Engineering 103 --
Section 35 -- Group 12
Background
In
this Engineering 103 class, the goal of the term was to build a model bridge
out of K'nex pieces with the lowest cost-to-strength ratio. What this means is
that the cost of the bridge was to be divided by the number of pounds the
bridge could hold before breaking. The lower this number, the stronger and more
cost effective the bridge.
Throughout
the term, the class learned about effective and ineffective bridge designs,
famous bridge failures, how to calculate tension and compression in certain
members of the bridge, and how to put all of this information together to build
the best possible bridge. The first few weeks of the term were spent
familiarizing ourselves with basic truss designs and the West Point Bridge
Design software. This software was useful in the beginning because it showed
what bridges were realistic, where the bridges would break, and how much
tension/compression was on each member. This allowed the class to get a greater
understanding of how bridges work before actually modeling, analyzing, and
testing one.
After
using the West Point Bridge Design software, the class moved on to building a
24-inch bridge out of K'nex pieces. This allowed everyone to see how K'nex
differ from theoretical software and understand how things were more likely to
break in the medium that we would be using for the final bridge. Working with
K'nex also allowed us to examine the bridge after it broke to determine what
aspects of the bridge could be improved.
Finally,
the class learned how to analyze the physics of bridges to come up with our own
compression/tension values and we had to modify our bridge to meet the criteria
of the class: at least 36 inches long, 3.5 inches wide, and two inches high.
The bridge also could only be supported on each end by the table – no support
beams in the middle.
Over
the course of the term the class learned how to plan and design a bridge via
software and modeling, how to use various bridge design software, the physics
behind bridge design, how to determine where the bridge failed and how to fix
it. We expanded our knowledge of how the design process works from beginning to
end.
Design Process
In
the first phase of the design process, each team member worked individually
using West Point Bridge Designer. The intention was to make an inexpensive truss
bridge that had high compression and tension force to strength ratios on its
members. Triangles, the strongest geometrical shape, were used. Constraints
included pricing per joint and per member, as well as a restriction to 2 support
points allowed, one at each end. The goal was to create a bridge that was
inexpensive (goal cost: $200,000 or less), and remain intact through the WPBD’s
load test. However, while going through the design process, it was difficult to
create a strong bridge that also was inexpensive. However, when the three
designs were pooled together for ideas, the group design was close to the goal
price.
Once
the second phase of the design process began, the goals had to be changed. The
West Point Bridge designer was no longer used. Instead, the medium was K’nex
building pieces. These pieces behaved very differently from the ideal
conditions in the WPBD program. The new goal was clear: build a bridge that
balanced structural integrity with low cost. Many individual designs were made,
at first by educated guessing, and later with strategic member and joint
placement derived from previous test results. Load tests with buckets of sand
showed that bridges tended to fail at the gusset plate joints in the center of
the bridge, where the load was directly applied. The Method of Joints was applied to a simple, 7-member truss section, and to the K'nex design. The Method of Joints is a system of equations made from free-body diagrams that calculates the force on each member and determines whether the force is tension or compression. Results were then checked using the John Hopkins University Bridge Designer for verification that hand calculations were correct. These calculations showed which members experienced the most force when a certain load was applied, and how the members would react to the applied force. It was useful in predicting how the
Each
phase concluded with the individual designs being brought together in a final
design. With the WPBD, the designs could not be combined without sacrificing
structural integrity, so one design was picked by all and modified by the group.
The K’nex bridge had more combination options. Two designs were made, one
spanning 2 feet and the other spanning 3 feet. For the 2-foot bridge, the individual designs were combined so elements from each were
included in the final. It followed constrains of a width of at least 3.5” and a
height of at least 2” inches, with a space in the middle where cars would fit. For
the 3 feet bridge seen in Figures 1 through 6, the constraints were the same, plus
the testing site did not have grooved edges as with the previous testing site.
