find out the forces in membersa braced support

Question

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)