Analysis of Indeterminate Beams by Slope Deflection Method

1. Subject Name: Theory of Structures
Topic Name:Analysis of Indeterminate
Beams by Slope Deflection Method
Lecture No: 15
Dr.Omprakash Netula
Professor & HOD
Department of Civil Engineering
9/28/2017 Lecture Number, Unit Number 1

2. Applying the equilibrium conditions:
)3(062.1)2()
6.3
2
(
)2(062.1)2()
6.3
2
(5.4)2()
4.2
2
(
)1(05.4)2()
4.2
2
(



BCBCCB
CBBCBAB
BAABAB
EI
M
EIEI
EI
M




3. By solving equations (1, 2 & 3) for and substitute
the values into equations (a, b, c, d): CBA  ,,
0
.158.4
.158.4
0




CB
BC
BA
AB
M
iseanticlockwmkNM
clockwisemkNM
M

4. Shearing force and bending moment diagrams are shown in the
following figure.

5. Example (4)
Determine the moments at each joint of the frame shown in Fig.(7). EI
is constant.
Fig. (7)

6. MkNFEM
MkNFEM
CB
BC
.80
96
)8)(24(5
)(
.80
96
)8)(24(5
)(
2
2



7. Because ends A and D are fixed supports.
and since no sidesway will occur.0 CDBCAB 
CCCDDC
CCCDCD
BCBCBCCB
CBCBBCBC
BBABBA
BBABAB
EI
l
EI
M
EI
EI
M
EIEI
EI
M
EIEI
EI
M
EI
EI
M
EI
EI
M






1667.0)()
2
(
3334.0)2()
12
2
(
8025.05.080)2()
8
2
(
8025.05.080)2()
8
2
(
3334.0)2()
12
2
(
1667.0)()
12
2
(







8. Equilibrium conditions:
)2(08025.08334.0
0803334.025.05.0
0
)1(08025.08334.0
08025.05.03334.0
0








BC
CBC
CDCB
CB
CBB
BCBA
EI
Or
EIEIEI
MM
EIEI
Or
EIEIEI
MM





9. Solving simultaneously yields
EI
and
EI
CB
1.1371.137
 

10. Therefore,
seanticlokwimkNM
iseanticlockwmkNM
clockwisemkNM
iseanticlockwmkNM
clockwisemkNM
clockwisemkNM
DC
CD
CB
BC
BA
AB
.9.22
.7.45
.7.45
.7.45
.7.45
.9.22







11. Fig.(8)
The bending moment diagram is shown in Fig.(8).