Rod Design
Furthermore, the design of the brace that held the worm-drive in place at the end of the boom
changed from the original design. The new design was easier to manufacture and easier to
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connect. Since the purpose of the piece is to just keep the worm drive level, a small and simple
design was used. This is shown below in Figure 18.
Figure 18: Smaller Worm-Drive Brace
Lastly, a β€œload deck” was added to the mechanical system to help distribute the weight. The
original system seemed to hold but was deflecting beyond comfortable levels. The new β€œload
deck” now distributes the load from the three main bars to the four bottom bars. This greatly
increased the moment of inertia of the cart structure and greatly minimized the deflection of the
three main bars. This is shown below in Figure 19.
Figure 19: Added Load Deck for Stabilization
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4. Theoretical and Computational Validation
The team started its validation by considering the truss element structure as the most efficient
type of structure. The truss structure is straightforward to construct, perform hand calculations on,
and carries aesthetic value. Several iterations of truss systems were analyzed using SAP2000 and
RISA. However, the final design contained X-bracing due to increased stability and decreased
maximum deflection. Also, the added cables are designed to connect the tip of the crane at its
base. The most important reason for using cable was to decrease member forces, decreasing
maximum deflection, and increasing the load capacity of the structure. In order to determine how
the crane would respond to different external loads, the team analyzed the crane through
SAP2000. In performing such computer analysis, the firm was able to determine critical
information such as member forces, reactions and deflection. Since the structure can be
considered symmetric with the assumed simplifications, hand calculations for only one side of
the crane were performed. A truss analysis was performed with method of sections to determine
the axial force in each member, the virtual work method was performed to find deflections, and
Euler’s equation was used as a check for buckling.
These calculations were performed in order to find all axial forces in members, displacement of
the end nodes (where maximum displacement occurs), and buckling loads for each member that
is in compression. It also enabled the team to confirm the location of critical elements and
confirm that these members would not undergo critical buckling.
Although SAP is a functional program for analyzing structures, it was also very crucial for the
team to confirm all results by way of hand calculations. In confirming such results, the firm was
able to make simplifications to the crane that would not only streamline the confirmation process
but would also still produce appropriate results. Of these simplifications, perhaps the most
important one, was that the team considered the crane as a truss and thus the moments were
released at all joints. In addition the team also decided to chance the crane’s fixed end support to
be simply supported in order to allow the crane to be externally determinant. Similarly, the team
also removed one diagonal member for every X-brace in order to allow the crane to be internally
determinant. After successfully simplifying the crane, the team was able to perform a truss
analysis through the use of virtual work in conjunction with the method of sections. In
performing this truss analysis, the team was able to determine deflections, member axial forces,
maximum displacement of the end node, as well as check for buckling in any members.
Appendix B contains pages that show the hand calculations. The first three pages of hand
calculation show the detailed method of sections calculations for member axial forces, while the
next three pages show detailed virtual work calculations that utilize a P and Q system to
determine the deflection in the structure. The last three pages show the utilization of Euler’s
buckling to determine the critical buckling of each member. Equations 1 and 2 were the primary
used equations for deflection in the virtual work method and Euler’s buckling, respectively.
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π·π‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘› =
𝑃𝑄𝐿
𝐴𝐸
(πΈπ‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘› 1)
Where P = force from P-system, Q = force from Q-system, L = length of member, A = cross
sectional area, and E = Young’s modulus
π‘ƒπ‘π‘Ÿ =
πΈπΌπœ‹2
( 𝐾𝐿)2
( πΈπ‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘› 2)
Where E= Young’s Modulus, I = second moment of inertia, k= effective length, and L=
unbraced length of member.
4.1 Validation
From the hand calculations, it was determined that the simplified truss will experience a
maximum deflection of 0.54 inches, a critical buckling load of 13,083.1 lb. for the L-channels,
and 358.6 lb. for the HSS (round tube) members. From the hand calculations, it was validated
that the capacity of the structure will in fact be higher than its demand. In comparison with the
SAP2000 model analysis however, the team did notice that there were slight discrepancies in the
results. From the SAP2000 model analysis, it was determined that the maximum deflection was
0.0406 in. without the cable and 0.038 in. with the cable. Furthermore, it was also determined
that the hand calculated axial forces of the bracing members were much higher in comparison to
the results generated from the SAP model analysis. To be able to adequately compare the
different sets of results, the following was determined:
Percentage Error
π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š π·π‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘› π‘Šπ‘–π‘‘β„Žπ‘œπ‘’π‘‘ πΆπ‘Žπ‘π‘™π‘’ =
0.0406 βˆ’ 0.054
0.0406
βˆ— 100 = 33%
π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š π·π‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘› π‘€π‘–π‘‘β„Ž πΆπ‘Žπ‘π‘™π‘’ =
0.038 βˆ’ 0.054
0.038
βˆ— 100 = 42.1 %
Furthermore, the critical members (shown in Figure 20) were analyzed in SAP2000 and through
hand calculations via truss analysis. The comparison of these calculations are shown in Table 2.
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Figure 20: Critical Members of Structure
Table 2: Deflection Comparison
Member Member Force, Hand
Calculations (lbs)
Member Force, SAP
(lbs)
Percent Error (%)
1 30 31.3 4.2
2 -35 -34.7 0.9
3 -35 -32.6 7.4
4 -30 -26.3 14.1
5 -24 -25.2 4.8
For Euler’s buckling, the realization is made that the buckling loads are too high for the loads
provided from the gold weights that the crane is lifting. The low un-braced length (3 inches) and
moment of inertia of the section are the biggest factors in the high calculated buckling load.
Because of this, the team saw the high calculated loads as simply a check that the structure will
not fail due to buckling.
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The discrepancy in these results is due to the simplifications that were made for the hand
calculations. In removing one diagonal member for every pair of X-bracing, the team is reducing
the amount of structural members available to resist all forces present and thus it makes sense
that the hand calculated forces are higher. In addition to increasing the axial force within all of
the members, the removal of the diagonal member also increases the member’s deflection
significantly as can be seen from the calculated percentage errors. Furthermore, the axial forces
in all of the members were further increased by idealizing the connections as having released
moments. Lastly it must also be pointed out that in simplifying the fixed end support to be
simply supported, the reactions were also reduced in comparison to the results obtained from the
SAP2000 analysis. Smaller reactions sound like a great deal for any design engineer, but one
must first notice that if the forces are not going to the supports, they are going to the crane’s
members. Even though the results for some of the hand calculations largely deviate from the
results obtained through SAP2000, it is important to determine the source of error for such
discrepancy and come to a conclusion as to whether or not the simplifications made could be
justified.
In the end, the team came to an assured conclusion in defending the simplifications made for the
hand calculations thanks to the following reason. The most critical sections of the crane are the
L-channels that are located at the top, bottom, left, and right chords of the crane, as displayed
previously. These chords serve as the most critical sections of the crane because together they
make up the load path that funnels most of the forces into the supports.
In comparing the forces at the L-channels for both the hand calculations and the SAP analysis, it
was determined that there is a very small deviation. This comparison allowed the team to feel
reassured about the simplifications made for the hand calculations and ultimately allowed the
hand calculations to serve as validation for the SAP results.
Since the hand calculations were made using a very conservative and simplified approach, the
firm determined that there was a sufficient capacity-to-demand ratio (factor of safety) for the
structure where no changes would be required. Hence, the configuration and modeling of the
crane were not changed. Furthermore, the previous design iterations that the team conducted in
the initial design phase eliminated any questionable design concept implementations that dealt
with how the cables and x-braces were handled.
As for changes to the crane itself, the hand calculations confirmed that there was some zero force
members in the simplified hand calculation model. In reality, these β€œzero force” members carry a
small force and contribute to the overall stability of the crane. In turn, the team decided that since
the members have a small load, members with a smaller cross-sectional area would be more
economic and better for spatial placement. The same conclusions were reached on vertical
bracing on top part of the crane (horizontal arm).
P a g e | 25
4.2 Mechanical System
For the mechanical system, the velocity and load capacity of critical members were calculated
with hand calculations. The velocity calculation used dynamic principles and was performed in
order to provide an adequate time estimates for the raising and lowering of the lifting platform,
which is needed for the Robopro programming. The main assumption that was made was there is
no dissipation (loss) of forces within the mechanical system. Furthermore, other insignificant
quantities like friction were ignored. The critical members were simplified as simply supported
beams with point loads on the center and the ends.
The velocity calculation yielded that the lifting of the platform occurs at one fourth of the
velocity of the motor. The calculation for velocity and the figure displaying the relevant
members can be seen below in Equation 3 and Figure 1, respectively.
Figure 21: Relevant Members for Velocity Calculation
4 βˆ— 𝑆2 + 𝑆1 = 𝑙 π‘π‘Žπ‘π‘™π‘’ (Equation 3)
4 βˆ— 𝑣2 + 𝑣1 = 0
𝑣2 = βˆ’ (
1
4
) βˆ— 𝑣1
Figure 22 below shows the start of the load path for the critical members of the mechanical
system. The lifting platform first disperses the load, W, to the supporting bracket in figure 22
below. The bracket disperses half the load, W/2, to each of the two pulleys on one side of the
crane.
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Figure 22: Loads Applied on Bracket
Figure 3 below shows the load being transferred from the bracket into the pulley wheels, and
lastly the string. Each pulley wheel has half the initial load of which half is dispersed to left and
right side of the string at each pulley wheel resulting in a load of W/4 in each side of the string
Figure 23: Load Transfer from Pulley Wheels into Attached Strings
The resulting force to the upper pulley shows that the final tension load on the motor is a load of
W/4. Therefore, the tension in the string that connects directly to the motor is 4 times lower the
total weight lifted by the crane. Hence the mechanical advantage is 4:1, thus an appropriate
motor was selected. This interaction is shown below in Figure 24.
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Figure 24: Final Pulley and Tension Load in String which is connected to the Motor
Figure 25 below shows the loading conditions that the critical rod member was analyzed for. The
loading has two point loads on each end to account for the connections to the wheel axles and
two central point loads to account for the force resultant from the lifting platform and the
attached weights. Figure 25 also contains the corresponding shear and moment diagrams.
Figure 25: Moment and Shear Diagrams
P a g e | 28
The following calculations were made to determine the critical force that the rod can handle. The
stress was calculated using equation below. Since the critical load capacity is larger than the
applied load, the design choice was validated.
𝜎 π‘šπ‘Žπ‘₯ =
𝑀 π‘šπ‘Žπ‘₯βˆ—π‘
𝐼
(Equation 4)
𝜎 π‘šπ‘Žπ‘₯ =
(
13π‘Š
20
) βˆ— (
5
2 βˆ— 32
)
πœ‹
32
βˆ— ((
5
32
)
4
βˆ’ (
4
32
)
4
)
= 1470 βˆ— π‘Š
π‘Šπ‘šπ‘Žπ‘₯ =
73244
1470
= 49.8 𝑙𝑏
Since the tube can handle about 50 lbs before kinking, a load of 15 lbs is well inside the safe
range.
5. Member and Connection Design
5.1. Member Design
The small scale model was enlarged and rescaled in order to for its members and connections to
be designed according to AISC.
Loading factor calculations for 10 lb load carrying model:
Assuming a 40 ton load for the real scale crane one can determine the scale factor (SF) from
Equation 5 below:
𝑆𝐹 =
π‘Žπ‘π‘‘π‘’π‘Žπ‘™ π‘™π‘œπ‘Žπ‘‘ π‘π‘Žπ‘Ÿπ‘Ÿπ‘¦π‘–π‘›π‘” π‘π‘Žπ‘π‘Žπ‘π‘–π‘‘π‘¦
π‘π‘Ÿπ‘œπ‘‘π‘œπ‘‘π‘¦π‘π‘’ π‘π‘Žπ‘Ÿπ‘Ÿπ‘¦π‘–π‘›π‘” π‘π‘Žπ‘π‘Žπ‘π‘–π‘‘π‘¦
(Equation 5)
𝑆𝐹 =
40(2000 𝑙𝑏𝑠)
10 𝑙𝑏𝑠
= 8000
From this, one can also determine the length scaling factor (SFL) through Equation 6 below:
𝑆𝐹𝐿 = √ 𝑆𝐹 = √8000 = 90 (Equation 6)
Likewise, one can determine the bending scale factor (SFB) through Equation 7 below:
𝑆𝐹𝐡 = 𝑆𝐹𝐿3
= 729,000 (Equation 7)
Below in Figure 26-A, one can find the two critical members that will be analyzed and designed
for this report. Critical member #1 is subjected to tension and bending while critical member #2
is subjected to compression and bending.
P a g e | 29
Figure 26A: Section Cut of the Crane Highlighting the Two Critical Members
Scaling for the critical tension and bending member (Member #1):
Using the appropriate scale factors, the following values were attained:
𝐹𝑇 = 0.024 π‘˜π‘–π‘π‘ (8000) = 192 π‘˜π‘–π‘π‘  (π‘‡π‘’π‘›π‘ π‘–π‘œπ‘› π‘“π‘œπ‘Ÿπ‘π‘’)
𝑀1 = 9.012 Γ— 10βˆ’5
π‘˜π‘–π‘ βˆ™ 𝑓𝑑 (729,000) = 66 π‘˜π‘–π‘ βˆ™ 𝑓𝑑
𝑀2 = 6.829 Γ— 10βˆ’5
π‘˜π‘–π‘ βˆ™ 𝑓𝑑 (729,000) = 50 π‘˜π‘–π‘ βˆ™ 𝑓𝑑
𝐿 π‘šπ‘’π‘šπ‘π‘’π‘Ÿ = 0.25 𝑓𝑑 (90) = 22.5 𝑓𝑑
The bending moment diagram for member #1 can be seen in Figure 26B below. Critical values
from this figure will be used for future calculations.
P a g e | 30
Figure 26B: Bending moment diagram for member #1
Scaling for the critical compression and bending member (Member #2):
Using the appropriate scale factors the following values were attained:
𝐹𝐢 = βˆ’0.02 π‘˜π‘–π‘π‘ (8000) = βˆ’176 π‘˜π‘–π‘π‘ 
𝑀1 = 2.922 Γ— 10βˆ’4
π‘˜π‘–π‘ βˆ™ 𝑓𝑑 (729,000) = βˆ’ 213 π‘˜π‘–π‘ βˆ™ 𝑓𝑑
𝑀2 = 5.317 Γ— 10βˆ’5
π‘˜π‘–π‘ βˆ™ 𝑓𝑑 (729,000) = 24 π‘˜π‘–π‘ βˆ™ 𝑓𝑑
𝐿 π‘šπ‘’π‘šπ‘π‘’π‘Ÿ = 0.25 𝑓𝑑 (90) = 22.5 𝑓𝑑
The bending moment diagram for member #2 can be seen in Figure 27 below. Critical values
from this figure will be used for future calculations.
Moment
(kip-ft)
Member Length (ft)
P a g e | 31
Figure 27: Bending moment diagram for member #2
Design of critical member subject to bending and tension (Member #1):
The member design according to AISC has to be carried by performing four steps as shown
below:
1- Design for Tension capacity using AISCM Chapter D.
2- Design for Compression capacity using AISCM Chapter E.
3- Calculate member flexural capacity using AISCM Chapter F.
4- Check capacity of one compression critical and tension critical member subjected to
bending moment using AISCM Chapter H (Ignore Torsion forces).
Step 1: Design for Tension Capacity
First, the required gross area which prevents the yielding limit state is calculated:
𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ =
𝑃𝑒
Ρ„ 𝑑
𝐹𝑦
=
192
0.9 βˆ— 60
= 3.5 𝑖𝑛2
𝑦𝑖𝑒𝑙𝑑𝑖𝑛𝑔 π‘™π‘–π‘šπ‘–π‘‘ π‘ π‘‘π‘Žπ‘‘π‘’ 𝑃𝑛 = 𝐹𝑦 βˆ— 𝐴 𝑔 (𝐴𝐼𝑆𝐢𝑀 𝐷2 βˆ’ 1)
Second, the required effective area which prevents rupture limit state is calculated:
𝐴 𝑒 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ =
𝑃𝑒
Ρ„ 𝑑
𝐹𝑒
=
192
0.75 βˆ— 65
= 3.93 𝑖𝑛2
π‘…π‘’π‘π‘‘π‘’π‘Ÿπ‘’ π‘™π‘–π‘šπ‘–π‘‘ π‘ π‘‘π‘Žπ‘‘π‘’ 𝑃𝑛 = 𝐹𝑒 βˆ— 𝐴 𝑒 (𝐴𝐼𝑆𝐢𝑀 𝐷2 βˆ’ 2)
Moment
(kip-ft)
Member Length (ft)
P a g e | 32
By using the obtained required effective area above, and using shear lag factor U=0.6 from AISC
manual table D3.1 case 8, the net effective required area is calculated below:
𝐴 𝑛 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ =
𝐴 𝑒 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘
π‘ˆ
=
3.93
0.6
= 6.56 𝑖𝑛2
Then, the New 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ which is function of thickness will be:
𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘= 𝐴 𝑛 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ + βˆ‘ 𝑑 βˆ— 𝑑 = 6.56 + (1 βˆ— 1.125 βˆ— 𝑑)
Third, the slenderness requirement will be checked:
𝐿
π‘Ÿ π‘šπ‘–π‘›
≀ 300 π‘ π‘œ π‘Ÿ π‘šπ‘–π‘› =
𝐿
300
=
22.5 βˆ— 12
300
= 0.9 𝑖𝑛
The larger 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ from first and second step governs the design. Since the
𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ required from the second step is function of thickness, few single angle shapes with
different thicknesses are listed below in Table 3 to chosen from.
Table 3: Single Angle Shapes
Thickness 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘
YLS
𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘
RLS
Size 𝐴 𝑔 π‘π‘Ÿπ‘œπ‘£π‘–π‘‘π‘’π‘‘ π‘Ÿ π‘šπ‘–π‘›(π‘₯, 𝑦) π‘Ÿπ‘§
3
8⁄ 3.5 6.98 N/A N/A N/A N/A
1
2⁄ 3.5 7.12 L8*8*1
2⁄ 7.84 2.49 1.59
9
16⁄ 3.5 7.19 L8*6*9
16⁄ 7.61 1.78 1.3
5
8⁄ 3.5 7.26 L8*6*5
8⁄ 8.41 1.77 1.29
By considering slenderness requirement and the gross area requirement for YLS and RLS, all
above sections would be suitable to choose. But the section with same angle length will be
chosen in order to simplify the construction. So L8*8*1
2⁄ with Ag = 7.84 would be used for
tension member.
