Advanced Methods of Structural Analysis

9.1 Fundamental Idea of the Mixed Method 315

A

q

1

5 4

3

2

X 1

Z 2

a b

12 8m

8m

4m

q=6kN/m

1

54

3

2

A

stiffness 2EI

stiffness ZEI stiffness 2EI^

stiffness EI

d 11

12

12

X 1 =1

M 1

r′ 21

c d

Z 2 =1

d′ M^2

12

r 22

M 23 =1EI

0.5EI

M 21 = 0.5EI

0.25EI

q

A

MP^0 kNm

R 2 P

M2–3=32

MC=16

C

D 1 P

e

12.8

3.2

9.6

MP

kNm

q=6kN/m

3.2

12.8

MC=20.8

41.6

9.6

4.8

f

12

12

X 1 =1

M 1

16 20

g

Fig. 9.2(a)Design diagram;(b)primary system of the mixed method;(c)bending moment dia-
grams caused by forceX 1 D 1 ;(d)bending moment diagrams caused by displacementZ 2 D 1.
(e)Bending moment diagram in the primary system due to given load.(f)Resulting bending mo-
ment diagram and free body diagram for joint 2.(g)Unit bending moment diagram in primary
system of the force method