Advanced Methods of Structural Analysis

68 3 Multispan Beams and Trusses

Example 3.2.The structure in Fig.3.23is subjected to a uniformly distributed load
qwithin the entire spanL:Calculate the internal forcesTandDin the indicated
elements.

Solution.The thrust of the arch chain equals

HDqHDq

1

2

L

2d

f

D

qLd

f

;

whereHis area of the influence line forHunder the loadq. After that, the required
forceTaccording to (3.2)is

TD

H

cos ̨ 1

D

qLd

fcos ̨ 1

:

We can see that in order to decrease the forceTwe must increase the heightf
and/or decrease the angle ̨ 1.
To calculate forceD, we can use section 2-2 and consider the equilibrium of the
right part of the structure:

D!

X

YD 0 W

DsinˇCRBCTsin ̨ 1 D^0 !DD

1

sinˇ



qL

2



qLd

f

tan ̨ 1



:

Thus, this problem is solved using the fixed and moving load approaches: thrustH
is determined using corresponding influence lines, while internal forcesDandT
are computed usingHand the classical method of through sections.

3.5.3 Complex Trusses.............................................

Complex trusses are generated using special methods to connect rigid discs. These
methods are different from those used to create the simple trusses, three-hinged
trusses, etc. analyzed in the previous sections of this chapter. An example of a com-
plex truss is a Wichert truss.
Figure3.24presents a design diagram of a typical Wichert truss. As before, stat-
ical determinacy of the structure can be verified by the formulaWD2JSS 0 ,
whereJ,S,andS 0 are the number of hinged joints, members, and constraints of

Fig. 3.24 Wichert truss

B

C 1

A

1 2