Advanced Methods of Structural Analysis

11.2 Ancillary Diagrams 377

a

A

B

C

b 1

2

4

A

3

5

6

Fig. 11.9 Z-Pdiagram for truss

(4). All other joints of frame have two possible displacements (vertical and horizon-
tal) and two corresponding joint loads.
It is obvious thatZ-Pdiagram (Fig.11.9b) shows the positive possible displace-
ments and corresponding external loads in global coordinates.

11.2.3 Internal Forces-Deformation (S-e) Diagram

This diagram shows a numeration and positive directions of all unknown internal
forcesS, which corresponds to deformatione. Figure11.10a shows three bar ele-
ments from any truss. Since all connections are hinged, then for all members only
axial deformationsein local coordinates is possible; corresponding internal forces
are axial forces. The concept ofS-ediagram for truss is shown in Fig.11.10b.

Fig. 11.10 Concept ofS-e
diagram for truss

a i-th bar

j-th bar

b

Sj Sk

Si

Figure11.11a presents the design diagram of the truss (loading is not shown)
and numeration 1–8 of the members. The correspondingS-ediagram is shown in
Fig.11.11b. Thus, we show the arrows related to the intermediate part of the truss
member. This diagram contains the positive axial deformationeiand forceSiin
i-th member; the forceSiis constant along thei-th element.

a

1

2

3

5 4

6 7

8

b

1

2

3

5 4

6 7 8

Fig. 11.11 S-ediagram for truss