________________________________________________________________________
PROBLEM (11.36) A 0.5-m-long, 50-mm by 75-mm rectangular column is pinned at both
ends. If the stress-strain curve for the material is approximated as shown in Fig.P11.36, what is
the buckling load Pcr ?
SOLUTION
3
50 75 3.75 10Am
2
=×= × m50 14.4
23 23
b
A mm= ===
rI
500 14.4 34.7Lr== (inelastic buckling)
Use Eq. (11.12):
22
22
0.0082
( ) (34.7)
tt
cr t
EE E
Lr
ππ
σ
== = (1)
Elastic range: 9
0.0082(20 10 ) 164
cr
M
Pa
σ
=×=
Figure shows that E is not valid above 40 MPa.
Second range: 9
0.0082(20 10 ) 82
cr
M
Pa
σ
=×=
is not valid above 60 MPa.
1t
E
Third range: 9
0.0082(7.5 10 ) 61.5
cr
M
Pa
σ
=×=
N
is valid between 60 MPa and 75 MPa. Thus,
2t
E
63
61.5 10 (3.75 10 ) 231
cr
Pk
−
=× × =
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