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Section Method Problems

SECTION METHOD

 

 Determine the force in members  \(E F\) and  \(E F\)  of the  roof truss and state if the members are in tension of  compression. 

 

\( A_ y= \ I_y \)

\( +\uparrow \sum F_y=0 \)

\( y-6-12-12-12-12-12-6=0 \)

\( \rightarrow y=72 \quad \longrightarrow \quad A_ y=\frac{72}{2}=36 \mathrm{kN}= I_y \)

 

\( \tan \theta=\frac{3}{12}=\theta=14^{\circ} \)

\( \sum M_{L}=0\quad \longrightarrow F_{E F} \cos 14(6)-12(4)-(12)(8) \)

\( -6(12)+36(12)=0 \)

\(∴ F _{E F}=37.1 \mathrm{kN}\quad (c) \)

 

\( \stackrel{+}{\rightarrow} \sum F_{x}=0\quad \longrightarrow F_{EF}=F_{ED} \)

\( +\uparrow \sum F_ y=0 \longrightarrow\quad 17.1 sin 14(2)-12-F_{EL}=0 \)

\(∴ F_{E L}=5.95 \mathrm{kN}(T) \)

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