As shown in the Figure Q4, a beam with a length of L is fixed at...

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As shown in the Figure Q4, a beam with a length of L is fixed at point A and subject to a uniformly distributed vertical load of w per unit length. Point B is free to move. El is constant. (a) Derive the bending moment in the beam as a function of the position x (the distance to point B). (6 marks) -L (b) The bending strain energy for a beam is: U = 1 M dx. If a virtual vertical force of is applied on point B, derive the virtual complementary energy in the beam. (8 marks) (c) Solve for the vertical displacement of point B under the distributed load w (relative to the unloaded beam). (6 marks) B W X L Figure Q4 A As shown in the Figure Q4, a beam with a length of L is fixed at point A and subject to a uniformly distributed vertical load of w per unit length. Point B is free to move. El is constant. (a) Derive the bending moment in the beam as a function of the position x (the distance to point B). (6 marks) -L (b) The bending strain energy for a beam is: U = 1 M dx. If a virtual vertical force of is applied on point B, derive the virtual complementary energy in the beam. (8 marks) (c) Solve for the vertical displacement of point B under the distributed load w (relative to the unloaded beam). (6 marks) B W X L Figure Q4 A