Advanced Methods of Structural Analysis

3.5 Special Types of Trusses 61

ForceD 5 - 6 ,Main Truss: The SPLC Is Panel 5-7; Ritter’s Point Is at Infinity

PD 1 left at SPLC PD 1 right at SPLC

Dmain 5 - 6!
P
YrightD 0
!Dmain 5 - 6 sin ̨CRBD0;

D 5 main- 6!

P

YleftD 0 !Dmain 5 - 6 sin ̨CRAD0;

Dmain 5 - 6 D
1
sin ̨
RB!IL



D 5 main- 6



D

1

sin ̨

IL.RB/ D 5 main- 6 D

1

sin ̨

RA!IL



Dmain 5 - 6



D

1

sin ̨

IL.RA/

This influence line presents two parallel lines with ordinates1=sin ̨on the supports
and a connecting line within panel 5-7. Ordinate1=sin ̨on the right support is not
shown.
The influence line for internal forceDsec 5 - 40 is already known. The required influ-
ence line forD 40 - 5 is presented in Fig.3.18. We can see that if loadPis located at
joint 50 or within the portion 50 -7, then the secondary truss within panel 5-7 leads to
a significant increase of compressed forceD 40 - 5.

ForceU 50 - 5

Member 50 -5 belongs simultaneously to the main and to the secondary truss.
Therefore, an influence line should be constructed considering the main truss and
secondary truss 5- 40 -7- 50 :

U 50 - 5 DU 5 main- 7 CU 5 sec (^0) - 5 !IL.U 50 - 5 /DIL

U 5 main- 7

CIL

U 5 sec (^0) - 5

;
where IL

U 5 sec (^0) - 5

DIL

U 5 sec (^0) - 7

has already been considered above. The influence
line forU 50 - 5 is presented in Fig.3.18. We can see that if this truss is subjected to
any load within portions 1-5 and/or 7-13, the secondary trusses do not affect internal
forceU 50 - 5. The influence of the secondary truss in panel 5-7 on internal forceU 50 - 5
occurs only if any load is located within panel 5-7.

3.5 Special Types of Trusses...............................................

The following trusses are considered in this section: Three-hinged trusses, trusses
with a hinged chain, and complex trusses. Each of the above-mentioned trusses has
some peculiarities.

3.5.1 Three-Hinged Trusses........................................

A three-hinged truss is actually two trusses connected by the hingeCas shown in
Fig.3.20a. Both supports are pinned. The fundamental feature of this structure is
that horizontal reactions appear even if the structure is subjected to a vertical load