Advanced Methods of Structural Analysis

64 3 Multispan Beams and Trusses

ForceU 3 - 5 (Section 1-1, SPLC Is Panel 4-6; Ritter’s Point is 4)

PD 1 left at SPLC P= 1 right at SPLC

U 3 - 5!

P

M 4 rightD 0 U 3 - 5!

P

M 4 leftD 0

U 3 - 5 rCRB5dHfD 0 !U 3 - 5

D

1

r

.RB5dHf/

U 3 - 5 rRAdCHfD 0 !U 3 - 5

D

1

r

.RAdHf /

IL.U 3 - 5 /D
5d
r
IL.RB/
f
r
IL.H / .i/ IL.U 3 - 5 /D
d
r
IL.RA/
f
r
IL.H/ .ii/

The first term in formulas (i) and (ii) corresponds to a common nonthrusted truss
(such as a pinned-rolled truss with additional member 7-8). These formulas show
that the thrust decreases the internal force in member 3-5; such an influence of the
thrust on the distribution of the internal forces is typical for thrusted trusses.
For the construction of influence lineU 3 - 5 in the case ofPD 1 left at SPLC, we
need to find the difference.5d =r /IL.RB/.f =r /IL.H /. This step is carried out
graphically after both terms in this equation have been plotted (Fig.3.21a). Ordinate
abcorresponds to the first term in formula (i), while ordinatebccorresponds to the
second term in formula (i). Sinceab > bc, then the difference between the two
functions.5d =r /IL.RB/and.f =r /IL.H /leads to the positive ordinates for the
final IL.U 3 - 5 /within this part of the truss.
Similarly, we can find the difference.d =r /IL.RB/.f =r /IL.H /for the
case ofPD 1 right at SPLC. The specified ordinatenmshown in the final influence
line is

nmDngmgD

d

2r



f

r

l

4f

D

d

2r



3d

2r

D

d

r

:

Note that the ordinates of the influence line within the right portion are negative.
The final influence line forU 3 - 5 is shown in Fig.3.21b.
The influence line forU 3 - 5 shows that this element of the bottom chord in this
three-hinged truss may be tensile or compressed, depending on the location of the
load. This is because the thrust acts as shown in Fig.3.21, i.e., external forceP
tends to extend element 3-5, while thrustHtends to compress this element.

3.5.2 Trusses with a Hinged Chain.................................

Some examples of trusses with a hinged chain are presented in Fig.3.22. In all cases
these systems consist of two trusses,ACandCB, connected by hingeCand stiff-
ened by additional structures called a hinged chain. The hinged chain may be located
above or below the trusses. Vertical members (hangers or suspensions) connect the
hinged chain with the trusses. The connections between the members of the chain
and the hangers are hinged. In case (c), all the hinges of the hinged chain are located
on one line. In cases (a) and (b), a load is applied to the truss directly, while in case
(c), the load is applied to the joint of the hinged chain and then transmitted to the
truss.