Chapter 3.3, Problem 1P

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

To determine

Magnitudes of the force $F_1$ and $F_2$ for equilibrium.

Answer to Problem 1P

Magnitude of equilibrium forces $\left(F_1\right)$ and $\left(F_2\right)$ are $\underset{\_}{1.83\text{kN}}$ and $\underset{\_}{9.60\text{kN}}$.

Explanation of Solution

Given information:

• The given members of a truss are pin connected at joint O.
• The theta value has to fix at $60°$ with the member of $F_1$.

Show the free body diagram of the given truss as in Figure 1.

Determine the magnitude of equilibrium forces by applying the Equation of equilibrium.

Along horizontal direction:

$\begin{array}{l}{\displaystyle \sum F_x=0}\\ F_2\sin 70°+F_1\cos 60°-5\cos 30°-7\cos \theta =0\\ 0.9397F_2+0.5F_1-4.33-7\times \frac{4}{5}=0\\ 0.9397F_2+0.5F_1=9.930\end{array}$ (I)

Along vertical direction:

$\begin{array}{l}{\displaystyle \sum F_y=0}\\ F_2\cos 70°-F_1\sin 60°+5\sin 30°-7\sin \theta =0\\ 0.3420F_2-0.8660F_1+2.5-4.2=0\\ 0.3420F_2-0.8660F_1=1.7\end{array}$ (II)

Find the magnitude of equilibrium forces by solving the Equations (I) and (II).

$F_1=1.83\text{kN}$

$F_2=9.60\text{kN}$

Conclusion:

Thus, the equilibrium force $F_1$ is $\underset{\_}{1.83\text{kN}}$.

Thus, the equilibrium force $F_2$ is $\underset{\_}{9.60\text{kN}}$.