Buckling length of column frame

[rc2008]

Homework Statement

I started with at location at B, with equation of v = A sinwx + B coswx +MB/P – Vx/P,

MCD= 2EI/(0.5L) (2 ΘC+ ΘB) , where ΘD= -0.5 ΘC, MCD= 6EI ΘC/ L
MBA= 2(1.5EI)/L (2 ΘB+ ΘA) MBA= 6EI ΘB/ L

Relevant Equations

v = A sinwx + B coswx +MB/P – Vx/P

At B, MBA + MBC= 0

MBC= 2(EI)/L (2 ΘB+ ΘC) ,

MB= 10(EI)/L ( ΘB) + 2(EI)/L ( ΘC) = 0 , ΘC = -5 ΘB



BC1, v(0)=0, 0 = B-MB/P, B = MB/P



BC2, V’(0) = ΘB

ΘB = wA + V/P

A= ΘB/w + V/Pw



BC3 = V’(L) = ΘC

-5 ΘB = w (ΘB/w + V/Pw) coswL - w (MB/P) sinwL + V/P



I am stucked here, can someone enlighten me to proceed further to get the solution?