The forth step of tension member design is checking the block shear of the tension member.
Block shear is the nominal resistance of tension member from tearing out of connection.
The nominal capacity for block shear is lesser of:
𝑅 𝑛 = 0.6𝐹𝑒 𝐴 𝑛𝑣 + π‘ˆπ‘π‘  𝐹𝑒 𝑅𝐴 𝑛𝑑 ≀ 0.6𝐹𝑦 𝐴 𝑔𝑣 + π‘ˆπ‘π‘  𝐹𝑒 𝐴 𝑛𝑑 (𝐴𝐼𝑆𝐢𝑀 𝐽4 βˆ’ 5)
𝑅 𝑛 = 912 ≀ 433 π‘˜π‘–π‘π‘ 
P a g e | 33
ф𝑅 𝑛 = 0.75 βˆ— 433 = 324.7 β‰₯ 𝑃𝑒 = 192 𝑂. 𝐾
Step 2: Design for Compression
According to AISCM chapter E, the nominal compressive strength Pn, shall be determined based
on limit state of flexural buckling.
𝑃𝑛 = πΉπ‘π‘Ÿ 𝐴 𝑔 ( 𝐴𝐼𝑆𝐢𝑀 𝐸3 βˆ’ 1)
When
𝐾𝑙
π‘Ÿ
≀ 4.71√
𝐸
𝐹𝑦
:
πΉπ‘π‘Ÿ = (0.658
𝐹𝑦
𝐹𝑒 ) 𝐹𝑦 (𝐴𝐼𝑆𝐢𝑀 𝐸3 βˆ’ 2)
When
𝐾𝑙
π‘Ÿ
> 4.71√
𝐸
𝐹𝑦
:
𝐹𝒄𝒓 = 0.877 𝐹𝑒 (𝐴𝐼𝑆𝐢𝑀 𝐸3 βˆ’ 3)
And Fe can be calculated by formula below:
𝐹𝑒 =
πœ‹2
𝐸
(
𝐾𝐿
π‘Ÿ
)
2 (𝐴𝐼𝑆𝐢𝑀 𝐸3 βˆ’ 4)
So according to the above formulas,
𝐾𝑙
π‘Ÿ
=
22.5 βˆ— 12
1.59
= 169.8 > 4.71√
𝐸
𝐹𝑦
= 103.5
𝐹𝑒 =
πœ‹2
𝐸
(
𝐾𝐿
π‘Ÿ
)
2 = 9.92
𝐹𝒄𝒓 = 0.877 𝐹𝑒 = 0.877 βˆ— 9.92 = 8.7π‘˜π‘ π‘–
𝑃𝑛 = πΉπ‘π‘Ÿ 𝐴 𝑔 = 8.7 βˆ— 7.84 = 68.2 π‘˜π‘–π‘π‘ 
Step 3: Design for Flexure
The chosen section L8*8*1
2⁄ with Ag = 7.84 has flexural capacity as calculated below:
𝑀 𝑝 = 𝐹𝑦
𝐴
2
( 𝑦𝑐 + 𝑦𝑑) = 𝐹𝑦 𝑍 (𝐴𝐼𝑆𝐢𝑀 𝐹2 βˆ’ 1)
P a g e | 34
𝑀 𝑝 = (60 βˆ— 15.1) = 906 π‘˜π‘–π‘. 𝑖𝑛 βˆ—
1
12
= 75.5 π‘˜π‘–π‘. 𝑓𝑑
Ρ„ 𝑏
𝑀 𝑛 = 0.9 βˆ— 75.5 = 67.95 β‰₯ 𝑀 𝑒 = 66 π‘˜π‘–π‘. 𝑓𝑑 𝑂. 𝐾
Design of critical member subject to bending and compression (Member #2):
For the design of the critical member, it was assumed that the member would be made out of
A572 grade 50 steel. The following stress values were determined from AISCM.
𝐹𝑒 = 65 π‘˜π‘ π‘–
𝐹𝑦 = 50 π‘˜π‘ π‘–
After this assumption was made, it was crucial to determine the maximum moment (𝑀 𝑒) that the
member would be expected to withhold. From Figure 27, one can see that 𝑀 𝑒 for this member is
213 kip-ft.
The next step was to determine the effective lengths of the member in both the x and y directions.
From AISCM Chapter E it was determined that because the member is un-braced, the effective
lengths are equal in both directions. From this, one will get the following:
(𝐾𝐿) π‘₯ = (𝐾𝐿) 𝑦 = 22.5 𝑓𝑑
After determining the effective lengths, one must resort to the β€œM table” that was provided in SE
150 for calculating 𝑃𝑒(π‘’π‘ž) for the factored moment. The section of the β€œM table” relevant to the
type of steel being used for this design can be found in Table 4 below.
Table 4: M table Values Based on Member’s Effective Length and Steel Properties
𝐹𝑦 50 ksi
KL (ft) 10 12 14 16 18 20 22 and over
All
shapes
1.9 1.8 1.7 1.6 1.4 1.3 1.2
In the table above, KL is based on weak-axis buckling. Since it is known that the section is
angled, KL is taken with respect to π‘Ÿπ‘§ so the first approximation is made using Table 4-11 from
AISCM. In combination with this table, Equation 8 below will allow one to calculate𝑃𝑒(π‘’π‘ž).
𝑃𝑒(π‘’π‘ž) = 𝑃𝑒 + π‘šπ‘€ 𝑒 = 176 + 1.2(213) = 431.6 π‘˜π‘–π‘π‘  (Equation 8)
From here, one can now enter AISCM Table 4-22 with (𝐾𝐿) 𝑦 = 22.5 𝑓𝑑 and 𝑃𝑒(π‘’π‘ž) =
431.6 π‘˜π‘–π‘π‘ . From the table, one can designate the section to be L8 x 8 x 9/8” which has the
following factored nominal capacity, πœ™π‘ 𝑃𝑛 = 446 π‘˜π‘–π‘π‘ . Furthermore the length of the selected
member, (𝐾𝐿) 𝑧 = 8 𝑓𝑑, is less than the effective length, (𝐾𝐿) 𝑦, thus it is acceptable. Now one
must proceed to verify if the member satisfies the P-M interaction requirement.
P a g e | 35
𝑀 𝑒 = 𝐡1 𝑀 𝑛𝑑
From AISCM p.16-231
𝑃𝑒𝑙 =
πœ‹2 𝐸𝐼 π‘₯
(𝐾𝐿)2 =
πœ‹2(29000)(98.1)
(8Γ—12)2 = 3047 π‘˜π‘–π‘π‘  (Equation 9)
𝐡1 =
𝑐 π‘š
1βˆ’
𝑃 π‘Ÿ
𝑃 𝑒𝑙
=
1.0
1βˆ’
176
3047
= 1.06 β‰ˆ 1.0 (Equation 10)
Hence the p-𝛿 effect is insignificant and the following remains:
𝑀 𝑒 = 𝐡1 𝑀 𝑛𝑑 = 213 π‘˜π‘–π‘ βˆ’ 𝑓𝑑
We compute πœ™ 𝑏 𝑀 𝑛, here the beam is unbraced and thus 𝑐 𝑏 = 1.0 and 𝐿 𝑏 = 𝐿 𝑝 so:
𝑀 𝑛 = 𝑐 𝑏 [𝑀 𝑝 βˆ’ (𝑀 𝑝 βˆ’ πœ™ 𝑏 𝐡𝐹(𝐿 𝑏 βˆ’ 𝐿 𝑝))]
𝑀 𝑛 = 𝑐 𝑏 𝑀 𝑝
πœ™π‘€ 𝑛 = 0.9𝑀 𝑝 = 0.9𝐹𝑦 𝑧 = 0.9(50)(31.6)
πœ™π‘€ 𝑛 = 118 π‘˜π‘–π‘ βˆ’ 𝑓𝑑
P-, interaction from AISCS 16-73
π‘ƒπ‘Ÿ
πœ™π‘ 𝑃𝑛
=
176
446
= 0.33 > 0.2
Therefore according to AISCS 16-74 one must use Equation xx below:
π‘ƒπ‘Ÿ
πœ™π‘ 𝑃𝑛
+
8
9
π‘€π‘Ÿ
πœ™ 𝑏 𝑀 𝑛
= 0.33 +
8
9
213
118
= 1.93 > 1 𝑁𝑂 𝐺𝑂𝑂𝐷
𝑆𝐸𝐢𝑇𝐼𝑂𝑁 𝐼𝑆 𝑁𝑂𝑇 𝐴𝐢𝐢𝐸𝑃𝑇𝐴𝐡𝐿𝐸
The biggest angle section fails under the conditions given so it is necessary to go and choose a
different section. A W-shaped section is selected because it has a bigger plastic section modulus
and hence a higher moment capacity. From AISCM, it is deemed that the most economical
section is W21 x 44.
For W21 x 44:
0.45 +
8
9
213
358
= 0.98 > 1 π‘‚πΎπ΄π‘Œ
𝑆𝐸𝐢𝑇𝐼𝑂𝑁 𝐼𝑆 𝐴𝐢𝐢𝐸𝑃𝑇𝐴𝐡𝐿𝐸
P a g e | 36
One must then proceed to the iteration process once more to check if W21 x 44 passes the beam
column checks. The β€œm” factor remains the same at m = 1.2 and thus 𝑃𝑒(π‘’π‘ž) will still be 431.6
kips. Below one will find the iteration calculations for the W21 x 44 section.
𝑀 𝑒 = 𝐡1 𝑀 𝑛𝑑
From AISCM p.16-231
𝑃𝑒𝑙 =
πœ‹2 𝐸𝐼 π‘₯
(𝐾𝐿)2 =
πœ‹2(29000)(843)
(22.5Γ—12)2 = 3309 π‘˜π‘–π‘π‘  (Equation 11)
𝐡1 =
𝑐 π‘š
1βˆ’
𝑃 π‘Ÿ
𝑃 𝑒𝑙
=
1.0
1βˆ’
176
3309
= 1.05 β‰ˆ 1.0 (Equation 12)
Once again, the P-𝛿 effect is insignificant so this means that 𝑀 𝑒 remains 213 kips.
From the 𝑍 π‘₯ table on page 3-25 from AISCM, one can determine the following:
𝐿 𝑃 = 4.45 𝑓𝑑 > 𝐿 𝑏 = 0 𝑓𝑑 (π‘’π‘›π‘π‘Ÿπ‘Žπ‘π‘’π‘‘) (AISCM, 3-25)
Since this is the case, the following is also true,
πœ™ 𝑏 𝑀 𝑛 = πœ™ 𝑏 𝑀𝑏 = 358 π‘˜π‘–π‘ βˆ’ 𝑓𝑑
π‘€π‘Ÿπ‘₯ =
358
0.9
= 398 π‘˜π‘–π‘ βˆ’ 𝑓𝑑
Now one must check the P-M interaction along with AISCS Table 6-1 and 6-3. From AISCS p
6.51 one can get the following values for the W 21 x 44 section.
𝐿 𝑏 = 0 𝑓𝑑, 𝑝 = 1.98 Γ— 103( π‘˜π‘–π‘π‘ )βˆ’1
, π‘Žπ‘›π‘‘ 𝑏 π‘₯ = 2.48 Γ— 103( π‘˜π‘–π‘ βˆ’ 𝑓𝑑)βˆ’1
π‘π‘ƒπ‘Ÿ =
1
1.98 Γ— 103
Γ— 176 = 0.089 ≀ 0.2
Hence one has to check:
1
2
π‘π‘ƒπ‘Ÿ +
9
8
( 𝑏 π‘₯ π‘€π‘Ÿπ‘₯) ≀ 1.0
1
2
(0.089) +
9
8
(
398
2.48 Γ— 103
) = 0.22 ≀ 1.0 π‘‚πΎπ΄π‘Œ
From the calculations, it is finally determined that the W21 x 44 section will in fact work for this
design.
P a g e | 37
5.2. Connection Design:
Through SAP2000 structural analysis, it was determined that the critical joint is going to be a
horizontal gusset plate that serves as the connection between the base and arm of the crane. From
the structural analysis, it was determined that the axial force for this member is -0.00142 kips.
The location of this critical joint can be seen in Figure 28 below. Furthermore in Figure 29, a
detail of the critical horizontal gusset plate is provided.
Figure 28: Section cut of the crane highlighting the critical joint
Figure 29: Detail of the Horizontal Gusset Plate (inches)
P a g e | 38
Critical axial member loading:
𝐹 = βˆ’0.00142 π‘˜π‘–π‘π‘  (8000) = 11.36 π‘˜π‘–π‘π‘ 
𝐿 = 5 𝑖𝑛. (90) = 37.5 𝑓𝑑
𝑑 = 1.5 𝑖𝑛. (90) = 11.25 𝑓𝑑
where F = member axial force, L = length of the member and d = bolt diameter.
Through the use of sound engineering judgment, the team came to a conclusion that the critical
connections (one on each side) are located between the tower and arm of the crane. The team
made sure to confirm their reasoning through SAP analysis. From here, the team resorted to the
AISC manual in order to determine the appropriate bolt size, spacing and edge distance
limitations, tensile and shear strength of bolts, and bearing strength at both holes. In addition to
the assumption that a 40 ton load was being used, the team also assumed that A572 Grade 50
steel was used throughout the entire design.
Bolt Size
In determining what type of bolts to use for the design, the team referred to Table J3.2: Nominal
Strength of Fasteners and Threaded Parts as well as Table J3.3: Nominal Hole Dimensions.
Through the use of Table J3.2, it was determined that the team should continue the design with a
Group A bolt where the threads are excluded from the shear plane. From the different
descriptions available, this description matched the team’s crane connection the best. Through
this designation, the team determined the following values that will be required for further
calculations:
π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ 𝑇𝑒𝑛𝑠𝑖𝑙𝑒 π‘†π‘‘π‘Ÿπ‘’π‘›π‘”π‘‘β„Ž, 𝐹𝑛𝑑 = 90 π‘˜π‘ π‘–
π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ π‘†β„Žπ‘’π‘Žπ‘Ÿ π‘†π‘‘π‘Ÿπ‘’π‘›π‘”π‘‘β„Ž, 𝐹𝑛𝑣 = 54 π‘˜π‘ π‘– (AISC Table J3.2)
From Table J3.3, the team elected to ¾” diameter bolts as a starting point. If this bolt size does
not provide the required strength, then the bolt size will have to be reconsidered. Through the use
of these two tables, the team was able to select ¾” diameter A325 bolts.
Spacing
Per AISC J3.3 and J3.5, the team was able to check for the minimum and maximum spacing
requirements. From J3-3, the AISC manual requires that the distance between the centers of the
bolts shall not be less than 2 2/3 times the nominal diameter. In addition, J3-3 states that a
minimum spacing of 3 times the nominal diameter is preferable.
P a g e | 39
𝑠 π‘šπ‘–π‘› = {
8
3
𝑑 β†’
8
3
(.75") = 2"
3𝑑 β†’ 3(.75") = 2.25"
(AISC J3-3)
Furthermore, AISC J3-5 requires that the spacing not exceed a specific maximum spacing. From
AISC J3-5, the maximum spacing required shall be the minimum of 24 times the thickness of the
connected part or 12”.
𝑠 π‘šπ‘Žπ‘₯ = {
24(𝑑 𝐺𝑃) β†’ 24(3.6") = 86.4"
12"
(AISC J3-3)
where 𝑑 𝐺𝑃 = gusset plate thickness.
𝑑 𝐺𝑃 = 0.04" (90) = 3.6"
Due to the fact that the length of the gusset plate is 37.5 feet, the team elected to go with a
spacing of 86.4”. A larger spacing between the bolts will also aid the bolt’s shearing strength.
Minimum Edge Distance:
Per AISC J3-4, the minimum edge distance is determined based on the bolt diameter. The section
then refers one to Table J3.4 which lists all of the minimum edge distances for different bolt
sizes. From Table J3.4, the team determined that the minimum edge distance ought to be 1”.
Tensile and Shear Strength of Bolts:
Per AISC J3.4, the design tensile or shear strength can be determined from the bolt area and the
nominal stress.
πœ™π‘… 𝑛 = 𝐹𝑛 𝐴 𝑏 (J3-1)
where 𝐹𝑛 = nominal stress, 𝐴 𝑏 = bolt area, and πœ™ (strength reduction factor) = 0.75.
One can obtain both the tensile and shear strength of the bolt by using Equation J3-1 with the
respective nominal stresses for tensile and shear.
Tensile Strength:
𝐹𝑛𝑑 = 90 π‘˜π‘ π‘–, 𝐴 𝑏 = (
πœ‹
4
(3/4)2
) = 0.442 𝑖𝑛.2
π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘™π‘‘π‘  = 5 (J3-1)
πœ™π‘… 𝑛𝑑 = .75(90 π‘˜π‘ π‘–(0.442 𝑖𝑛.2 )) Γ— 5 π‘π‘œπ‘™π‘‘π‘ 
πœ™π‘… 𝑛𝑑 = 149.2 π‘˜π‘–π‘π‘  (𝑑𝑒𝑛𝑠𝑖𝑙𝑒 π‘π‘œπ‘™π‘‘ π‘ π‘‘π‘Ÿπ‘’π‘›π‘”π‘‘β„Ž)
P a g e | 40
Shear Strength:
𝐹𝑛𝑣 = 54 π‘˜π‘ π‘–, 𝐴 𝑏 = (
πœ‹
4
(3/4)2
) = 0.442 𝑖𝑛.2
π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘™π‘‘π‘  = 5 (J3-1)
πœ™π‘… 𝑛𝑑 = .75(54 π‘˜π‘ π‘–(0.442 𝑖𝑛.2 )) Γ— 5 π‘π‘œπ‘™π‘‘π‘ 
πœ™π‘… 𝑛𝑑 = 89.5 π‘˜π‘–π‘π‘  (π‘ β„Žπ‘’π‘Žπ‘Ÿ π‘π‘œπ‘™π‘‘ π‘ π‘‘π‘Ÿπ‘’π‘›π‘”π‘‘β„Ž)
Both the tensile and shear bolt strengths of the bolt are greater than the demand of 11.36 kips.
