Consider the pipe shown The forces F1 650 N F2 700 N and

Consider the pipe shown. The forces F1 = 650 N , F2 = 700 N , and F3= 800 N are parallel to the x, y, and z axes, respectively.

Part A: Determine the x, y, and z components of reaction at the fixed support A using scalar notation.(Express your answers using three significant figures separated by commas.)

Part B: Determine the x, y, and z components of moment of reaction at the fixed support A using scalar notation.(Express your answers using three significant figures separated by commas.)

1 m 0.75 m 10.5 m 0.75 m

Solution

A)

F1 is parallel to x-axis and it acts towards negative x-direction

so

Rx = F1

F2 is parallel to y-axis and it acts towards positive y-direction

Ry = -F2

F3 is parallel to z-axis and it acts towards negative z-direction

Rz = F3

Therefore the reactions at the supports are

(650, -700, 800)

B)

F1 is in xz plane, so moment about y-axis

My = 0.75 k X 650 (-i) = -487.5 j

F2 in yz plance so moment about x-axis

Mx = (0.75 + 0.5) k X (700 j ) = -875 i

Moment due to F3

M = (1.25 k + 1 j -0.75 i) X ( -800 k)

M = -800 i -600 j

Therefore the total moment about x-axis is

Mx\' = -875-800 = -1675

My\' = -487.5-600 = -1087.5

Mz\' = 0

The moment reactions are

(-1675, -1087.5, 0 )