among the plans subjected to the given loads shown in Fig. 2, in which plan the beam size can be the smallest; (Hint: you need to plot the bending moment diagrams of the following structures and make your selection on the basis of the maximum bending moment within the beams)

Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: ox = (M.I,M,L)y+(M,I.-M.I.) (1,1₂-13/2) where My and M₂ are bending moments applied to a cross-section, and where ly, lz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (iii) A Z--section beam has the cross-section shown overleaf (see Figure QB2). The second moments of area of the section about the y and z axes are given as;; ly = 1.12x106mm² and I₂ = 2.87x106 mm4. Show that lyz = 1.35x106 mm² (use the parallel axis theorem). 100 60 10 y -10 10 60 Figure QB2 N (iv) Bending moments Mz = 2.0 kNm and My = 0 kNm act on a cross- -section of the beam of part (iii). Obtain an expression for the bending stress and sketch the orientation of the neutral axis with reference to the y and z axes. What is the maximum tensile value of the axial bending stress and where does it occur?

Below presents a continuous beam with A being fixed and B is pinned and C has a roller. Take: E = 200 GPa 1 = 8 x 106mm Load = 2 kN A 5m B Using the following method: 2 KN + 2m + 2m |- You are tasked to analyze the continuous beam by calculating the: > the displacement on the beam at B and C and > the reaction at the supports Matrix Structural Analysis Use the following steps as a guide to analyze the beam: Matrix Structural Analysis ✓ Produce Notations ✓ Establish the known displacements and known external load ✓ Produce Member Stiffness Matrix ✓ Displacement and Load ✓ Calculating the displacement Calculating the reaction at the support

Write the number of elements, nodes required and degree of freedom to solve following truss using FEM (Use the best node/element numbering; Do not need to solve it!) Would ANSYS be able to solve the structure with given Boundary Conditions (BC)? If not, what should be done and why?