1. (40%) Use the stress function shown below to analyze a beam carrying a uniformly distributed...

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1. (40%) Use the stress function shown below to analyze a beam carrying a uniformly distributed transverse loading w along its top surface, as shown in Figure 1. O=Cx + C2xy+ Cy + C4xy + Cys (a) Identify how many independent coefficients in the stress function and show any necessary relationship between them. (b) List all boundary conditions of this problem. (c) Derive the expression of the stress components x, Oy, and Txy. (d) Compare the answer of (c) with the results obtained from the strength of materials you learned before. (e) Express the strain components through the stress-strain relations. (f) Derive the expression of displacement u and v through integration of the strain-displacement relations. (g) Find the maximum deflection of the beam and compare the answer with the results obtained from the strength of materials you learned before. w/ 4 2t y 21 WI Figure 1. 1. (40%) Use the stress function shown below to analyze a beam carrying a uniformly distributed transverse loading w along its top surface, as shown in Figure 1. O=Cx + C2xy+ Cy + C4xy + Cys (a) Identify how many independent coefficients in the stress function and show any necessary relationship between them. (b) List all boundary conditions of this problem. (c) Derive the expression of the stress components x, Oy, and Txy. (d) Compare the answer of (c) with the results obtained from the strength of materials you learned before. (e) Express the strain components through the stress-strain relations. (f) Derive the expression of displacement u and v through integration of the strain-displacement relations. (g) Find the maximum deflection of the beam and compare the answer with the results obtained from the strength of materials you learned before. w/ 4 2t y 21 WI Figure 1.