Please solve! Show full steps! The beam shown in the figure has lateral support provided at the supports and at

the free end. The concentrated loads shown consist of $50\%$ dead load and $50\%$

live load. Design the beam using A$992$ steel. The maximum allowable deflection

is $\frac{1}{360}$ of the main span.

Design a steel bearing plate for the right support if the beam will bear on a

reinforced concrete wall with $c$ of $4$ksi. In a direction perpendicular to the walt

the bearing plate may not be longer than $6$ inches.