Crane Design ProblemLearning Outcomes$1.$ Apply knowledge of shear and moment diagrams to a simple design scenario$\mathrm{.}2.$ Work effectively with other students taking into account input from all team members and recognizing different working styles$\mathrm{.}3.$ Explain how diversity $($of ideas and identities$)$ is relevant to engineering problem$-$solving.Demand vs$.$ CapacityIn design, we always need to satisfy the following inequality:Demand $<$ Capacity In Statics, we have only been considering the demand of the applied loads. But in design, we must compare this demand to the capacity $($or strength$)$ of each element in the system. Or$,$ in other words,the internal forces caused by the applied load must be less than the internal forces the material can withstand. For the capacity to barely meet the demand is not enough, we must also add in factors of safety to account for computational error, material defects, structure age, and construction errors. Problem OverviewYou have been hired by a boat manufacturer to design a support frame for a $35-$foot$-$long and $8-$ton capacity crane system $($crane $+$ hoist$)$ that they have purchased. Your specific task for this assignment is to design the $60-$foot$-$long rails for the system below to have enough capacity for the crane to lift $8-$tons. For this situation, we need to make sure the rail beam is adequate to carry two types of internal loads: shear forces and bending moments. Thus, you need to select a beam with: $1.$ ample shear force capacity to carry to resist the shear force developed by the applied loads and $2.$ ample bending moment capacity to resist the bending moment developed by the applied loads. It is essential to check both modes of failure. Additional Design Details: $$ The crane beam$$s length is $35$ feet, but the hoist cannot access the beam$$s outer $2\mathrm{.}5$ feet as the hoist would hit the rails. $$ The crane beam has a uniformly distributed weight of $3000$ pounds. $$ The $8-$ton hoist capacity includes the weight of the hoist. $$ When modeling the $60-$ft rails, assume a pin supports the rails at one end and a roller at the other. $$ The crane beam moves perpendicularly along the rails and cannot travel over the rail$$s outer $2$ feet as it would hit the columns. Pick a wide flange $($W$-$shape$)$ shape for the rail made from ASTM A $572$ Grade $50$ steel, meaning the steel has a yield strength of $50$ kips$/$in$2($ksi$).$ W$-$shapes are also commonly known as I$-$beams. The American Institute of Steel Construction $($AISC$)$ Steel Construction Manual tables on the next two pages provide the shear and bending moment capacity for a series of W$-$shape beams. Based on your Statics knowledge, your team should be able to determine the maximum moment and shear caused by the applied loads. However, you have likely never included factors of safety in your demand computations, nor computed the capacity of a beam. To help you with this process, each team member will be provided with a hint $$ representing the diverse knowledge of a design team. By bringing the hints together with your team members$$ previous knowledge, your team should have enough information to solve this problem. Deliverables: $$ Contact your team and have each person access a separate hint listed in the Week $$ Sketches turning this $3$D problem into $2$D beam FBD$$s of the worst$-$case loading scenario for each shear and moment. $$ Computations to find the maximum shear and moment under the worst$-$case loading scenario$($s$).$ Computations to increase the loading demand by the factor$($s$)$ of safety. $$ Short written description about how you chose the W$-$shape beam from the tables with ample capacity. $$ Computational check that the chosen beam's self$-$weight won$$t require you to choose one with greater capacity.