Advanced Methods of Structural Analysis

510 13 Stability of Elastic Systems

Ans.

ˇ

ˇ

ˇ

ˇ

' 2 . /C21:0

1:0 0:75' 1 .2/C3:5

ˇ

ˇ

ˇ

ˇD^0 ,1ADDh

r

P

EI

I 2BD

h

r

4P

EI

D2,minD2:097.

In problems 13.16–13.19 it is necessary to analyze the structure on the basis of
deformable design diagram. In all cases parameter

DnlDl

r

P

EI

Dl

r

kPcr

EI

:

13.16.The uniform free-clamped beam is subjected to axial compressive forceP
and lateral distributed loadq(Fig. P13.16). Calculate the vertical and angular dis-
placement at free end, and the bending moment at fixed support. Estimate effect of
axial load for different parameterK,

PDkPcr;PcrD

2 EI

4l^2

:

P

P

l

x

y

x

RB

q

y 0 B

Fig. P13.16

Ans. 0 D

ql^3

6 EI



6.sin/

^3 cos

Iy 0 D

ql^4

8 EI



8

^4



sinCcos 1

cos



^2

2



I

MBD

ql^2

2



2.cosCsin1/

^2 cos

13.17.The uniform beamABis subjected to axial compressive forcePand lateral
uniform distributed loadq(Fig. P13.17). Calculate slope at the support, the deflec-
tion and bending moment at the middle of the beam. Estimate effect of axial load
for different parametersk,

PDkPcr;PcrD

2 EI

l^2

:

q

l

P

Fig. P13.17