A1 Oil Rig Structure Design After finishing ENGRD2020, you are selected to participate in the design of a new oil rig off shore. The geometry of the proposed oil rig design is illustrated in the right figure below and simplified to a 2D form (drawing not to scale). The parameters related to the geometry are given in the following table. Major loads considered in the design are the self-weight of the square-profile beam (cross-section side dimension a) used for the platform and the point load from the onboard crane (value given in table). The entire platform sits on top of 2 columns at locations specified in the drawing. Both columns share the same design (cross-section side dimension b and end type) and are made of the same material as the platform. The material chosen for this oil rig is steel, given its availability, weldability and low cost (p = 8050 kg/m, E = 200 GPa, fail 350 MPa, Tfail 175 MPa). LNG AN OIL TANKER A L L2 W b H ???? '? M C. lb Pinned end or 10 Fixed end P crane B NC. .? Given Parameter Value Li 20 m L2 5 m Find a H Perane wo g Total budget Material cost 100 m 5 000 kN Platform Beam Profile Dependent 9.81 m/s $900 000 $4.000/m $20000 per end Pinned End cost Fixed End cost $50 000 per end b End type (same for both columns) overall m The different parts of this problem are designed to guide you through the process to set up the optimization/iterative design. 1. Find expressions for the internal shear and moment for each segment of the platform beam in terms of L1, L2, Wo, P and x (where 0 x L1 + L2). 2. Draw the moment and shear diagrams of the platform beam for the hypothetical case a = 1 m and wo specific to steel. Identify the values and locations of maximum shear and normal stress. 3. Calculate the maximum allowable dimension b for the given total cost and the hypothetical case of a = 1m and pinned ends. Using 6 and the reactions at points A and B from part 2, determine the factor of safety of the structure against buckling. 4. What are the possible modes of failure in this oil rig design? Keep in mind that we don't yet know the likelihood of each one, so list everything. 5. With the fixed total budget and the given loading condition, find an optimal design in terms of dimension a, dimension b and end type that achieves the largest overall factor of safety.