Find out the forces in members:
A braced support ABC is loaded as illustrated. Find out the forces in members AB, BC, BD and AD by the method of joints. Check out the results by graphical method of solution.
Solution
Method of Joints
Supposing the direction of the required forces as shown in the figure.
Joint A
Resolving the forces vertically,
f_{AB} sin 60^{o} = 1000
∴ f_{AB} = 1154 kg (tension) Further, solving the forces horizontally,
f_{AD} = f_{AB} cos 60^{o} = 577 kg (comp.)
Joint B
Resolving the forces vertically,
f_{DB} sin 60^{o} = f_{BA} sin 60^{o}
∴ f_{DB} = f_{BA} = f_{AB} = 1154 kg (comp.)
And, resolving the forces horizontally,
f_{BC} = f_{DB }cos 60^{o} + f_{BA }cos 60^{o}
= (1154 × 0.5) + (1154 × 0.5) = 1154 kg (tension)