54 3 Multispan Beams and Trusses
The left-hand portion of influence line forU 5 - 7 is obtained by multiplying all ordi-
nates of influence line forRBby a constant factor6d= h. The right-hand portion of
influence line forU 5 - 7 is obtained by multiplying all ordinates of influence line for
RAby a constant factor3d= h. Connecting line runs between points 5 and 7. The
forceU 5 - 7 is tensile for any location of load on the truss.
ForceV 6 - 7 (Section 2-2, Equilibrium of Joint 6, Fig.3.14b)
P
PXD^0 !O^4 -^6 cos'CO^6 -^8 cos'D^0 !O^4 -^6 DO^6 -^8 ;
Y D 0 !V 6 - 7 2O 4 - 6 sin'D 0 !V 6 - 7 D2O 4 - 6 sin'!IL.V 6 - 7 /
D 2 sin'IL.O 4 - 6 /The influence line forV 6 - 7 is obtained by multiplying all ordinates of influence
line forO 4 - 6 by a constant factor ( 2 sin'). The maximum ordinate of this influ-
ence line equals to.3d =r /sin'D 1. This result may be obtained using the other
approach: if loadP D 1 is located at point 7, then internal forces in all vertical
members (exceptV 6 - 7 /and diagonal members are zero; equilibrium equation of
joint 7 leads toV 6 - 7 D 1.
ForceU 1 - 3 (Section 3-3, Equilibrium of Joint 1, Fig.3.14b)
PD 1 applied at joint 1 PD 1 applied at joint 3 or to the right of joint 3
U 1 - 3!
P
M 2 leftD 0
!U 1 - 3
h
3 C^1 dRA
dD0;U 1 - 3!
P
M 2 leftD 0 !U 1 - 3
h
3
RAdD0;RAD^1 !U 1 - 3 D^0 !IL.U 1 - 3 /D^0 U 1 - 3 D
3d
hRA
!IL.U 1 - 3 /D3d
hIL.RA
/The right-hand portion of influence line forU 1 - 3 is obtained by multiplying all ordi-
nates of influence line forRAby a constant factor.3d = h/. Connecting line connects
the joints 1 and 3.
All the above-mentioned influence lines are presented in Fig.3.14c.
3.4 Trusses with Subdivided Panels.......................................
Trusses with subdivided panels present are simple trusses with additional mem-
bers. Figure3.15a shows the Pratt truss with two additional members within each
panel; for first panel they are 3-kandk-n. Figure3.15b shows the Parker truss with
three additional members within each panel; they area-b,a-candb-c. In both ex-
amples additional elements divide a panel (vertical memberk-nin first case and
inclined membersa-candb-cin the second case). In the analysis of such trusses,