402 11 Matrix Stiffness Method
PD 1 at the section 2
(uD0:333; D0:667/
PD 1 at the section 4
(uD0:667;D0:333/
Matrix proceduresZED&
Z 1
Z 2'
DK^1 EPD
l
45 EI"
7 2
27#l&
0:1480
0'
D l2
304:05EI&
7
2'ZED&
Z 1
Z 2'
DK^1 EPD
l
45 EI"
7 2
27#l&
0:1851
0'
D l2
243:11EI&
7
2'ES 2 D2(^66)
(^66)
(^66)
M 1
M 2
M 3
M 4
3
(^77)
(^77)
(^77)
2
DkAQ TEZDEIl
2
(^66)
(^64)
30
42
24
03
3
(^77)
(^75)
l
2
304:05EI
&
7
2
'
Dl
2
(^66)
(^66)
(^66)
0:06907
0:07893
0:01973
0:01973
3
(^77)
(^77)
(^77)
ES 2 D
2
(^66)
(^66)
(^66)
M 1
M 2
M 3
M 4
3
(^77)
(^77)
(^77)
2
DQkATZEDEIl
2
(^66)
(^64)
30
42
24
03
3
(^77)
(^75)
l
2
243:11EI
&
7
2
'
Dl
2
(^66)
(^66)
(^66)
0:08638
0:09872
0:02468
0:02468
3
(^77)
(^77)
(^77)
Bending moment at the sections 6 and 12ESDES 1 CES 2
ESDl
2
(^66)
(^66)
(^66)
0:1480
0
0
0
3
(^77)
(^77)
(^77)
Cl
2
(^66)
(^66)
(^66)
0:06907
0:07893
0:01973
0:01973
3
(^77)
(^77)
(^77)
Dl
2
(^66)
(^66)
(^66)
0:07893
0:07893
0:01973
0:01973
3
(^77)
(^77)
(^77)
ESDl
2
(^66)
(^66)
(^66)
0:1851
0
0
0
3
(^77)
(^77)
(^77)
Cl
2
(^66)
(^66)
(^66)
0:08638
0:09872
0:02468
0:02468
3
(^77)
(^77)
(^77)
Dl
2
(^66)
(^66)
(^66)
0:09872
0:09872
0:02468
0:02468
3
(^77)
(^77)
(^77)
The signs of the bending moments should be treated according toS-ediagram and
general rules of the bending moments. If the loadPD 1 is placed at point 2, then
ordinates of influence lines for bending moments at sections6.B/and2.C /are
given in Fig.11.25c.
If the loadP D 1 is placed at point 4, then ordinates of influence lines for
bending moments at the same sections are following:M 4 BD0:09872lI M 4 CD
0:02468l.
Load PD 1 in the second spanThe bending moment diagram in the primary
system of displacement method and equivalent joint-load diagram are shown in
Fig.11.25d.
Now for any positionuof unit loadPin the second span, we can compile the
vectorPof the external joint loads (using theJ-LandZ-Pdiagrams) and vector
S 1 of unknown internal forces in the first state (using theMP^0 andS-ediagrams).