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MENG 4326 HCCS Optimization of Truss Worksheet

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MENG 4326 Exam 1 Part b (40 Points) You are hired by an engineering firm to certify and, if needed, improve upon the initial design of a space truss. The initial design of the structure is given in figure below. The truss is made of A36 steel with 𝐸 = 200 πΊπ‘ƒπ‘Ž, yield stress of πœŽπ‘¦ = 250π‘€π‘ƒπ‘Ž and density of 𝜌 = 8000 π‘˜π‘”/π‘š3. The current price of A36 steel is $0.75 per kg. The team that originally designed this bridge used a factor of safety (FS) of FS = 2.5 for all design purposes and they made sure that 𝐹𝑆. 𝜎 < πœŽπ‘¦ 𝑖𝑛 π‘Žπ‘™π‘™ π‘’π‘™π‘’π‘šπ‘’π‘›π‘‘π‘  … (1π‘Ž) 𝐹𝑆. |𝜎| < πœ‹2𝐸 𝑑 2 8 (𝐿 ) 𝑖𝑛 π‘‘β„Žπ‘’ π‘’π‘™π‘’π‘šπ‘’π‘›π‘‘ π‘€π‘–π‘‘β„Ž π‘π‘œπ‘šπ‘π‘Ÿπ‘’π‘ π‘ π‘–π‘£π‘’ π‘ π‘‘π‘Ÿπ‘’π‘ π‘  … (1𝑏) Where d is the diameter and L being the length of the member. In the initial design, all bars have a diameter of 30mm. 1. Utilizing the Finite element method find out if the initial design truly satisfy conditions outlined in Equation 1a and Equation 1b? If not, clearly state which elements do not satisfy those conditions? 2. If the initial design is not acceptable, you should improve the design as many times as needed to finally land of a design that meets the conditions in Equation 1. The only design parameter you can change is the diameter of bars. Beware that only bars with 30mm, 35mm and 40mm in diameter are available in the market. To minimize confusion at the construction site, you can only use a maximum of 2 different types bars in your design. MENG 4326 Exam 1 Part b (40 Points) 3. Moreover, you should try to minimize the cost of construction. Report the final cost for the material used in your design. Note: Make sure to upload all analysis files you generated along with the report. Let’s say the initial design does not satisfy some of the criteria and you want to improve the design. Clearly state how you are going to modify the design and why you think that modification is going to help satisfy the design criteria.
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