378 11 Matrix Stiffness Method
For beams we will denote thesectionswith unknown internal forces. Fig-
ure11.12a shows a continuous beam. TheS-ediagram is presented in Fig.11.12b;
this diagram contains internal moments in vicinity of supports. The positive mo-
ment rotates the intermediate portion of span around opposite end clockwise. These
moments are shown by solid lines; they are transmitted on the adjacent portion with
opposite directions (shown by dotted arrows). Figure11.12c contains a diagramS-e
of positive internal forces.
abc
S 2S (^1) S
3 S 5
S 4
12345
S-e diagram
Fig. 11.12 Concept ofS-ediagram for continuous beam
For frames, as for beams, we will denote thesectionswith unknown internal
forces. The required internal forces are bending moments at the ends of each mem-
ber. Figure11.13a shows the frame; the joints are labeled asi,j,k.TheS-ediagram
is presented in Fig.11.13b; this diagram contains internal moments infinitely close
to the fixed support and rigid joint. The positive moment rotate theintermediatepor-
tion of member around opposite end clockwise. These moments are shown by solid
lines; they transmitted on the adjacent portion with opposite directions (shown by
dotted arrows). The diagramS-eof positive internal forces is shown in Fig.11.13c.
a
i j
k
b Si
Sk
Sj c
Si
Sk
Sj
Fig. 11.13 S-ediagram for frame
We can see that diagram (b) shows the type of internal loads, while the diagram
(c) shows positive directions of unknown internal forces. Later both diagram (b) and
diagram (c) are referred together simply asS-ediagram.
Summary The joint-load (J-L), displacement-load (Z-P), and internal forces-
deformation (S-e) diagrams deal with similar concepts. For this concept, theJ-L
andZ-Pdiagrams uses the termload, while forS-ediagram termforces.Forthese
concepts, the different symbols are used; they areL,P,andS.The symbolLis
used for presentation of the given loading by equivalent joint loads. The symbol
Pis used for presentation of thetypeof the load, which corresponds to possible
displacements Z. The symbolSis used for presentation of thetypeof the unknown
internal forcesS.