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