The door is supported by compression member AB Determine the

The door is supported by compression member AB. Determine the magnitude of the force in member AB (as it acts at point A) along diagonal OC if the force in this member is 200 N.

Solution

F =8 kN

F makes an angle of 35⁰ and 65⁰ with the z-axis

it project onto xy plane = FCos(35) = 8000*Cos(35)

                                      = 6553.22 N

z-component = FSin(35) = 4588.61 N

xy- component makes angle of 60⁰ with x-axis

x-component = 6553.22*Cos(60) = 3276.61 N

y-Component = 6553.22Sin(60) = 5675.26 N

Vector of F

F = 2294.31 i^ +3974.85 j^ + 4588.61 k^

Projection on to the x-axis is the x-component = 2294.31 N

Projection on to line OA

Line OA makes an angle of 30⁰ with the xy-component (6553.22N)

projection onto OA = 6553.22Cos(30)

                               = 5675.26 N