Advanced Methods of Structural Analysis

11.8 Analysis of Statically Indeterminate Trusses 411

Vector has five entries because the given structure allows five possible joint dis-
placements. The first entry of this matrix (0) means that in the possible direction 1
the active force is absent.

b 2

3

1 4

5

Z-P diagram

c S-e diagram

2

1

6

3

4

5

a

F 2 =2kN

F 1 =4kN

d

d

A

B

C

D

d Joint A

P 1

S 2

S 4

S 6

Joint C

P 4

P 5

S 3 S 5

S 6

Joint B

P 2

P 3

S 1

S (^4) S
5
e
XD
YD
S 1
S 2 S^3
Fig. 11.28 (a-c) Truss and correspondingZ-PandS-ediagrams; (d) Free-body diagram for each
joint; (e) Computation of reactions at0 supportD
To construct the static matrix let us show theS-ediagram (Fig.11.28c). Then we
need to consider free body diagram for joints which have possible displacements
(all joints except the pinned supportD) and express the possible forcesP 1 – P 5 in
terms of unknown internal forcesS 1 – S 6. This step is presented in Fig.11.28d.
Joint AW
X
YD 0 !P 1 DS 2 0:707S 4
Joint BW
X
YD 0 !P 2 D0:707S 4 CS 5
X
XD 0 !P 3 DS 1 C0:707S 4
Joint CW
X
YD 0 !P 4 D0:707S 3 S 5
X
XD 0 !P 5 D0:707S 3 CS 6