Determine the plastic moment Mp of a steel beam of the cross section shown, assuming the steel to be elastoplastic with a yield strength of 230 MPa. 50 inm 30 inm 10 mm 10 mm HH 10 mm 30 mm The plastic moment of the steel beam is KN-m.

Please provide step-by-step calculations, also draw the nodes showing temperatures l A rectangular cross-section bar is held in steady conditions at different temperatures on each of its 4 sides. There is no internal heat generation, and the material properties are constant in all directions at all temperatures. The cross section has an aspect ratio of 1.5, with its longest side measuring 2.5 m in the x direction. It is split into 4 nodes in the x direction and 3 nodes in the y direction. The node numbering starts from (1,1) in the bottom left hand corner. The temperatures of the faces are held constant as follows: left hand side = 428 K, right hand side = 506 K, top side = 367 K, and bottom side = 298 K. The initial guess for the temperature of the internal nodes is 301 K. Using the Jacobi method to iterate, complete the following sentences.  a) The temperature of node (3,2) after the 2nd iteration is _____ K. b) The temperature of node (3,2) after the 3rd iteration is _____ K.

(b) Find the natural frequencies and mode shapes. (c) Calculate the natural frequencies and mode shapes with m₁ = m2 = 2 kg and k₁ = k2 = 3000 N/m. You can just use the formula you obtained in (b).

3. Determine the displacement of an eight-cylinder engine having a bore of 3.25 in and a stroke of 3 in.