ME104Q THE ENGINEERING OF BRIDGES FALL 2018

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1 Prof. R. Perucchio PROJECT 1 part 2 Design of a Cantilever Truss Bridge Assigned Wednesday Oct 2, due Thursday Nov 1 Objectives: 1. Design and build an optimized cantilever truss bridge according to specifications. 2. Measure forces and deformations in the PASCO model representing the bridge. 3. Compute truss forces for the same bridge using the Dr. Frame CAE software. 4. Practice correlating computed with measured results. 5. Practice report writing. Design Objective: The goal is to design a structurally optimized model, which is light yet stiff when tested and which transmits the smallest possible axial forces. The PASCO models will be tested in the lab. For each model, we will: 1. weigh the truss; 2. apply at the free end a load of 29.4 N (3 kg mass), record the deflection of the structure at the load point, and then compute the load/displacement ratio (i.e., the stiffness) of the structure; 3. insert load cells and measure the maximum axial forces transmitted by the truss; 4. finally compute the load/displacement ratio (i.e., the stiffness) and the truss efficiency as efficiency = stiffness/(weight x max axial force). Your goal is to maximize the efficiency of your truss. Therefore, you need to maximize the stiffness and minimize the weight and the internal forces. The score for the model testing (30 points total) is assigned as follows 20 points max based on stiffness/mass ratio. 10 points max based on the magnitude of the internal forces. Truss Specifications: 1. Bridge must be a cantilever truss statically determinate designed to fit in the design envelope. 2. Overall dimensions: Must span 6 bays (75 cm total), with each bay corresponding to a number 3 beam (12.5 cm for each bay). 3. Support constraints: As shown in the design envelope in Fig. 1, the red beams are mandatory to span the bridge. There will be a pin at the green square. A single roller can be placed anywhere on the black line (3 bays deep). The entire configuration should fit into the blue outline, meaning 2 bays max above the road deck and 3 bays max below the bottom of the lowest possible roller configuration. 4. The fully constrained end must fit into the vertical supports in the test rig available in the lab (see Fig. 2). 5. Loading constraints: On the free end, the 3D structure must have at least one transversal element where a live load of 29.4 N (3 kg mass) will be applied. 6. The 3D structure must consist of two identical 2D trusses (front and back) connected by transversal elements (use number 3 beams for the connection). 7. Any joint introduced in the physical model must correspond to a mechanical hinge. 1

2 Pre-Laboratory Work Expected: Students will continue to work within the same design teams formed for Project 1. Register for a team lab session during which the PASCO model will be tested. (Registration form circulated electronically). All team members must attend the same session. Construct the model prior to the lab session. Members of each design team are expected to work in collaboration. Design and build the bridge PASCO model according to the design specifications given above. Note: each team must build one model only. Hint, Dr. Frame can be useful when designing your bridge. Lab Report: Each team member must submit an independently written report. Briefly describe the design objective and the approach followed in achieving this objective. Describe your 2D truss design with figures (drawings) and tables (force values). Be as accurate as possible in your drawings. Analyze your truss using Dr.Frame for live and dead loads separately. For the dead loads, compute the joint loads due to the mass of each bar (mass table for the PASCO is attached) and inclusive of half the mass of each cross-beam (which connects the two 2D trusses in the third dimension), apply loads to joints, and compute forces on each truss element and reactions at supports. Present the results of the truss analysis. Include three separate figures from Dr. Frame showing 1) the truss geometry (with element dimensions and joint labels), 2) the element forces and the support reactions for the live load, and 3) the element forces and the support reactions for the dead loads. Include also tables showing the forces acting on each element and the total weight of your truss. Discuss and interpret the test and analyze results. A. The team will compare the results obtained from the lab experiments and the numerical model with applied loads. B. Explain possible sources of discrepancies and error. C. Why was your truss successful and how could it be improved? Formatting: The report must be typewritten (either single or 1.5 lines spacing). Your name, date, course, name of instructor and an illustration (if relevant) go on the cover page. Each figure and table must be numbered and must have a caption. In the text, refer to a figure or table by its number (ex., fig. 1, tab. 3). Number the pages and staple them together. Timetable: Oct 1 Project is assigned. Please contact the TAs if you want to inspect the vertical support (used to hold the truss model) or check your model in the rig before testing. 2

3 Oct Sign up form circulated electronically and TAs available to check the PASCO models during regular office hours (checking the model is highly recommended) Oct Lab testing of the PASCO models. Nov 1 Report is due at class time. Figure 1: Design envelope- the red beams are mandatory to span the bridge. The green square is a pin. A single roller can be placed anywhere on the black line (3 bays deep). The entire bridge must fit into the blue outline, meaning 2 bays max above the road deck and 3 bays max below the bottom of the lowest possible roller configuration. 3

4 ME104Q THE ENGINEERING OF BRIDGES FALL 2018 PROJECT 1.part.2 (a) (b) (c) Fig.2. VerAcal support used to lock the constrained end of the canalever truss with truss installed (a) ; ( b) and (c) show, respecavely, support configuraaons with maximum and minimum distance between hinge and roller.

5 Prof. R. Perucchio PROJECT 1 part 2 Design of a Cantilever Truss Bridge 1 October 2018 PASCO Element Mass (grams) Screw I-beam I-beam I-beam I-beam I-beam Full Round Joint Full Round Angle Joint Half Round Angle Joint Table Mass of PASCO elements to be used in computing the dead loads for truss analysis via Dr.FRAME 1