Finite element method for civil engineering
You are a structural engineer working in a housing project that is building three storey bungalow units. A typical main frame ABCDEFGH that the architect is proposing is provided in FIGURE Q1. The architect would like to keep the structural elements to a minimum and hence has proposed that it must consist of six columns (AB, BC, CD, EF, FG and GH) of equal length and three beams (BG, CF and DE), also of equal length. The height of the columns, LCC = 3.05 m, the length of the beams, LBB = 5.4m, factored imposed load of FBG kN/m = 3.25 on beam BG, factored imposed load of FCF,DE kN/m = 4.3 on beams CF and DE and a point load of X kN = -55.0 due to wind at beam column junctions B, C and D. As it is easiest to transport to the site, the architect decided to construct the frame from steel and want to fabricate all connections as fixed connections.
1. Your technical director, who believes in optimisation of structures for weight (least material), has asked you to size all of the members of the frame such that no members exceed their yield stress while minimizing the weight of the whole structure. She asked you to use the simple finite element program that you use in the office. Use necessary simplifications backed by solid reasoning and choose only standard steel cross-sections.
2. While you are working on this project at home, your father, who is a retired earthquake specialist, is concerned that you are not considering any dynamic loading. To allay these fears, you have decided to perform a dynamic analysis, the first step of which you have decided will be the computation of mode shapes and their associated frequencies. Compute the frequencies of the first 5 mode shapes and their associated mode shapes by modifying the simple program from QUESTION 1.
3. Once you presented your initial design of the frame, a senior engineer has raised some concerns about the simple beam column finite element solution that you have used. With justification, evaluate the validity of the solution adopted with respect to the structural stability, material behaviour and magnitude of the final deflections.
