Advanced Methods of Structural Analysis

Problems 509

13.13.Design diagram of the frames with deformable cross bar are presented in
Fig. P13.13. Derive the equation for critical load.

l

P

EI

kEI

h

l

P

EI

kEI

h

ab

Fig. P13.13

Ans. (a)3k

h

l

C



tan

D0; Dh

r

P

EI

;(b)tanD3k

h
l
13.14.The frame with absolutely rigid cross bar is presented in Fig. P13.14. Derive
the stability equation and calculate the critical load.

l 1

P

EI

EI=∞

h kEI kEI

l 2

Fig. P13.14

Ans. 

1 . /C2kD0; Dh

r

P

EI

.IfkD 1 ,thenD2:67:PcrD

7:13EI

h^2

.

13.15.Design diagram of the frame is presented in Fig. P13.15. Relationship be-
tween two forces is constant. Derive the stability equation and find critical load.

l=6m

4 P

l=6m

P

EI EI

3 EI 3 EI

h=

4m

1

2

A B

Fig. P13.15