ENGR 211 Bridge Design Project Preliminary Design of Single-Span Truss Bridge for Truck Loading Select Optimum Material and Cross-Section Satisfy Allowable Tensile Stress and Buckling Criteria Satisfy Minimum Cost Criteria Utilize the West Point Bridge Designer Program

Typical Single-Span Truss Bridge “Pratt Through Truss” h 6 bays, or 24 m long 4 m typ.

General Scope of Assignment The 24 m single-span truss bridge must support the load of a moving truck with a weight of 40, 000 lb. To simplify the design, we restrict the design so that the lower span has 7 equally spaced joints. These joints cannot be moved or eliminated. See restrictions on other joints as presented later. Your job is to complete the remainder of the truss structure, and design the most economical bridge that satisfies essential design criteria by making the following design choices:

General Scope of Assignment Choose the location of the other joints and place members connecting these joints. Choose the "best" combination of materials (A36 carbon steel or A572 high strength steel), cross-section geometry (solid rectangle or tube), and the cross-section size (varies, mm). Optimize your design for minimum bridge material cost (see program for cost algorithm).

General Scope of Assignment Design constraints include: Tension in members cannot exceed a tensile strength that would cause failure by material yielding, and Compressive force in members cannot exceed a compressive strength that would cause failure by member buckling.

AASHTO H20-44 Cargo Truck The AASHTO H20-44 cargo truck has two axles spaced 14 feet (approximately 4.3 meters) apart. The front axle load is 8,000 pounds (approximately 3,600 kg) and the rear axle load is 32,000 pounds (approximately 14,500 kg). When designing a bridge for an AASHTO H20-44 loading, the designer must ensure that all members in the structure can carry the forces generated by this loading, no matter where the hypothetical H20-44 truck is positioned on the bridge. The design program does this for you by spreading the weight over two (or more) adjacent nodes. The design program does multiple analyses to simulate the truck moving across the bridge.

The Design Process Once you select the joints and members connecting the joints, the design program will make an initial selection for the material (carbon steel), cross-section type (solid rectangle) and cross-section size (120x120 mm). The program than performs a systematic truss analysis to determine the internal force in each truss member (tension or compression).

The Design Process Failure Analysis If the member is in tension, the program checks to see if the member stress (force/cross-sectional area) exceeds the tensile strength (allowable stress) for the material that has been selected for that member (failure due to the material "yielding" or becoming inelastic). If the member is in compression, the program checks to see if the compressive force exceeds the compressive strength of the member (failure due to physical buckling). After the program completes the analysis, you may check you design in three windows at the bottom of the screen.

The Design Process Checking Your Analysis: The program provides several output “windows” Load Test Results (click on right i at the bottom) Cost Summary Member List Examples of these are shown below:

Load Test Results

Member List

Cost Summary Cost Algorithm Note that different materials and cross-sections have different costs per kg of member. Each connection (joint) has a cost. An overall product cost is added.

The Re-Design Process If the member fails by yielding, it has failed the following test where P is the tensile force in the member, is an empirical constant, is the yield stress for the material and A is the cross-sectional area of the member. Therefore, to reduce the possibility of failure by material yielding, you may make one or all of the following changes to your design: Choose a material with a higher yield stress , or Choose a cross-sectional area, A, for the member that is larger.

The Re-Design Process If the member fails by buckling, it has failed the following test: where P is the compressive force in the member, is an empirical constant depending on end conditions, E is Young's modulus of elasticity for the material, I is the moment of inertia of the cross-section, and L is the length of the member. For a rectangular cross-section of dimension bxh, ; and for a tube with outer diameter Do and inner diameter Di, . Therefore, to reduce the possibility of failure by member buckling, you may make one or all of the following changes to your design: Choose a material with a larger Young's modulus (E), Choose a cross-section with a larger moment of inertia (I) which means increasing the cross-sectional area, or Make the member shorter (L).

The Re-Design Process If the member is over-designed, e.g., the tensile force is much less then the allowed tensile strength, then we may re-design the member using ideas opposite to that in the above paragraphs. For example, if the tensile force is much less then the allowed tensile strength, choose a cross-sectional area that is smaller, OR a material with a lower yield stress if cheaper. There will typically be several options in which to re-design, so the design process is iterative, or is a trade-off study between the various options.

Tensile Yielding of an Elastic Material

Elastic Buckling of a Rod

Teams Have Different Problems Each team is to work a different problem according to the following schedule: Teams 1-5: All member joints you add must be greater than 4.5 meters and less than 6.5 m in height. NO restriction on horizontal location (except those at 0 meters, which are fixed). NO restriction on the number of joints or members you use. Teams 6-10: As above, but 5.0 to 7.0 meters. Teams 11-15: As above, but 5.5 to 7.5 meters. Teams 16-21: As above, but 6.0 to 8.0 meters.

2-Member Teams You are to work in teams of two. Therefore, from your current team of four, the following two sub-teams are defined: Arrange your team alphabetically; then Team A is the first two in the alphabetical list; Team B is the other two team members. Thus, if you are on team 7, we now have two 2-person teams for the design project: 7A and 7B.

Report Requirements Formal written report (word processed document) consisting of Summary (short) of the design problem and your design results and recommendations, and cost [this is what your boss would read to determine if the rest of the report is worth reading], Description of the design problem, requirements, truss loading, etc., General description of how a truss analysis is conducted, Description of procedure that your individual team took to reach your final design, trade-off studies you did, etc., Summary and discussion of the final design details and the cost (the program will print these for you), with references to design program results contained in the appendix, and an Appendix containing a printed copy of the truss drawing, member list window, the cost summary window, and the load test results window.

Project Grading Maximum score - 100 points Satisfactory design - 25% Design report - 35% Lowest Cost post design - 40%. Two teams with the lowest cost designs will receive full credit (40%), next three lowest cost designs will receive 80% of maximum available design score (80% of 40%), remaining teams with the highest cost designs will receive 60% of the maximum available design score, and Failure to meet the assigned design scope or assigned team problem will automatically place your team in the lowest category (even if you have the best design!).

Due Date Thursday, November 30, 10 AM (no exceptions!)