Advanced Methods of Structural Analysis

500 13 Stability of Elastic Systems

each member areP 1 DN 0 CP,whereN 0 is axial force in specified member as
a result of the stage 1 andPis external compressive load. Since for all columns
N 0 D 0 then for left and right columns, the axial force equals to given loadP.

F^1

2

i=0.2EI

i=0.333E

PPZ^1 Z^2

l=6m

h=5m

6m

F=30kN^1

P= 180 kN P= 180 kN

ABC

2 EI

EI

ab

1 2

M 1

Z 1 =1

r 11

r 21

3 i=1EI

3 i=1EI

3 i=1EI

1

r 11

3 i=1EI

(^12) r 21
c
Z 2 =1
12
r 12
r 22
MB
M 2
MA MC
d
Z 2 =1
0.01435EI 0.024EI
(^12)
r 22
r 12
0.01435EI
e
63.64(50.0) 68.31(50.0)
F
63.64(50.0)
MP
P= 180 kN P= 180 kN
f
Fig. 13.25 (a, b) Design diagram of the frame and primary system. (c) Unit bending moment
diagram due toZ 1 D 1 and calculation of unit reactions. (d) Unit bending moment diagram due to
Z 2 D 1 and unit reactions. (e) Free body diagram and computation of the unit reactions. (f)Final
bending moment diagram
Parameters of compressive load
Dl
r
P
EI