Calculate distribution factor member OA for the shown figure.

Joint O is connected to the four-member OA, OB, OC, and OD where far end is supported by vertical guided roller, vertical roller support, fixed support, and horizontal roller support respectively.
Stiffness for OA is \(\frac{EI}{L} \)
Stiffness for OB is 0
Stiffness for OC is \(\frac{4EI}{L} \)
Stiffness for OD is \(\frac{3EI}{L} \)
Therefore stiffness for joint O is the sum of the stiffness for all the members connected to it.
Stiffness for the joint O is \(\frac{EI}{L}+0+\frac{4EI}{L}+\frac{3EI}{L}=\frac{8EI}{L} \)
Distribution factor for member OA=\(\frac{Stiffness \, of \, member \, OA}{Stiffness \, of \, rigid \, joint}=\frac{\frac{EI}{L}}{\frac{8EI}{L}}=\frac{1}{8} \)