With this being said, the bolts will not fail under the current loading conditions.
Bearing Strength at bolt holes:
Per AISC J3.10, the bearing strength at bolt holes can be calculated for different conditions.
From all of the conditions listed, the team decided that the following equation best agreed with
the connection design:
πœ™π‘… 𝑛 = 1.2𝑙 𝑐 𝑑𝐹𝑒 ≀ 2.4𝑑𝑑𝐹𝑒 (J3-6a)
Where 𝑙 𝑐 = clear distance (in direction of force), 𝑑 = thickness of connected material, 𝑑 = bolt
diameter, 𝐹𝑒= material tensile strength, and πœ™(strength reduction factor) = 0.75
𝑙 𝑐 = 86.4 (distance between holes), Fu=65 ksi, t=tGP=3.6", 𝑑 = 3/4"
πœ™π‘… 𝑛 = 1.2(86.4)(3.6)(65) ≀ 2.4 (
3
4
) (3.6)(65)
πœ™π‘… 𝑛 = 24,261.12 π‘˜π‘–π‘π‘  ≀ 421.2 π‘˜π‘–π‘π‘ 
πœ™π‘… 𝑛 = 421.2 π‘˜π‘–π‘π‘  π‘π‘’π‘Ÿ π‘π‘œπ‘™π‘‘
Thus the total bearing strength for all five bolts will be:
πœ™π‘… 𝑛 = 5(421.2) = 2106 π‘˜π‘–π‘π‘ 
Since the bearing strength of the bolts is greater than the demand, the design is acceptable.
Final Design of Critical Members and Connections:
It was observed that the angle-shaped section failed under the given conditions for the member
subjected to flexure and compression. For conservative purposes, the W21 x 44 section was
chosen for both the tension and compression members since its capacity is larger than that of the
L8 x 8 x 1/2. Moreover this design adds symmetry to the structure, which is a plus because it
drastically simplifies the construction process. Finally, the bolt size and spacing was determined
P a g e | 41
for the critical connection. From the calculations provided, the design team chose A325 bolts
with a ¾” diameter at a spacing of 86.4”.
6. Structural Performance
6.1 Assumptions
The model was analyzed with SAP2000 using fixed supports for the foundation of the crane
because the foundation will be bolted to the rotation table. The connections of the crane base and
arm were also modeled as fixed with no moment release because the construction phase of the
project involved connections with bolts, washers and epoxy for the critical connections, while all
connections were fixed using 4-40 bolts, #4 washers and #4 nuts. Furthermore, the SAP2000
model has members connected at their centroids rather realistic pinned binding.
The pulley was modeled as an external roller with an un-deformed cable. Instead of the rope
being fixed to the structure, a roller was added so the tension forces could be transferred all the
way down to the base so that the compression forces in base could be relieved, creating a more
desirable and realistic load path.
Furthermore, loading conditions were done in individual iterations with the structure being
assumed to be fully fixed, fully pinned and having full moment release in order to compare the
individual deflection contributions from axial and lateral forces. Thus, the decision was made to
model the structure’s connections as fully fixed because it was the closest to real world behavior.
6.2 Analysis
In order to analyze the structure, the team applied the weight of the golden cargo by having two
point loads of 5 pounds applied at the end of the boom as critical loads. These two loads
represent the permanent loads, as shown below in Figure 30. Furthermore, torsional loads are
also present when the structure is rotating in the theta direction when considering a 3D polar
axis of (R,Θ,Z) directions (Figure 31)
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Figure 30: Permanent Point Loads
Figure 31: Torsional Loads
P a g e | 43
The primary load originates at the end of the crane’s arm due to the weight of the cargo.
The load then travels through the diagonal and horizontal members at the right of the crane’s arm
to the left towards the crane’s tower. The load then travels vertically downward through the
vertical and diagonal members of the tower. Finally, the loads are transferred from the tower into
the base of the structure and then into the ground. The string also transfers part of the load, from
the end of the cranes arm to the tip of the tower, to the base of the tower, and finally into the
ground. Figure 32 displays the load path described.
Figure 32: Load Path
Next, a SAP2000 was done in order to analyze the vertical (point load) and torsional (rotational)
loading. A primary analysis was done using only the vertical loading. The red members are in
compression while the blue members are in tension, as is customary with SAP2000 analysis.
Figure 33 shows the analysis results for critical members based on the vertical loading analysis.
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Figure 33: Vertical Loading Analysis
A Second analysis was performed using a load combination taking into account torsion and
vertical loading, as shown below in Figure 34.
Figure 34: Combined Loading
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It is evident that when the torsional loads are applied, the axial forces in the members increase
considerably. However the first analysis would be more accurate since the crane is moving at a
very slow pace. The structures critical members are discussed in the validation section on page
21.
6.3 Failure Modes
From the analysis performed, a conclusion can be drawn as to how the crane will fail when
placed under critical loads. The first and most probable failure mode would happen at the tension
member at the top of the boom. Since the member at that connection had a hole it is possible that
it would fail under tension due to stress concentration, yielding of the member. The bolt being
stronger block shear would be observed in this mode as well.
The second mode of failure could occur at the connection where five members intersect with a
compression force of 30 lbs. This connection is critical and supports a large load. However the
team heavily reinforced this connection by adding an aluminum plate at that location which
increased the strength of the material. The third possible failure could occur at the maximum
compression member of 30 lb. Buckling is a possibility as well, but it is highly improbable (see
hand calculations for reference). The fourth possible failure could happen at the base because it
is only supported by three bolts hence creating a stress concentrations in the connections, block
shear can be observed in this failure mode as well. Figure 35 below shows the location of the
failure modes described.
Figure 35: Possible Failure Modes
P a g e | 46
7. Predicted Final Test Results
After acquiring a range for the predictions from the hand calculations section presented in
section 5, SAP2000, Solidworks and engineering intuition developed from previous coursework,
a factor of was used to increase the hand calculated deflection of 0.015 in to the official
prediction of 0.15 in. This correction factor accounts for the imperfections that are present in the
real world structure as opposed to its virtual counterpart. The virtual model on SAP2000 assumes
that connections and members are fabricated perfectly and the connections are fully rigid while
the real world structure could suffer from construction flaws.
Furthermore, the correction factor also accounts for any yielding from the fatigue that might
have occurred during testing . The structure was tested for a total of six hours in order to fully
calibrate the RoboPro program and ensure that that the mechanical system was fully operational .
The results are shown below in Figure 36 which were acquired after applying the loads at the end
of the crane to get the max deflection.
Figure 36: Deflection Predictions Generated From SAP2000
As for the prediction of the maximum load, an FEA analysis was done on the critical connections
shown below in Figure 37.
According to SAP and the assumptions taken into account
Max deflection is 0.15 inches
P a g e | 47
Figure 37: Maximum Load FEA
This member was chosen because it carries the most tension force and it is also deformed in
order for the connections to be properly installed. A finite element analysis was done in
solidworks with Aluminum 6061-T6 Material properties until the member reached its yielding
strength of 39,885 Psi. The team's final prediction of the maximum load that structure can hold
for the provided loading connections is 17 lbs.
8. Final Test Results
The final test results yielded were in accordance with the group's original goals of designing a
structure that was able to carry a high load with little deflection. This was evident by the team's
success in carrying the a total of forty-one (41) gold weights successfully from the port to the
warehouse for an unloading rate of 2.48 kg/min, which was first among the team's competing.
Furthermore, the deflection measurement was also very close to the team's prediction where the
measured deflection under 15 N was 0.17 in. as compared to the 0.15 in. predicted deflection for
a percent error of 11.71 %. The peak load was measured to be 65.58 lbs, as opposed to the 17 lb
prediction, resulting in a percent error of 227%. This was largely a result of the loading that
tested the top of the boom, whereas the crane was designed to be tested at the bottom of the
boom, where the L-channels are located. The failure location is shown below in Figure 38.
P a g e | 48
Figure 38: Member Failure at the Top of the Boom
Moreover, the crane was aesthetically pleasing, coming in second place with an overall
aesthetics score of 94.25%. The deciding factor was the cost, which was too high when
compared to the other groups. However, this was a direct result of unexpected testing and
material fees, which would not be as important on a large scale real world project. The team's
results are summarized in Table 3 below.
Table 3: Summarized Results
Quantity Score Placement
Unloading Rate 2.48 kg/min 1st
Aesthetics Score 94.25 % 3rd
Peak Load 65.58 3rd
Deflection at 15N 0.17 in 8th
Measured Deflection 4.35 in 15th
Structure Weight 2543.0 g 16th
Virtual Cost $263,802.60 15th
Structural Capacity $3,979 8th
Structural Economy $381,678 11th
Structural Performance $14,880 5th
Overall Performance $400,536 11th
The first critical failure that occurred was the rupture of the cables used to hold the crane down at
the base. However, since the crane was designed to go beyond the required loading, the structure
maintained a peak load past the rupture. Another contributing factor was that one of the base
plates that connected the crane to the table was not a perfect 90 degrees as the other two were,
causing a problem with the stability of the structure . Since the cables were no longer present to
resist deflection at peak load, the peak load deflection measurement suffered as a result (4.35).
P a g e | 49
9. RoboPro
To control the mechanical system of the crane, RoboPro was utilized to create a script capable of
managing the all the motors and sensors. For the script’s first iteration, the program primarily
consisted of three distinct control pathways (Figure 39), which would all run simultaneously to
independently control the radial, vertical, and theta directions. The leftmost path, outlined in blue,
was used control the rotation of the crane. The middle path, outlined in red, was used to control
the winch’s motion. Finally, the green path was used to specify the translation along the boom by
use of the worm drive. For all three pathways, the first step was to return to predefined home
positions which relied on hard mounted sensors upon the crane’s body. With this setup, the
program would be able to reliably start in the same location, regardless of the current position of
mechanical system. As the program continued, all three pathways would synchronize by waiting
for predefined inputs such as switch activations signaling the completion of a specific task. For
example, in the middle of the program, all three logic lines wait for I6 to complete a number of
counts. I6 refers to a revolution counter attached to the winch, so all 3 paths would wait for the
winch to complete a certain number of revolutions before continuing on their individual
subroutines. This would ensure that no step would interfere with any other step, such as
activating the worm drive before the magnets were picked up. Finally, after all steps were
completed, the crane would stop moving instead of returning to a home position because the
initial steps of the program would negate the necessity of resetting the crane.
Figure 39: Preliminary Robopro script
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However, during practice sessions several challenges were discovered with using RoboPro to
control the crane. The most immediate problem was the necessity of calibrating the number of
revolutions needed to raise and lower the winch as well as the precise placement of the switches.
In order to determine the crane calibrations, a time consuming trial and error method must be
used. Additionally, as each calibration was determined, the RoboPro program had to be manually
updated to reflect the new values and the switches required time for their adhesive mounts to
cure. With time during each practice session being extremely limited, it was a race against time
in order to update the script. While rushing to update the script, some changes weren’t
implemented properly and other bugs were introduced. Because of this, it was decided to rewrite
another script from scratch, with the intent of simplifying the logic paths as well as making any
updates easier to implement.
In the second revision of the script (Figure 40), the program was streamlined in order to reduce
complexity and probability of additional bugs as well as incorporating all the calibrations
determined during practice sessions. The basic logic behind the program is the same, in which
the crane starts by resetting to a home position. However the biggest change is the reduction of
steps of the winch subroutine, outlined in green. This was achieved by determining many of the
steps which slowed down the winch’s spooling speed was unnecessary to stably carry the loads,
even that of the gold weights. Because of this, many steps were eliminated which allowed for
better synchronization between all three individual subroutines.
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Figure 40: Revised RoboPro Script
10. Budget
The projected budget of $126,500 as seen in Table 4 below was far less than the actual budget of
$228,900 as seen in Table 5. The projected budget compared to the actual budget by way of
percent increase increased by 81%. The colossal difference in the budget was mainly due to
unexpected expenses and an underestimation of the quantity of material that would be necessary
for the completion of a successful crane. The projected budget was base on the initial design,
which changed a few times before and during construction. The changes in design led to major
unforeseen expenses for instance the mechanical system was originally going to have 20 parts
and it now has over 40 parts.
The structural system, which is primarily constructed of aluminum tubing and sheet material,
was only projected to have 25 thirty-six inch long tubes but the crane used over 50 thirty-six inch
long tubes. Fees for testing were also unexpected since the team planned to only test the crane
during the bonus and free testing weeks and earn the $5000 bonus. Instead the team only tested
P a g e | 52
during charged, expensive, and ridiculously expensive testing weeks due to an absence in
material availability, construction delays, and unrealistic expectations in regards to the amount of
time that was needed for testing to insure the crane was working properly. The doubling of the
quantity of many of the components of the crane and other unforeseen expenses can be seen to
account for the 81% increase in the budget. In the end, the largest project expense was for the
aluminum tubing and aluminum sheet material parts that were the primary components of the
structural and auxiliary systems of the crane and together cost $171,300 or 75% of the actual
budget.
Table 4: Detailed Projected Budget
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Table 5: Detailed Actual Budget
11. Challenges
As with any large scale engineering project, there are challenges in creating a schedule for a
large team with no conflicts. This was the case for the team as other projects and tasks would
often interfere with planned group meetings. In order to circumvent this, the CEO appointed
team members to their specific tasks while also assigning alternate roles in which the team
members would experts in one field and consultants in another. This ensured that when a primary
team member was unavailable to attend a group meeting, someone with knowledge of the
situation would be present.
Since the design was fairly simple, the structural system was constructed fairly easily, except for
the simple deviations explained in the conceptual design section of the report. As for the
mechanical system, one main challenge in building the system was that the mechanical design
creates various focused point loads on the rail of crane which in turn makes the rail a critical
member with potential of failure. This in turn circumvented by increasing the number of wheels
on rail for proper weight distribution. The force is less concentrated along the track rather than
having two critical points.
Furthermore, considering that the firm aims to transfer the highest weights possible, there is the
matter of rocking and tilt on the magnet platform that could be a safety and structural hazard.
The main challenge was ensuring that the transfer platform experienced as little vibrational
P a g e | 54
rocking as possible. This is due to the turbulence generated from the transient vibrational motion,
which raises the risk of the cart assembly falling off the track. This was dealt with by mounting a
total of four (two on each side) 10 in. long, 5/32 in. diameter force-stabilization bars to the 3" x
7" aluminum plate that will hold the electro magnets. This, along with the added eight wheels
(four on each side) lessens the motion with the platform and ultimately leads to a more safe and
accurate transfer of the weights with minimum rocking and tilt.
Finally, there was the matter of designing a rail system completely exposed on the top while still
being well supported. In order for this to work, small cross sectional brackets that were inserted
into the angle brackets so that the rods would be supported from the underside while leaving the
exposed in order for the cart to translate about the rail without obstruction.
12. Ethics
As an engineer, one has both social and professional obligations that one must uphold in order to
lead an appropriate and ethical practice. In 1914, the American Society of Civil Engineers
(ASCE) adopted a code of ethics in hopes of promoting the reputation and ethics of the
engineering profession. For over 100 years now the ASCE Code of Ethics has served as the
model for professional conduct of all civil engineers. The Code of Ethics is comprised of seven
canons that seek to provide all necessary guidance in hopes of leading an ethical engineering
career. Among these seven canons, there are two in particular that had extensive influence on all
of the engineers working on the crane project.
Due to the amount of work and size of the crane project, the engineering team was comprised of
ten members that all had different responsibilities based on their areas of expertise. Based on a
member’s particular skill set, such member was placed into one of the four subsets of teams:
either design, construction, mechanical systems, or documentation. The rationale behind the
specialization process is to ensure that members are only working within areas of their expertise.
As per the second canon of the ASCE Code of Ethics, β€œEngineers shall perform services only in
areas of their competence”. This canon limits engineers to the work that they may perform
during their career in hopes of preserving the safety and wellbeing of the public. In regards to the
crane project, members of the engineering team were only assigned work that they would be
comfortable in completing. This canon sanctioned a certain degree of accountability to all
members of the engineering team as they were expected to always produce deliverables that met
the standard of competent engineering. Team members were encouraged to seek assistance from
other team members whenever they experienced trouble performing their work. By working
together, team members were able to come an agreeable conclusion that would have to
ultimately be confirmed by either the project engineer or the CEO. Team members could have
chosen to lie or not confirm their analysis with consultants, which would have resulted in the
project being labeled a failure.
As an engineer, one must be able to claim all responsibility for their work. Within this huge
burden of responsibility, lies the safety and wellbeing of the public. Serving as the paramount
P a g e | 55
objective with all engineering projects, the safety and wellbeing of the public must always
remain the driving factor behind all engineering design. For this reason, the first canon of the
ASCE Code of Ethics states that "engineers shall hold paramount the safety, health and welfare
of the public and shall strive to comply with the principles of sustainable development in the
performance of their professional duties". With this canon serving as the primary objective, the
engineering team sought to design a structure that would provide adequate redundancy and
minimal deflection. In order to satisfy this design criteria, the team designed a structure that
would incorporate cable systems to help support the primary truss configuration of the crane.
Together, the two structural systems work cohesively to provide maximum stiffness and
ultimately minimal deflection of the crane. Furthermore, the crane's ability to be supported by
two different structural systems adds a degree of redundancy to the overall crane design. If the
structural supporting cables were to somehow fail, the crane would still be able to operate as a
result of the main structural support coming from the crane's trusses.
13. Life Long Learning
13.1. Musco Arts Center Lecture
In the Chapman University Musco Center for the Arts lecture by Lori Jue from KPFF-LA, the
design to construction process was thoroughly explained. It is the responsibility of the structural
and design engineers to ensure that the construction manager is fully aware of what the drawings
and plans convey on paper. Furthermore, plans should be as detailed as possible with little to no
guess work involved as it can create situations where complications could arise that can derail
the fabrication schedule.
