Calculate distribution factor member OB 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, fixed support, the free end, and fixed support respectively.
Stiffness for OA is \(\frac{EI}{L} \)
Stiffness for OB is \(\frac{4EI}{L} \)
Stiffness for OC is 0
Stiffness for OD is \(\frac{4EI}{L} \)
Therefore stiffness for joint O is the sum of the stiffness for all the members connected to it.
Stiffness for the joint O is \(\frac{EI}{L}+0+\frac{4EI}{L}+\frac{4EI}{L}=\frac{9EI}{L} \)
Distribution factor for member OB=\(\frac{Stiffness \, of \, member \, OB}{Stiffness \, of \, rigid \, joint}=\frac{\frac{4EI}{L}}{\frac{9EI}{L}}=\frac{4}{9} \)