Nov 7, 2014 Kevin R. Kline, PE, District Executive PennDOT Engineering District 2-0 1924 Daisy Street - P.O. Box 342 Clearfield County, PA 16830 Dear Mr. Kline: Reference. PennDOT Engineering District 2-0, Statement of Work, subj: Concept Design for Vehicle Bridge over Spring Creek along Puddintown Road in College Township, Centre County, PA, revision #1, dated February 10, 2014. Statement of Problem. A flood has washed away a vital bridge for College Township over the Spring Creek. A crucial access point for the county, it’s vital for transport to the Mount Nittany Medical Center. Without this bridge, heavy traffic stress is put on the State College area, and emergency vehicles have limited access. Objective. PennDOT has begun an urgent project to design and construct a bridge to replace the bridge destroyed in the flood. Design Criteria. The new bridge must include standard abutments, be only one span, have a deck of medium strength concrete, and no cable anchorages. It must support the weight of two AASHTO H20-44 trucks, one in each lane, at the same time and must be 20 meters tall and span 40 meters. Technical Approach.

Phase 1: Economic Efficiency. The cost of a replacement bridge was determined using the West Point Bridge Design software. Using the WPBD software, a replacement bridge was systematically designed to ensure that the cost was as low as possible while still meeting all requirements and being able to support a dead and live load.

Phase 2: Structural Efficiency. Both a Howe and Warren truss prototype bridge was built using standard Popsicle sticks. The bridges were then tested until failure when they collapsed. To determine structural efficiency, the weight of the bridge itself was divided by the weight the bridge supported at failure.

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Results.

Phase 1: Economic Efficiency. The Howe Truss cost $326,392.87, compared to the price of our Warren Truss design, which cost $240,056.42. The Warren design used only 2 more members, making it much more economically efficient. Please refer to Attachment 1 starting on page 3 for a more detailed analysis.

Phase 2: Structural Efficiency. < Reference Attachment 2 and briefly summarize the results detailed in Attachment 2.> Best Solution. The best solution between the two bridges designed by our team was the Howe Truss Bridge. While it was the more expensive bridge, it was much more structurally efficient as well. The Howe Truss cost close to $90,000.00 more to construct, but had a structural efficiency value of 424.573 compared to the Warren value of 156.214. Because the Howe Truss was considerably stronger, we recommend this bridge due to the greater safety it provides. Refer to Attachments 1 and 2 for a more in depth analysis of both bridges. Conclusions and Recommendations. In conclusion, we recommend the Howe Truss Bridge to replace the bridge washed away in the flood. The greater efficiency of the Howe Truss is worth the increased price. We recommend to begin construction of our Howe Truss Bridge design as soon as possible to allow for normal traffic patterns to resume. Respectfully, Fletcher Bucolo Engineering Student EDSGN100 Design Team #6 College of Engineering Penn State University

Thomas Greene Engineering Student EDSGN100 Design Team #6 College of Earth and Mineral Sciences Penn State University

John Gruber Engineering Student EDSGN100 Design Team #6 College of Earth and Mineral Sciences Penn State University

Mike Hadesty Engineering Student EDSGN100 Design Team #6 College of Earth and Mineral Sciences Penn State University

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ATTACHMENT 1 Phase 1: Economic Efficiency

Howe Truss.

Figure 1: Howe Truss Bridge

In determining the cost efficiency of the bridge, a variety of bridge designs were tested

to ensure that the cheapest and strongest bridge was built. It was decided that quenched and tempered steel was the most expensive and the strongest material; therefore, this material was only used for the hip verticals and verticals. While carbon steel is the cheapest material, we decided it was too weak to use extensively in the final bridge; it was only used in the end posts. High strength steel composed the rest of the bridge, being the middle ground of both cost and strength.

