Bridge Design Project Using the West Point Bridge Design Program

Bridge Design Project using the West Point Bridge Design Program

Consider the design of a 24 m single span truss bridge that must support the load of a moving truck with a weight of 40, 000 lb. To assist you in the design process, we have available the West Point Bridge Design Program. The program is available on the laptops in 103 Zachry, or you may download and install on your personal computer by going to the link on the class web page. To simplify the design, the design program assumes that the lower span will have 7 equally spaced joints. These joints can not be moved or eliminated. 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:  Choose the location of the other joints and place members connecting these joints. For example, five equally spaced joints have been placed at the top with members connecting these joints as shown below.

Typical Bridge Truss

 Choose the "best" combination of  materials (A36 carbon steel, A572 high strength steel, or 2014-T6 aluminum alloy)**,  cross-section geometry (solid rectangle or tube)** and the  cross-section size (varies, mm)**. ** See Design Scope at the end of this document before proceeding.  Optimize your design for minimum bridge cost (see program for cost algorythm).  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.

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.

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 1 internal force in each truss member (tension or compression). 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:

 Load Test Results (click on right i at the bottom)  Cost Summary  Member List

The load test results window will provide various information about each member: Size, cross- section type, material used, length, compressive force, compressive strength, status (OK or buckled), tensile force, tensile strength and status (OK or yielded). If a member has failed, you must redesign it to prevent buckling (if the member is in compression) or material yielding (if the member is in tension). In order to prevent member failure, consider the following.  2 EI If the member fails by buckling, it has failed the following test: P   where P is the L2 compressive force in the member,  is an empirical constant, 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 3 a rectangular cross-section of dimension bxh, I bh /12 ; and for a tube with outer diameter Do and 4 4 inner diameter Di, I ( Do  D i ) . 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.

If the member fails by yielding, it has failed the following test P  y A where P is the tensile force in the member,  is an empirical constant,  y 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  y or  Choose a cross-sectional area for the member that is larger.

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. E.G., 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).

Examples of the member list, cost summary and load test results are shown below.

2 3 4 In this design program, the cost algorithm is provided in the first table of data (example shown above). Notice that the cost depends upon the type of material used, the weight of each material, the number of joints used and a per-unit assembly cost. While not included here, the cost of the bridge supports, abutments, piles, etc. should also be included in practice. For further information on cost, click the help button. Note that carbon steel is cheaper than aluminum alloy (by the lb or kg), solid bars are cheaper than tubes. However, aluminum weighs less then steel. The weight of the structure is included as loads at the joints. Also, note that Aluminum has a higher tensile strength then does HS steel; and HS steel has a greater tensile strength than does carbon steel (affects tensile failure). Steel has a higher Young's modulus of elasticity than does aluminum (affects buckling failure). In order to optimize the structure for minimum cost, it is necessary to juggle all of these parameters so as achieve minimum cost but at the same time satisfy the engineering design constraints on compressive failure and tensile strength. This iteration process is called a design trade-off study.

Program Help The design program has extensive help information: For example; the design process, how to use the program, moving or removing joints (nodes) or members, changing member sizes and materials, what does the red and blue member color mean when you run an analysis, how is the failure analysis done, how is weight of truck treated, etc. Be sure you use the help menu!

Design Scope. While a design engineer might have complete flexibility in varying all of the parameters allowed by this design program, it is prudent to begin your study of the design process by limiting the number of variables. Consequently, for purposes of this design, we will limit ourselves as follows:

 Truss Geometry: When you start the design program, choose a single span truss, then choose "none." The none means that you have complete flexibility over all joint locations except that the lower 7 fixed joints located 4 m apart cannot be removed or relocated.  Material: Only A36 carbon steel or A572 high strength steel may be used (even though the design program allows the use of 2014-T6 aluminum alloy). In practice, steel and aluminum are rarely used together due to cost, fabrication differences, and corrosion between steel and aluminum.  Cross-sectional Shape: You may use rectangular bars or hollow tubes.  Cross-sectional Size: Any size allowed by the program may be used.  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, but 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.

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.

5 When you are satisfied with your bridge design, you are to submit the following report:

Formal written report (word processed document) consisting of  Summary (short) of the design problem and your design results/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.

Your grade will be computed in the following manner:  Maximum score - 100 points  Bridge design - 25%  Design report - 35%  Lowest Cost design - 40%. The amount of credit received for lowest cost design will depend upon your design. The two teams with the lowest cost design will receive full credit (40 points). The three teams with the next lowest cost design will receive 80% of maximum available score (32 points). The five teams with the highest cost design will receive 60% of the maximum available score (24 points). Designs for each of the specified minimum heights will be consider separately. Thus teams 1-5 are competing against each other, etc. 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)