Advanced Methods of Structural Analysis

Problems 505

Ans.PcrD

k 1 .l 1 Cl 2 /^2 Ck 2 l 22

l 1 Cl 2 .1C ̨/

:

13.2.Two absolutely rigid bodies.EI D1/connected by hinge at point C
(Fig. P13.2). Stiffness coefficient of each elastic support isk. Derive the stability
equation, find critical forces and corresponding shapes.

k

l

P

k

l

EI=• C

Fig. P13.2

Ans.P 1 crD

3 

p

5

2

klD0:3819klI P 2 crD

3 C

p

5

2

klD2:6180kl:

13.3.Design diagram of two-story frame withelastic constraints between adjacent
absolutely rigid members is shown in Fig. P13.3. Calculate the critical load using
energy method.

P

k (^1) h
l
h
k 2
k 3
Fig. P13.3
Ans.PcrD
k 1 Ck 2 Ck 3
2h
:
13.4.Pinned-pinned beam with elastic support A is subjected to axial compressive
forceP (Fig. P13.4). The restoring moment in rotational spring isM Dk'0.
Derive the stability equation. Apply thedouble integration and initial parameter
methods.