Table 1: Cost Calculation

High strength steel was used for the majority of the bridge because it was cheaper than quenched and tempered steel, but not as strong. To compensate for this, the width of the steel rod was increased in areas under high stress. Quenched and tempered steel in the verticals was used because those members were under some of the highest tension forces, so this material was selected for its strength. Carbon fiber steel is light but weak, and only used in the end posts.

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These two members were under an intermediate compression force. The top chords are made of high strength steel and are under the highest compression forces in the bridge. This material was used because it is cheaper than quenched and tempered steel but was still able to withstand the force. The end posts were designed with quenched and tempered steel because this material is the strongest of the three steels; the end posts are under the highest tension forces in the bridge. Table 2: Load Test Report

Member #3 is under the highest compression force with a compression force/strength value of 0.87. The piece is a top chord made of high strength steel measuring 150mm x 150mm x 4m. Please see Table Three on page 5 for more details.

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Table 3: Member Detail Report

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Warren Truss.

Figure 2: Warren Truss Bridge

After many different structural variations and analyses of various member types, we were able to construct what we are confident is the bridge model with the greatest cost to strength ratio. This means that our bridge is perfectly sound structurally, while still achieving the lowest possible cost. Typically, making the cross sections tubes as opposed to solid beams was the cheaper option, and carbon steel was typically the cheapest material to build with, however this was not always the case. Because of this, we constructed our bridge by using the most cost efficient strut for each location. This strategy is what allowed us to construct such an efficient bridge. Table 4: Cost Calculation

Carbon steel bars were used for the majority (23/39) of the struts because of their relatively low price compared to other materials, without having to compromise the overall strength of the bridge. Additionally, we used tubular struts opposed to solid bars whenever they could be used without sacrificing the structural integrity of the bridge, since they were often the cheaper option. Finally, we reduced the width of struts whenever it was an option, as this reduced the overall weight of the member, effectively reducing the cost as well. However,

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we made sure that whenever we took steps to decrease the overall cost of the bridge, we were not making dangerous decisions for the sake of a lowered price. Our bridge was tested extensively to ensure that our cost-cutting decisions would not result in an unstable bridge. Table 5: Load Test Report

Member #39 is under the highest compression force, with a compression force/strength value of 0.97. This member is a top cord made of carbon steel with a solid cross section and measuring 160mm x 160mm x 4m. A more in depth analysis of this member can be seen in Table 6.

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Table 6: Member Detail Report

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ATTACHMENT 2 Phase 2: Structural Efficiency

Howe Truss.

Prototype Bridge. The standard design for the Howe truss was used for construction. 50 out of 60 available Popsicle sticks were used along with 3-5 g of Elmer’s glue. Hot glue was used for all struts and floor beams. It was decided that 50 Popsicle could be used without compromising structural efficacy of the Howe truss while saving on overall costs. The final dimensions’ for the Howe truss: Height - 4.125 in, Width – 4.5 in, Length 12.5 in.

Figure 3: Before Testing Load Testing. Load test results are displayed below, in Table 7, from most to least

structurally efficient. Our Howe truss was able to hold a total of 30,536.77 grams for a structural efficiency of 424.5787 per gram of bridge weight, which is 109.87 per gram of bridge weight above the average. Please see page 10, Table 7 for a detailed chart.

Forensic Analysis. Our Howe Bridge failed at a bottom cord glued joint, labeled 13B and 3C. After this joint failed, the center vertical collapsed. When weight was added to the bridge, the bridge began to twist at the previously mentioned joint. The bridge was able to stand until the twisting on the joint overcame the glue holding it together.

Figure 4: After Testing

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Table 7: Load Test Results Results.

Table 8: Graph of Structural Efficiencies

Design Team No.

Height (in.)

Width (in.)

Length (in.)

