1. RPI Master’s Project Stephen Ganz – August 2012 Structural Analysis of Bridge Gusset Plates: Steel vs. Composite

2. Problem Description The objective of this project is to compare the performance differences in metallic and composite plates by performing structural analyses on the vertical section of a Warren truss bridge Material performance is based on stresses and deflections The materials chosen are A36 Carbon Steel and HexPly 8552 IM7 prepreg composite This will be accomplished by comparing results from computer generated Finite Element Analyses. Requirements for the bridge is based on federal and state regulations

3. Steps to Completion Develop Bridge Model Develop Gusset Plate Detail Dimensions Calculated loads based on bridge model –Dead Load –Live load Constructed a working 2D FEA model of a Warren truss bridge Perform a Mesh Study Determine Best Evaluation Method to Analyze Composite Plates Run Analyses & Compare Results based on FS and Deflections

4. Bridge and Plate Details As previously mentioned, the vertical section is a Warren Truss with verticals. It’s length was arbitrarily chosen, but it’s height and width are based on state and federal requirements Gusset plates were selected to be 2 inches thick

5. Loads Loads were based on the overall dimensions of the bridge model as well as state and federal requirements for vehicles. This included weights of the trusses, sidewalks, snow, vehicles and road deck. Total Load (W) is 576,636 lbs Total Dead Load 297,201 lbs Trusses – 101,721 lbs Sidewalk – 43,500 lbs Roadway – 205,200 lbs Floor and Roof Joists – 98,759 lbs Total Live Load – 279,435 lbs Vehicles – 188,235 lbs Snow – 182,400 lbs

6. Model Development The best way to produce accurate results is to include the truss members –By using a coarse mesh for the trusses their presence comes at very little computing cost –Tie constraints bond the the trusses to the plates to simulate a weld A B C D E F G H IiIi J K L W 5W 5 W 5W 5 W 5W 5 W 5W 5 W 5W 5 Pinned End Roller End Loads were applied as surface tractions (psi) at the 5 locations shown

7. Mesh Study & Failure Method Mesh studies were carried for both steel and composite models –This was done by varying the mesh density of the plates until a convergence of stress or TSAI-WU criteria was observed Developing an accurate way of calculating Factors of Safety for the composites (CFAILURE)

8. CFAILURE This field output request has been selected as the tool to provide the necessary results from FEA to base composite failure on CFAILURE is a built in feature in Abaqus that can allow the user to view results based on Maximum Stress Theory, Maximum Strain Theory, Tsai- Hill and Tsai-Wu criterion Factors of safety are calculated as 1/TSAIW for each layer Defining the failure stresses in Abaqus (Edit Material -> Suboptions -> Fail Stress)

9. FEA Results A36 Steel ModelComposite Models [0 15 30 45 60 75 90]S [0 45 90]S [0 90]S Shown here are the maximum values for stress in the A36 Steel Model and maximum TSAIW values in the composite models Factors of Safety for Steel are based on Von Mises stress Factors of Safety for Composite model are based on TSAIW values

10. Deflections Illustrated x100 A36 Steel Model Composite Models [0 15 30 45 60 75 90]S [0 45 90]S [0 90]S The best performing composite model deformed nearly twice as much as A36 steel.

11. Factors of Safety The table below lists the factors of safety based on failure for all the FEA models. The factors of safety are based on peak stresses or maximum TSAIW values for that particular model Steel displayed the highest factor of safety, outperforming the best composite by approximately 30%. Table 4: Factors of Safety Steel ModelVon-Mises StressMax allowableFS A36 Carbon Steel12668580004.58 Composite ModelsTSAIWMax allowableFS HexPly [0 90]S0.29613.38 HexPly [0 45 90]S0.28613.50 HexPly [0 15 30 45 60 75 90]S0.40012.50

12. Deflections Illustrated x100 The best performing composite model deformed nearly twice as much as A36 steel. Table 5: Deflections Steel ModelU magnitudeU1U2 A36 Carbon Steel0.4540.180-0.447 Composite Models HexPly [0 90]S0.8900.329-0.879 HexPly [0 45 90]S0.8330.331-0.816 HexPly [0 15 30 45 60 75 90]S0.9440.377-0.921 Lowest % over steel183%

13. Outcomes The A36 Carbon Steel Gusset plates outperformed those made from HexPly 8552 IM7 Carbon Fiber composite material based on failure margin and deflections This is primarily due to ther orthotropic nature of composites –HexPly 8552 IM7 is much stronger than steel when loaded longitudinally, but it is only about half as strong as A36 in the transverse directions. Composites do have desirable qualities, but they are not suited for this application in which a plate is loaded in up to 6 different directions.

14. References 1.Kulicki, J.M. “Bridge Engineering Handbook.” Boca Raton: CRC Press, 2000. 2.Abaqus Technology Brief TB-09-BRIDGE-1. “Failure Analysis of Minneapolis I-35W Bridge Gusset Plates,” Revised: December, 2009. Web. July, 2012. http://imechanica.org/files/Architecture-SIMULIA-Tech-Brief-09-Failure-Analysis-Minneapolis- Full.pdf http://imechanica.org/files/Architecture-SIMULIA-Tech-Brief-09-Failure-Analysis-Minneapolis- Full.pdf 3.Meyers, M. M. “Safety and Reliability of Bridge Structures.” CRC Press, 2009. 4.Najjar, Walid S., DeOrtentiis, Frank. “Gusset Plates in Railroad Truss Bridges – Finite Element Analysis and Comparison with Whitmore Testing.” Briarcliff Manor, New York, 2010. 5.State of Connecticut Department of Transportation. “Bridge Design Manual.” Newington, CT 2003. 6.Kinlan, Jeff. “Structural Comparison of a Composite and Steel Truss Bridge.” Rensselaer Polytechnic Institute, Hartford, CT, April, 2012. Web. July, 2012. http://www.ewp.rpi.edu/hartford/~ernesto/SPR/Kinlan-FinalReport.pdf http://www.ewp.rpi.edu/hartford/~ernesto/SPR/Kinlan-FinalReport.pdf 7.Budynas, Richard G. and Nisbett, J. Keith. “Shigley’s Mechanical Engineering Design 9 th Edition.” McGraw-Hill, New York, NY, 2011.

15. References 8.American Standard for Testing and Materials - Standard Specification for Carbon Structural Steel, ASTM A36/A36 M. ASTM International, West Conshohocken, PA 2008. 9.Gibson, Ronald F. “Principles of Composite Material Mechanics Second Edition.” Boca Raton, FL: Taylor and Francis Group, 2007. 10.Abaqus/CAE 6.9EF-1. “Abaqus User Manual.” Dassault Systèmes, Providence, RI, 2009. 11.Portland Cement Association. Unit Weights, 2012. Web. July 2012 http://www.cement.org/tech/faq_unit_weights.asp http://www.cement.org/tech/faq_unit_weights.asp 12.Beer, Johnston. “Vector Mechanics for Engineers Statics and Dynamics 7 th Edition.” New York, NY. McGraw-Hill, 2004.