Advanced Methods of Structural Analysis

11.6 Analysis of Continuous Beams 397

l 1 =6m l 2 =4m l 3 =4m

Δ 2

j 0

A

EI 1 =1EI 0 BD2EI 0 C 2EI 0

a

b

M^0

Δ

MBA

MAB

MCB MCD

MBC

A

B

C

c

MBC–MBA=

0.02667EI 0

MCB–MCD=

0.015EI 0

Joint-load diagram

eS

1

S 1

S 2

S 2

S 3

S 3

S 4

S 4

S 5

S 5

S-e diagram

d

Z-P diagram^12

f

M, kNm

(factor 10–^4 EI 0 )

96

98

174

Fig. 11.24 (a) Settlements of supports. Design diagram of continuous beam; (b,c)Conversionof
effect due to settlementof support to the joint-load moments; (d,e) Continuous beam; (f)Final
bending moment diagram and correspondingZ-PandS-ediagrams

Stiffness matrix Stiffness matricesfor finite elementsAB,BC,andCDin local
coordinates are

k 1 D

EI 1

l 1



42

24

D

EI 0

6



42

24

DEI 0



0:667 0:333

0:333 0:667

;

k 2 D

EI 2

l 2



42

24

D

2 EI 0

4



42

24

DEI 0



21

12

;

k 3 D

EI 3

l 3

Œ3D

2 EI 0

4

Œ3DEI 0 Œ1:5 :