Advanced Methods of Structural Analysis

Problems 507

x

k

l

M 0

Q 0

EI N

ky 1

Fig. P13.7

Ans. tannlDnl



1 

n^2 l^2 EI

kl^3



;nD

r

N

EI

13.8.The uniform beam with overhang is subjected to axial compressive forceP
(Fig. P13.8). Derive the stability equation. Use the initial parameter method.

l

P

a

EI

Fig. P13.8

Ans.nl .tannlCtanna/Dtannltanna,nD

r

P

EI

13.9.The uniform pinned-clamped beam with intermediate hingeCis subjected
to axial compressive forceP(Fig. P13.9). Derive the stability equation by initial
parameter method. Calculate the critical load and trace elastic curve; (a) Consider
the special cases.aD0; aDl/.

l

P

a

CEI

Fig. P13.9

Ans. sinna Œnlcosn.la/sinn.la/D 0

13.10.The uniform pinned-pinned beam with elastic support is subjected to axial
compressed forceP(Fig. P13.10); stiffness coefficient of elastic support isk.The
total length of the beam islDl 1 Cl 2. Derive the stability equation. Use the initial
parameter method. Consider two special cases; (a)kD 0 ;(b)l 1 Dl 2 andkD1.