Question

A simply supported prismatic beam is loaded with a load applied at an angle at point F as shown below The beams connecting points CE and EF can be considered rigid (l-very large). The magnitude of the applied load P is 75kN. NOTE: You must use your student number to calculate the magnitude of the angle, α, and the length EF using the expressions below. The angle, α, is given in degrees and the unit for length EF is m 0.24m α-61.8 degrees P1 0.15m 100mm 50mm 0.25m> 25mm Section B-B Not to scale 0.50m 1.00m You are a consultant engineer tasked with evaluating the beam. To do this you must a) Construct the shear force, axial force and bending moment diagrams Hint: You should break down the load P into horizontal and vertical components and then convert the horizontal and vertical forces (at point F) to equivalent forces and moments (at Point C) b) Calculate the magnitudes of the axial force, shear force and bending moment at Section B-B c) Plot the stress distributions overthe height of the beam at Section B-B. Note, the stresses will not be constant. Plot graphs of the principal stresses, σ1 and σ2, and the maximum in-plane shear stress, mao, showing how they vary over the height of the beam at section B-B Ensure that you document the process used to create the graphs. Make sure that all equations are clearly referenced. Hint: It is more convenient to define the y axis from the centroid of the beam's cross-section d) Calculate the stresses at Point P1 at Section B-B. Using the stresses at Point P1 construct Mohr's circle and calculate the maximum in-plane shear stress and the angle associated with the maximum in-plane shear stress. Verify that your result is consistent with your answer for (c). Draw an RVE for the resultant stress state associated with the maximum in-plane shear stress

Answer 1

団 Af point ! 26 .635 MPa 仄 bh C-%)