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

**Problem 241**

Locate the amount and position of the resultant of the loads acting on the Fink truss in Fig. P-241.

**Solution 241**

$a = 3 \sin 30^\circ$

$a = 1.5 \, \text{ m}$

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

$b = a \cos 60^\circ$

$b = 1.5 \cos 60^\circ$

$b = 0.75 \, \text{ m}$

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*