The members of a truss are pin connected at joint O. Determine the magnitudes of F₁ and F₂ for equilibrium. Set θ=60.

Solution:

Free-body diagram:

Equations of Equilibrium:

Take the sum of horizontal forces considering forces to the right positive, and equate to zero.

\begin {aligned}


\sum{F}_x &= 0 & \\

F_1 \cos{60 \degree}+F_2 \sin{70 \degree}-5\cos{30 \degree}-\dfrac{4}{5}\left(7\right) &= 0 &\\

0.5F_1+0.9397F_2&=9.9301 &(1)\\

\end {aligned}

Take the sum of vertical forces considering upward forces positive, and equate to zero.

\begin{aligned}

\sum F_y&=0 &\\

-F_1\sin60\degree+F_2\cos70\degree+5\sin30\degree-\dfrac{3}{5}\left(7\right)&=0 &\\

-0.8660F_1+0.3420F_2&=1.7 &(2)\\

\end{aligned}

Now, we have two equations with two unknowns F_1 and F_2 . So, we have a system of two equations. We can solve this using algebra, or we can directly use our calculator with this capability. The answers are

F_1=1.83 \: \text{kN}\\
F_2=9.60 \: \text{kN}