In terms of the crane, it was important to have a project engineer present during construction.
Since the initial designs were simply straight lines connected at member centroids and
centerlines generated from SAP2000, the presence of a project engineer and the occasional
supervision of the design engineer helped the team’s contractor properly visualize the members
and connections of the crane in a three-dimensional aspect.
13.2 Integrated Design Lecture
In the integrated Design and Introduction to Architecture lecture by Ms.Daniela Deutsch from
the Woodbury and New Schools of Architecture a focus was made on integrated design. In
previous years, the architect would traditionally design the structure, then hand it off to the
structural engineer who would then bring in the electrical and mechanical engineers along with
the other trades. In recent times, the focus has shifted to everyone being involved in the project
from day one where the architect and engineers lay out the design and decide on a mutually
beneficial solution for all the problems that the design team is faced.
This relates to the design of the crane as the team decided that the design engineer, the
mechanical engineer, the RoboPro designer and head of construction should work on the initial
design together, ensuring that the final design would be feasible for each department. This
ultimately benefited the team by allowing the mechanical system to perfectly fit along with
P a g e | 56
structural system with little complications. While the different departments were ultimately
allowed to work in stages to complete their respective parts, it was crucial to have a cohesive unit
that kept in communications regarding modifications and feasibility of the other systems.
13.3 Temporary Structures Lecture
The Temporary Structures and the Construction Industry Lecture by Mr. Chong Kim from DH
Charles Engineering covered the importance of temporary structures during the construction
times. Oftentimes, false-work will be needed to keep the structure upright as other integral
members are either installed or repaired. Furthermore, it was also emphasized that a qualified
structural engineer needed to be onsite at times to ensure that everything is being constructed to
code and up to the satisfaction of the design engineer and the architect.
For the Robo-Crane, there were two false work structures that were created in order to ensure the
proper construction and stability of the crane. One of the two was made of wooden beams
connected at 90 degrees acting as a counterweight at the on the boom. Since there was no table to
simulate the ones provided by the port authority, it was necessary to keep the crane upright
during installation of the truss members on the boom and the base. Since there was a large
overturning moment due to the long arm of the crane, the two wooden beams ensured that the
crane would not fall over. Furthermore the team fabricated a plastic base that simulated the
Dover table provided by the port authority. The plastic base was then clamped down to a wooden
plank to simulate the testing day conditions and allow for easier access during the installation of
the mechanical system. The plastic base is show below in Figure 40. Since the mechanical
system deals a great deal with intricately placed parts on the boom, the previously used wooden
beams needed to be removed to allow for full access.
Figure 40: Plastic Base Used to Hold Structure During Construction
P a g e | 57
14. Conclusion
Overall, the project was an appropriate simulation of a real world engineering project in that a
design process was undertaken that covered all the typical steps in a design procedure. An initial
brainstorm lead to preliminary designs being evaluated with modeling programs such as
SAP2000, Solidworks and RISA. This iterative process ultimately led to a final design being
picked with limited deflection and efficient functionality all while being easy to fabricate and
adjust should complications arise during construction.
As expected, complications did occur as with any large scale real world project. The project and
construction engineers had to think on the fly and create solutions for problems that were not
necessarily discussed or accounted for in the original design, as discussed earlier in the report.
Finally, the structure was tested multiple times for its functionality and stiffness, similar to how a
building must pass inspection and code checks before being inhabited or put in us.
In terms of a broader academic scope, the project was an appropriate capstone project as it
covered a broad spectrum of classes including but not limited to statics, dynamics (relating to the
swinging in the mechanical system), vibrations (allowing the system to properly dampen before
dropping the weights), CAD modeling and analysis (analyzing and iterating designs as well as
analyzing the final design to ensure it met the necessary demands) , steel design (connection
design)as well as seismic design (designing for a given load to ensure minimum movement in the
structure). This project can extend into future coursework that is oriented around design where
the problem statements or client demands are vague and the engineer has to come up with an
entire design from scratch. What this ultimately does is it mold critical thinkers that are able to
take on challenges with little hesitation as the prior experience ultimately builds both the
confidence and knowledge to succeed in the real world.
References
Jue, Lori. "Chapman University Musco Center for the Arts." SE 140 Guest Lecture. UCSD, La
Jolla. 21 Apr. 2015. Lecture.
Deutsch, Daniela. "Integrated Design." SE 140 Guest Lecture. UCSD, La Jolla. 12 May 2015.
Lecture.
Kim, Chong. "Temporary Structures: DH Charles Engineering." SE 140 Guest Lecture. UCSD,
La Jolla. 7 May 2015. Lecture.
Steel Construction Manual. Fourteenth ed. N.p.: AISC, 2011. Print.
Van Den Einde. Robo Crane Competition 2015 Rules. La Jolla: SE 140 - Van Den Einde, 2015.
PDF.
Van Den Einde. Catalog Prices V14-1. La Jolla: SE 140 - Van Den Einde, 2015. PDF.
Van Den Einde. Conceptual Design Presentation Requirements. La Jolla: SE 140 - Van Den
Einde, 2015. PDF.
P a g e | 58
Van Den Einde. Conceptual Design & Analysis Report Requirements. La Jolla: SE 140 - Van
Den Einde, 2015. PDF.
Van Den Einde. Mechanical Design Report Requirements. La Jolla: SE 140 - Van Den Einde,
2015. PDF.
Van Den Einde. Analysis Validation Report (Hand Calculations) Requirements. La Jolla: SE 140
- Van Den Einde, 2015. PDF.
Van Den Einde. Motion Simulation Requirements. La Jolla: SE 140 - Van Den Einde, 2015. PDF.
Van Den Einde. Cost and Constraints for Aluminum Sheet Material. La Jolla: SE 140 - Van Den
Einde, 2015. PDF.
Van Den Einde. AISC Compliance Design. La Jolla: SE 140 - Van Den Einde, 2015. PDF.
Van Den Einde. SE 140 ROBO CRANE COMPETITION FINAL REPORT GUIDELINES. La
Jolla: SE 140 - Van Den Einde, 2015. PDF.
Appendix A:
Project Schedule/Timeline:
The project was on schedule for the most part. All the deliverables were completed by the
specified and planned dates. The main deviations from the schedule were for the primary
fabrication and the amount and dates of testing for the crane. The main reason for the delay in
fabrication was due to the unexpected time to receive the water jet parts from the fabricators and
the finalization of the design also took longer than expected. The delay in fabrication led to a
delay in testing. The original schedule planned for testing during Bonus and Free Testing weeks
for a total of two hours of testing. The construction delays pushed the initial testing to the
Charged Testing week for an interval of two hours. Following the initial testing it was realized
that additional testing was a must to insure the crane functioned as desired for the competition.
So testing was also conducted during the Expensive and Ridiculously Expensive testing weeks
each for an interval of two hours resulting in a total of six hours of testing over three weeks. A
detailed Gantt Chart can be seen below in Figure 41 and the corresponding Figure 42 shows the
dates in tabular form for the Gantt Chart. Table 6 then compares the planned schedule as laid out
on the Gantt Chart with the actual start and completion dates for the major deadlines and
milestones and whether they were achieved or delayed.
The items that were on the critical path and critical to completion of the project by the required
deadline and in accordance to the project schedule was mainly in sync with the deliverable
deadlines. The proposal presentation insured that the team was on track with our initial design
and plans. Next, the design and analysis report required the completion of the structural system
design and analysis. Following that the mechanical system design report assured that the
mechanical system design and analysis was completed. Thereafter, the initial RoboPro design
P a g e | 59
was completed for validation by the team’s supervisors. The supervisors would confirm that the
logic was sound and that the program would work during testing with only minor modifications.
The analysis validation was completed next and insured that the SAP analysis was reasonable
when compared to our hand calculations and would closely reflect our testing data. Afterwards,
the preliminary SolidWorks motion simulation was done to demonstrate the planned motions of
the crane and to see if there were any possible issues with the desired path for transporting the
cargo. Soon after, the steel connection report was completed in accordance with AISC to insure
that the design for the critical connections and members would satisfy their demand loads. All of
these critical steps insured that fabrication, testing, and performance during the competition
would be exceptional and completed by the deadline.
Table 6: Planned vs. Actual Schedule and Whether They Were Achieved or Delayed
P a g e | 60
Figure 41: Gantt Chart in Tabular Form
P a g e | 61
Figure 42: Gantt Chart for Major Deadlines and Milestones
P a g e | 62
Team Hours:
In Table 7 below are the team’s hours for the project. For simplification the time sheet was
organized by each school week of the quarter and the main tasks for the respective week are
listed accordingly. Team members have their own column in the table and listed the hours that
they worked each week. At the bottom of the table is the total hours spent on the project for each
respective team member and below that is their Working Hour Factor (WH). The Working Hour
Factor is calculated as follows, the team member’s hours divided by the average of the team’s
hours; maximum value is 1.10. Furthermore, the table also shows that each member contributed
100% effort to the project.
Table 7: Team Hours
P a g e | 63
RoboPro Program:
Figure 43: RoboPro Program
Bill of Materials:
The β€œDetailed Actual Budget’ table above lists all of the raw materials to purchase in order to
construct the crane. Once the materials are purchased the bill of materials in Table 8 and Table 9
can be used to construct the structural and mechanical system respectively. The tables list all
parts and quantities need in order to replicate the final design. The bills of material were
produced via SolidWorks from the team’s completed SolidWorks assembly.
P a g e | 64
Table 8: Bill of Material for the Structural System
P a g e | 65
Table 9: Bill of Material for the Mechanical System
P a g e | 66
Project Drawings:
Figures 43 to 45 show the relevant dimensions for the front, top and side views of the crane,
respectively.
Figure 43: Front View
P a g e | 67
Figure 44: Side View
P a g e | 68
Figure 45: Top View of Boom
Furthermore, Figures 46 and 47 show the relevant information for the L-channel and HSS round
sections, respectively.
Figure 16: L-channel Cross Sections
Figure 47: Circular HSS Cross Sections
P a g e | 69
Mechanical System:
Figures 47 and 48 show the relevant mechanical system dimensions:
Figure 47: H-Plate Dimensions
Figure 48: Mechanical System Dimensions
P a g e | 70
Multi-Media:
A video of the solidworks motion simulation can be found here:
https://www.youtube.com/watch?v=DBjk6-jTyH8&feature=youtu.be
A comprehensive cloud file can be found at the following link:
https://drive.google.com/folderview?id=0ByEi_zHS4ioofnN0RUJxeGJGbURpZzRIRlFpdDJud
ThtWXdHNXliWVZyRkFzU3JZWXlCa1E&usp=sharing
P a g e | 71
Appendix B:
Hand Calculations Detail:
P a g e | 72
P a g e | 73
P a g e | 74
P a g e | 75
P a g e | 76
P a g e | 77
P a g e | 78

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Team01_FinalReport

  • 1. P a g e | 1 United Design Compilation: Final Design Report SE 140 Dr. Van Den Einde May 29th , 2015 Team 1:
  • 2. P a g e | 2 Table of Contents Acknowledgements:.................................................................................................................................. 4 1. Introduction and Project Purpose ....................................................................................................... 5 2. Company Mission & Team Responsibilities: ...................................................................................... 5 3. Conceptual Design ............................................................................................................................... 9 3.1 Structural System.............................................................................................................................. 9 3.1.1 Structural Deviations................................................................................................................ 14 3.2 Mechanical System ......................................................................................................................... 15 3.1.1 Mechanical Deviations............................................................................................................. 18 4. Theoretical and Computational Validation ...................................................................................... 21 4.1 Validation ....................................................................................................................................... 22 4.2 Mechanical System ......................................................................................................................... 25 5. Member and Connection Design........................................................................................................ 28 5.1. Member Design.............................................................................................................................. 28 5.2. Connection Design:........................................................................................................................ 37 6. Structural Performance...................................................................................................................... 41 6.1 Assumptions ................................................................................................................................... 41 6.2 Analysis .......................................................................................................................................... 41 6.3 Failure Modes ................................................................................................................................. 45 7. Predicted Final Test Results............................................................................................................... 46 8. Final Test Results................................................................................................................................ 47 9. RoboPro............................................................................................................................................... 49 10. Budget................................................................................................................................................ 51 11. Challenges.......................................................................................................................................... 53 12. Ethics ................................................................................................................................................. 54 13. Life Long Learning........................................................................................................................... 55 13.1. Musco Arts Center Lecture .......................................................................................................... 55 13.2 Integrated Design Lecture ............................................................................................................. 55 13.3 Temporary Structures Lecture....................................................................................................... 56 14. Conclusion ......................................................................................................................................... 57 References................................................................................................................................................ 57 Appendix A: ............................................................................................................................................ 58
  • 3. P a g e | 3 Project Schedule/Timeline: ................................................................................................................... 58 Team Hours: ......................................................................................................................................... 62 RoboPro Program: ................................................................................................................................ 63 Bill of Materials:................................................................................................................................... 63 Project Drawings: ................................................................................................................................. 66 Multi-Media:......................................................................................................................................... 70 Appendix B:............................................................................................................................................. 71 Hand Calculations Detail: ...................................................................................................................... 71
  • 4. P a g e | 4 Acknowledgements: The team would like to thank Dr. Van Den Einde, Mr. Steve Porter and the SE 140 TAs for their continued efforts in providing the skills and tools needed to complete the SE Senior Capstone Project. A project that covers four years of curriculum and learning also needed time, effort and patience to complete but it was ultimately doable due to your continued efforts and assistance, and for that, you have our gratitude. Thank You, United Engineering (Team 1)
  • 5. P a g e | 5 1. Introduction and Project Purpose The Port Authority for the City of San Diego has asked the firm to replace an aging crane that is used to transfer cargo from docked ships at the port. They have also asked the assembled team to build the stiffest possible crane, which will have limited deflection, and an efficient transfer time for the cargo to go from the ships to warehouse. The team started out with the goal of creating a crane that took into consideration the materials properties, material cost, practicability and aesthetics all while having an efficient structural and mechanical system. Ultimately the safety of the public was paramount, which is why the final crane design was fabricated with the goal of carrying the cargo with the highest weight at a slow but efficient time in order to ensure that all systems have a chance to dampen and lessen unnecessary motion. 2. Company Mission & Team Responsibilities: The team’s mission was to design and build a crane for the Port Authority of San Diego that was able to pick up the heaviest cargo (the gold weights) while having a structural system with minimum deflection and a slower paced mechanical system to ensure that the structural system would not fatigue while in use. A well-paced and secure mechanical system ensures that the operator has complete control of the crane; this limits swinging of the cargo and in turn secures the safety of the public. Furthermore, the team also aimed to design a structural system that carried the cargo over neighboring cruise ship terminal property. United Engineering is qualified to perform the tasks for the crane project due to the team’s competency in the pertinent engineering principles along with its diverse disciplinary focus. The team having nearly completed UCSD’s SE program and with eight of the ten team members having been accepted into graduate school programs, concepts surrounding structural analysis, dynamics, modeling, and steel connection design are quite clear after years of practice. The team’s mechanical engineer, Andrey Uvarov, is a top student in the Aerospace department and has contributed his expertise to micro aspects of the project while those with focuses in Civil and Geotechnical Engineering have concentrated on the macro aspects such as the structural system of the crane.
  • 6. P a g e | 6 Table 1 below lists the team members and their contributions to the project. Table 1: Member Contributions Member Title Contribution Farshad Alimohamadi Project Engineer As Project engineer, Mr. Alimohamadi had a hand in all three phases: design, construction and testing. This included the design of members and connections, aiding in fabrication as well as helping on the Solidworks modeling and motion simulations. Documents Contributed To: 1. Conceptual Design Report 2. Water Jet DXF Submission 3. Solidworks Motion Study 4. Final Report and Presentation Jorge Balderrama Integrated Designer As the integrated designer, Mr. Balderrama contributed to the Solidworks modeling, steel connection design as well as ensuring that the crane’s aesthetics were planned correctly by having proper placement of members and proper wire management. Documents Contributed To: 1. Hand Calculations Report 2. Steel Member and Connection Design Report 3. Final Report and Presentation Ryan Bourdette CEO/CFO Mr. Bourdette was the CEO during the project; this included creating schedules as well as handling of any conflicts that arose during the design, construction and testing phases. Mr. Bourdette also kept in communication with the port authority when questions or concerns arose. In a project that includes ten members, it was important for everyone be aware of their responsibilities and deadlines in order for the deliverables to be turned in a timely and efficient manner. Furthermore, as acting CFO Mr. Bourdette created an initial estimation of the budget and then kept track of the accumulated costs during construction and testing. Documents Contributed To: 1. Conceptual Design Report 2. Analysis Validation Report 3. Final Report and Presentation Javier Construction As the main construction engineer, Mr. Buenas was responsible
  • 7. P a g e | 7 Buenas Engineer for the fabrication of the crane as well as the installation of the mechanical system. Having what is arguably the most important part in the project, Mr. Buenas used his experience in the construction industry to provide the team with state of the art tools and techniques to ensure a structurally sound crane would be built to the satisfaction of the design engineer. Mr. Buenas was also responsible for the parts of the technical documents that were related to his involvement. Documents Contributed To: 1. Conceptual Design Report 2. Final Report and Presentation Mohamed Elgabaly Structural Designer As the structural designer, Mr. Elgabaly provided the design iterations needed to create a structure with minimum deflection and proper rigidity. This includes the placement of diagonal members on both the arm and the boom as well as the inclusion of cables for increased stiffness. This process included SAP2000 revisions as well as a sound grasp of engineering principles in order to make the necessary changes. Documents Contributed To: 1. Conceptual Design Report 2. Analysis Validation Report 3. Solidworks Motion Simulation 4. Final Report and Presentation William Fuentes Structural Analyst As the structural analyst, Mr. Fuentes was responsible for checking the designs provided by the structural designer and mechanical engineer. This included a proper understanding of the structure’s load path while identifying the critical members and connections by using SAP2000, RISA and hand calculations. Documents Contributed To: 1. Hand Calculations Report 2. Steel Member and Connection Design Report 3. Final Report and Presentation Sinan Habeeb Technical Writer Mr. Habeeb was responsible for all deliverables to the port authority in a timely manner while also presenting explanations provided by group members in a technical and professional manner. Documents Contributed To: 1. Conceptual Design Report
  • 8. P a g e | 8 2. Mechanical Systems Design Report 3. Analysis Validation Report 4. Steel Members and Connection Design Report 5. Pre-Test Report 6. Final Report and Presentation Alan Haduong Control Engineer As the lead controls engineer, Mr. Haduong was responsible for the creation of a Robo-Pro program that moved the crane in the R, Theta and Z directions to the satisfaction of the mechanical Engineer. Mr. Haduong also worked closely with Mr. Uvarov in order to complete all schematics related to the mechanical system as well as the Robo-Pro program. Documents Contributed To: 1. Robo-Pro Submission 2. Mechanical Design Report 3. Final Report and Presentation Ata Mohseni Integrated Designer As the second integrated designer, Mr. Mohseni communicated with the structural designer and mechanical designer to ensure that the final design can accommodate structural loads and mechanical systems. Mr. Mohseni was also responsible for ensuring that proper assumptions were made for the validation reports as well as the steel connection report. Furthermore, he was also responsible for the final report drawings. Documents Contributed To: 1. Conceptual Design Report 2. Analysis Validation Report 3. Final Report and Presentation Andrey Uvarov Mechanical Engineer As the lead mechanical engineer, Mr. Uvarov was responsible for the design and fabrication of the mechanical system including placement of pulleys, winches, sensors and other related portions. Furthermore, Mr. Uvarov was responsible for the corresponding calculations related to the mechanical system such as dynamic response, friction, swinging as well as load balancing. Lastly, Mr. Uvarov worked closely with Mr. Haduong in order to finish the Robo-Pro and mechanical collaboration. 1. Robo-Pro Submission 2. Mechanical Design Report 3. Final Report and Presentation
  • 9. P a g e | 9 3. Conceptual Design 3.1 Structural System The team wanted to focus on providing the client with a crane that had an emphasis on structural rigidity, aesthetics and of course cost effectiveness. The firm has also hired a mechanical engineer for the design of the mechanical system components, ensuring the safe transfer of cargo at the port at an efficient rate. The structure is also focused on constructability, featuring 0.75” long L-channel brackets for the outer members on the base of the arm and 0.25” diameter tubes for the internal bracing as well as the outer bracing for the arm. The first initial design was focused on stiffness to limit deflection at the highest load while also having sufficient room for the mechanical component. The first design, shown in Figure 1, had no x-bracing in the tower in order to reduce material consumption. The design also had a cable system connected at the arm of the crane in order to limit compression at the bottom of the structure. The plan was to pre-tension the cables to relieve the loads on the critical members of the structure. Figure 1: First Design Iteration However, since analysis of the first model yielded very high compression loads in the tower, the decision was made to add x-bracing members, as shown in Figure 2. This would ensure that base of the crane had enough support and bracing to resist buckling loads.