Estimate Bridge weight (grams)

Actual Bridge Weight (grams)

LOAD at Failure (lbs)

Structural Efficiency (Estimated)

Structural efficiency (Actual)

1 4 4.625 13.5 85 77.2 81.1 432.781 476.508 6 3.625 4.5 12.5 82.67 71.9 67.3 369.261 424.573 3 4.625 4.5 14.875 113.78 90.8 67.2 267.8981 335.699 8 4.25 4.5 12.875 87.02 81.4 55.9 291.3795 311.497 2 3.875 4.625 13 85.64 80.2 53.4 282.8335 302.018 5 4.125 4.625 13.5 90.8 88.2 36 179.8386 185.14 7 4 4.5 13.25 91.53 81.8 30.2 149.6614 167.463 4 4.325 4.5 11.25 96.78 84.3 0 0 AVG 4.103125 4.546875 13.09375 91.6525 81.975 55.87143 281.9504 314.6997

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Design Team No.

Structural Efficiency (Actual)

Difference of Average Howe

1 476.508 206.307857 2 302.018 31.8178571 3 335.699 65.4988571 4 0 -270.20014 5 185.14 -85.060143 6 424.573 154.372857 7 167.463 -102.73714 8 311.497 41.2968571

Table 9: Structural Efficiency Compared to Average Howe

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Warren Truss.

Prototype Bridge. To build this bridge we used 45 popsicle sticks arranged in a Warren Truss bridge type, along with 2-4 grams of Elmer’s glue to fasten the sticks together. The method used for this bridge design was to create a downward camber for the bridge. This way the bridge would be able to have room to bend before the bridge was completely horizontal. Theoretically, this would add to the structural efficiency of the bridge. Another design aspect of the bridge was to build all top cords, bottom cords, diagonal, end posts, floor beams, and struts vertical with respect to direction of gravity. This way every member would be experiencing force on its strongest side. The only way to do this with popsicle sticks and glue was to cut notches in the bottom cords to act as a place holder for the floor beams. These notches were cut on each side of the bridge in each bottom cord at two locations. See Figure 5 for a detailed look at the notches.

Figure 5: Highlights, in red boxes, the notches cut out on the bottom cords to hold the Floor Beams in a vertical position. For terminology purposes, Figure 6 shows a blown up diagram of the notches.

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Figure 6: Notch cut in the popsicle stick in an attempt to make the bridge stronger.

Herein, the “direction of cut” is used to describe the above diagram

The notches were cut into the bottom cords at about one half of the width of the popsicle stick. During construction, tests were done to determine if the notches in the stick were stable. No conclusive evidence was found to determine that the notches were any less stable in the direction of the cut. However the notches provided a huge loss in structural integrity when forces were exerted on the popsicle stick perpendicular to the direction of cut.

The bridge was built with four diagonals and two end posts for a total length of 12.5 inches. Width and height of the bridge were 4.5 and 4.875 inches, respectively. This was done in an attempt to keep the bridge short and compact to try and increase structural efficiency.

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Load Testing. Load testing results from all Design Teams are displayed below in Table

10. Table 10 shows an isolated table of Design Team 6’s Warren Truss bridge results with the averages across all design teams. Design Team 6’s Bridge fell way below the average of the class, at about 121.525 less than the average.

Table 10: Results of bridge loading for the Warren Truss Bridges. Design Team 1 bridge design had the highest structural efficiency of 453.593. This is

because the bridge failed at 80.8 pounds which is 36650.26 grams. Therefore, for each gram weight of the bridge it supported 453.593 grams. This is a good efficiency for a bridge design, and shows that engineered bridges work well and do what they are designed to do. The average actual structural efficiency for the Warren Truss was 277.739. This average was below the average for the Howe Truss Bridge, which was 314.00. This shows that the Howe Truss is a more efficient bridge to build, not including the cost factor, which is laid out Attachment 1.

Below is a table showing the highest to lowest actual structural efficiencies of all bridge

types across all design teams. The “H” in the team number column denotes Howe Truss, while the “W” denotes a Warren Truss Bridge.

Design Team No.

Height (in.)

Width (in.)

Length (in.)

