241 Finding the resultant of vertical forces acting on the Fink truss

$\sin 30^\circ = \dfrac{a}{3}$

$a = 3 \sin 30^\circ$

$a = 1.5 \, \text{ m}$
 

 

$\cos 60^\circ = \dfrac{b}{a}$

$b = a \cos 60^\circ$

$b = 1.5 \cos 60^\circ$

$b = 0.75 \, \text{ m}$
 

Magnitude of resultant
$R = \Sigma F_v$

$R = 2(890) + 2(1335) + 1780 + 8900$

$R = 15\,130 \, \text{ N}$       downward
 

Location of resultant
$Rd = \Sigma Fx$

$Rd = 1335(3 - b) + 8900(3) + 1780(4.5) + 1335(6 + b) + 890(9)$

$15\,130d = 1335(3 - 0.75) + 8900(3) + 1780(4.5) + 1335(6 + 0.75) + 890(9)$

$15\,130d = 1335(2.25) + 8900(3) + 1780(4.5) + 1335(6.75) + 890(9)$

$15\,130d = 54\,735$

$d = 3.62 \, \text{ m}$       to the right of A
 

Thus, R = 15 130 N downward at 3.62 m to the right of left support.           answer