Advanced Methods of Structural Analysis

10.3 Comparison of the Force and Displacements Methods 357

Case of

n

D

1

ı^11

X

C 1

ı1P

D

0

r^11

Z

C 1

r1P

D

0

Primary unknown

X

1

D

ı1Pı^11

ı1P

is function,

ı^11

is number

Z

1

D

r1Pr^11

r1P

is function,

r^11

is number

Influence line for primary

unknown

IL

.X

/ 1

D

(^1) ı^11
IL
.ı
1P
/
IL
.Z
/ 1
D
(^1) r^11
IL
.r
1P
/
Influence line for internal
forces at section
k
M
k
D
M
k
IL
.X
/ 1
C
IL
M
 (^0) k
Q
k
D
Q
k
IL
.X
/ 1
C
IL
Q
 0 k
N
k
D
N
k
IL
.X
/ 1
C
IL
N
 (^0) k
M
k
D
M
k
IL
.Z
/ 1
C
IL
M
 (^0) k
Q
k
D
Q
k
IL
.Z
/ 1
C
IL
Q
 0 k
N
k
D
N
k
IL
.Z
/ 1
C
IL
N
 (^0) k
Unit internal forces
M
 k
Q
k;
N
 k
Bending moment (shear, axial forces) at section
k
of primary
system of the
Fo rc e
method caused by primary unknown
X
1
D
1
Bending moment (shear, axial
forces) at section
k
of primary
system of the
Displacement
method caused by primaryunknown
Z
D 1
1
IL
M
 (^0) k
IL
Q
 (^0) k
IL
N
 (^0) k
Influence line for bending moment (shear, axial forces) at section
k
in primary system of the
Fo rc e
method. These influence lines
are
linear
Influence line for bending moment
(shear, axial forces) at sectionk
in primary system of the
Displacement
method. These
influence lines are
curvilinear