  • 10. P a g e | 10 Figure 2: Second Design Iteration A third design iteration was done with an added pulley on the top of the tower instead of having the cables tied to the structural members. This was done to allow for the moment to be transferred to the end of the crane, acting as a counter-weight. Unnecessary zero-force members that were connected to the end of the arm were also removed. Furthermore, the decision was made to add JB weld epoxy to the connections to ensure structural rigidity, as shown in Figure 3. However, the final design did not feature epoxy on the members as the bolts and washers were deemed satisfactory in holding and distributing the maximum 10 lbs of force (gold weights) on the structure.
  • 11. P a g e | 11 Figure 3: Third Design Iteration with Added Pulley After doing three different iterations, the location of the critical sections were known and where axial forces needed to be decreased and the members that were not critical in load reduction. Reinforcement was added for torsional and lateral loading at the tip of the boom. The pre- tensioned cables were also expanded to the bottom of the base to further transfer the loading to the crane’s foundation. The boom also features straight track members that were added to support against torsion and other lateral forces, as shown in Figure 4. Figure 4: Added Lateral Support These changes also aid in creating an easy installation platform for the mechanical system. The final design keeps the L-brackets, cross bracing and extended cables from previous iterations as
  • 12. P a g e | 12 shown below in Figure 5. Figure 6 shows relevant dimensions of the crane while Figure 7 display a 2D and 3D views generated from solidworks. Figure 5: Final Design with Dimensions Figure 6: Relevant Dimensions
  • 13. P a g e | 13 Figure 7: 2D and 3D Views of Final Design
  • 14. P a g e | 14 3.1.1 Structural Deviations As with any other large-scale project, there were some deviations between the final design documents and the actual fabricated design. For starters, it was realized that the water-jet members would be better used for the mechanical system rather than the top members of the crane’s arm. Thus, 0.25” diameter rods were used for the top of the crane’s arm during construction and subsequent testing. Additionally, the worm drive that was needed for the mechanical system to function would occasionally pull off of motor when heavy weights were applied. The construction engineer circumvented this issue by adding an extra member at the end of the boom that pushed against the worm-drive and hold it in place, as shown below in Figure 8. Figure 8: Added Plate to Support Worm Drive Furthermore, since the winch for the pulley used in the mechanical system would occasionally become unspooled and the mounting bracket would rotate around the bottom member, an additional diagonal member was added at the top to ensure that the winch remained in place, as shown below in Figure 9.
  • 15. P a g e | 15 Figure 9: Members Added to Stabilize Winch Lastly, the worm drive needed stabilization as it spun. At times it would come unhinged at its connection to the motor and also encounter large deflections due to the cargo. So a flattened tube was wrapped around the worm drive to support it. This is shown below in Figure 10. Figure 10: Added Worm-drive Support 3.2 Mechanical System The mechanical system design that the team used was externally mounted. It features H-plate panels that house four stabilization bars and a plate assembly suspended with cables. This design was chosen because of its robustness. Since the goal was to lift the largest amount of weight, the design has a large cross section and multiple mechanisms to prevent shaking and rotations. 2D and 3D image of the mechanical system are presented below in Figure 11.
  • 16. P a g e | 16 Figure 11: 2D and 3D View of Mechanical System In order to move the cargo from its initial position to the target destination, three degrees of motion were considered. The first degree of motion, here forth referred to as β€œTheta”, is the degree of rotation about the turntable. For the next degree of freedom, the distance along the crane’s boom is to be considered and will be referred to as the β€œRadial Distance”. The final degree of motion is the vertical distance from the table surface and will be referred to as the β€œHeight”. By bolting the crane’s base to the rotating turntable provided, Theta is controlled simply through the use of a Robopro script. However, there is potential for the cargo load to oscillate during the transit, which will cause a different Theta than that of the crane’s boom. In order to resist this additional motion, four force-stabilization rods were attached to the lift platform that will be used to stabilize the load and prevent swinging (Figure 12). Figure 12: Four Added Stabilization Rods The radial distance is controlled through the use of a worm drive and nut attached (Figure 13) to a cart. This cart uses a set of wheels (Figure 14) to traverse along a track attached to the exterior
  • 17. P a g e | 17 of the crane’s boom. With a motor mounted within the crane to rotate the worm drive, the cart will be able to adjust its radial distance to accurately drop the cargo onto the target location, which is set to a different radial distance than that of its starting location. Figure 13: Worm-drive Attached to Cart Figure 14: Wheels Used By Mechanical System Transfer Cargo Finally, in order to pick up the cargo from its initial cradle and traverse over the wall, a motor controlled winch will be used to adjust the lift platform’s height (Figure 15). The winch will be
  • 18. P a g e | 18 mounted to the turntable, and a system of pulleys will be used to redirect the line to the correct position and to allow the platform to raise and lower. Figure 15: Lift Platform Previous iterations of the design had a total of two wheels on each side being used, but in order to reduce force concentration two additional wheels were added to each side. There was also a matter of only two pulleys being used to lift the weights on the platform, which only gave the design a 1:1 mechanical advantage. This was corrected by adding a third pulley for a more advantageous 2:1 mechanical operation. Figure 16 below shows this early design. Figure 16: Early Iteration of Mechanical System 3.1.1 Mechanical Deviations As with the structural system, the mechanical system also had deviations during construction than the original planned drawings. For starters, the team original planned for only a single rail, the team later decided to add a top rail as well in order to add additional stability for the cart
  • 19. P a g e | 19 system. If the weights shook or shifted, the top rail would provide some resistance. Furthermore, some lubrication was added in order to allow the wheels to translate with very little friction. This is shown below in Figure 17A. Figure 17A: Double Rail System There was also an issue with the force stabilizing bars being too long, thus the decision was made to use a telescoping design. The goal was to have the larger tube fixed to the β€œH-panels” and allow the smaller tube to slide in and out freely. Because the fixed rod was extended below the β€œH-panel”, the smaller tube did not have to be as long as the original design. This design is shown below in Figure 17B. Figure 17B: Telescoping Rod Design Furthermore, the design of the brace that held the worm-drive in place at the end of the boom changed from the original design. The new design was easier to manufacture and easier to
  • 20. P a g e | 20 connect. Since the purpose of the piece is to just keep the worm drive level, a small and simple design was used. This is shown below in Figure 18. Figure 18: Smaller Worm-Drive Brace Lastly, a β€œload deck” was added to the mechanical system to help distribute the weight. The original system seemed to hold but was deflecting beyond comfortable levels. The new β€œload deck” now distributes the load from the three main bars to the four bottom bars. This greatly increased the moment of inertia of the cart structure and greatly minimized the deflection of the three main bars. This is shown below in Figure 19. Figure 19: Added Load Deck for Stabilization
  • 21. P a g e | 21 4. Theoretical and Computational Validation The team started its validation by considering the truss element structure as the most efficient type of structure. The truss structure is straightforward to construct, perform hand calculations on, and carries aesthetic value. Several iterations of truss systems were analyzed using SAP2000 and RISA. However, the final design contained X-bracing due to increased stability and decreased maximum deflection. Also, the added cables are designed to connect the tip of the crane at its base. The most important reason for using cable was to decrease member forces, decreasing maximum deflection, and increasing the load capacity of the structure. In order to determine how the crane would respond to different external loads, the team analyzed the crane through SAP2000. In performing such computer analysis, the firm was able to determine critical information such as member forces, reactions and deflection. Since the structure can be considered symmetric with the assumed simplifications, hand calculations for only one side of the crane were performed. A truss analysis was performed with method of sections to determine the axial force in each member, the virtual work method was performed to find deflections, and Euler’s equation was used as a check for buckling. These calculations were performed in order to find all axial forces in members, displacement of the end nodes (where maximum displacement occurs), and buckling loads for each member that is in compression. It also enabled the team to confirm the location of critical elements and confirm that these members would not undergo critical buckling. Although SAP is a functional program for analyzing structures, it was also very crucial for the team to confirm all results by way of hand calculations. In confirming such results, the firm was able to make simplifications to the crane that would not only streamline the confirmation process but would also still produce appropriate results. Of these simplifications, perhaps the most important one, was that the team considered the crane as a truss and thus the moments were released at all joints. In addition the team also decided to chance the crane’s fixed end support to be simply supported in order to allow the crane to be externally determinant. Similarly, the team also removed one diagonal member for every X-brace in order to allow the crane to be internally determinant. After successfully simplifying the crane, the team was able to perform a truss analysis through the use of virtual work in conjunction with the method of sections. In performing this truss analysis, the team was able to determine deflections, member axial forces, maximum displacement of the end node, as well as check for buckling in any members. Appendix B contains pages that show the hand calculations. The first three pages of hand calculation show the detailed method of sections calculations for member axial forces, while the next three pages show detailed virtual work calculations that utilize a P and Q system to determine the deflection in the structure. The last three pages show the utilization of Euler’s buckling to determine the critical buckling of each member. Equations 1 and 2 were the primary used equations for deflection in the virtual work method and Euler’s buckling, respectively.
  • 22. P a g e | 22 π·π‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘› = 𝑃𝑄𝐿 𝐴𝐸 (πΈπ‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘› 1) Where P = force from P-system, Q = force from Q-system, L = length of member, A = cross sectional area, and E = Young’s modulus π‘ƒπ‘π‘Ÿ = πΈπΌπœ‹2 ( 𝐾𝐿)2 ( πΈπ‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘› 2) Where E= Young’s Modulus, I = second moment of inertia, k= effective length, and L= unbraced length of member. 4.1 Validation From the hand calculations, it was determined that the simplified truss will experience a maximum deflection of 0.54 inches, a critical buckling load of 13,083.1 lb. for the L-channels, and 358.6 lb. for the HSS (round tube) members. From the hand calculations, it was validated that the capacity of the structure will in fact be higher than its demand. In comparison with the SAP2000 model analysis however, the team did notice that there were slight discrepancies in the results. From the SAP2000 model analysis, it was determined that the maximum deflection was 0.0406 in. without the cable and 0.038 in. with the cable. Furthermore, it was also determined that the hand calculated axial forces of the bracing members were much higher in comparison to the results generated from the SAP model analysis. To be able to adequately compare the different sets of results, the following was determined: Percentage Error π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š π·π‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘› π‘Šπ‘–π‘‘β„Žπ‘œπ‘’π‘‘ πΆπ‘Žπ‘π‘™π‘’ = 0.0406 βˆ’ 0.054 0.0406 βˆ— 100 = 33% π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š π·π‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘› π‘€π‘–π‘‘β„Ž πΆπ‘Žπ‘π‘™π‘’ = 0.038 βˆ’ 0.054 0.038 βˆ— 100 = 42.1 % Furthermore, the critical members (shown in Figure 20) were analyzed in SAP2000 and through hand calculations via truss analysis. The comparison of these calculations are shown in Table 2.
  • 23. P a g e | 23 Figure 20: Critical Members of Structure Table 2: Deflection Comparison Member Member Force, Hand Calculations (lbs) Member Force, SAP (lbs) Percent Error (%) 1 30 31.3 4.2 2 -35 -34.7 0.9 3 -35 -32.6 7.4 4 -30 -26.3 14.1 5 -24 -25.2 4.8 For Euler’s buckling, the realization is made that the buckling loads are too high for the loads provided from the gold weights that the crane is lifting. The low un-braced length (3 inches) and moment of inertia of the section are the biggest factors in the high calculated buckling load. Because of this, the team saw the high calculated loads as simply a check that the structure will not fail due to buckling.
  • 24. P a g e | 24 The discrepancy in these results is due to the simplifications that were made for the hand calculations. In removing one diagonal member for every pair of X-bracing, the team is reducing the amount of structural members available to resist all forces present and thus it makes sense that the hand calculated forces are higher. In addition to increasing the axial force within all of the members, the removal of the diagonal member also increases the member’s deflection significantly as can be seen from the calculated percentage errors. Furthermore, the axial forces in all of the members were further increased by idealizing the connections as having released moments. Lastly it must also be pointed out that in simplifying the fixed end support to be simply supported, the reactions were also reduced in comparison to the results obtained from the SAP2000 analysis. Smaller reactions sound like a great deal for any design engineer, but one must first notice that if the forces are not going to the supports, they are going to the crane’s members. Even though the results for some of the hand calculations largely deviate from the results obtained through SAP2000, it is important to determine the source of error for such discrepancy and come to a conclusion as to whether or not the simplifications made could be justified. In the end, the team came to an assured conclusion in defending the simplifications made for the hand calculations thanks to the following reason. The most critical sections of the crane are the L-channels that are located at the top, bottom, left, and right chords of the crane, as displayed previously. These chords serve as the most critical sections of the crane because together they make up the load path that funnels most of the forces into the supports. In comparing the forces at the L-channels for both the hand calculations and the SAP analysis, it was determined that there is a very small deviation. This comparison allowed the team to feel reassured about the simplifications made for the hand calculations and ultimately allowed the hand calculations to serve as validation for the SAP results. Since the hand calculations were made using a very conservative and simplified approach, the firm determined that there was a sufficient capacity-to-demand ratio (factor of safety) for the structure where no changes would be required. Hence, the configuration and modeling of the crane were not changed. Furthermore, the previous design iterations that the team conducted in the initial design phase eliminated any questionable design concept implementations that dealt with how the cables and x-braces were handled. As for changes to the crane itself, the hand calculations confirmed that there was some zero force members in the simplified hand calculation model. In reality, these β€œzero force” members carry a small force and contribute to the overall stability of the crane. In turn, the team decided that since the members have a small load, members with a smaller cross-sectional area would be more economic and better for spatial placement. The same conclusions were reached on vertical bracing on top part of the crane (horizontal arm).
  • 25. P a g e | 25 4.2 Mechanical System For the mechanical system, the velocity and load capacity of critical members were calculated with hand calculations. The velocity calculation used dynamic principles and was performed in order to provide an adequate time estimates for the raising and lowering of the lifting platform, which is needed for the Robopro programming. The main assumption that was made was there is no dissipation (loss) of forces within the mechanical system. Furthermore, other insignificant quantities like friction were ignored. The critical members were simplified as simply supported beams with point loads on the center and the ends. The velocity calculation yielded that the lifting of the platform occurs at one fourth of the velocity of the motor. The calculation for velocity and the figure displaying the relevant members can be seen below in Equation 3 and Figure 1, respectively. Figure 21: Relevant Members for Velocity Calculation 4 βˆ— 𝑆2 + 𝑆1 = 𝑙 π‘π‘Žπ‘π‘™π‘’ (Equation 3) 4 βˆ— 𝑣2 + 𝑣1 = 0 𝑣2 = βˆ’ ( 1 4 ) βˆ— 𝑣1 Figure 22 below shows the start of the load path for the critical members of the mechanical system. The lifting platform first disperses the load, W, to the supporting bracket in figure 22 below. The bracket disperses half the load, W/2, to each of the two pulleys on one side of the crane.
  • 26. P a g e | 26 Figure 22: Loads Applied on Bracket Figure 3 below shows the load being transferred from the bracket into the pulley wheels, and lastly the string. Each pulley wheel has half the initial load of which half is dispersed to left and right side of the string at each pulley wheel resulting in a load of W/4 in each side of the string Figure 23: Load Transfer from Pulley Wheels into Attached Strings The resulting force to the upper pulley shows that the final tension load on the motor is a load of W/4. Therefore, the tension in the string that connects directly to the motor is 4 times lower the total weight lifted by the crane. Hence the mechanical advantage is 4:1, thus an appropriate motor was selected. This interaction is shown below in Figure 24.
  • 27. P a g e | 27 Figure 24: Final Pulley and Tension Load in String which is connected to the Motor Figure 25 below shows the loading conditions that the critical rod member was analyzed for. The loading has two point loads on each end to account for the connections to the wheel axles and two central point loads to account for the force resultant from the lifting platform and the attached weights. Figure 25 also contains the corresponding shear and moment diagrams. Figure 25: Moment and Shear Diagrams
  • 28. P a g e | 28 The following calculations were made to determine the critical force that the rod can handle. The stress was calculated using equation below. Since the critical load capacity is larger than the applied load, the design choice was validated. 𝜎 π‘šπ‘Žπ‘₯ = 𝑀 π‘šπ‘Žπ‘₯βˆ—π‘ 𝐼 (Equation 4) 𝜎 π‘šπ‘Žπ‘₯ = ( 13π‘Š 20 ) βˆ— ( 5 2 βˆ— 32 ) πœ‹ 32 βˆ— (( 5 32 ) 4 βˆ’ ( 4 32 ) 4 ) = 1470 βˆ— π‘Š π‘Šπ‘šπ‘Žπ‘₯ = 73244 1470 = 49.8 𝑙𝑏 Since the tube can handle about 50 lbs before kinking, a load of 15 lbs is well inside the safe range. 5. Member and Connection Design 5.1. Member Design The small scale model was enlarged and rescaled in order to for its members and connections to be designed according to AISC. Loading factor calculations for 10 lb load carrying model: Assuming a 40 ton load for the real scale crane one can determine the scale factor (SF) from Equation 5 below: 𝑆𝐹 = π‘Žπ‘π‘‘π‘’π‘Žπ‘™ π‘™π‘œπ‘Žπ‘‘ π‘π‘Žπ‘Ÿπ‘Ÿπ‘¦π‘–π‘›π‘” π‘π‘Žπ‘π‘Žπ‘π‘–π‘‘π‘¦ π‘π‘Ÿπ‘œπ‘‘π‘œπ‘‘π‘¦π‘π‘’ π‘π‘Žπ‘Ÿπ‘Ÿπ‘¦π‘–π‘›π‘” π‘π‘Žπ‘π‘Žπ‘π‘–π‘‘π‘¦ (Equation 5) 𝑆𝐹 = 40(2000 𝑙𝑏𝑠) 10 𝑙𝑏𝑠 = 8000 From this, one can also determine the length scaling factor (SFL) through Equation 6 below: 𝑆𝐹𝐿 = √ 𝑆𝐹 = √8000 = 90 (Equation 6) Likewise, one can determine the bending scale factor (SFB) through Equation 7 below: 𝑆𝐹𝐡 = 𝑆𝐹𝐿3 = 729,000 (Equation 7) Below in Figure 26-A, one can find the two critical members that will be analyzed and designed for this report. Critical member #1 is subjected to tension and bending while critical member #2 is subjected to compression and bending.
  • 29. P a g e | 29 Figure 26A: Section Cut of the Crane Highlighting the Two Critical Members Scaling for the critical tension and bending member (Member #1): Using the appropriate scale factors, the following values were attained: 𝐹𝑇 = 0.024 π‘˜π‘–π‘π‘ (8000) = 192 π‘˜π‘–π‘π‘  (π‘‡π‘’π‘›π‘ π‘–π‘œπ‘› π‘“π‘œπ‘Ÿπ‘π‘’) 𝑀1 = 9.012 Γ— 10βˆ’5 π‘˜π‘–π‘ βˆ™ 𝑓𝑑 (729,000) = 66 π‘˜π‘–π‘ βˆ™ 𝑓𝑑 𝑀2 = 6.829 Γ— 10βˆ’5 π‘˜π‘–π‘ βˆ™ 𝑓𝑑 (729,000) = 50 π‘˜π‘–π‘ βˆ™ 𝑓𝑑 𝐿 π‘šπ‘’π‘šπ‘π‘’π‘Ÿ = 0.25 𝑓𝑑 (90) = 22.5 𝑓𝑑 The bending moment diagram for member #1 can be seen in Figure 26B below. Critical values from this figure will be used for future calculations.
  • 30. P a g e | 30 Figure 26B: Bending moment diagram for member #1 Scaling for the critical compression and bending member (Member #2): Using the appropriate scale factors the following values were attained: 𝐹𝐢 = βˆ’0.02 π‘˜π‘–π‘π‘ (8000) = βˆ’176 π‘˜π‘–π‘π‘  𝑀1 = 2.922 Γ— 10βˆ’4 π‘˜π‘–π‘ βˆ™ 𝑓𝑑 (729,000) = βˆ’ 213 π‘˜π‘–π‘ βˆ™ 𝑓𝑑 𝑀2 = 5.317 Γ— 10βˆ’5 π‘˜π‘–π‘ βˆ™ 𝑓𝑑 (729,000) = 24 π‘˜π‘–π‘ βˆ™ 𝑓𝑑 𝐿 π‘šπ‘’π‘šπ‘π‘’π‘Ÿ = 0.25 𝑓𝑑 (90) = 22.5 𝑓𝑑 The bending moment diagram for member #2 can be seen in Figure 27 below. Critical values from this figure will be used for future calculations. Moment (kip-ft) Member Length (ft)
  • 31. P a g e | 31 Figure 27: Bending moment diagram for member #2 Design of critical member subject to bending and tension (Member #1): The member design according to AISC has to be carried by performing four steps as shown below: 1- Design for Tension capacity using AISCM Chapter D. 2- Design for Compression capacity using AISCM Chapter E. 3- Calculate member flexural capacity using AISCM Chapter F. 4- Check capacity of one compression critical and tension critical member subjected to bending moment using AISCM Chapter H (Ignore Torsion forces). Step 1: Design for Tension Capacity First, the required gross area which prevents the yielding limit state is calculated: 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ = 𝑃𝑒 Ρ„ 𝑑 𝐹𝑦 = 192 0.9 βˆ— 60 = 3.5 𝑖𝑛2 𝑦𝑖𝑒𝑙𝑑𝑖𝑛𝑔 π‘™π‘–π‘šπ‘–π‘‘ π‘ π‘‘π‘Žπ‘‘π‘’ 𝑃𝑛 = 𝐹𝑦 βˆ— 𝐴 𝑔 (𝐴𝐼𝑆𝐢𝑀 𝐷2 βˆ’ 1) Second, the required effective area which prevents rupture limit state is calculated: 𝐴 𝑒 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ = 𝑃𝑒 Ρ„ 𝑑 𝐹𝑒 = 192 0.75 βˆ— 65 = 3.93 𝑖𝑛2 π‘…π‘’π‘π‘‘π‘’π‘Ÿπ‘’ π‘™π‘–π‘šπ‘–π‘‘ π‘ π‘‘π‘Žπ‘‘π‘’ 𝑃𝑛 = 𝐹𝑒 βˆ— 𝐴 𝑒 (𝐴𝐼𝑆𝐢𝑀 𝐷2 βˆ’ 2) Moment (kip-ft) Member Length (ft)
  • 32. P a g e | 32 By using the obtained required effective area above, and using shear lag factor U=0.6 from AISC manual table D3.1 case 8, the net effective required area is calculated below: 𝐴 𝑛 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ = 𝐴 𝑒 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ π‘ˆ = 3.93 0.6 = 6.56 𝑖𝑛2 Then, the New 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ which is function of thickness will be: 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘= 𝐴 𝑛 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ + βˆ‘ 𝑑 βˆ— 𝑑 = 6.56 + (1 βˆ— 1.125 βˆ— 𝑑) Third, the slenderness requirement will be checked: 𝐿 π‘Ÿ π‘šπ‘–π‘› ≀ 300 π‘ π‘œ π‘Ÿ π‘šπ‘–π‘› = 𝐿 300 = 22.5 βˆ— 12 300 = 0.9 𝑖𝑛 The larger 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ from first and second step governs the design. Since the 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ required from the second step is function of thickness, few single angle shapes with different thicknesses are listed below in Table 3 to chosen from. Table 3: Single Angle Shapes Thickness 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ YLS 𝐴 𝑔 π‘Ÿπ‘’π‘žπ‘’π‘–π‘Ÿπ‘’π‘‘ RLS Size 𝐴 𝑔 π‘π‘Ÿπ‘œπ‘£π‘–π‘‘π‘’π‘‘ π‘Ÿ π‘šπ‘–π‘›(π‘₯, 𝑦) π‘Ÿπ‘§ 3 8⁄ 3.5 6.98 N/A N/A N/A N/A 1 2⁄ 3.5 7.12 L8*8*1 2⁄ 7.84 2.49 1.59 9 16⁄ 3.5 7.19 L8*6*9 16⁄ 7.61 1.78 1.3 5 8⁄ 3.5 7.26 L8*6*5 8⁄ 8.41 1.77 1.29 By considering slenderness requirement and the gross area requirement for YLS and RLS, all above sections would be suitable to choose. But the section with same angle length will be chosen in order to simplify the construction. So L8*8*1 2⁄ with Ag = 7.84 would be used for tension member. The forth step of tension member design is checking the block shear of the tension member. Block shear is the nominal resistance of tension member from tearing out of connection. The nominal capacity for block shear is lesser of: 𝑅 𝑛 = 0.6𝐹𝑒 𝐴 𝑛𝑣 + π‘ˆπ‘π‘  𝐹𝑒 𝑅𝐴 𝑛𝑑 ≀ 0.6𝐹𝑦 𝐴 𝑔𝑣 + π‘ˆπ‘π‘  𝐹𝑒 𝐴 𝑛𝑑 (𝐴𝐼𝑆𝐢𝑀 𝐽4 βˆ’ 5) 𝑅 𝑛 = 912 ≀ 433 π‘˜π‘–π‘π‘ 
  • 33. P a g e | 33 ф𝑅 𝑛 = 0.75 βˆ— 433 = 324.7 β‰₯ 𝑃𝑒 = 192 𝑂. 𝐾 Step 2: Design for Compression According to AISCM chapter E, the nominal compressive strength Pn, shall be determined based on limit state of flexural buckling. 𝑃𝑛 = πΉπ‘π‘Ÿ 𝐴 𝑔 ( 𝐴𝐼𝑆𝐢𝑀 𝐸3 βˆ’ 1) When 𝐾𝑙 π‘Ÿ ≀ 4.71√ 𝐸 𝐹𝑦 : πΉπ‘π‘Ÿ = (0.658 𝐹𝑦 𝐹𝑒 ) 𝐹𝑦 (𝐴𝐼𝑆𝐢𝑀 𝐸3 βˆ’ 2) When 𝐾𝑙 π‘Ÿ > 4.71√ 𝐸 𝐹𝑦 : 𝐹𝒄𝒓 = 0.877 𝐹𝑒 (𝐴𝐼𝑆𝐢𝑀 𝐸3 βˆ’ 3) And Fe can be calculated by formula below: 𝐹𝑒 = πœ‹2 𝐸 ( 𝐾𝐿 π‘Ÿ ) 2 (𝐴𝐼𝑆𝐢𝑀 𝐸3 βˆ’ 4) So according to the above formulas, 𝐾𝑙 π‘Ÿ = 22.5 βˆ— 12 1.59 = 169.8 > 4.71√ 𝐸 𝐹𝑦 = 103.5 𝐹𝑒 = πœ‹2 𝐸 ( 𝐾𝐿 π‘Ÿ ) 2 = 9.92 𝐹𝒄𝒓 = 0.877 𝐹𝑒 = 0.877 βˆ— 9.92 = 8.7π‘˜π‘ π‘– 𝑃𝑛 = πΉπ‘π‘Ÿ 𝐴 𝑔 = 8.7 βˆ— 7.84 = 68.2 π‘˜π‘–π‘π‘  Step 3: Design for Flexure The chosen section L8*8*1 2⁄ with Ag = 7.84 has flexural capacity as calculated below: 𝑀 𝑝 = 𝐹𝑦 𝐴 2 ( 𝑦𝑐 + 𝑦𝑑) = 𝐹𝑦 𝑍 (𝐴𝐼𝑆𝐢𝑀 𝐹2 βˆ’ 1)
  • 34. P a g e | 34 𝑀 𝑝 = (60 βˆ— 15.1) = 906 π‘˜π‘–π‘. 𝑖𝑛 βˆ— 1 12 = 75.5 π‘˜π‘–π‘. 𝑓𝑑 Ρ„ 𝑏 𝑀 𝑛 = 0.9 βˆ— 75.5 = 67.95 β‰₯ 𝑀 𝑒 = 66 π‘˜π‘–π‘. 𝑓𝑑 𝑂. 𝐾 Design of critical member subject to bending and compression (Member #2): For the design of the critical member, it was assumed that the member would be made out of A572 grade 50 steel. The following stress values were determined from AISCM. 𝐹𝑒 = 65 π‘˜π‘ π‘– 𝐹𝑦 = 50 π‘˜π‘ π‘– After this assumption was made, it was crucial to determine the maximum moment (𝑀 𝑒) that the member would be expected to withhold. From Figure 27, one can see that 𝑀 𝑒 for this member is 213 kip-ft. The next step was to determine the effective lengths of the member in both the x and y directions. From AISCM Chapter E it was determined that because the member is un-braced, the effective lengths are equal in both directions. From this, one will get the following: (𝐾𝐿) π‘₯ = (𝐾𝐿) 𝑦 = 22.5 𝑓𝑑 After determining the effective lengths, one must resort to the β€œM table” that was provided in SE 150 for calculating 𝑃𝑒(π‘’π‘ž) for the factored moment. The section of the β€œM table” relevant to the type of steel being used for this design can be found in Table 4 below. Table 4: M table Values Based on Member’s Effective Length and Steel Properties 𝐹𝑦 50 ksi KL (ft) 10 12 14 16 18 20 22 and over All shapes 1.9 1.8 1.7 1.6 1.4 1.3 1.2 In the table above, KL is based on weak-axis buckling. Since it is known that the section is angled, KL is taken with respect to π‘Ÿπ‘§ so the first approximation is made using Table 4-11 from AISCM. In combination with this table, Equation 8 below will allow one to calculate𝑃𝑒(π‘’π‘ž). 𝑃𝑒(π‘’π‘ž) = 𝑃𝑒 + π‘šπ‘€ 𝑒 = 176 + 1.2(213) = 431.6 π‘˜π‘–π‘π‘  (Equation 8) From here, one can now enter AISCM Table 4-22 with (𝐾𝐿) 𝑦 = 22.5 𝑓𝑑 and 𝑃𝑒(π‘’π‘ž) = 431.6 π‘˜π‘–π‘π‘ . From the table, one can designate the section to be L8 x 8 x 9/8” which has the following factored nominal capacity, πœ™π‘ 𝑃𝑛 = 446 π‘˜π‘–π‘π‘ . Furthermore the length of the selected member, (𝐾𝐿) 𝑧 = 8 𝑓𝑑, is less than the effective length, (𝐾𝐿) 𝑦, thus it is acceptable. Now one must proceed to verify if the member satisfies the P-M interaction requirement.
  • 35. P a g e | 35 𝑀 𝑒 = 𝐡1 𝑀 𝑛𝑑 From AISCM p.16-231 𝑃𝑒𝑙 = πœ‹2 𝐸𝐼 π‘₯ (𝐾𝐿)2 = πœ‹2(29000)(98.1) (8Γ—12)2 = 3047 π‘˜π‘–π‘π‘  (Equation 9) 𝐡1 = 𝑐 π‘š 1βˆ’ 𝑃 π‘Ÿ 𝑃 𝑒𝑙 = 1.0 1βˆ’ 176 3047 = 1.06 β‰ˆ 1.0 (Equation 10) Hence the p-𝛿 effect is insignificant and the following remains: 𝑀 𝑒 = 𝐡1 𝑀 𝑛𝑑 = 213 π‘˜π‘–π‘ βˆ’ 𝑓𝑑 We compute πœ™ 𝑏 𝑀 𝑛, here the beam is unbraced and thus 𝑐 𝑏 = 1.0 and 𝐿 𝑏 = 𝐿 𝑝 so: 𝑀 𝑛 = 𝑐 𝑏 [𝑀 𝑝 βˆ’ (𝑀 𝑝 βˆ’ πœ™ 𝑏 𝐡𝐹(𝐿 𝑏 βˆ’ 𝐿 𝑝))] 𝑀 𝑛 = 𝑐 𝑏 𝑀 𝑝 πœ™π‘€ 𝑛 = 0.9𝑀 𝑝 = 0.9𝐹𝑦 𝑧 = 0.9(50)(31.6) πœ™π‘€ 𝑛 = 118 π‘˜π‘–π‘ βˆ’ 𝑓𝑑 P-, interaction from AISCS 16-73 π‘ƒπ‘Ÿ πœ™π‘ 𝑃𝑛 = 176 446 = 0.33 > 0.2 Therefore according to AISCS 16-74 one must use Equation xx below: π‘ƒπ‘Ÿ πœ™π‘ 𝑃𝑛 + 8 9 π‘€π‘Ÿ πœ™ 𝑏 𝑀 𝑛 = 0.33 + 8 9 213 118 = 1.93 > 1 𝑁𝑂 𝐺𝑂𝑂𝐷 𝑆𝐸𝐢𝑇𝐼𝑂𝑁 𝐼𝑆 𝑁𝑂𝑇 𝐴𝐢𝐢𝐸𝑃𝑇𝐴𝐡𝐿𝐸 The biggest angle section fails under the conditions given so it is necessary to go and choose a different section. A W-shaped section is selected because it has a bigger plastic section modulus and hence a higher moment capacity. From AISCM, it is deemed that the most economical section is W21 x 44. For W21 x 44: 0.45 + 8 9 213 358 = 0.98 > 1 π‘‚πΎπ΄π‘Œ 𝑆𝐸𝐢𝑇𝐼𝑂𝑁 𝐼𝑆 𝐴𝐢𝐢𝐸𝑃𝑇𝐴𝐡𝐿𝐸
  • 36. P a g e | 36 One must then proceed to the iteration process once more to check if W21 x 44 passes the beam column checks. The β€œm” factor remains the same at m = 1.2 and thus 𝑃𝑒(π‘’π‘ž) will still be 431.6 kips. Below one will find the iteration calculations for the W21 x 44 section. 𝑀 𝑒 = 𝐡1 𝑀 𝑛𝑑 From AISCM p.16-231 𝑃𝑒𝑙 = πœ‹2 𝐸𝐼 π‘₯ (𝐾𝐿)2 = πœ‹2(29000)(843) (22.5Γ—12)2 = 3309 π‘˜π‘–π‘π‘  (Equation 11) 𝐡1 = 𝑐 π‘š 1βˆ’ 𝑃 π‘Ÿ 𝑃 𝑒𝑙 = 1.0 1βˆ’ 176 3309 = 1.05 β‰ˆ 1.0 (Equation 12) Once again, the P-𝛿 effect is insignificant so this means that 𝑀 𝑒 remains 213 kips. From the 𝑍 π‘₯ table on page 3-25 from AISCM, one can determine the following: 𝐿 𝑃 = 4.45 𝑓𝑑 > 𝐿 𝑏 = 0 𝑓𝑑 (π‘’π‘›π‘π‘Ÿπ‘Žπ‘π‘’π‘‘) (AISCM, 3-25) Since this is the case, the following is also true, πœ™ 𝑏 𝑀 𝑛 = πœ™ 𝑏 𝑀𝑏 = 358 π‘˜π‘–π‘ βˆ’ 𝑓𝑑 π‘€π‘Ÿπ‘₯ = 358 0.9 = 398 π‘˜π‘–π‘ βˆ’ 𝑓𝑑 Now one must check the P-M interaction along with AISCS Table 6-1 and 6-3. From AISCS p 6.51 one can get the following values for the W 21 x 44 section. 𝐿 𝑏 = 0 𝑓𝑑, 𝑝 = 1.98 Γ— 103( π‘˜π‘–π‘π‘ )βˆ’1 , π‘Žπ‘›π‘‘ 𝑏 π‘₯ = 2.48 Γ— 103( π‘˜π‘–π‘ βˆ’ 𝑓𝑑)βˆ’1 π‘π‘ƒπ‘Ÿ = 1 1.98 Γ— 103 Γ— 176 = 0.089 ≀ 0.2 Hence one has to check: 1 2 π‘π‘ƒπ‘Ÿ + 9 8 ( 𝑏 π‘₯ π‘€π‘Ÿπ‘₯) ≀ 1.0 1 2 (0.089) + 9 8 ( 398 2.48 Γ— 103 ) = 0.22 ≀ 1.0 π‘‚πΎπ΄π‘Œ From the calculations, it is finally determined that the W21 x 44 section will in fact work for this design.
