A simply supported beam carries a uniformly distributed load as shown in the following figure. The deflection, 8, along the beam is governed by the following equation: WX (L'-2 Lx? + x') 24 EI x is the distance from the support A; L is the total length of the beam; w is the load per unit length; E is the Young's modulus of the beam, and I is the moment of inertia of the section of beam. where (Hint: w, L, E and I are constant parameters) Prove that: the maximum deflection is at the mid-span of the beam, (a) that is at x = ; and 5 wL (b) the maximum deflection is 384 EI A max