3.3 Simple Trusses 53
and 7; connecting line is always a straight line. The completed influence line is
presented in Fig.3.14c. As can be seen, the elementO 4 - 6 is always compressed
for any location of the moving load. Maximum internal forceO 4 - 6 occurs when
concentrated load is located at point 7.It is very convenient to represent all information related to construction of influ-
ence lines in tabulated form as follows.
ForceO 4 - 6 (Section 1-1, SPLC Is Panel 5-7, Ritter’s Point 7)
PD 1 left at SPLC PD 1 right at SPLC
O 4 - 6!
P
M 7 rightD 0 !O 4 - 6 rCRB3dD0; O 4 - 6!
P
M 7 leftD 0 !O 4 - 6 rCRA3dD0;
O 4 - 6 D3d
rRB
!IL.O 4 - 6 /D3d
rIL
.RB/ O 4 - 6 D3d
rRA
!IL.O 4 - 6 /D3d
r IL.RA
/Analytical expressions for influence lines of internal forces for the remaining
elements of the truss are obtained in the same manner as above. From now on we
will be presenting analytical expressions for construction of influence lines in tabu-
lated form. The tabulated form contains all necessary information for construction
of influence line.
ForceD 4 - 7 (Section 1-1, SPLC Is Panel 5-7, Ritter’s Point 1)
PD 1 left at SPLC PD 1 right at SPLC
D 4 - 7!P
M 1 rightD 0 !D 4 - 7 r 1 CRB6dD0; D 4 - 7!P
M 1 leftD 0 !D 4 - 7 r 1 D0;
D 4 - 7 D
6d
r 1
RB!IL.D 4 - 7 /D
6d
r 1
IL.RB/ D 4 - 7 D 0 !IL.D 4 - 7 /D 0The left-hand portion of influence line forD 4 - 7 is obtained by multiplying all or-
dinates of influence line forRBby a constant factor (6d=r 1 ). Ordinates of the
right-hand portion of influence line forD 4 - 7 are zeros. Connecting line connects
the joints 5 and 7. Thus, if any load is located within portion 7-12, then internal
force in memberD 4 - 7 does not arise. Maximum forceD 4 - 7 occurs, if loadPis
placed at joint 5.
ForceU 5 - 7 (Section 1-1, SPLC Is Panel 5-7, Ritter’s Point 4)
PD 1 left at SPLC PD 1 right at SPLC
U 5 - 7!P
M 4 rightD 0 !U 5 - 7
2
3
hRB4dD0; U 5 - 7!P
M 4 leftD 0 !U 5 - 7
2
3
hRA2dD0;
U 5 - 7 D
6d
h
RB!IL.U 5 - 7 /D
6d
h
IL.RB/ U 5 - 7 D
3d
h
RA!IL.U 5 - 7 /D
3d
h
IL.RA/