Advanced Methods of Structural Analysis

13.6 Compressed Rods with Lateral Loading 501

for columns are

ADCD5;000 .mm/

vu

u

u

t

18  104 .N /

2  105



N

mm^2



22:2 106 .mm^4 /

D1:007IBD0:

Parameters of compressive load for cross bar are

leftD6;000 .mm/

vu

u

u

t

2  103 .N /

2  105



N

mm^2



 2 22:2 106 .mm^4 /

D0:0028I

rightD0:0020:

According Table A.25, we can assumeADCD1:0andleftDrightD0:0.
Canonical equations of the displacement method are:

r 11 Z 1 Cr 12 Z 2 CR1PD0;

r 21 Z 1 Cr 22 Z 2 CR2PD0:

(a)

The bending moment diagramM 1 in the primary system due to the rotation of
induced constraint 1 is shown in Fig.13.25c. Since parametersfor cross bars are
zero, then this member may be considered without effect of compressive load, so
the bending moment diagram is bounded by straight lines. It is obvious that

r 11 D 2 EI



kN m

rad



andr 21 D0:

Figure13.25d presents the bending moment diagramM 2 in the primary system
due to the linear displacement of induced constraint 2. For columnsAandC,we
need to take into account parameterbecause these members are subjected to axial
forces. Therefore, bending moment diagrams along these members are curvilinear.
The corrected functionsaccording Table A.25 are ' 1 . / D ' 1 .1:0/ D
0:9313; 1 . /D
1 .1:0/D0:5980.
Specified ordinates of the bending moment diagram are

MADMCD

3i

l

' 1 . /D

3 0:2EI

5

0:9313D0:1118EI;

MBD

3i

l

D

3 0:2EI

5

D0:12EI:

Shear forces at specified sections are

QADQCD

3i

l^2

1 . /D

3 0:2EI

52

0:5980D0:01435EI;

QBD

3i

l^2

D

3 0:2EI

52

D0:024EI: