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FIGURE P11.9
11.11 Determine the critic
al
load
P
for the stepped column of Fig. P11.11, with a varying
axial force. Assume
P
b
=
m P
, where
m
is a prescribed constant of proportionality.
FIGURE P11.11
11.12 A beam column with axial force
P
is subject to a concentrated transverse force
P
1
at
midspan
(
L
/
2
)
. If both ends are fixed, find the deflection at midspan.
12
P
EI
1
/
2
P
1
L
3
192
EI
(
2
−
2 cos
β
−
β
sin
β)
L
2
Answer:
w(
L
/
2
)
=
β
=
β
3
sin
β
11.13 Find the critical value of
P
of the frame of Fig. P11.13. Use consistent geometric
stiffness matrices.
Hint:
Only the vertical bar is subject to an axial force.
Answer:
P
cr
≈
12 700 kN
FIGURE P11.13
0tofind the value of
M
∗
that buckles the
11.14 For the frame of Fig. P11.14, use det
K
=
frame
M
cr
=
Answer:
33
.
535 MNm.
11.15 Solve problem 11.14 using
(
K
lin
+
λ
K
geo
)
V
=
0.
Answer:
M
cr
=
41
.
587 MNm.
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