40 kN

A B 10 kN/m

2EI EI

3m 3m 9m

θa = 0

θa = 6 Mab - 6 Mba - 1/16 x 40 x 6^2

3 (2 EI) 6 (2EI)

θa = 1 Mab + -0.5 Mba + -90

θba = -6 Mab + 6 Mba + 1/16 x 40 x 6^2

6 (2 EI) 3 (2EI)

θba = -0.5 Mab + 1 Mba + 90

θbc = 9 Mbc + - 9 Mcb + -1/24 x 10 x 9^3

3 (EI) 6 EI

= 3 Mbc + -1.5 Mcb + -303.75

= 3 Mbc + 180 + -303.75

θcb = -1.5 Mbc + 3 Mcb + 303.75

= -1.5 Mbc + -360 + 303.75

= -1.5 Mbc + -56.25

θa = 1 Mab + -0.5 Mba + -90 =

1 Mab + -0.5 Mbc = 90

-0.5 Mab + 1 Mba + 90 = 3 Mbc

-0.5 Mab + 1 Mba -3 Mbc

-0.5 Mab + 1 Mba + 3 (Mba +50)

-0.5 Mab + 4 Mba = -363.75

1 -0.5 Mab = 90

-0.5 4 Mba = -363.75

1.066667 0.133333 Mab = 47.5

0.133333 0.266667 Mba = -85

40 -85

47.5 -35

Va -6.25 Vb 6.25

Va 20 Vb 20

Va total = 13.75 Vb 45

Vb -17.2222

Vb total = 54.02778
 27.77778

A B +

13.75 -

-26.25 -26.25
 40 kN

C D

EI

3m

Mba + Mbc = -50

Mcd = P.L = 40 x3 = 120

Mcb = -Mcd

Mcb = -120

Mcb = -120

0
 Mba + Mbc = -50

+ 180 + -303.75

= -213.75

= -213.75

-120

Vc 17.22222

Vc 40

Vc 45

Vc total = 102.2222
 40

C + D

-62.2222