800 lbft 500 Ibft 12 ft Solution Now First Lets Find the res

Solution

>> Now, First Let\'s Find the resultant of these Distributed Loadings.

>> Let F1be the resultant of tiangular distributed loading

As,F1 = Area under this = (1/2)*800*12 = 4800 lb

and, it will act 12 - (12/3) = 8 ft from A

>>

Now, here, we do one thing that let\'s make this trapezoidal distribution a rectangular distribution, i.. uniform distribution by subtracting a triangular portion of load with maximum height (800 - 500 ) = 300 lb/ft for 9 ft

Later, we wil add loading due to this triangle

>> Let, F2 = Resultant of uniform distributed load of 500 lb/ft

=> F2 = 500*9 = 4500 lb

and, it acts at 12 + 9/2 = 16.5 ft

>> Let, F3 = Resulatnt of Load due to subtracted triangular loading.of height of 300 lb/ft for 9 ft

=> F3 = (1/2)*300*9 = 1350 lb

and, it will act at 12 + 9/3 = 15 ft from A

>> Now, Let Reactions are Ra & Rb

=> As, under Equilibrium, Net Forces = 0

=> Ra + Rb = F1 + F2 + F3 = 4800 + 4500 + 1350 = 10650 lb .....(1)........

>> Also, Moment about A, Ma = 0

=> 4800*8 - 12*Rb + 4500*16.5 + 1350*15 = 0

=> Solving, Rb = 11075 lb

and, from (1), Ra = - 425 lb