Bridge Girders Adria Hogan Benedictine High School Richmond, VA Developed with funding from the American Council of Engineering Companies of Virginia and the MathScience Innovation Center. Question Where should the girders that support bridges be spliced in order to preserve their strength? Grade/Subject Grade Six Science, Physical Science, Algebra 1 Virginia Standards of Learning: 2010 Science 6 (6.1); 2010 Physical Science (PS.1, PS.10); 2009 Algebra I (A.7) 21st Century Curriculum Engineering: Design and Build (2.22, 2.23); Civil Engineering (4.41, 4.43, 4.45) Background Bridges bring people and vehicles safely across a span. Safety depends on strength. Bridges are only as strong as the individual structures of which they are made. How do engineers design the supports of large structures using single or multiple supports? Reducing costs is important to any engineer designing a project, and bridge projects are no exception. A good way to reduce construction costs is to splice or join large girders together to create single large steel girders needed to span highways. The critical question—where to splice the girders together—must be answered. Loads are divided into 2 categories. Dead load is the weight of the material making up the bridge. They do not change. Live load is the weight of the things on the bridge. Live loads are dynamic (they change). Bridge designers must design with the maximum live load in mind. Moment is the force of an object on the supporting member. In the case of a bridge, the further out the object is from the support, the greater the moment. Therefore, the largest downward vertical moment is found at the middle of the span and the largest upward vertical moment is found at the supporting members. Safety Remember to follow your regular classroom rules for labs and activities. Materials Bridge Girders TI-83 or another graphing calculator, paper, pencil Popsicle Sticks Masking Tape http://mathinscience.info ©MathScience Innovationn Center, 2007 Procedure Pennies Objects that will provide 5”-10” vertical height (chairs) 1. Tape together 3 popsicle sticks end to end. 2. Place the chairs 1 popsicle stick length apart and tape the sticks to the chairs at the ends. You will have a stick on either side that is unused. 3. Load the stick with pennies in increments of 10 at the center of the stick and record how many pennies are needed to break the tape at the end. 4. Place the chairs 2 popsicle-stick-lengths-apart and tape the sticks to the chairs at the ends. You will have a stick on one side that is unused. 5. Load the sticks with pennies in increments of 10 at the center of the stick and record how many pennies are needed to break the tape at the end or the middle. 6. Move the sticks and re-tape them to the chairs so that they are taped to the chair at the middle of the sticks on both sides. 7. Load the sticks with pennies in increments of 10 at the center of the chair space and record how many pennies are needed to break the tape at the end or the middle. Be sure the push down on the end of the stick that is outside the chair space as much as the moment on the inside of the chair space. 8. Move the sticks and re-tape them to the chairs so that they are taped to the chair at the end of the sticks on both sides. 9. Load the sticks with pennies in increments of 10 at the center of the chair space and record. Data Analysis/ Results Bridge Girders # Sticks Arrangement of Sticks http://mathinscience.info # of Pennies at Break Point ©MathScience Innovationn Center, 2007 The graph represents the moment of a bridge girder. The vertical supports are at 0 and 6.28 (0 and 2 ) on the x axis. As an object moves further away from the vertical supports, the girders deflect. The popsicle sticks in the activity represent the splices in the steel girders used to hold up a bridge. Conclusions/ Questions Based on the table of data compiled, where is it best to splice girders for bridge supports? In theory, it is best to splice them where the forces pushing up and balanced by the forces pushing down. On the graph, that occurs where the curve crosses the x axis. References http://www.pbs.org/wgbh/buildingbig/educator/act_columns_ei.html http://www.asce.org/kids/ MathScience Innovation Center Information on educational programs available to students, teachers and school divisions and procedures for registering for programs. http://msinnovation.info Bridge Girders http://mathinscience.info ©MathScience Innovationn Center, 2007