Advanced Methods of Structural Analysis

416 11 Matrix Stiffness Method

EI

ll

q

(^012)
a P
EI
ll
0 1 2
D
c
EI
ll
0 1 2
b q
Fig. P11.1
Ans:.a/Z 1 D
ql^3
56 EI
;M 1 D
ql^2
14


C

I.b/Z 1 D
ql^3
84 EI
;M 1 D
ql^2
28
I
.c/Z 1 D
3P l^2
112 EI
:
11.2.The uniform three-span beam with different spans is subjected to uniformly
distributed loadq(Fig. P11.2). The flexural rigidity of the beam isEI. Determine the
angle of rotation at support 1 and the bending moments at specified points. Compare
the result with data in TableA.12.
EI
l 1 =1.2l 2 l 2 l 3 =0.6l 2
q
(^012)
Fig. P11.2
Ans.M 1 D0:0734ql 12
11.3.The uniform three-span beam with equal spanslis subjected to the settlement
of support 1 as shown in Fig. P.11.3. The flexural rigidity of the beam isEI. Deter-
mine the angle of rotation at support 1 and the bending moments at specified points.
Compare with data at the Table A18.
EI
(^012) D
l
Fig. P11.3
Ans.M 1 D3:6
EI
l^2
; M 2 D2:4
EI
l^2

11.4.Design diagram of the uniform two-span continuous beam is presented in
Fig.P11.4. Construct the influence line for angle of rotation and bending moment
at the supportB(section 6). Compare with data at the TableA.9