  • 37. P a g e | 37 5.2. Connection Design: Through SAP2000 structural analysis, it was determined that the critical joint is going to be a horizontal gusset plate that serves as the connection between the base and arm of the crane. From the structural analysis, it was determined that the axial force for this member is -0.00142 kips. The location of this critical joint can be seen in Figure 28 below. Furthermore in Figure 29, a detail of the critical horizontal gusset plate is provided. Figure 28: Section cut of the crane highlighting the critical joint Figure 29: Detail of the Horizontal Gusset Plate (inches)
  • 38. P a g e | 38 Critical axial member loading: 𝐹 = βˆ’0.00142 π‘˜π‘–π‘π‘  (8000) = 11.36 π‘˜π‘–π‘π‘  𝐿 = 5 𝑖𝑛. (90) = 37.5 𝑓𝑑 𝑑 = 1.5 𝑖𝑛. (90) = 11.25 𝑓𝑑 where F = member axial force, L = length of the member and d = bolt diameter. Through the use of sound engineering judgment, the team came to a conclusion that the critical connections (one on each side) are located between the tower and arm of the crane. The team made sure to confirm their reasoning through SAP analysis. From here, the team resorted to the AISC manual in order to determine the appropriate bolt size, spacing and edge distance limitations, tensile and shear strength of bolts, and bearing strength at both holes. In addition to the assumption that a 40 ton load was being used, the team also assumed that A572 Grade 50 steel was used throughout the entire design. Bolt Size In determining what type of bolts to use for the design, the team referred to Table J3.2: Nominal Strength of Fasteners and Threaded Parts as well as Table J3.3: Nominal Hole Dimensions. Through the use of Table J3.2, it was determined that the team should continue the design with a Group A bolt where the threads are excluded from the shear plane. From the different descriptions available, this description matched the team’s crane connection the best. Through this designation, the team determined the following values that will be required for further calculations: π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ 𝑇𝑒𝑛𝑠𝑖𝑙𝑒 π‘†π‘‘π‘Ÿπ‘’π‘›π‘”π‘‘β„Ž, 𝐹𝑛𝑑 = 90 π‘˜π‘ π‘– π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ π‘†β„Žπ‘’π‘Žπ‘Ÿ π‘†π‘‘π‘Ÿπ‘’π‘›π‘”π‘‘β„Ž, 𝐹𝑛𝑣 = 54 π‘˜π‘ π‘– (AISC Table J3.2) From Table J3.3, the team elected to ¾” diameter bolts as a starting point. If this bolt size does not provide the required strength, then the bolt size will have to be reconsidered. Through the use of these two tables, the team was able to select ¾” diameter A325 bolts. Spacing Per AISC J3.3 and J3.5, the team was able to check for the minimum and maximum spacing requirements. From J3-3, the AISC manual requires that the distance between the centers of the bolts shall not be less than 2 2/3 times the nominal diameter. In addition, J3-3 states that a minimum spacing of 3 times the nominal diameter is preferable.
  • 39. P a g e | 39 𝑠 π‘šπ‘–π‘› = { 8 3 𝑑 β†’ 8 3 (.75") = 2" 3𝑑 β†’ 3(.75") = 2.25" (AISC J3-3) Furthermore, AISC J3-5 requires that the spacing not exceed a specific maximum spacing. From AISC J3-5, the maximum spacing required shall be the minimum of 24 times the thickness of the connected part or 12”. 𝑠 π‘šπ‘Žπ‘₯ = { 24(𝑑 𝐺𝑃) β†’ 24(3.6") = 86.4" 12" (AISC J3-3) where 𝑑 𝐺𝑃 = gusset plate thickness. 𝑑 𝐺𝑃 = 0.04" (90) = 3.6" Due to the fact that the length of the gusset plate is 37.5 feet, the team elected to go with a spacing of 86.4”. A larger spacing between the bolts will also aid the bolt’s shearing strength. Minimum Edge Distance: Per AISC J3-4, the minimum edge distance is determined based on the bolt diameter. The section then refers one to Table J3.4 which lists all of the minimum edge distances for different bolt sizes. From Table J3.4, the team determined that the minimum edge distance ought to be 1”. Tensile and Shear Strength of Bolts: Per AISC J3.4, the design tensile or shear strength can be determined from the bolt area and the nominal stress. πœ™π‘… 𝑛 = 𝐹𝑛 𝐴 𝑏 (J3-1) where 𝐹𝑛 = nominal stress, 𝐴 𝑏 = bolt area, and πœ™ (strength reduction factor) = 0.75. One can obtain both the tensile and shear strength of the bolt by using Equation J3-1 with the respective nominal stresses for tensile and shear. Tensile Strength: 𝐹𝑛𝑑 = 90 π‘˜π‘ π‘–, 𝐴 𝑏 = ( πœ‹ 4 (3/4)2 ) = 0.442 𝑖𝑛.2 π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘™π‘‘π‘  = 5 (J3-1) πœ™π‘… 𝑛𝑑 = .75(90 π‘˜π‘ π‘–(0.442 𝑖𝑛.2 )) Γ— 5 π‘π‘œπ‘™π‘‘π‘  πœ™π‘… 𝑛𝑑 = 149.2 π‘˜π‘–π‘π‘  (𝑑𝑒𝑛𝑠𝑖𝑙𝑒 π‘π‘œπ‘™π‘‘ π‘ π‘‘π‘Ÿπ‘’π‘›π‘”π‘‘β„Ž)
  • 40. P a g e | 40 Shear Strength: 𝐹𝑛𝑣 = 54 π‘˜π‘ π‘–, 𝐴 𝑏 = ( πœ‹ 4 (3/4)2 ) = 0.442 𝑖𝑛.2 π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘™π‘‘π‘  = 5 (J3-1) πœ™π‘… 𝑛𝑑 = .75(54 π‘˜π‘ π‘–(0.442 𝑖𝑛.2 )) Γ— 5 π‘π‘œπ‘™π‘‘π‘  πœ™π‘… 𝑛𝑑 = 89.5 π‘˜π‘–π‘π‘  (π‘ β„Žπ‘’π‘Žπ‘Ÿ π‘π‘œπ‘™π‘‘ π‘ π‘‘π‘Ÿπ‘’π‘›π‘”π‘‘β„Ž) Both the tensile and shear bolt strengths of the bolt are greater than the demand of 11.36 kips. With this being said, the bolts will not fail under the current loading conditions. Bearing Strength at bolt holes: Per AISC J3.10, the bearing strength at bolt holes can be calculated for different conditions. From all of the conditions listed, the team decided that the following equation best agreed with the connection design: πœ™π‘… 𝑛 = 1.2𝑙 𝑐 𝑑𝐹𝑒 ≀ 2.4𝑑𝑑𝐹𝑒 (J3-6a) Where 𝑙 𝑐 = clear distance (in direction of force), 𝑑 = thickness of connected material, 𝑑 = bolt diameter, 𝐹𝑒= material tensile strength, and πœ™(strength reduction factor) = 0.75 𝑙 𝑐 = 86.4 (distance between holes), Fu=65 ksi, t=tGP=3.6", 𝑑 = 3/4" πœ™π‘… 𝑛 = 1.2(86.4)(3.6)(65) ≀ 2.4 ( 3 4 ) (3.6)(65) πœ™π‘… 𝑛 = 24,261.12 π‘˜π‘–π‘π‘  ≀ 421.2 π‘˜π‘–π‘π‘  πœ™π‘… 𝑛 = 421.2 π‘˜π‘–π‘π‘  π‘π‘’π‘Ÿ π‘π‘œπ‘™π‘‘ Thus the total bearing strength for all five bolts will be: πœ™π‘… 𝑛 = 5(421.2) = 2106 π‘˜π‘–π‘π‘  Since the bearing strength of the bolts is greater than the demand, the design is acceptable. Final Design of Critical Members and Connections: It was observed that the angle-shaped section failed under the given conditions for the member subjected to flexure and compression. For conservative purposes, the W21 x 44 section was chosen for both the tension and compression members since its capacity is larger than that of the L8 x 8 x 1/2. Moreover this design adds symmetry to the structure, which is a plus because it drastically simplifies the construction process. Finally, the bolt size and spacing was determined
  • 41. P a g e | 41 for the critical connection. From the calculations provided, the design team chose A325 bolts with a ¾” diameter at a spacing of 86.4”. 6. Structural Performance 6.1 Assumptions The model was analyzed with SAP2000 using fixed supports for the foundation of the crane because the foundation will be bolted to the rotation table. The connections of the crane base and arm were also modeled as fixed with no moment release because the construction phase of the project involved connections with bolts, washers and epoxy for the critical connections, while all connections were fixed using 4-40 bolts, #4 washers and #4 nuts. Furthermore, the SAP2000 model has members connected at their centroids rather realistic pinned binding. The pulley was modeled as an external roller with an un-deformed cable. Instead of the rope being fixed to the structure, a roller was added so the tension forces could be transferred all the way down to the base so that the compression forces in base could be relieved, creating a more desirable and realistic load path. Furthermore, loading conditions were done in individual iterations with the structure being assumed to be fully fixed, fully pinned and having full moment release in order to compare the individual deflection contributions from axial and lateral forces. Thus, the decision was made to model the structure’s connections as fully fixed because it was the closest to real world behavior. 6.2 Analysis In order to analyze the structure, the team applied the weight of the golden cargo by having two point loads of 5 pounds applied at the end of the boom as critical loads. These two loads represent the permanent loads, as shown below in Figure 30. Furthermore, torsional loads are also present when the structure is rotating in the theta direction when considering a 3D polar axis of (R,Θ,Z) directions (Figure 31)
  • 42. P a g e | 42 Figure 30: Permanent Point Loads Figure 31: Torsional Loads
  • 43. P a g e | 43 The primary load originates at the end of the crane’s arm due to the weight of the cargo. The load then travels through the diagonal and horizontal members at the right of the crane’s arm to the left towards the crane’s tower. The load then travels vertically downward through the vertical and diagonal members of the tower. Finally, the loads are transferred from the tower into the base of the structure and then into the ground. The string also transfers part of the load, from the end of the cranes arm to the tip of the tower, to the base of the tower, and finally into the ground. Figure 32 displays the load path described. Figure 32: Load Path Next, a SAP2000 was done in order to analyze the vertical (point load) and torsional (rotational) loading. A primary analysis was done using only the vertical loading. The red members are in compression while the blue members are in tension, as is customary with SAP2000 analysis. Figure 33 shows the analysis results for critical members based on the vertical loading analysis.
  • 44. P a g e | 44 Figure 33: Vertical Loading Analysis A Second analysis was performed using a load combination taking into account torsion and vertical loading, as shown below in Figure 34. Figure 34: Combined Loading
  • 45. P a g e | 45 It is evident that when the torsional loads are applied, the axial forces in the members increase considerably. However the first analysis would be more accurate since the crane is moving at a very slow pace. The structures critical members are discussed in the validation section on page 21. 6.3 Failure Modes From the analysis performed, a conclusion can be drawn as to how the crane will fail when placed under critical loads. The first and most probable failure mode would happen at the tension member at the top of the boom. Since the member at that connection had a hole it is possible that it would fail under tension due to stress concentration, yielding of the member. The bolt being stronger block shear would be observed in this mode as well. The second mode of failure could occur at the connection where five members intersect with a compression force of 30 lbs. This connection is critical and supports a large load. However the team heavily reinforced this connection by adding an aluminum plate at that location which increased the strength of the material. The third possible failure could occur at the maximum compression member of 30 lb. Buckling is a possibility as well, but it is highly improbable (see hand calculations for reference). The fourth possible failure could happen at the base because it is only supported by three bolts hence creating a stress concentrations in the connections, block shear can be observed in this failure mode as well. Figure 35 below shows the location of the failure modes described. Figure 35: Possible Failure Modes
  • 46. P a g e | 46 7. Predicted Final Test Results After acquiring a range for the predictions from the hand calculations section presented in section 5, SAP2000, Solidworks and engineering intuition developed from previous coursework, a factor of was used to increase the hand calculated deflection of 0.015 in to the official prediction of 0.15 in. This correction factor accounts for the imperfections that are present in the real world structure as opposed to its virtual counterpart. The virtual model on SAP2000 assumes that connections and members are fabricated perfectly and the connections are fully rigid while the real world structure could suffer from construction flaws. Furthermore, the correction factor also accounts for any yielding from the fatigue that might have occurred during testing . The structure was tested for a total of six hours in order to fully calibrate the RoboPro program and ensure that that the mechanical system was fully operational . The results are shown below in Figure 36 which were acquired after applying the loads at the end of the crane to get the max deflection. Figure 36: Deflection Predictions Generated From SAP2000 As for the prediction of the maximum load, an FEA analysis was done on the critical connections shown below in Figure 37. According to SAP and the assumptions taken into account Max deflection is 0.15 inches
  • 47. P a g e | 47 Figure 37: Maximum Load FEA This member was chosen because it carries the most tension force and it is also deformed in order for the connections to be properly installed. A finite element analysis was done in solidworks with Aluminum 6061-T6 Material properties until the member reached its yielding strength of 39,885 Psi. The team's final prediction of the maximum load that structure can hold for the provided loading connections is 17 lbs. 8. Final Test Results The final test results yielded were in accordance with the group's original goals of designing a structure that was able to carry a high load with little deflection. This was evident by the team's success in carrying the a total of forty-one (41) gold weights successfully from the port to the warehouse for an unloading rate of 2.48 kg/min, which was first among the team's competing. Furthermore, the deflection measurement was also very close to the team's prediction where the measured deflection under 15 N was 0.17 in. as compared to the 0.15 in. predicted deflection for a percent error of 11.71 %. The peak load was measured to be 65.58 lbs, as opposed to the 17 lb prediction, resulting in a percent error of 227%. This was largely a result of the loading that tested the top of the boom, whereas the crane was designed to be tested at the bottom of the boom, where the L-channels are located. The failure location is shown below in Figure 38.
  • 48. P a g e | 48 Figure 38: Member Failure at the Top of the Boom Moreover, the crane was aesthetically pleasing, coming in second place with an overall aesthetics score of 94.25%. The deciding factor was the cost, which was too high when compared to the other groups. However, this was a direct result of unexpected testing and material fees, which would not be as important on a large scale real world project. The team's results are summarized in Table 3 below. Table 3: Summarized Results Quantity Score Placement Unloading Rate 2.48 kg/min 1st Aesthetics Score 94.25 % 3rd Peak Load 65.58 3rd Deflection at 15N 0.17 in 8th Measured Deflection 4.35 in 15th Structure Weight 2543.0 g 16th Virtual Cost $263,802.60 15th Structural Capacity $3,979 8th Structural Economy $381,678 11th Structural Performance $14,880 5th Overall Performance $400,536 11th The first critical failure that occurred was the rupture of the cables used to hold the crane down at the base. However, since the crane was designed to go beyond the required loading, the structure maintained a peak load past the rupture. Another contributing factor was that one of the base plates that connected the crane to the table was not a perfect 90 degrees as the other two were, causing a problem with the stability of the structure . Since the cables were no longer present to resist deflection at peak load, the peak load deflection measurement suffered as a result (4.35).
