PAGE 7 ME2112 QUESTION 4 (TOTAL: 25 MARKS) Figure Q4 shows a uniform cylindrical beam ABC of length 4L, built in at the left end A, and supported by a roller at B, a distance of 3L from A. A uniformly-distributed load of w N/m is applied from B to C. The beam is made of a material that has a Young's modulus of E, a shear modulus of G, a Poisson's ratio of v and its weight can be neglected. The second moment of area and polar second moment of area of the shaft cross-section are I and J respectively. (Use only the quantities relevant to this problem.) (a) (b) (c) (d) Sketch as accurately as possible, the deflected shape of the beam, ensuring that any curved or straight portions, positive or negative deflections, inflexion points, etc, relative to the unloaded state are correctly depicted. (A plastic ruler may help you visualise this.) (2 marks) Sketch the bending moment distribution, ensuring that it corresponds to the deflected shape of the beam. (3 marks) Sketch the shear force distribution, ensuring that it corresponds to the bending moment diagram. (2 marks) Calculate all the reactions in terms of the uniformly-distributed applied load w N/m. (Judicious and appropriate use of a plastic ruler may help you determine the directions of the reactions.) (e) Determine the maximum upward deflection in the beam. w N/m B C 3L mm. L Figure Q4 (13 marks) (5 marks)