Editing Structural analysis (section)

====Method of joints====
This type of method uses the force balance in the x and y directions at each of the joints in the truss structure. 
:[[Image:Truss Structure Analysis, Method of Joints2.png|border|350x450px]]

At A,
:<math>\sum F_y=0=R_{Ay}+F_{AD}\sin(60)=5+F_{AD}\frac{\sqrt{3} }{2} \Rightarrow F_{AD}=-\frac{10}{\sqrt{3}}</math>
:<math>\sum F_x=0=R_{Ax}+F_{AD}\cos(60)+F_{AB}=0-\frac{10}{\sqrt{3} }\frac{1}{2}+F_{AB} \Rightarrow F_{AB}=\frac{5}{\sqrt{3}}</math>
At D,
:<math>\sum F_y=0=-10-F_{AD}\sin(60)-F_{BD}\sin(60)=-10-\left(-\frac{10}{\sqrt{3}}\right)\frac{\sqrt{3} }{2}-F_{BD}\frac{\sqrt{3}}{2} \Rightarrow F_{BD}=-\frac{10}{\sqrt{3}}</math>
:<math>\sum F_x=0=-F_{AD}\cos(60)+F_{BD}\cos(60)+F_{CD}=-\frac{10}{\sqrt{3}}\frac{1}{2}+\frac{10}{\sqrt{3} }\frac{1}{2}+F_{CD} \Rightarrow F_{CD}=0</math>
At C,
:<math>\sum F_y=0=-F_{BC} \Rightarrow F_{BC}=0</math>

Although the forces in each of the truss elements are found, it is a good practice to verify the results by completing the remaining force balances.
:<math>\sum F_x=-F_{CD}=-0=0 \Rightarrow verified</math>
At B,
:<math>\sum F_y=R_B+F_{BD}\sin(60)+F_{BC}=5+\left(-\frac{10}{\sqrt{3}}\right)\frac{\sqrt{3} }{2}+0=0 \Rightarrow verified</math>
:<math>\sum F_x=-F_{AB}-F_{BD}\cos(60)=\frac{5}{\sqrt{3}}-\frac{10}{\sqrt{3}}\frac{1}{2}=0 \Rightarrow verified</math>