Advanced Methods of Structural Analysis

576 Appendix

The left recursive relationship fornext.nC1/span in terms of theprevious leftfoci
quotientknLis as follows

knLC 1 D 2 C

ln

lnC 1



2 

1

knL



:

The right recursive relationship forprevious.n1/-thspanintermsofthenext
rightfoci quotientknRis

kRn 1 D 2 C

ln

ln 1



2 

1

kRn



:

Case a.Iftheveryleftsupport 0 is pinned then the left focus for thefirstspan coin-
cides with support 0 and theleftfocus quotient becomesk 1 LD.M 1 =M 0 /D1.
Similarly, if the veryrightsupport is pinned then for thelastspan, therightfocus
quotient isklastR D1.

Case b. If the very left support 0 is clamped, then the left focus quotient is for
first span equals two. It means that if a very left support is clamped and first span
is unloaded then a moment at the clamped support is twice less than in the next
pinned support. Similarly, if a last support is clamped and last span is unloaded then
a moment at the clamped support is twice less than in the previous pinned support.
If load is applied only within one spanlnthen distribution of bending moments
is shown below. The left foci points on right spans and right foci points on left spans
are not shown. The nil pointsc 1 andc 2 , which are located within a loaded span, are
not foci.