Advanced Methods of Structural Analysis

56 3 Multispan Beams and Trusses

The main purpose of a secondary truss is to transmit a load, which is applied

between the jointsof a main truss,to the jointsof a main truss.

How can we distinguish between the main and the secondary trusses? The rule is

that elements of the secondary truss are connected with the main truss in such a way

that averticalload, which acts on the joint of the secondary truss, is transmitted only

as averticalload to the joints of the main truss. The secondary trusses in Fig.3.15

are shown by dotted lines. Figure3.15a also shows an incorrect presentation of a

secondary truss, since in this case the vertical, as well as thehorizontal reactions

are transmitted to the joints of the main truss.

Auxiliary trusses add joints to the loaded chord and serve different goals:

1.Secondary elements (i.e., the elements of the auxiliary truss) transmit loads ap-
plied to the lower (or upper) chord to the joints of the same chord of the main
truss (Fig.3.15a, b).
2.Secondary elements transmit loads applied to the upper (or lower) chord to the
joints of the other chord of the main truss (Fig.3.15c).
3.Vertical elements of an auxiliary truss can divide acompressedmember of
the upper chord, leading to increased load-carrying capacity of this element
(Fig.3.15c).
It is possible to have a combination of two types of auxiliary trusses so that a load is
transmitted to both chords of the main truss as shown in Fig.3.15d. In this case hinge
6 belongs to bottom auxiliary truss 5-8-7-6, while hinge 4 belongs to top auxiliary
truss 1-2-3-4. Members 3-4 and 7-8 have no common points. If loadPis located
at point 4, then the load is transmitted to theupperchord (to joints 1 and 2) of the
main truss. If loadPis located at point 6, then the load is transmitted to thelower
chord (to joints 5 and 7) of the main truss. If loadPis located between points 4 and
6, then part of the load is transmitted to joint 4 and part to joint 6, and from there it
is transmitted from joint 4 to an upper chord and from joint 6 to lower chord.

Kinematical Analysis

For kinematical analysis of the truss in Fig.3.15a, we show the initial rigid disc

1-3-k. Each subsequent hinge is connected using two bars with hinges at the ends,

thus part 1-2-4-3 of the truss presents a rigid disc. The next joint cannot be obtained

in this way, so instead consider the truss from the right where the base rigid triangle

is 6-7-n. Similarly, each subsequent hinge is connected using two bars with hinges

at the ends, so part 5-6-7-4 presents a second rigid disc. Both discs are connected by

hinge 4 and member 2-5 according to Fig.3.9; this compound truss is geometrically

unchangeable. The trusses in Fig.3.15b,c can be analyzed in a similar way.

For all the design diagrams presented in Fig.3.15, the relationshipSD2JS 0

is satisfied. For example, for structures (a,c)SD 33 andJD 18 ; for structures (b,d)

SD 25 ,andJD 14. All these structures are statically determinate and geometri-

cally unchangeable compound trusses.