(Solved): 1.Cantilever Beams: a. Determine, using an \( \mathrm{FBD} \), bending moment function (at a dista ...

1.Cantilever Beams: a. Determine, using an \( \mathrm{FBD} \), bending moment function (at a distance \( \mathrm{x} \) ) for a cantilever beam of length \( \mathrm{L} \) and a point load \( \mathrm{W} \). The load is applied at the free end of the cantilever. b. Obtain a function for the deflection of the beam in terms of position \( \mathrm{x} \). What is the maximum deflection of the beam? E and I are given. c. If the (cantilever) beam extends beyond the point load and there are no loads on the extended part, what is the shape of the deflection of the extended part of the beam? 2. Simply Supported Beams: a. Determine, using a FBD, bending moment function (at a distance \( \mathrm{x} \) ) for a simply supported beam of length \( \mathrm{L} \) with load \( \mathrm{W} \) at the center. The load is applied at midspan. b. Obtain a function for the deflection of the beam in terms of position \( \mathrm{x} \). What is the maximum deflection of the beam? 3. If the bending moment is constant on a beam section, what is the radius of curvature of the beam in that section in terms of \( \mathrm{M}, \mathrm{E} \) and \( \mathrm{I} \).