The final design for this length was different from the previous one. After
much revisiting and editing, the initial 2 feet bridge was exhausted of all
options. In an attempt to hold more weight, a more expensive bridge was made
that utilized X-cross sections instead of the right triangles previously used. This
final design was predicted to fail at 25 pounds, with the middle members
dislocating from the gusset plates.
Description of Final Bridge:
Figure 1: Plan Drawing of the Final Bridge Design
Figure 2: Elevation Drawing of the Final Bridge Design
Figure 3: Excel Spreadsheet Bill of Materials
The overall cost of
our bridge according to the Truss Bill of Materials (Figure 3) was $342,000.
Figure 4: Plan Photograph of the Final K'nex Bridge
Figure 5: Elevation Photograph of the Final K’Nnex Bridge
Figure 6: Final K’nex Bridge Ready to be Tested
Testing Results
Our
final bridge design held 13.6 pounds. Though this was not as great as the
predicted carrying capacity of 25 pounds, it still gave us a cost to weight ratio
of 25,147.06 dollars/pound. This load at breaking point was not unreasonable low
considering the low cost of the bridge. The bridge failed in two places,
in each of these two places a member popped out of a joint. The failures
occurred at the bottom edge of the middle of the bridge and at the bottom of
one of the ends of the bridge. In each of these places the joint that the
member popped out of was a 360-grooved gusset plate. The bridge
twisted only slightly when it failed and it did fail graceful as the bridge did
not completely fall apart or break in half and no pieces went flying off when
the two members popped out. Its only slight twist was a compliment to the
stability of the bridge, while many other bridges seemed to twist almost into
two pieces.
Conclusions
The
bridge behaved as expected. It failed in the middle where the load was applied
by members dislocating from the gusset plates. However, it failed much sooner
than expected, at 13.6 pounds instead of the expected 25. One reason for this
was that the bridge was very box-like. In other words, the only supports came
from each face of the rectangular truss. There were no diagonal supports that
traversed through the center opening. The bridge would have been far more
expensive if these extra supports had been added, but it is possible the design
would have held enough weight for the cost to strength ratio to improve,
meaning the design was more efficient. It is difficult to know what the other
outcomes would have been without more tests.
Working with both West Point Bridge Designer and the K'nex pieces throughout the design process, it was apparent that the two methods had many differences but also a few similarities. The West Point Bridge Designer has informative
stress test simulations and takes multiple factors into account when
calculating cost (like material type, length, and density). Members can be any
size, made from one of three materials, and can be hollow or solid. All
connecting pieces are the same size and weight, but can connect at any angle
and it is possible to connect a great number of members to one connecting piece
in the drawing board.
K’nex bridges are very different. K’nex pieces
are all made from the same solid plastic material. There is a limited variety
of members each at a set size that cannot be changed. Connector pieces, known
as gussets, are different as well. They have a certain amount of slots at
specific angles that fit the member pieces. The K’nex kit has more artistic
freedom than the WPBD, since with K’nex a design doesn’t have to be symmetrical
on both sides and the perpendicular connecting pieces can be drafted by the
user.
There
are a few similarities between the two. Both use straight members that can bend
a bit to support a design up to a certain breaking point. They both have the
possibility to create different shapes not limited to triangles, but triangles are consistently the strongest structures. They both bring new challenges to creating a design that prompt the designer to think things through to determine the best course of action.
Future Work
If our group was to design another version of the bridge, we would
completely scrap the design we’ve been trying to work with from the beginning
and we would work to make our bridge as strong as it can possibly be. This
seems to be the best technique since the average class price ranges from
$300,000 dollars to $900,000 dollars, but the weights range from 10 to 100
pounds, and the cost-to-strength ratio was anywhere from $8,000 dollars a pound
to $27,000 dollars a pound. With this in mind, it makes more sense to spend the
extra few hundred thousand dollars to get 20-40 extra pounds of weight.
Our future bridge design would probably also be less about what we
think is unique and might work, and more about strengthening what has been
proven to work in the past. These tried and true designs have weathered
centuries of use, and thus would likely be a better option than anything our
group could think up on the spot.
