Microsoft Word - MIET XXXXXXXXXXTask 1f.docx Solid Mechanics 3 Assessment Task 1f - 2019 Milestone f (Due by week 9) Question 1 A beam made of an elastic-plastic material, for which the yield stress...

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Microsoft Word - MIET2490-2019 Task 1f.docx Solid Mechanics 3 Assessment Task 1f - 2019 Milestone f (Due by week 9) Question 1 A beam made of an elastic-plastic material, for which the yield stress is 300 MPa, has the cross section shown below. The beam is loaded about the horizontal axis of its cross-section by the bending moment M. Calculate the maximum elastic moment Me and the plastic moment Mp. Also determine and sketch the distribution of the residual stresses in the beam after the plastic moment Mp is applied and then released, showing all significant values. (10 marks) Question 2 A beam shown below is made of an elastic-plastic material for which the yield stress is 200 MPa. a. Calculate the maximum elastic moment Me and the plastic moment Mp. b. Calculate and sketch, showing all significant values, the distribution of the residual stresses in the beam after the plastic moment Mp is applied and then released. c. Calculate the bending moment that would cause the flanges to yield completely, while the web stays elastic. (10 marks) Question 3 A beam with the shown channel-section is made of an elastic-plastic material for which σy = 250 MPa. Calculate the maximum elastic moment Me and the plastic moment Mp and determine the shape factor for the cross section of the beam. Also determine and sketch, showing all significant values, the distribution of the residual stresses in the beam after the plastic moment MP is applied and then released. (10 marks) Question 4 The continuous beam shown in Figure has a plastic moment MP. Sketch the mode of failure showing clearly the locations of plastic hinges and determine the magnitude of the load P for plastic collapse in terms of MP. L = 8.0 m. (7 marks) Question 5 The unsymmetrical frame shown below in figure is having both bases pinned as shown. The beam has a plastic moment MP. Sketch the mode of failure showing clearly the locations of plastic hinges and determine the magnitude of the load P, in terms of MP and the given dimensions, for plastic collapse of the frame. (8 marks) Question 6 The frame shown in Figure is built using a beam having a plastic moment MP. Sketch ALL possible modes of collapse showing clearly the locations of plastic hinges in each mode and calculate ALL corresponding magnitudes of collapse loads and finally determine the magnitude of the critical load P which will cause the frame to collapse. L = 3.0 m. (15 marks)