Advanced Methods of Structural Analysis

11.7 Analysis of Redundant Frames 407

q=2kN/m 4m 6m

5m

3m

1

2

1

P=8kN

A

B

(^1) C
ab
4.1667
15.36 P
q MP^0
1
Z-P diagram
2
cd
S-e diagram
1
2
3
4
e
15.36kNm
4.1667kNm
1
5 q/2=5
5.0
5.0
q
fg
11.1993
Joint-load (J-L) diagram
5.0
h
1
P 1
S 2
S 4 S 3
i
S (^2) S 1 /h 1 +S 2 /h 1
(S 1 +S 2 )/h 1
(S 1 +S 2 )/h 1
S 4 /h 2
S 4
S 1
P 2
j
1
3 2
2 EI
EI
EI
Fig. 11.27 (a,b) Etalon frame. Design diagram and calculation of fixed end moments; (c,d)Z-P
andS-ediagrams; (e–g) Calculation of equivalent joint moment and force and joint-load diagram;
(h,i) Construction of a static matrix; (j) Finite elements
M 1 ADMA 1 D
ql 12 A
12
D4:1667kNmI M 1 BD 0 I
M 1 CD
Pl
2


1 ^2

D
8  10
2
0:6

1 0:6^2

D15:36kNm: