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
Œ3D
2 EI 0
4
Œ3DEI 0 Œ1:5 :