An engineering department is tasked with assessing a floor beam in a tool-making factory for the installation of a new machine. The design manager needs to know the maximum permissible load to avoid plastic collapse of the floor beam with a factor of safety of 4. The floor beam is 5m long and may be regarded as simply-supported at each end. The floor is already loaded with a machine which exerts a load of 20 kN at the location shown (1m from end A) in Fig. Q11. The new machine is to be located 2m from end B. Neglect dead weight of the beam and assume that local buckling of the beam section is not a critical mode of failure. a) First determine 3 possible collapse mechanisms (one plastic hinge) to assess. Draw a basic sketch of each of these showing the loads acting on the mechanism and location of the plastic hinge. b) Determine the critical collapse mode and corresponding maximum value of P that satisfies the design criteria to avoid plastic collapse of the floor beam with a factor of safety of 4 if the floor beam section has a plastic moment capacity, M, of 200 kNm. (Ans: 40 kN) Im 20 kN P. 2m B Sm Fig. Q11