# Members of a truss are connected to the gusset plate

The members of a truss are connected to the gusset plate. If the forces are concurrent at point O, determine the magnitudes of F and T for equilibrium. Take ϴ = 30°.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

#### Solution:

Let us first draw the free body diagram of the gusset plate.

We will assume forces going $\rightarrow^+$ to be positive and $\uparrow+$ to be positive.

Now, we can write the equations of equilibrium for the x-axis forces.

$\sum \text{F}_\text{x}=0$

$8+5\text{sin}\,(45^0)-T\text{cos}\,(30^0)=0$

Solve for T

$T=13.32$ kN

Next, we will write the equations of equilibrium for the y-axis forces.

$\sum \text{F}_\text{y}=0$

$F-T\text{sin}\,(30^0)-5\text{cos}\,(45^0)=0$

##### We already figured out the value for T. Substitute the value of T and solve for F.

$F=10.2$ kN