  • 49. P a g e | 49 9. RoboPro To control the mechanical system of the crane, RoboPro was utilized to create a script capable of managing the all the motors and sensors. For the script’s first iteration, the program primarily consisted of three distinct control pathways (Figure 39), which would all run simultaneously to independently control the radial, vertical, and theta directions. The leftmost path, outlined in blue, was used control the rotation of the crane. The middle path, outlined in red, was used to control the winch’s motion. Finally, the green path was used to specify the translation along the boom by use of the worm drive. For all three pathways, the first step was to return to predefined home positions which relied on hard mounted sensors upon the crane’s body. With this setup, the program would be able to reliably start in the same location, regardless of the current position of mechanical system. As the program continued, all three pathways would synchronize by waiting for predefined inputs such as switch activations signaling the completion of a specific task. For example, in the middle of the program, all three logic lines wait for I6 to complete a number of counts. I6 refers to a revolution counter attached to the winch, so all 3 paths would wait for the winch to complete a certain number of revolutions before continuing on their individual subroutines. This would ensure that no step would interfere with any other step, such as activating the worm drive before the magnets were picked up. Finally, after all steps were completed, the crane would stop moving instead of returning to a home position because the initial steps of the program would negate the necessity of resetting the crane. Figure 39: Preliminary Robopro script
  • 50. P a g e | 50 However, during practice sessions several challenges were discovered with using RoboPro to control the crane. The most immediate problem was the necessity of calibrating the number of revolutions needed to raise and lower the winch as well as the precise placement of the switches. In order to determine the crane calibrations, a time consuming trial and error method must be used. Additionally, as each calibration was determined, the RoboPro program had to be manually updated to reflect the new values and the switches required time for their adhesive mounts to cure. With time during each practice session being extremely limited, it was a race against time in order to update the script. While rushing to update the script, some changes weren’t implemented properly and other bugs were introduced. Because of this, it was decided to rewrite another script from scratch, with the intent of simplifying the logic paths as well as making any updates easier to implement. In the second revision of the script (Figure 40), the program was streamlined in order to reduce complexity and probability of additional bugs as well as incorporating all the calibrations determined during practice sessions. The basic logic behind the program is the same, in which the crane starts by resetting to a home position. However the biggest change is the reduction of steps of the winch subroutine, outlined in green. This was achieved by determining many of the steps which slowed down the winch’s spooling speed was unnecessary to stably carry the loads, even that of the gold weights. Because of this, many steps were eliminated which allowed for better synchronization between all three individual subroutines.
  • 51. P a g e | 51 Figure 40: Revised RoboPro Script 10. Budget The projected budget of $126,500 as seen in Table 4 below was far less than the actual budget of $228,900 as seen in Table 5. The projected budget compared to the actual budget by way of percent increase increased by 81%. The colossal difference in the budget was mainly due to unexpected expenses and an underestimation of the quantity of material that would be necessary for the completion of a successful crane. The projected budget was base on the initial design, which changed a few times before and during construction. The changes in design led to major unforeseen expenses for instance the mechanical system was originally going to have 20 parts and it now has over 40 parts. The structural system, which is primarily constructed of aluminum tubing and sheet material, was only projected to have 25 thirty-six inch long tubes but the crane used over 50 thirty-six inch long tubes. Fees for testing were also unexpected since the team planned to only test the crane during the bonus and free testing weeks and earn the $5000 bonus. Instead the team only tested
  • 52. P a g e | 52 during charged, expensive, and ridiculously expensive testing weeks due to an absence in material availability, construction delays, and unrealistic expectations in regards to the amount of time that was needed for testing to insure the crane was working properly. The doubling of the quantity of many of the components of the crane and other unforeseen expenses can be seen to account for the 81% increase in the budget. In the end, the largest project expense was for the aluminum tubing and aluminum sheet material parts that were the primary components of the structural and auxiliary systems of the crane and together cost $171,300 or 75% of the actual budget. Table 4: Detailed Projected Budget
  • 53. P a g e | 53 Table 5: Detailed Actual Budget 11. Challenges As with any large scale engineering project, there are challenges in creating a schedule for a large team with no conflicts. This was the case for the team as other projects and tasks would often interfere with planned group meetings. In order to circumvent this, the CEO appointed team members to their specific tasks while also assigning alternate roles in which the team members would experts in one field and consultants in another. This ensured that when a primary team member was unavailable to attend a group meeting, someone with knowledge of the situation would be present. Since the design was fairly simple, the structural system was constructed fairly easily, except for the simple deviations explained in the conceptual design section of the report. As for the mechanical system, one main challenge in building the system was that the mechanical design creates various focused point loads on the rail of crane which in turn makes the rail a critical member with potential of failure. This in turn circumvented by increasing the number of wheels on rail for proper weight distribution. The force is less concentrated along the track rather than having two critical points. Furthermore, considering that the firm aims to transfer the highest weights possible, there is the matter of rocking and tilt on the magnet platform that could be a safety and structural hazard. The main challenge was ensuring that the transfer platform experienced as little vibrational
  • 54. P a g e | 54 rocking as possible. This is due to the turbulence generated from the transient vibrational motion, which raises the risk of the cart assembly falling off the track. This was dealt with by mounting a total of four (two on each side) 10 in. long, 5/32 in. diameter force-stabilization bars to the 3" x 7" aluminum plate that will hold the electro magnets. This, along with the added eight wheels (four on each side) lessens the motion with the platform and ultimately leads to a more safe and accurate transfer of the weights with minimum rocking and tilt. Finally, there was the matter of designing a rail system completely exposed on the top while still being well supported. In order for this to work, small cross sectional brackets that were inserted into the angle brackets so that the rods would be supported from the underside while leaving the exposed in order for the cart to translate about the rail without obstruction. 12. Ethics As an engineer, one has both social and professional obligations that one must uphold in order to lead an appropriate and ethical practice. In 1914, the American Society of Civil Engineers (ASCE) adopted a code of ethics in hopes of promoting the reputation and ethics of the engineering profession. For over 100 years now the ASCE Code of Ethics has served as the model for professional conduct of all civil engineers. The Code of Ethics is comprised of seven canons that seek to provide all necessary guidance in hopes of leading an ethical engineering career. Among these seven canons, there are two in particular that had extensive influence on all of the engineers working on the crane project. Due to the amount of work and size of the crane project, the engineering team was comprised of ten members that all had different responsibilities based on their areas of expertise. Based on a member’s particular skill set, such member was placed into one of the four subsets of teams: either design, construction, mechanical systems, or documentation. The rationale behind the specialization process is to ensure that members are only working within areas of their expertise. As per the second canon of the ASCE Code of Ethics, β€œEngineers shall perform services only in areas of their competence”. This canon limits engineers to the work that they may perform during their career in hopes of preserving the safety and wellbeing of the public. In regards to the crane project, members of the engineering team were only assigned work that they would be comfortable in completing. This canon sanctioned a certain degree of accountability to all members of the engineering team as they were expected to always produce deliverables that met the standard of competent engineering. Team members were encouraged to seek assistance from other team members whenever they experienced trouble performing their work. By working together, team members were able to come an agreeable conclusion that would have to ultimately be confirmed by either the project engineer or the CEO. Team members could have chosen to lie or not confirm their analysis with consultants, which would have resulted in the project being labeled a failure. As an engineer, one must be able to claim all responsibility for their work. Within this huge burden of responsibility, lies the safety and wellbeing of the public. Serving as the paramount
  • 55. P a g e | 55 objective with all engineering projects, the safety and wellbeing of the public must always remain the driving factor behind all engineering design. For this reason, the first canon of the ASCE Code of Ethics states that "engineers shall hold paramount the safety, health and welfare of the public and shall strive to comply with the principles of sustainable development in the performance of their professional duties". With this canon serving as the primary objective, the engineering team sought to design a structure that would provide adequate redundancy and minimal deflection. In order to satisfy this design criteria, the team designed a structure that would incorporate cable systems to help support the primary truss configuration of the crane. Together, the two structural systems work cohesively to provide maximum stiffness and ultimately minimal deflection of the crane. Furthermore, the crane's ability to be supported by two different structural systems adds a degree of redundancy to the overall crane design. If the structural supporting cables were to somehow fail, the crane would still be able to operate as a result of the main structural support coming from the crane's trusses. 13. Life Long Learning 13.1. Musco Arts Center Lecture In the Chapman University Musco Center for the Arts lecture by Lori Jue from KPFF-LA, the design to construction process was thoroughly explained. It is the responsibility of the structural and design engineers to ensure that the construction manager is fully aware of what the drawings and plans convey on paper. Furthermore, plans should be as detailed as possible with little to no guess work involved as it can create situations where complications could arise that can derail the fabrication schedule. In terms of the crane, it was important to have a project engineer present during construction. Since the initial designs were simply straight lines connected at member centroids and centerlines generated from SAP2000, the presence of a project engineer and the occasional supervision of the design engineer helped the team’s contractor properly visualize the members and connections of the crane in a three-dimensional aspect. 13.2 Integrated Design Lecture In the integrated Design and Introduction to Architecture lecture by Ms.Daniela Deutsch from the Woodbury and New Schools of Architecture a focus was made on integrated design. In previous years, the architect would traditionally design the structure, then hand it off to the structural engineer who would then bring in the electrical and mechanical engineers along with the other trades. In recent times, the focus has shifted to everyone being involved in the project from day one where the architect and engineers lay out the design and decide on a mutually beneficial solution for all the problems that the design team is faced. This relates to the design of the crane as the team decided that the design engineer, the mechanical engineer, the RoboPro designer and head of construction should work on the initial design together, ensuring that the final design would be feasible for each department. This ultimately benefited the team by allowing the mechanical system to perfectly fit along with
  • 56. P a g e | 56 structural system with little complications. While the different departments were ultimately allowed to work in stages to complete their respective parts, it was crucial to have a cohesive unit that kept in communications regarding modifications and feasibility of the other systems. 13.3 Temporary Structures Lecture The Temporary Structures and the Construction Industry Lecture by Mr. Chong Kim from DH Charles Engineering covered the importance of temporary structures during the construction times. Oftentimes, false-work will be needed to keep the structure upright as other integral members are either installed or repaired. Furthermore, it was also emphasized that a qualified structural engineer needed to be onsite at times to ensure that everything is being constructed to code and up to the satisfaction of the design engineer and the architect. For the Robo-Crane, there were two false work structures that were created in order to ensure the proper construction and stability of the crane. One of the two was made of wooden beams connected at 90 degrees acting as a counterweight at the on the boom. Since there was no table to simulate the ones provided by the port authority, it was necessary to keep the crane upright during installation of the truss members on the boom and the base. Since there was a large overturning moment due to the long arm of the crane, the two wooden beams ensured that the crane would not fall over. Furthermore the team fabricated a plastic base that simulated the Dover table provided by the port authority. The plastic base was then clamped down to a wooden plank to simulate the testing day conditions and allow for easier access during the installation of the mechanical system. The plastic base is show below in Figure 40. Since the mechanical system deals a great deal with intricately placed parts on the boom, the previously used wooden beams needed to be removed to allow for full access. Figure 40: Plastic Base Used to Hold Structure During Construction
  • 57. P a g e | 57 14. Conclusion Overall, the project was an appropriate simulation of a real world engineering project in that a design process was undertaken that covered all the typical steps in a design procedure. An initial brainstorm lead to preliminary designs being evaluated with modeling programs such as SAP2000, Solidworks and RISA. This iterative process ultimately led to a final design being picked with limited deflection and efficient functionality all while being easy to fabricate and adjust should complications arise during construction. As expected, complications did occur as with any large scale real world project. The project and construction engineers had to think on the fly and create solutions for problems that were not necessarily discussed or accounted for in the original design, as discussed earlier in the report. Finally, the structure was tested multiple times for its functionality and stiffness, similar to how a building must pass inspection and code checks before being inhabited or put in us. In terms of a broader academic scope, the project was an appropriate capstone project as it covered a broad spectrum of classes including but not limited to statics, dynamics (relating to the swinging in the mechanical system), vibrations (allowing the system to properly dampen before dropping the weights), CAD modeling and analysis (analyzing and iterating designs as well as analyzing the final design to ensure it met the necessary demands) , steel design (connection design)as well as seismic design (designing for a given load to ensure minimum movement in the structure). This project can extend into future coursework that is oriented around design where the problem statements or client demands are vague and the engineer has to come up with an entire design from scratch. What this ultimately does is it mold critical thinkers that are able to take on challenges with little hesitation as the prior experience ultimately builds both the confidence and knowledge to succeed in the real world. References Jue, Lori. "Chapman University Musco Center for the Arts." SE 140 Guest Lecture. UCSD, La Jolla. 21 Apr. 2015. Lecture. Deutsch, Daniela. "Integrated Design." SE 140 Guest Lecture. UCSD, La Jolla. 12 May 2015. Lecture. Kim, Chong. "Temporary Structures: DH Charles Engineering." SE 140 Guest Lecture. UCSD, La Jolla. 7 May 2015. Lecture. Steel Construction Manual. Fourteenth ed. N.p.: AISC, 2011. Print. Van Den Einde. Robo Crane Competition 2015 Rules. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Van Den Einde. Catalog Prices V14-1. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Van Den Einde. Conceptual Design Presentation Requirements. La Jolla: SE 140 - Van Den Einde, 2015. PDF.
  • 58. P a g e | 58 Van Den Einde. Conceptual Design & Analysis Report Requirements. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Van Den Einde. Mechanical Design Report Requirements. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Van Den Einde. Analysis Validation Report (Hand Calculations) Requirements. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Van Den Einde. Motion Simulation Requirements. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Van Den Einde. Cost and Constraints for Aluminum Sheet Material. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Van Den Einde. AISC Compliance Design. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Van Den Einde. SE 140 ROBO CRANE COMPETITION FINAL REPORT GUIDELINES. La Jolla: SE 140 - Van Den Einde, 2015. PDF. Appendix A: Project Schedule/Timeline: The project was on schedule for the most part. All the deliverables were completed by the specified and planned dates. The main deviations from the schedule were for the primary fabrication and the amount and dates of testing for the crane. The main reason for the delay in fabrication was due to the unexpected time to receive the water jet parts from the fabricators and the finalization of the design also took longer than expected. The delay in fabrication led to a delay in testing. The original schedule planned for testing during Bonus and Free Testing weeks for a total of two hours of testing. The construction delays pushed the initial testing to the Charged Testing week for an interval of two hours. Following the initial testing it was realized that additional testing was a must to insure the crane functioned as desired for the competition. So testing was also conducted during the Expensive and Ridiculously Expensive testing weeks each for an interval of two hours resulting in a total of six hours of testing over three weeks. A detailed Gantt Chart can be seen below in Figure 41 and the corresponding Figure 42 shows the dates in tabular form for the Gantt Chart. Table 6 then compares the planned schedule as laid out on the Gantt Chart with the actual start and completion dates for the major deadlines and milestones and whether they were achieved or delayed. The items that were on the critical path and critical to completion of the project by the required deadline and in accordance to the project schedule was mainly in sync with the deliverable deadlines. The proposal presentation insured that the team was on track with our initial design and plans. Next, the design and analysis report required the completion of the structural system design and analysis. Following that the mechanical system design report assured that the mechanical system design and analysis was completed. Thereafter, the initial RoboPro design
  • 59. P a g e | 59 was completed for validation by the team’s supervisors. The supervisors would confirm that the logic was sound and that the program would work during testing with only minor modifications. The analysis validation was completed next and insured that the SAP analysis was reasonable when compared to our hand calculations and would closely reflect our testing data. Afterwards, the preliminary SolidWorks motion simulation was done to demonstrate the planned motions of the crane and to see if there were any possible issues with the desired path for transporting the cargo. Soon after, the steel connection report was completed in accordance with AISC to insure that the design for the critical connections and members would satisfy their demand loads. All of these critical steps insured that fabrication, testing, and performance during the competition would be exceptional and completed by the deadline. Table 6: Planned vs. Actual Schedule and Whether They Were Achieved or Delayed
  • 60. P a g e | 60 Figure 41: Gantt Chart in Tabular Form
  • 61. P a g e | 61 Figure 42: Gantt Chart for Major Deadlines and Milestones
  • 62. P a g e | 62 Team Hours: In Table 7 below are the team’s hours for the project. For simplification the time sheet was organized by each school week of the quarter and the main tasks for the respective week are listed accordingly. Team members have their own column in the table and listed the hours that they worked each week. At the bottom of the table is the total hours spent on the project for each respective team member and below that is their Working Hour Factor (WH). The Working Hour Factor is calculated as follows, the team member’s hours divided by the average of the team’s hours; maximum value is 1.10. Furthermore, the table also shows that each member contributed 100% effort to the project. Table 7: Team Hours
  • 63. P a g e | 63 RoboPro Program: Figure 43: RoboPro Program Bill of Materials: The β€œDetailed Actual Budget’ table above lists all of the raw materials to purchase in order to construct the crane. Once the materials are purchased the bill of materials in Table 8 and Table 9 can be used to construct the structural and mechanical system respectively. The tables list all parts and quantities need in order to replicate the final design. The bills of material were produced via SolidWorks from the team’s completed SolidWorks assembly.
  • 64. P a g e | 64 Table 8: Bill of Material for the Structural System
  • 65. P a g e | 65 Table 9: Bill of Material for the Mechanical System
  • 66. P a g e | 66 Project Drawings: Figures 43 to 45 show the relevant dimensions for the front, top and side views of the crane, respectively. Figure 43: Front View
  • 67. P a g e | 67 Figure 44: Side View
  • 68. P a g e | 68 Figure 45: Top View of Boom Furthermore, Figures 46 and 47 show the relevant information for the L-channel and HSS round sections, respectively. Figure 16: L-channel Cross Sections Figure 47: Circular HSS Cross Sections
  • 69. P a g e | 69 Mechanical System: Figures 47 and 48 show the relevant mechanical system dimensions: Figure 47: H-Plate Dimensions Figure 48: Mechanical System Dimensions
  • 70. P a g e | 70 Multi-Media: A video of the solidworks motion simulation can be found here: https://www.youtube.com/watch?v=DBjk6-jTyH8&feature=youtu.be A comprehensive cloud file can be found at the following link: https://drive.google.com/folderview?id=0ByEi_zHS4ioofnN0RUJxeGJGbURpZzRIRlFpdDJud ThtWXdHNXliWVZyRkFzU3JZWXlCa1E&usp=sharing
  • 71. P a g e | 71 Appendix B: Hand Calculations Detail:
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