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°.

members of a truss are connected to the gusset plate

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.

members of a truss are connected to 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

 

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 3, question 3-5.

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