Estimate Bridge weight (grams)

Actual Bridge Weight (grams)

LOAD at Failure (lbs)

Structural Efficiency (Estimated)

Structural Efficiency (Actual)

1 4 4.5 13.25 90.9 80.8 80.8 403.194 453.593 2 4 3.875 13.5 89.78 85 62.7 316.777 334.591 3 4.25 5.25 13 73.05 68.8 33.4 207.392 220.204 4 4 4.375 11.5 88.5 75.6 54.2 277.794 325.195 5 3.875 4.5 13.125 86.01 78 67.5 355.976 392.532 6 4.875 4.5 12.5 75.81 63.3 21.8 130.436 156.214 7 3.875 4.75 13 91.53 82.7 28.6 141.732 156.865 8 3.875 4.5 13.5 75.98 71 28.6 170.739 182.715

AVG 4.09375 4.53125 12.921875 83.945 75.65 47.2 250.50504 277.739

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Table 11: Highest to lowest Structural Efficiencies of all Design Teams and Bridge Types. A Howe Truss by Design Team 1 was the highest. Forensic Analysis.

Forensic analysis showed failure of the bridge occurred on a bottom cord of the bridge. As load was applied to the bridge, it started to twist. Because of this twist the members were taking load on an axis that was designed to take almost zero pounds of force. When the bridge started to bend, the notch on the bottom cord started to take load. Because of the missing area of the stick, it was weaker, and failed at a small amount of weight. The bridge failed at 20 pounds of load, relativity small compared to all other bridges.

Figure 7: Failure, highlighted in a red box. It occurred on the bottom side of the bridge.

Design Team No.

Height (in.)

Width (in.)

Length (in.)

Estimate Bridge weight (grams)

Actual Bridge Weight (grams)

LOAD at Failure (lbs)

Structural Efficiency (Estimated)

Structural efficiency (Actual)

1H 4 4.625 13.5 85 77.2 81.1 432.7809995 476.508 1W 4 4.5 13.25 90.9 80.8 80.8 403.194 453.593 6H 3.625 4.5 12.5 82.67 71.9 67.3 369.2609508 424.573 5W 3.875 4.5 13.125 86.01 78 67.5 355.976 392.532 3H 4.625 4.5 14.875 113.78 90.8 67.2 267.8980798 335.699 2W 4 3.875 13.5 89.78 85 62.7 316.777 334.591 4W 4 4.375 11.5 88.5 75.6 54.2 277.794 325.195 8H 4.25 4.5 12.875 87.02 81.4 55.9 291.3794948 311.497 2H 3.875 4.625 13 85.64 80.2 53.4 282.8335049 302.018 3W 4.25 5.25 13 73.05 68.8 33.4 207.392 220.204 5H 4.125 4.625 13.5 90.8 88.2 36 179.8385985 185.140 8W 3.875 4.5 13.5 75.98 71 28.6 170.739 182.715 7H 4 4.5 13.25 91.53 81.8 30.2 149.6613773 167.463 7W 3.875 4.75 13 91.53 82.7 28.6 141.732 156.865 6W 4.875 4.5 12.5 75.81 63.3 21.8 130.436 156.214 4H 4.325 4.5 11.25 96.78 84.3 0 0.000

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Results. Results of all of the Warren Bridges are shown below in Table 12 and Figure 8.

Another table, Table 12, shows the difference between each Warren Truss bridge and the average of the Warren Truss structural efficiency (277.700). A positive value shows that the bridge was better than the average Howe Truss, while a negative value shows that the bridge was worse than the average Howe Truss.

Table 12: Diffrence between each Warren Truss bridge and the average.

Figure 9: Bar graph of the Strucural Effiencencys of the Bridges. Numbers are used from

the above table.

Design Team No.

Structural Efficiency (Actual)

Difference of Average Warren

1 453.593 175.854 2 334.591 56.852375 3 220.204 -57.534625 4 325.195 47.456375 5 392.532 114.793375 6 156.214 -121.52463 7 156.865 -120.87363 8 182.715 -95.023625

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