sm11 3 4

________________________________________________________________________
PROBLEMS (11.3 and 11.4) Determine the critical load Pcr for the rigid bar-spring
system shown in Figs. P11.3 and P11.4, where k represents the linear spring constant.
SOLUTION (11.3)
Bar AB
P
0: 0
B
MPLLR θ
=
−=
∑
,
R
P
θ
=
(1)
Bar BC
0:
C
M
=
∑
0
22
LL
PL RL k
θ
θ
−
−+ =
or 4
kL
RP
θ
θ =− + (2)
From Eqs.(1) and (2):
1
8
cr
Pk=L
SOLUTION (11.4)
Bar AB
0:
B
M=
∑
0,
R
aPa RP
θ
θ
−
== (1)
System ABC
0: (2 ) ( ) 0
C
MRakaa θ
=
−=
∑
1
2
R
ka
θ
= (2)
From Eqs.(1) and (2):
1
2
cr
Pk a=
A
C
B
L
R
θ
B
R
L
θ
kL
θ
L
R
R
a
θ
A
a
Fk=
a
θ
B
θ
P
a
C
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.