EXAMPLE $4\mathrm{.}7$ A beam carries vertical concentrated loads as shown in Figure $4\mathrm{.}12$a$.$ The beam is pin$-$supported at $\backslash ($ A $\backslash )$ and supported by a roller on a horizontal surface at $\backslash ($ B $\backslash ).$ A beam of this type with the indicated supports is called a simple beam. The supports are called simple supports. The reactions at the supports are assumed to be parallel to the loads. Calculate the reactions at each support. Neglect the weight of the beam.