Subject: Structure Analysis 2

Topic: Moment Distribution Method

Difficulty: Hard

1) Fixed End Moments (FEM's)

$M_{ab} = \frac{-wl^2}{12} = \frac{-45*4^2}{12} = -60 KN.m$

$M_{ba} = \frac{wl^2}{12} = \frac{45*4^2}{12} = 60 KN.m$

$M_{bc} = 0$

$M_{cb} = 0$

2) Stiffness(K):

$K_{BA} = \frac{4EI}{l} = \frac{4EI}{4} = EI$ [K_B]

$K_{BC} = \frac{3EI}{l} = \frac{3EI}{6} = \frac{1}{2}EI$ [K_B]

Total Stiffness:

$K_B = K_{BA} + K_{BC}$

$=\frac{1}{2}EI + EI = \frac{3}{2}EI$

3) Distribution Factor:

$(D.F)_{BA} = \frac{K_{BA}}{K_B} = \frac{1EI}{\frac{3EI}{2}} = \frac{2}{3}$

$(D.F)_{BC} = \frac{K_{BC}}{K_B} = \frac{\frac{1EI}{2}}{\frac{3EI}{2}} = \frac{1}{3}$

4) Distribution Factor:

5) BMD: